text:
@testset "1.1.1.3 (a+b x)^m (c+d x)^n (e+f x)^p" begin
    (A, B, a, b, c, d, e, f, m, n, p, x, ) = @variables A B a b c d e f m n p x

    #= ::Package:: =#

    #= ::Title:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x)^n*(c+d*x)^p=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x)^n*(c+d*x)^p*when*b*c+a*d=0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x)^n*(c+d*x)^p*when*b*c+a*d=0=#

    @test_int [x^2/((-1 + x)^2*(1 + x)^2), x, 3, x/(2*(1 - x^2)) - atanh(x)/2]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x)^1*(c+d*x)^p*when*b*c+a*d=0=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(a + b*x)*(a*c - b*c*x)^3*x^2, x, 2, (1/3)*a^4*c^3*x^3 - (1/2)*a^3*b*c^3*x^4 + (1/3)*a*b^3*c^3*x^6 - (1/7)*b^4*c^3*x^7]
    @test_int [(a + b*x)*(a*c - b*c*x)^3*x^1, x, 2, (1/2)*a^4*c^3*x^2 - (2/3)*a^3*b*c^3*x^3 + (2/5)*a*b^3*c^3*x^5 - (1/6)*b^4*c^3*x^6]
    @test_int [(a + b*x)*(a*c - b*c*x)^3*x^0, x, 2, -((a*c^3*(a - b*x)^4)/(2*b)) + (c^3*(a - b*x)^5)/(5*b)]

    @test_int [(a + b*x)*(a*c - b*c*x)^3/x^1, x, 2, -2*a^3*b*c^3*x + (2/3)*a*b^3*c^3*x^3 - (1/4)*b^4*c^3*x^4 + a^4*c^3*log(x)]
    @test_int [(a + b*x)*(a*c - b*c*x)^3/x^2, x, 2, -((a^4*c^3)/x) + a*b^3*c^3*x^2 - (1/3)*b^4*c^3*x^3 - 2*a^3*b*c^3*log(x)]
    @test_int [(a + b*x)*(a*c - b*c*x)^3/x^3, x, 1, -((c^3*(a - b*x)^4)/(2*x^2))]
    @test_int [(a + b*x)*(a*c - b*c*x)^3/x^4, x, 2, -((a^4*c^3)/(3*x^3)) + (a^3*b*c^3)/x^2 - b^4*c^3*x + 2*a*b^3*c^3*log(x)]
    @test_int [(a + b*x)*(a*c - b*c*x)^3/x^5, x, 2, -((a^4*c^3)/(4*x^4)) + (2*a^3*b*c^3)/(3*x^3) - (2*a*b^3*c^3)/x - b^4*c^3*log(x)]

    @test_int [(a + b*x)*(a*c - b*c*x)^3/x^6, x, 2, -((a^4*c^3)/(5*x^5)) + (a^3*b*c^3)/(2*x^4) - (a*b^3*c^3)/x^2 + (b^4*c^3)/x]
    @test_int [(a + b*x)*(a*c - b*c*x)^3/x^7, x, 2, -((a^4*c^3)/(6*x^6)) + (2*a^3*b*c^3)/(5*x^5) - (2*a*b^3*c^3)/(3*x^3) + (b^4*c^3)/(2*x^2)]
    @test_int [(a + b*x)*(a*c - b*c*x)^3/x^8, x, 2, -((a^4*c^3)/(7*x^7)) + (a^3*b*c^3)/(3*x^6) - (a*b^3*c^3)/(2*x^4) + (b^4*c^3)/(3*x^3)]

    @test_int [(a + b*x)*(a*c - b*c*x)^4*x^4, x, 2, (1/5)*a^5*c^4*x^5 - (1/2)*a^4*b*c^4*x^6 + (2/7)*a^3*b^2*c^4*x^7 + (1/4)*a^2*b^3*c^4*x^8 - (1/3)*a*b^4*c^4*x^9 + (1/10)*b^5*c^4*x^10]
    @test_int [(a + b*x)*(a*c - b*c*x)^4*x^3, x, 2, (1/4)*a^5*c^4*x^4 - (3/5)*a^4*b*c^4*x^5 + (1/3)*a^3*b^2*c^4*x^6 + (2/7)*a^2*b^3*c^4*x^7 - (3/8)*a*b^4*c^4*x^8 + (1/9)*b^5*c^4*x^9]

    @test_int [(a + b*x)*(a*c - b*c*x)^4*x^2, x, 2, -((2*a^3*c^4*(a - b*x)^5)/(5*b^3)) + (5*a^2*c^4*(a - b*x)^6)/(6*b^3) - (4*a*c^4*(a - b*x)^7)/(7*b^3) + (c^4*(a - b*x)^8)/(8*b^3)]
    @test_int [(a + b*x)*(a*c - b*c*x)^4*x^1, x, 2, -((2*a^2*c^4*(a - b*x)^5)/(5*b^2)) + (a*c^4*(a - b*x)^6)/(2*b^2) - (c^4*(a - b*x)^7)/(7*b^2)]
    @test_int [(a + b*x)*(a*c - b*c*x)^4*x^0, x, 2, -((2*a*c^4*(a - b*x)^5)/(5*b)) + (c^4*(a - b*x)^6)/(6*b)]

    @test_int [(a + b*x)*(a*c - b*c*x)^4/x^1, x, 2, -3*a^4*b*c^4*x + a^3*b^2*c^4*x^2 + (2/3)*a^2*b^3*c^4*x^3 - (3/4)*a*b^4*c^4*x^4 + (1/5)*b^5*c^4*x^5 + a^5*c^4*log(x)]
    @test_int [(a + b*x)*(a*c - b*c*x)^4/x^2, x, 2, -((a^5*c^4)/x) + 2*a^3*b^2*c^4*x + a^2*b^3*c^4*x^2 - a*b^4*c^4*x^3 + (1/4)*b^5*c^4*x^4 - 3*a^4*b*c^4*log(x)]
    @test_int [(a + b*x)*(a*c - b*c*x)^4/x^3, x, 2, -((a^5*c^4)/(2*x^2)) + (3*a^4*b*c^4)/x + 2*a^2*b^3*c^4*x - (3/2)*a*b^4*c^4*x^2 + (1/3)*b^5*c^4*x^3 + 2*a^3*b^2*c^4*log(x)]
    @test_int [(a + b*x)*(a*c - b*c*x)^4/x^4, x, 2, -((a^5*c^4)/(3*x^3)) + (3*a^4*b*c^4)/(2*x^2) - (2*a^3*b^2*c^4)/x - 3*a*b^4*c^4*x + (1/2)*b^5*c^4*x^2 + 2*a^2*b^3*c^4*log(x)]
    @test_int [(a + b*x)*(a*c - b*c*x)^4/x^5, x, 2, -((a^5*c^4)/(4*x^4)) + (a^4*b*c^4)/x^3 - (a^3*b^2*c^4)/x^2 - (2*a^2*b^3*c^4)/x + b^5*c^4*x - 3*a*b^4*c^4*log(x)]
    @test_int [(a + b*x)*(a*c - b*c*x)^4/x^6, x, 2, -((a^5*c^4)/(5*x^5)) + (3*a^4*b*c^4)/(4*x^4) - (2*a^3*b^2*c^4)/(3*x^3) - (a^2*b^3*c^4)/x^2 + (3*a*b^4*c^4)/x + b^5*c^4*log(x)]

    @test_int [(a + b*x)*(a*c - b*c*x)^4/x^7, x, 2, -((c^4*(a - b*x)^5)/(6*x^6)) - (7*b*c^4*(a - b*x)^5)/(30*a*x^5)]
    @test_int [(a + b*x)*(a*c - b*c*x)^4/x^8, x, 2, -((a^5*c^4)/(7*x^7)) + (a^4*b*c^4)/(2*x^6) - (2*a^3*b^2*c^4)/(5*x^5) - (a^2*b^3*c^4)/(2*x^4) + (a*b^4*c^4)/x^3 - (b^5*c^4)/(2*x^2)]
    @test_int [(a + b*x)*(a*c - b*c*x)^4/x^9, x, 2, -((a^5*c^4)/(8*x^8)) + (3*a^4*b*c^4)/(7*x^7) - (a^3*b^2*c^4)/(3*x^6) - (2*a^2*b^3*c^4)/(5*x^5) + (3*a*b^4*c^4)/(4*x^4) - (b^5*c^4)/(3*x^3)]

    @test_int [(a + b*x)*(a*c - b*c*x)^5*x^4, x, 2, (1/5)*a^6*c^5*x^5 - (2/3)*a^5*b*c^5*x^6 + (5/7)*a^4*b^2*c^5*x^7 - (5/9)*a^2*b^4*c^5*x^9 + (2/5)*a*b^5*c^5*x^10 - (1/11)*b^6*c^5*x^11]
    @test_int [(a + b*x)*(a*c - b*c*x)^5*x^3, x, 2, (1/4)*a^6*c^5*x^4 - (4/5)*a^5*b*c^5*x^5 + (5/6)*a^4*b^2*c^5*x^6 - (5/8)*a^2*b^4*c^5*x^8 + (4/9)*a*b^5*c^5*x^9 - (1/10)*b^6*c^5*x^10]

    @test_int [(a + b*x)*(a*c - b*c*x)^5*x^2, x, 2, -((a^3*c^5*(a - b*x)^6)/(3*b^3)) + (5*a^2*c^5*(a - b*x)^7)/(7*b^3) - (a*c^5*(a - b*x)^8)/(2*b^3) + (c^5*(a - b*x)^9)/(9*b^3)]
    @test_int [(a + b*x)*(a*c - b*c*x)^5*x^1, x, 2, -((a^2*c^5*(a - b*x)^6)/(3*b^2)) + (3*a*c^5*(a - b*x)^7)/(7*b^2) - (c^5*(a - b*x)^8)/(8*b^2)]
    @test_int [(a + b*x)*(a*c - b*c*x)^5*x^0, x, 2, -((a*c^5*(a - b*x)^6)/(3*b)) + (c^5*(a - b*x)^7)/(7*b)]

    @test_int [(a + b*x)*(a*c - b*c*x)^5/x^1, x, 2, -4*a^5*b*c^5*x + (5/2)*a^4*b^2*c^5*x^2 - (5/4)*a^2*b^4*c^5*x^4 + (4/5)*a*b^5*c^5*x^5 - (1/6)*b^6*c^5*x^6 + a^6*c^5*log(x)]
    @test_int [(a + b*x)*(a*c - b*c*x)^5/x^2, x, 2, -((a^6*c^5)/x) + 5*a^4*b^2*c^5*x - (5/3)*a^2*b^4*c^5*x^3 + a*b^5*c^5*x^4 - (1/5)*b^6*c^5*x^5 - 4*a^5*b*c^5*log(x)]
    @test_int [(a + b*x)*(a*c - b*c*x)^5/x^3, x, 2, -((a^6*c^5)/(2*x^2)) + (4*a^5*b*c^5)/x - (5/2)*a^2*b^4*c^5*x^2 + (4/3)*a*b^5*c^5*x^3 - (1/4)*b^6*c^5*x^4 + 5*a^4*b^2*c^5*log(x)]
    @test_int [(a + b*x)*(a*c - b*c*x)^5/x^4, x, 1, -((c^5*(a - b*x)^6)/(3*x^3))]
    @test_int [(a + b*x)*(a*c - b*c*x)^5/x^5, x, 2, -((a^6*c^5)/(4*x^4)) + (4*a^5*b*c^5)/(3*x^3) - (5*a^4*b^2*c^5)/(2*x^2) + 4*a*b^5*c^5*x - (1/2)*b^6*c^5*x^2 - 5*a^2*b^4*c^5*log(x)]
    @test_int [(a + b*x)*(a*c - b*c*x)^5/x^6, x, 2, -((a^6*c^5)/(5*x^5)) + (a^5*b*c^5)/x^4 - (5*a^4*b^2*c^5)/(3*x^3) + (5*a^2*b^4*c^5)/x - b^6*c^5*x + 4*a*b^5*c^5*log(x)]
    @test_int [(a + b*x)*(a*c - b*c*x)^5/x^7, x, 2, -((a^6*c^5)/(6*x^6)) + (4*a^5*b*c^5)/(5*x^5) - (5*a^4*b^2*c^5)/(4*x^4) + (5*a^2*b^4*c^5)/(2*x^2) - (4*a*b^5*c^5)/x - b^6*c^5*log(x)]

    @test_int [(a + b*x)*(a*c - b*c*x)^5/x^8, x, 2, -((c^5*(a - b*x)^6)/(7*x^7)) - (4*b*c^5*(a - b*x)^6)/(21*a*x^6)]
    @test_int [(a + b*x)*(a*c - b*c*x)^5/x^9, x, 3, -((c^5*(a - b*x)^6)/(8*x^8)) - (5*b*c^5*(a - b*x)^6)/(28*a*x^7) - (5*b^2*c^5*(a - b*x)^6)/(168*a^2*x^6)]
    @test_int [(a + b*x)*(a*c - b*c*x)^5/x^10, x, 2, -((a^6*c^5)/(9*x^9)) + (a^5*b*c^5)/(2*x^8) - (5*a^4*b^2*c^5)/(7*x^7) + (a^2*b^4*c^5)/x^5 - (a*b^5*c^5)/x^4 + (b^6*c^5)/(3*x^3)]
    @test_int [(a + b*x)*(a*c - b*c*x)^5/x^11, x, 2, -((a^6*c^5)/(10*x^10)) + (4*a^5*b*c^5)/(9*x^9) - (5*a^4*b^2*c^5)/(8*x^8) + (5*a^2*b^4*c^5)/(6*x^6) - (4*a*b^5*c^5)/(5*x^5) + (b^6*c^5)/(4*x^4)]
    @test_int [(a + b*x)*(a*c - b*c*x)^5/x^12, x, 2, -((a^6*c^5)/(11*x^11)) + (2*a^5*b*c^5)/(5*x^10) - (5*a^4*b^2*c^5)/(9*x^9) + (5*a^2*b^4*c^5)/(7*x^7) - (2*a*b^5*c^5)/(3*x^6) + (b^6*c^5)/(5*x^5)]

    @test_int [(a + b*x)*(a*c - b*c*x)^6/x^8, x, 2, -((a^7*c^6)/(7*x^7)) + (5*a^6*b*c^6)/(6*x^6) - (9*a^5*b^2*c^6)/(5*x^5) + (5*a^4*b^3*c^6)/(4*x^4) + (5*a^3*b^4*c^6)/(3*x^3) - (9*a^2*b^5*c^6)/(2*x^2) + (5*a*b^6*c^6)/x + b^7*c^6*log(x)]

    @test_int [(a + b*x)*(a*c - b*c*x)^6/x^9, x, 2, -((c^6*(a - b*x)^7)/(8*x^8)) - (9*b*c^6*(a - b*x)^7)/(56*a*x^7)]
    @test_int [(a + b*x)*(a*c - b*c*x)^6/x^10, x, 3, -((c^6*(a - b*x)^7)/(9*x^9)) - (11*b*c^6*(a - b*x)^7)/(72*a*x^8) - (11*b^2*c^6*(a - b*x)^7)/(504*a^2*x^7)]
    @test_int [(a + b*x)*(a*c - b*c*x)^6/x^11, x, 4, -((c^6*(a - b*x)^7)/(10*x^10)) - (13*b*c^6*(a - b*x)^7)/(90*a*x^9) - (13*b^2*c^6*(a - b*x)^7)/(360*a^2*x^8) - (13*b^3*c^6*(a - b*x)^7)/(2520*a^3*x^7)]
    @test_int [(a + b*x)*(a*c - b*c*x)^6/x^12, x, 2, -((a^7*c^6)/(11*x^11)) + (a^6*b*c^6)/(2*x^10) - (a^5*b^2*c^6)/x^9 + (5*a^4*b^3*c^6)/(8*x^8) + (5*a^3*b^4*c^6)/(7*x^7) - (3*a^2*b^5*c^6)/(2*x^6) + (a*b^6*c^6)/x^5 - (b^7*c^6)/(4*x^4)]
    @test_int [(a + b*x)*(a*c - b*c*x)^6/x^13, x, 2, -((a^7*c^6)/(12*x^12)) + (5*a^6*b*c^6)/(11*x^11) - (9*a^5*b^2*c^6)/(10*x^10) + (5*a^4*b^3*c^6)/(9*x^9) + (5*a^3*b^4*c^6)/(8*x^8) - (9*a^2*b^5*c^6)/(7*x^7) + (5*a*b^6*c^6)/(6*x^6) - (b^7*c^6)/(5*x^5)]

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^(m/2)*(a+b*x)^n*(c+d*x)^p*when*b*c+a*d=0=#

    @test_int [(e*x)^(5/2)/((a + b*x)*(a*c - b*c*x)), x, 6, -((2*e*(e*x)^(3/2))/(3*b^2*c)) - (a^(3/2)*e^(5/2)*atan((sqrt(b)*sqrt(e*x))/(sqrt(a)*sqrt(e))))/(b^(7/2)*c) + (a^(3/2)*e^(5/2)*atanh((sqrt(b)*sqrt(e*x))/(sqrt(a)*sqrt(e))))/(b^(7/2)*c)]
    @test_int [(e*x)^(3/2)/((a + b*x)*(a*c - b*c*x)), x, 6, -((2*e*sqrt(e*x))/(b^2*c)) + (sqrt(a)*e^(3/2)*atan((sqrt(b)*sqrt(e*x))/(sqrt(a)*sqrt(e))))/(b^(5/2)*c) + (sqrt(a)*e^(3/2)*atanh((sqrt(b)*sqrt(e*x))/(sqrt(a)*sqrt(e))))/(b^(5/2)*c)]
    @test_int [(e*x)^(1/2)/((a + b*x)*(a*c - b*c*x)), x, 5, -((sqrt(e)*atan((sqrt(b)*sqrt(e*x))/(sqrt(a)*sqrt(e))))/(sqrt(a)*b^(3/2)*c)) + (sqrt(e)*atanh((sqrt(b)*sqrt(e*x))/(sqrt(a)*sqrt(e))))/(sqrt(a)*b^(3/2)*c)]
    @test_int [1/((e*x)^(1/2)*(a + b*x)*(a*c - b*c*x)), x, 5, atan((sqrt(b)*sqrt(e*x))/(sqrt(a)*sqrt(e)))/(a^(3/2)*sqrt(b)*c*sqrt(e)) + atanh((sqrt(b)*sqrt(e*x))/(sqrt(a)*sqrt(e)))/(a^(3/2)*sqrt(b)*c*sqrt(e))]
    @test_int [1/((e*x)^(3/2)*(a + b*x)*(a*c - b*c*x)), x, 6, -(2/(a^2*c*e*sqrt(e*x))) - (sqrt(b)*atan((sqrt(b)*sqrt(e*x))/(sqrt(a)*sqrt(e))))/(a^(5/2)*c*e^(3/2)) + (sqrt(b)*atanh((sqrt(b)*sqrt(e*x))/(sqrt(a)*sqrt(e))))/(a^(5/2)*c*e^(3/2))]
    @test_int [1/((e*x)^(5/2)*(a + b*x)*(a*c - b*c*x)), x, 6, -(2/(3*a^2*c*e*(e*x)^(3/2))) + (b^(3/2)*atan((sqrt(b)*sqrt(e*x))/(sqrt(a)*sqrt(e))))/(a^(7/2)*c*e^(5/2)) + (b^(3/2)*atanh((sqrt(b)*sqrt(e*x))/(sqrt(a)*sqrt(e))))/(a^(7/2)*c*e^(5/2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x)^n*(c+d*x)^p*when*b*c+a*d=0*and*m*symbolic=#

    @test_int [(e*x)^m*(1 + a*x)^4*(2 - 2*a*x)^3, x, 2, (8*(e*x)^(1 + m))/(e*(1 + m)) + (8*a*(e*x)^(2 + m))/(e^2*(2 + m)) - (24*a^2*(e*x)^(3 + m))/(e^3*(3 + m)) - (24*a^3*(e*x)^(4 + m))/(e^4*(4 + m)) + (24*a^4*(e*x)^(5 + m))/(e^5*(5 + m)) + (24*a^5*(e*x)^(6 + m))/(e^6*(6 + m)) - (8*a^6*(e*x)^(7 + m))/(e^7*(7 + m)) - (8*a^7*(e*x)^(8 + m))/(e^8*(8 + m))]
    @test_int [(e*x)^m*(1 + a*x)^3*(2 - 2*a*x)^2, x, 2, (4*(e*x)^(1 + m))/(e*(1 + m)) + (4*a*(e*x)^(2 + m))/(e^2*(2 + m)) - (8*a^2*(e*x)^(3 + m))/(e^3*(3 + m)) - (8*a^3*(e*x)^(4 + m))/(e^4*(4 + m)) + (4*a^4*(e*x)^(5 + m))/(e^5*(5 + m)) + (4*a^5*(e*x)^(6 + m))/(e^6*(6 + m))]
    @test_int [(e*x)^m*(1 + a*x)^2*(2 - 2*a*x)^1, x, 2, (2*(e*x)^(1 + m))/(e*(1 + m)) + (2*a*(e*x)^(2 + m))/(e^2*(2 + m)) - (2*a^2*(e*x)^(3 + m))/(e^3*(3 + m)) - (2*a^3*(e*x)^(4 + m))/(e^4*(4 + m))]
    @test_int [(e*x)^m/((1 + a*x)^1*(2 - 2*a*x)^2), x, 5, ((e*x)^(1 + m)*HypergeometricFunctions._₂F₁(2, (1 + m)/2, (3 + m)/2, a^2*x^2))/(4*e*(1 + m)) + (a*(e*x)^(2 + m)*HypergeometricFunctions._₂F₁(2, (2 + m)/2, (4 + m)/2, a^2*x^2))/(4*e^2*(2 + m))]
    @test_int [(e*x)^m/((1 + a*x)^2*(2 - 2*a*x)^3), x, 5, ((e*x)^(1 + m)*HypergeometricFunctions._₂F₁(3, (1 + m)/2, (3 + m)/2, a^2*x^2))/(8*e*(1 + m)) + (a*(e*x)^(2 + m)*HypergeometricFunctions._₂F₁(3, (2 + m)/2, (4 + m)/2, a^2*x^2))/(8*e^2*(2 + m))]
    @test_int [(e*x)^m/((1 + a*x)^3*(2 - 2*a*x)^4), x, 5, ((e*x)^(1 + m)*HypergeometricFunctions._₂F₁(4, (1 + m)/2, (3 + m)/2, a^2*x^2))/(16*e*(1 + m)) + (a*(e*x)^(2 + m)*HypergeometricFunctions._₂F₁(4, (2 + m)/2, (4 + m)/2, a^2*x^2))/(16*e^2*(2 + m))]

    @test_int [(e*x)^m*(a + b*x)^4*(a*d - b*d*x)^3, x, 2, (a^7*d^3*(e*x)^(1 + m))/(e*(1 + m)) + (a^6*b*d^3*(e*x)^(2 + m))/(e^2*(2 + m)) - (3*a^5*b^2*d^3*(e*x)^(3 + m))/(e^3*(3 + m)) - (3*a^4*b^3*d^3*(e*x)^(4 + m))/(e^4*(4 + m)) + (3*a^3*b^4*d^3*(e*x)^(5 + m))/(e^5*(5 + m)) + (3*a^2*b^5*d^3*(e*x)^(6 + m))/(e^6*(6 + m)) - (a*b^6*d^3*(e*x)^(7 + m))/(e^7*(7 + m)) - (b^7*d^3*(e*x)^(8 + m))/(e^8*(8 + m))]
    @test_int [(e*x)^m*(a + b*x)^3*(a*d - b*d*x)^2, x, 2, (a^5*d^2*(e*x)^(1 + m))/(e*(1 + m)) + (a^4*b*d^2*(e*x)^(2 + m))/(e^2*(2 + m)) - (2*a^3*b^2*d^2*(e*x)^(3 + m))/(e^3*(3 + m)) - (2*a^2*b^3*d^2*(e*x)^(4 + m))/(e^4*(4 + m)) + (a*b^4*d^2*(e*x)^(5 + m))/(e^5*(5 + m)) + (b^5*d^2*(e*x)^(6 + m))/(e^6*(6 + m))]
    @test_int [(e*x)^m*(a + b*x)^2*(a*d - b*d*x)^1, x, 2, (a^3*d*(e*x)^(1 + m))/(e*(1 + m)) + (a^2*b*d*(e*x)^(2 + m))/(e^2*(2 + m)) - (a*b^2*d*(e*x)^(3 + m))/(e^3*(3 + m)) - (b^3*d*(e*x)^(4 + m))/(e^4*(4 + m))]
    @test_int [(e*x)^m/((a + b*x)^1*(a*d - b*d*x)^2), x, 5, ((e*x)^(1 + m)*HypergeometricFunctions._₂F₁(2, (1 + m)/2, (3 + m)/2, (b^2*x^2)/a^2))/(a^3*d^2*e*(1 + m)) + (b*(e*x)^(2 + m)*HypergeometricFunctions._₂F₁(2, (2 + m)/2, (4 + m)/2, (b^2*x^2)/a^2))/(a^4*d^2*e^2*(2 + m))]
    @test_int [(e*x)^m/((a + b*x)^2*(a*d - b*d*x)^3), x, 5, ((e*x)^(1 + m)*HypergeometricFunctions._₂F₁(3, (1 + m)/2, (3 + m)/2, (b^2*x^2)/a^2))/(a^5*d^3*e*(1 + m)) + (b*(e*x)^(2 + m)*HypergeometricFunctions._₂F₁(3, (2 + m)/2, (4 + m)/2, (b^2*x^2)/a^2))/(a^6*d^3*e^2*(2 + m))]
    @test_int [(e*x)^m/((a + b*x)^3*(a*d - b*d*x)^4), x, 5, ((e*x)^(1 + m)*HypergeometricFunctions._₂F₁(4, (1 + m)/2, (3 + m)/2, (b^2*x^2)/a^2))/(a^7*d^4*e*(1 + m)) + (b*(e*x)^(2 + m)*HypergeometricFunctions._₂F₁(4, (2 + m)/2, (4 + m)/2, (b^2*x^2)/a^2))/(a^8*d^4*e^2*(2 + m))]

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(e*x)^m*(a + b*x)*(a*c - b*c*x)^4, x, 2, (a^5*c^4*(e*x)^(1 + m))/(e*(1 + m)) - (3*a^4*b*c^4*(e*x)^(2 + m))/(e^2*(2 + m)) + (2*a^3*b^2*c^4*(e*x)^(3 + m))/(e^3*(3 + m)) + (2*a^2*b^3*c^4*(e*x)^(4 + m))/(e^4*(4 + m)) - (3*a*b^4*c^4*(e*x)^(5 + m))/(e^5*(5 + m)) + (b^5*c^4*(e*x)^(6 + m))/(e^6*(6 + m))]
    @test_int [(e*x)^m*(a + b*x)*(a*c - b*c*x)^3, x, 2, (a^4*c^3*(e*x)^(1 + m))/(e*(1 + m)) - (2*a^3*b*c^3*(e*x)^(2 + m))/(e^2*(2 + m)) + (2*a*b^3*c^3*(e*x)^(4 + m))/(e^4*(4 + m)) - (b^4*c^3*(e*x)^(5 + m))/(e^5*(5 + m))]
    @test_int [(e*x)^m*(a + b*x)*(a*c - b*c*x)^2, x, 2, (a^3*c^2*(e*x)^(1 + m))/(e*(1 + m)) - (a^2*b*c^2*(e*x)^(2 + m))/(e^2*(2 + m)) - (a*b^2*c^2*(e*x)^(3 + m))/(e^3*(3 + m)) + (b^3*c^2*(e*x)^(4 + m))/(e^4*(4 + m))]
    @test_int [(e*x)^m*(a + b*x)*(a*c - b*c*x)^1, x, 3, (a^2*c*(e*x)^(1 + m))/(e*(1 + m)) - (b^2*c*(e*x)^(3 + m))/(e^3*(3 + m))]
    @test_int [(e*x)^m*(a + b*x)/(a*c - b*c*x)^1, x, 2, -((e*x)^(1 + m)/(c*e*(1 + m))) + (2*(e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (b*x)/a))/(c*e*(1 + m))]
    @test_int [(e*x)^m*(a + b*x)/(a*c - b*c*x)^2, x, 2, (2*(e*x)^(1 + m))/(c^2*e*(a - b*x)) - ((1 + 2*m)*(e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (b*x)/a))/(a*c^2*e*(1 + m))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(e*x)^m*(a*c - b*c*x)^3/(a + b*x), x, 7, -((7*a^2*c^3*(e*x)^(1 + m))/(e*(1 + m))) + (4*a*b*c^3*(e*x)^(2 + m))/(e^2*(2 + m)) - (b^2*c^3*(e*x)^(3 + m))/(e^3*(3 + m)) + (8*a^2*c^3*(e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((b*x)/a)))/(e*(1 + m))]
    @test_int [(e*x)^m*(a*c - b*c*x)^2/(a + b*x), x, 5, -((3*a*c^2*(e*x)^(1 + m))/(e*(1 + m))) + (b*c^2*(e*x)^(2 + m))/(e^2*(2 + m)) + (4*a*c^2*(e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((b*x)/a)))/(e*(1 + m))]
    @test_int [(e*x)^m*(a*c - b*c*x)^1/(a + b*x), x, 2, -((c*(e*x)^(1 + m))/(e*(1 + m))) + (2*c*(e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((b*x)/a)))/(e*(1 + m))]
    @test_int [(e*x)^m/((a + b*x)*(a*c - b*c*x)^1), x, 2, ((e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, (1 + m)/2, (3 + m)/2, (b^2*x^2)/a^2))/(a^2*c*e*(1 + m))]
    @test_int [(e*x)^m/((a + b*x)*(a*c - b*c*x)^2), x, 5, ((e*x)^(1 + m)*HypergeometricFunctions._₂F₁(2, (1 + m)/2, (3 + m)/2, (b^2*x^2)/a^2))/(a^3*c^2*e*(1 + m)) + (b*(e*x)^(2 + m)*HypergeometricFunctions._₂F₁(2, (2 + m)/2, (4 + m)/2, (b^2*x^2)/a^2))/(a^4*c^2*e^2*(2 + m))]
    @test_int [(e*x)^m/((a + b*x)*(a*c - b*c*x)^3), x, 5, (e*x)^(1 + m)/(4*a^2*c^3*e*(a - b*x)^2) + ((2 - m)*(e*x)^(1 + m))/(4*a^3*c^3*e*(a - b*x)) + ((e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((b*x)/a)))/(8*a^4*c^3*e*(1 + m)) + ((1 - 4*m + 2*m^2)*(e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (b*x)/a))/(8*a^4*c^3*e*(1 + m))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x)^n*(c+d*x)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x)^1*(c+d*x)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^4*(a + b*x)*(A + B*x), x, 2, (1/5)*a*A*x^5 + (1/6)*(A*b + a*B)*x^6 + (1/7)*b*B*x^7]
    @test_int [x^3*(a + b*x)*(A + B*x), x, 2, (1/4)*a*A*x^4 + (1/5)*(A*b + a*B)*x^5 + (1/6)*b*B*x^6]
    @test_int [x^2*(a + b*x)*(A + B*x), x, 2, (1/3)*a*A*x^3 + (1/4)*(A*b + a*B)*x^4 + (1/5)*b*B*x^5]
    @test_int [x^1*(a + b*x)*(A + B*x), x, 2, (1/2)*a*A*x^2 + (1/3)*(A*b + a*B)*x^3 + (1/4)*b*B*x^4]

    @test_int [x^0*(a + b*x)*(A + B*x), x, 2, a*A*x + ((A*b + a*B)*x^2)/2 + (b*B*x^3)/3]

    @test_int [((a + b*x)*(A + B*x))/x^1, x, 2, (A*b + a*B)*x + (1/2)*b*B*x^2 + a*A*log(x)]
    @test_int [((a + b*x)*(A + B*x))/x^2, x, 2, -((a*A)/x) + b*B*x + (A*b + a*B)*log(x)]
    @test_int [((a + b*x)*(A + B*x))/x^3, x, 2, -((a*A)/(2*x^2)) - (A*b + a*B)/x + b*B*log(x)]

    @test_int [((a + b*x)*(A + B*x))/x^4, x, 2, -((a*A)/(3*x^3)) - (A*b + a*B)/(2*x^2) - (b*B)/x]
    @test_int [((a + b*x)*(A + B*x))/x^5, x, 2, -((a*A)/(4*x^4)) - (A*b + a*B)/(3*x^3) - (b*B)/(2*x^2)]
    @test_int [((a + b*x)*(A + B*x))/x^6, x, 2, -((a*A)/(5*x^5)) - (A*b + a*B)/(4*x^4) - (b*B)/(3*x^3)]

    @test_int [x^4*(a + b*x)^2*(A + B*x), x, 2, (1/5)*a^2*A*x^5 + (1/6)*a*(2*A*b + a*B)*x^6 + (1/7)*b*(A*b + 2*a*B)*x^7 + (1/8)*b^2*B*x^8]
    @test_int [x^3*(a + b*x)^2*(A + B*x), x, 2, (1/4)*a^2*A*x^4 + (1/5)*a*(2*A*b + a*B)*x^5 + (1/6)*b*(A*b + 2*a*B)*x^6 + (1/7)*b^2*B*x^7]
    @test_int [x^2*(a + b*x)^2*(A + B*x), x, 2, (1/3)*a^2*A*x^3 + (1/4)*a*(2*A*b + a*B)*x^4 + (1/5)*b*(A*b + 2*a*B)*x^5 + (1/6)*b^2*B*x^6]
    @test_int [x^1*(a + b*x)^2*(A + B*x), x, 2, (1/2)*a^2*A*x^2 + (1/3)*a*(2*A*b + a*B)*x^3 + (1/4)*b*(A*b + 2*a*B)*x^4 + (1/5)*b^2*B*x^5]

    @test_int [x^0*(a + b*x)^2*(A + B*x), x, 2, ((A*b - a*B)*(a + b*x)^3)/(3*b^2) + (B*(a + b*x)^4)/(4*b^2)]

    @test_int [((a + b*x)^2*(A + B*x))/x^1, x, 3, 2*a*A*b*x + (1/2)*A*b^2*x^2 + (B*(a + b*x)^3)/(3*b) + a^2*A*log(x)]
    @test_int [((a + b*x)^2*(A + B*x))/x^2, x, 2, -((a^2*A)/x) + b*(A*b + 2*a*B)*x + (1/2)*b^2*B*x^2 + a*(2*A*b + a*B)*log(x)]
    @test_int [((a + b*x)^2*(A + B*x))/x^3, x, 2, -((a^2*A)/(2*x^2)) - (a*(2*A*b + a*B))/x + b^2*B*x + b*(A*b + 2*a*B)*log(x)]
    @test_int [((a + b*x)^2*(A + B*x))/x^4, x, 2, -((a^2*A)/(3*x^3)) - (a*(2*A*b + a*B))/(2*x^2) - (b*(A*b + 2*a*B))/x + b^2*B*log(x)]

    @test_int [((a + b*x)^2*(A + B*x))/x^5, x, 2, -((A*(a + b*x)^3)/(4*a*x^4)) + ((A*b - 4*a*B)*(a + b*x)^3)/(12*a^2*x^3)]

    @test_int [((a + b*x)^2*(A + B*x))/x^6, x, 2, -((a^2*A)/(5*x^5)) - (a*(2*A*b + a*B))/(4*x^4) - (b*(A*b + 2*a*B))/(3*x^3) - (b^2*B)/(2*x^2)]
    @test_int [((a + b*x)^2*(A + B*x))/x^7, x, 2, -((a^2*A)/(6*x^6)) - (a*(2*A*b + a*B))/(5*x^5) - (b*(A*b + 2*a*B))/(4*x^4) - (b^2*B)/(3*x^3)]
    @test_int [((a + b*x)^2*(A + B*x))/x^8, x, 2, -((a^2*A)/(7*x^7)) - (a*(2*A*b + a*B))/(6*x^6) - (b*(A*b + 2*a*B))/(5*x^5) - (b^2*B)/(4*x^4)]

    @test_int [x^4*(a + b*x)^3*(A + B*x), x, 2, (1/5)*a^3*A*x^5 + (1/6)*a^2*(3*A*b + a*B)*x^6 + (3/7)*a*b*(A*b + a*B)*x^7 + (1/8)*b^2*(A*b + 3*a*B)*x^8 + (1/9)*b^3*B*x^9]
    @test_int [x^3*(a + b*x)^3*(A + B*x), x, 2, (1/4)*a^3*A*x^4 + (1/5)*a^2*(3*A*b + a*B)*x^5 + (1/2)*a*b*(A*b + a*B)*x^6 + (1/7)*b^2*(A*b + 3*a*B)*x^7 + (1/8)*b^3*B*x^8]
    @test_int [x^2*(a + b*x)^3*(A + B*x), x, 2, (1/3)*a^3*A*x^3 + (1/4)*a^2*(3*A*b + a*B)*x^4 + (3/5)*a*b*(A*b + a*B)*x^5 + (1/6)*b^2*(A*b + 3*a*B)*x^6 + (1/7)*b^3*B*x^7]

    @test_int [x^1*(a + b*x)^3*(A + B*x), x, 2, -((a*(A*b - a*B)*(a + b*x)^4)/(4*b^3)) + ((A*b - 2*a*B)*(a + b*x)^5)/(5*b^3) + (B*(a + b*x)^6)/(6*b^3)]
    @test_int [x^0*(a + b*x)^3*(A + B*x), x, 2, ((A*b - a*B)*(a + b*x)^4)/(4*b^2) + (B*(a + b*x)^5)/(5*b^2)]

    @test_int [((a + b*x)^3*(A + B*x))/x^1, x, 3, 3*a^2*A*b*x + (3/2)*a*A*b^2*x^2 + (1/3)*A*b^3*x^3 + (B*(a + b*x)^4)/(4*b) + a^3*A*log(x)]
    @test_int [((a + b*x)^3*(A + B*x))/x^2, x, 2, -((a^3*A)/x) + 3*a*b*(A*b + a*B)*x + (1/2)*b^2*(A*b + 3*a*B)*x^2 + (1/3)*b^3*B*x^3 + a^2*(3*A*b + a*B)*log(x)]
    @test_int [((a + b*x)^3*(A + B*x))/x^3, x, 2, -((a^3*A)/(2*x^2)) - (a^2*(3*A*b + a*B))/x + b^2*(A*b + 3*a*B)*x + (1/2)*b^3*B*x^2 + 3*a*b*(A*b + a*B)*log(x)]
    @test_int [((a + b*x)^3*(A + B*x))/x^4, x, 2, -((a^3*A)/(3*x^3)) - (a^2*(3*A*b + a*B))/(2*x^2) - (3*a*b*(A*b + a*B))/x + b^3*B*x + b^2*(A*b + 3*a*B)*log(x)]
    @test_int [((a + b*x)^3*(A + B*x))/x^5, x, 3, -((a^3*B)/(3*x^3)) - (3*a^2*b*B)/(2*x^2) - (3*a*b^2*B)/x - (A*(a + b*x)^4)/(4*a*x^4) + b^3*B*log(x)]

    @test_int [((a + b*x)^3*(A + B*x))/x^6, x, 2, -((A*(a + b*x)^4)/(5*a*x^5)) + ((A*b - 5*a*B)*(a + b*x)^4)/(20*a^2*x^4)]

    @test_int [((a + b*x)^3*(A + B*x))/x^7, x, 2, -((a^3*A)/(6*x^6)) - (a^2*(3*A*b + a*B))/(5*x^5) - (3*a*b*(A*b + a*B))/(4*x^4) - (b^2*(A*b + 3*a*B))/(3*x^3) - (b^3*B)/(2*x^2)]
    @test_int [((a + b*x)^3*(A + B*x))/x^8, x, 2, -((a^3*A)/(7*x^7)) - (a^2*(3*A*b + a*B))/(6*x^6) - (3*a*b*(A*b + a*B))/(5*x^5) - (b^2*(A*b + 3*a*B))/(4*x^4) - (b^3*B)/(3*x^3)]
    @test_int [((a + b*x)^3*(A + B*x))/x^9, x, 2, -((a^3*A)/(8*x^8)) - (a^2*(3*A*b + a*B))/(7*x^7) - (a*b*(A*b + a*B))/(2*x^6) - (b^2*(A*b + 3*a*B))/(5*x^5) - (b^3*B)/(4*x^4)]
    @test_int [((a + b*x)^3*(A + B*x))/x^10, x, 2, -((a^3*A)/(9*x^9)) - (a^2*(3*A*b + a*B))/(8*x^8) - (3*a*b*(A*b + a*B))/(7*x^7) - (b^2*(A*b + 3*a*B))/(6*x^6) - (b^3*B)/(5*x^5)]

    @test_int [x^5*(a + b*x)^5*(A + B*x), x, 2, (a^5*A*x^6)/6 + (a^4*(5*A*b + a*B)*x^7)/7 + (5*a^3*b*(2*A*b + a*B)*x^8)/8 + (10*a^2*b^2*(A*b + a*B)*x^9)/9 + (a*b^3*(A*b + 2*a*B)*x^10)/2 + (b^4*(A*b + 5*a*B)*x^11)/11 + (b^5*B*x^12)/12]
    @test_int [x^4*(a + b*x)^5*(A + B*x), x, 2, (a^5*A*x^5)/5 + (a^4*(5*A*b + a*B)*x^6)/6 + (5*a^3*b*(2*A*b + a*B)*x^7)/7 + (5*a^2*b^2*(A*b + a*B)*x^8)/4 + (5*a*b^3*(A*b + 2*a*B)*x^9)/9 + (b^4*(A*b + 5*a*B)*x^10)/10 + (b^5*B*x^11)/11]

    @test_int [x^3*(a + b*x)^5*(A + B*x), x, 2, -((a^3*(A*b - a*B)*(a + b*x)^6)/(6*b^5)) + (a^2*(3*A*b - 4*a*B)*(a + b*x)^7)/(7*b^5) - (3*a*(A*b - 2*a*B)*(a + b*x)^8)/(8*b^5) + ((A*b - 4*a*B)*(a + b*x)^9)/(9*b^5) + (B*(a + b*x)^10)/(10*b^5)]
    @test_int [x^2*(a + b*x)^5*(A + B*x), x, 2, (a^2*(A*b - a*B)*(a + b*x)^6)/(6*b^4) - (a*(2*A*b - 3*a*B)*(a + b*x)^7)/(7*b^4) + ((A*b - 3*a*B)*(a + b*x)^8)/(8*b^4) + (B*(a + b*x)^9)/(9*b^4)]
    @test_int [x^1*(a + b*x)^5*(A + B*x), x, 2, -((a*(A*b - a*B)*(a + b*x)^6)/(6*b^3)) + ((A*b - 2*a*B)*(a + b*x)^7)/(7*b^3) + (B*(a + b*x)^8)/(8*b^3)]
    @test_int [x^0*(a + b*x)^5*(A + B*x), x, 2, ((A*b - a*B)*(a + b*x)^6)/(6*b^2) + (B*(a + b*x)^7)/(7*b^2)]

    @test_int [((a + b*x)^5*(A + B*x))/x^1, x, 3, 5*a^4*A*b*x + 5*a^3*A*b^2*x^2 + (10/3)*a^2*A*b^3*x^3 + (5/4)*a*A*b^4*x^4 + (1/5)*A*b^5*x^5 + (B*(a + b*x)^6)/(6*b) + a^5*A*log(x)]
    @test_int [((a + b*x)^5*(A + B*x))/x^2, x, 2, -((a^5*A)/x) + 5*a^3*b*(2*A*b + a*B)*x + 5*a^2*b^2*(A*b + a*B)*x^2 + (5/3)*a*b^3*(A*b + 2*a*B)*x^3 + (1/4)*b^4*(A*b + 5*a*B)*x^4 + (1/5)*b^5*B*x^5 + a^4*(5*A*b + a*B)*log(x)]
    @test_int [((a + b*x)^5*(A + B*x))/x^3, x, 2, -((a^5*A)/(2*x^2)) - (a^4*(5*A*b + a*B))/x + 10*a^2*b^2*(A*b + a*B)*x + (5/2)*a*b^3*(A*b + 2*a*B)*x^2 + (1/3)*b^4*(A*b + 5*a*B)*x^3 + (1/4)*b^5*B*x^4 + 5*a^3*b*(2*A*b + a*B)*log(x)]
    @test_int [((a + b*x)^5*(A + B*x))/x^4, x, 2, -((a^5*A)/(3*x^3)) - (a^4*(5*A*b + a*B))/(2*x^2) - (5*a^3*b*(2*A*b + a*B))/x + 5*a*b^3*(A*b + 2*a*B)*x + (1/2)*b^4*(A*b + 5*a*B)*x^2 + (1/3)*b^5*B*x^3 + 10*a^2*b^2*(A*b + a*B)*log(x)]
    @test_int [((a + b*x)^5*(A + B*x))/x^5, x, 2, -((a^5*A)/(4*x^4)) - (a^4*(5*A*b + a*B))/(3*x^3) - (5*a^3*b*(2*A*b + a*B))/(2*x^2) - (10*a^2*b^2*(A*b + a*B))/x + b^4*(A*b + 5*a*B)*x + (1/2)*b^5*B*x^2 + 5*a*b^3*(A*b + 2*a*B)*log(x)]
    @test_int [((a + b*x)^5*(A + B*x))/x^6, x, 2, -((a^5*A)/(5*x^5)) - (a^4*(5*A*b + a*B))/(4*x^4) - (5*a^3*b*(2*A*b + a*B))/(3*x^3) - (5*a^2*b^2*(A*b + a*B))/x^2 - (5*a*b^3*(A*b + 2*a*B))/x + b^5*B*x + b^4*(A*b + 5*a*B)*log(x)]
    @test_int [((a + b*x)^5*(A + B*x))/x^7, x, 3, -((a^5*B)/(5*x^5)) - (5*a^4*b*B)/(4*x^4) - (10*a^3*b^2*B)/(3*x^3) - (5*a^2*b^3*B)/x^2 - (5*a*b^4*B)/x - (A*(a + b*x)^6)/(6*a*x^6) + b^5*B*log(x)]

    @test_int [((a + b*x)^5*(A + B*x))/x^8, x, 2, -((A*(a + b*x)^6)/(7*a*x^7)) + ((A*b - 7*a*B)*(a + b*x)^6)/(42*a^2*x^6)]
    @test_int [((a + b*x)^5*(A + B*x))/x^9, x, 3, -((A*(a + b*x)^6)/(8*a*x^8)) + ((A*b - 4*a*B)*(a + b*x)^6)/(28*a^2*x^7) - (b*(A*b - 4*a*B)*(a + b*x)^6)/(168*a^3*x^6)]

    @test_int [((a + b*x)^5*(A + B*x))/x^10, x, 2, -((a^5*A)/(9*x^9)) - (a^4*(5*A*b + a*B))/(8*x^8) - (5*a^3*b*(2*A*b + a*B))/(7*x^7) - (5*a^2*b^2*(A*b + a*B))/(3*x^6) - (a*b^3*(A*b + 2*a*B))/x^5 - (b^4*(A*b + 5*a*B))/(4*x^4) - (b^5*B)/(3*x^3)]
    @test_int [((a + b*x)^5*(A + B*x))/x^11, x, 2, -((a^5*A)/(10*x^10)) - (a^4*(5*A*b + a*B))/(9*x^9) - (5*a^3*b*(2*A*b + a*B))/(8*x^8) - (10*a^2*b^2*(A*b + a*B))/(7*x^7) - (5*a*b^3*(A*b + 2*a*B))/(6*x^6) - (b^4*(A*b + 5*a*B))/(5*x^5) - (b^5*B)/(4*x^4)]
    @test_int [((a + b*x)^5*(A + B*x))/x^12, x, 2, -((a^5*A)/(11*x^11)) - (a^4*(5*A*b + a*B))/(10*x^10) - (5*a^3*b*(2*A*b + a*B))/(9*x^9) - (5*a^2*b^2*(A*b + a*B))/(4*x^8) - (5*a*b^3*(A*b + 2*a*B))/(7*x^7) - (b^4*(A*b + 5*a*B))/(6*x^6) - (b^5*B)/(5*x^5)]

    @test_int [x^10*(a + b*x)^10*(A + B*x), x, 2, (1/11)*a^10*A*x^11 + (1/12)*a^9*(10*A*b + a*B)*x^12 + (5/13)*a^8*b*(9*A*b + 2*a*B)*x^13 + (15/14)*a^7*b^2*(8*A*b + 3*a*B)*x^14 + 2*a^6*b^3*(7*A*b + 4*a*B)*x^15 + (21/8)*a^5*b^4*(6*A*b + 5*a*B)*x^16 + (42/17)*a^4*b^5*(5*A*b + 6*a*B)*x^17 + (5/3)*a^3*b^6*(4*A*b + 7*a*B)*x^18 + (15/19)*a^2*b^7*(3*A*b + 8*a*B)*x^19 + (1/4)*a*b^8*(2*A*b + 9*a*B)*x^20 + (1/21)*b^9*(A*b + 10*a*B)*x^21 + (1/22)*b^10*B*x^22]
    @test_int [x^9*(a + b*x)^10*(A + B*x), x, 2, (1/10)*a^10*A*x^10 + (1/11)*a^9*(10*A*b + a*B)*x^11 + (5/12)*a^8*b*(9*A*b + 2*a*B)*x^12 + (15/13)*a^7*b^2*(8*A*b + 3*a*B)*x^13 + (15/7)*a^6*b^3*(7*A*b + 4*a*B)*x^14 + (14/5)*a^5*b^4*(6*A*b + 5*a*B)*x^15 + (21/8)*a^4*b^5*(5*A*b + 6*a*B)*x^16 + (30/17)*a^3*b^6*(4*A*b + 7*a*B)*x^17 + (5/6)*a^2*b^7*(3*A*b + 8*a*B)*x^18 + (5/19)*a*b^8*(2*A*b + 9*a*B)*x^19 + (1/20)*b^9*(A*b + 10*a*B)*x^20 + (1/21)*b^10*B*x^21]

    @test_int [x^8*(a + b*x)^10*(A + B*x), x, 2, (a^8*(A*b - a*B)*(a + b*x)^11)/(11*b^10) - (a^7*(8*A*b - 9*a*B)*(a + b*x)^12)/(12*b^10) + (4*a^6*(7*A*b - 9*a*B)*(a + b*x)^13)/(13*b^10) - (2*a^5*(2*A*b - 3*a*B)*(a + b*x)^14)/b^10 + (14*a^4*(5*A*b - 9*a*B)*(a + b*x)^15)/(15*b^10) - (7*a^3*(4*A*b - 9*a*B)*(a + b*x)^16)/(8*b^10) + (28*a^2*(A*b - 3*a*B)*(a + b*x)^17)/(17*b^10) - (2*a*(2*A*b - 9*a*B)*(a + b*x)^18)/(9*b^10) + ((A*b - 9*a*B)*(a + b*x)^19)/(19*b^10) + (B*(a + b*x)^20)/(20*b^10)]
    @test_int [x^7*(a + b*x)^10*(A + B*x), x, 2, -((a^7*(A*b - a*B)*(a + b*x)^11)/(11*b^9)) + (a^6*(7*A*b - 8*a*B)*(a + b*x)^12)/(12*b^9) - (7*a^5*(3*A*b - 4*a*B)*(a + b*x)^13)/(13*b^9) + (a^4*(5*A*b - 8*a*B)*(a + b*x)^14)/(2*b^9) - (7*a^3*(A*b - 2*a*B)*(a + b*x)^15)/(3*b^9) + (7*a^2*(3*A*b - 8*a*B)*(a + b*x)^16)/(16*b^9) - (7*a*(A*b - 4*a*B)*(a + b*x)^17)/(17*b^9) + ((A*b - 8*a*B)*(a + b*x)^18)/(18*b^9) + (B*(a + b*x)^19)/(19*b^9)]
    @test_int [x^6*(a + b*x)^10*(A + B*x), x, 2, (a^6*(A*b - a*B)*(a + b*x)^11)/(11*b^8) - (a^5*(6*A*b - 7*a*B)*(a + b*x)^12)/(12*b^8) + (3*a^4*(5*A*b - 7*a*B)*(a + b*x)^13)/(13*b^8) - (5*a^3*(4*A*b - 7*a*B)*(a + b*x)^14)/(14*b^8) + (a^2*(3*A*b - 7*a*B)*(a + b*x)^15)/(3*b^8) - (3*a*(2*A*b - 7*a*B)*(a + b*x)^16)/(16*b^8) + ((A*b - 7*a*B)*(a + b*x)^17)/(17*b^8) + (B*(a + b*x)^18)/(18*b^8)]
    @test_int [x^5*(a + b*x)^10*(A + B*x), x, 2, -((a^5*(A*b - a*B)*(a + b*x)^11)/(11*b^7)) + (a^4*(5*A*b - 6*a*B)*(a + b*x)^12)/(12*b^7) - (5*a^3*(2*A*b - 3*a*B)*(a + b*x)^13)/(13*b^7) + (5*a^2*(A*b - 2*a*B)*(a + b*x)^14)/(7*b^7) - (a*(A*b - 3*a*B)*(a + b*x)^15)/(3*b^7) + ((A*b - 6*a*B)*(a + b*x)^16)/(16*b^7) + (B*(a + b*x)^17)/(17*b^7)]
    @test_int [x^4*(a + b*x)^10*(A + B*x), x, 2, (a^4*(A*b - a*B)*(a + b*x)^11)/(11*b^6) - (a^3*(4*A*b - 5*a*B)*(a + b*x)^12)/(12*b^6) + (2*a^2*(3*A*b - 5*a*B)*(a + b*x)^13)/(13*b^6) - (a*(2*A*b - 5*a*B)*(a + b*x)^14)/(7*b^6) + ((A*b - 5*a*B)*(a + b*x)^15)/(15*b^6) + (B*(a + b*x)^16)/(16*b^6)]
    @test_int [x^3*(a + b*x)^10*(A + B*x), x, 2, -((a^3*(A*b - a*B)*(a + b*x)^11)/(11*b^5)) + (a^2*(3*A*b - 4*a*B)*(a + b*x)^12)/(12*b^5) - (3*a*(A*b - 2*a*B)*(a + b*x)^13)/(13*b^5) + ((A*b - 4*a*B)*(a + b*x)^14)/(14*b^5) + (B*(a + b*x)^15)/(15*b^5)]
    @test_int [x^2*(a + b*x)^10*(A + B*x), x, 2, (a^2*(A*b - a*B)*(a + b*x)^11)/(11*b^4) - (a*(2*A*b - 3*a*B)*(a + b*x)^12)/(12*b^4) + ((A*b - 3*a*B)*(a + b*x)^13)/(13*b^4) + (B*(a + b*x)^14)/(14*b^4)]
    @test_int [x^1*(a + b*x)^10*(A + B*x), x, 2, -((a*(A*b - a*B)*(a + b*x)^11)/(11*b^3)) + ((A*b - 2*a*B)*(a + b*x)^12)/(12*b^3) + (B*(a + b*x)^13)/(13*b^3)]
    @test_int [x^0*(a + b*x)^10*(A + B*x), x, 2, ((A*b - a*B)*(a + b*x)^11)/(11*b^2) + (B*(a + b*x)^12)/(12*b^2)]

    @test_int [((a + b*x)^10*(A + B*x))/x^1, x, 3, 10*a^9*A*b*x + (45*a^8*A*b^2*x^2)/2 + 40*a^7*A*b^3*x^3 + (105*a^6*A*b^4*x^4)/2 + (252*a^5*A*b^5*x^5)/5 + 35*a^4*A*b^6*x^6 + (120*a^3*A*b^7*x^7)/7 + (45*a^2*A*b^8*x^8)/8 + (10*a*A*b^9*x^9)/9 + (A*b^10*x^10)/10 + (B*(a + b*x)^11)/(11*b) + a^10*A*log(x)]
    @test_int [((a + b*x)^10*(A + B*x))/x^2, x, 2, -((a^10*A)/x) + 5*a^8*b*(9*A*b + 2*a*B)*x + (15/2)*a^7*b^2*(8*A*b + 3*a*B)*x^2 + 10*a^6*b^3*(7*A*b + 4*a*B)*x^3 + (21/2)*a^5*b^4*(6*A*b + 5*a*B)*x^4 + (42/5)*a^4*b^5*(5*A*b + 6*a*B)*x^5 + 5*a^3*b^6*(4*A*b + 7*a*B)*x^6 + (15/7)*a^2*b^7*(3*A*b + 8*a*B)*x^7 + (5/8)*a*b^8*(2*A*b + 9*a*B)*x^8 + (1/9)*b^9*(A*b + 10*a*B)*x^9 + (1/10)*b^10*B*x^10 + a^9*(10*A*b + a*B)*log(x)]
    @test_int [((a + b*x)^10*(A + B*x))/x^3, x, 2, -((a^10*A)/(2*x^2)) - (a^9*(10*A*b + a*B))/x + 15*a^7*b^2*(8*A*b + 3*a*B)*x + 15*a^6*b^3*(7*A*b + 4*a*B)*x^2 + 14*a^5*b^4*(6*A*b + 5*a*B)*x^3 + (21/2)*a^4*b^5*(5*A*b + 6*a*B)*x^4 + 6*a^3*b^6*(4*A*b + 7*a*B)*x^5 + (5/2)*a^2*b^7*(3*A*b + 8*a*B)*x^6 + (5/7)*a*b^8*(2*A*b + 9*a*B)*x^7 + (1/8)*b^9*(A*b + 10*a*B)*x^8 + (1/9)*b^10*B*x^9 + 5*a^8*b*(9*A*b + 2*a*B)*log(x)]
    @test_int [((a + b*x)^10*(A + B*x))/x^4, x, 2, -((a^10*A)/(3*x^3)) - (a^9*(10*A*b + a*B))/(2*x^2) - (5*a^8*b*(9*A*b + 2*a*B))/x + 30*a^6*b^3*(7*A*b + 4*a*B)*x + 21*a^5*b^4*(6*A*b + 5*a*B)*x^2 + 14*a^4*b^5*(5*A*b + 6*a*B)*x^3 + (15/2)*a^3*b^6*(4*A*b + 7*a*B)*x^4 + 3*a^2*b^7*(3*A*b + 8*a*B)*x^5 + (5/6)*a*b^8*(2*A*b + 9*a*B)*x^6 + (1/7)*b^9*(A*b + 10*a*B)*x^7 + (1/8)*b^10*B*x^8 + 15*a^7*b^2*(8*A*b + 3*a*B)*log(x)]
    @test_int [((a + b*x)^10*(A + B*x))/x^5, x, 2, -((a^10*A)/(4*x^4)) - (a^9*(10*A*b + a*B))/(3*x^3) - (5*a^8*b*(9*A*b + 2*a*B))/(2*x^2) - (15*a^7*b^2*(8*A*b + 3*a*B))/x + 42*a^5*b^4*(6*A*b + 5*a*B)*x + 21*a^4*b^5*(5*A*b + 6*a*B)*x^2 + 10*a^3*b^6*(4*A*b + 7*a*B)*x^3 + (15/4)*a^2*b^7*(3*A*b + 8*a*B)*x^4 + a*b^8*(2*A*b + 9*a*B)*x^5 + (1/6)*b^9*(A*b + 10*a*B)*x^6 + (1/7)*b^10*B*x^7 + 30*a^6*b^3*(7*A*b + 4*a*B)*log(x)]
    @test_int [((a + b*x)^10*(A + B*x))/x^6, x, 2, -((a^10*A)/(5*x^5)) - (a^9*(10*A*b + a*B))/(4*x^4) - (5*a^8*b*(9*A*b + 2*a*B))/(3*x^3) - (15*a^7*b^2*(8*A*b + 3*a*B))/(2*x^2) - (30*a^6*b^3*(7*A*b + 4*a*B))/x + 42*a^4*b^5*(5*A*b + 6*a*B)*x + 15*a^3*b^6*(4*A*b + 7*a*B)*x^2 + 5*a^2*b^7*(3*A*b + 8*a*B)*x^3 + (5/4)*a*b^8*(2*A*b + 9*a*B)*x^4 + (1/5)*b^9*(A*b + 10*a*B)*x^5 + (1/6)*b^10*B*x^6 + 42*a^5*b^4*(6*A*b + 5*a*B)*log(x)]
    @test_int [((a + b*x)^10*(A + B*x))/x^7, x, 2, -((a^10*A)/(6*x^6)) - (a^9*(10*A*b + a*B))/(5*x^5) - (5*a^8*b*(9*A*b + 2*a*B))/(4*x^4) - (5*a^7*b^2*(8*A*b + 3*a*B))/x^3 - (15*a^6*b^3*(7*A*b + 4*a*B))/x^2 - (42*a^5*b^4*(6*A*b + 5*a*B))/x + 30*a^3*b^6*(4*A*b + 7*a*B)*x + (15/2)*a^2*b^7*(3*A*b + 8*a*B)*x^2 + (5/3)*a*b^8*(2*A*b + 9*a*B)*x^3 + (1/4)*b^9*(A*b + 10*a*B)*x^4 + (1/5)*b^10*B*x^5 + 42*a^4*b^5*(5*A*b + 6*a*B)*log(x)]
    @test_int [((a + b*x)^10*(A + B*x))/x^8, x, 2, -((a^10*A)/(7*x^7)) - (a^9*(10*A*b + a*B))/(6*x^6) - (a^8*b*(9*A*b + 2*a*B))/x^5 - (15*a^7*b^2*(8*A*b + 3*a*B))/(4*x^4) - (10*a^6*b^3*(7*A*b + 4*a*B))/x^3 - (21*a^5*b^4*(6*A*b + 5*a*B))/x^2 - (42*a^4*b^5*(5*A*b + 6*a*B))/x + 15*a^2*b^7*(3*A*b + 8*a*B)*x + (5/2)*a*b^8*(2*A*b + 9*a*B)*x^2 + (1/3)*b^9*(A*b + 10*a*B)*x^3 + (1/4)*b^10*B*x^4 + 30*a^3*b^6*(4*A*b + 7*a*B)*log(x)]
    @test_int [((a + b*x)^10*(A + B*x))/x^9, x, 2, -((a^10*A)/(8*x^8)) - (a^9*(10*A*b + a*B))/(7*x^7) - (5*a^8*b*(9*A*b + 2*a*B))/(6*x^6) - (3*a^7*b^2*(8*A*b + 3*a*B))/x^5 - (15*a^6*b^3*(7*A*b + 4*a*B))/(2*x^4) - (14*a^5*b^4*(6*A*b + 5*a*B))/x^3 - (21*a^4*b^5*(5*A*b + 6*a*B))/x^2 - (30*a^3*b^6*(4*A*b + 7*a*B))/x + 5*a*b^8*(2*A*b + 9*a*B)*x + (1/2)*b^9*(A*b + 10*a*B)*x^2 + (1/3)*b^10*B*x^3 + 15*a^2*b^7*(3*A*b + 8*a*B)*log(x)]
    @test_int [((a + b*x)^10*(A + B*x))/x^10, x, 2, -((a^10*A)/(9*x^9)) - (a^9*(10*A*b + a*B))/(8*x^8) - (5*a^8*b*(9*A*b + 2*a*B))/(7*x^7) - (5*a^7*b^2*(8*A*b + 3*a*B))/(2*x^6) - (6*a^6*b^3*(7*A*b + 4*a*B))/x^5 - (21*a^5*b^4*(6*A*b + 5*a*B))/(2*x^4) - (14*a^4*b^5*(5*A*b + 6*a*B))/x^3 - (15*a^3*b^6*(4*A*b + 7*a*B))/x^2 - (15*a^2*b^7*(3*A*b + 8*a*B))/x + b^9*(A*b + 10*a*B)*x + (1/2)*b^10*B*x^2 + 5*a*b^8*(2*A*b + 9*a*B)*log(x)]
    @test_int [((a + b*x)^10*(A + B*x))/x^11, x, 2, -((a^10*A)/(10*x^10)) - (a^9*(10*A*b + a*B))/(9*x^9) - (5*a^8*b*(9*A*b + 2*a*B))/(8*x^8) - (15*a^7*b^2*(8*A*b + 3*a*B))/(7*x^7) - (5*a^6*b^3*(7*A*b + 4*a*B))/x^6 - (42*a^5*b^4*(6*A*b + 5*a*B))/(5*x^5) - (21*a^4*b^5*(5*A*b + 6*a*B))/(2*x^4) - (10*a^3*b^6*(4*A*b + 7*a*B))/x^3 - (15*a^2*b^7*(3*A*b + 8*a*B))/(2*x^2) - (5*a*b^8*(2*A*b + 9*a*B))/x + b^10*B*x + b^9*(A*b + 10*a*B)*log(x)]
    @test_int [((a + b*x)^10*(A + B*x))/x^12, x, 3, -(a^10*B)/(10*x^10) - (10*a^9*b*B)/(9*x^9) - (45*a^8*b^2*B)/(8*x^8) - (120*a^7*b^3*B)/(7*x^7) - (35*a^6*b^4*B)/x^6 - (252*a^5*b^5*B)/(5*x^5) - (105*a^4*b^6*B)/(2*x^4) - (40*a^3*b^7*B)/x^3 - (45*a^2*b^8*B)/(2*x^2) - (10*a*b^9*B)/x - (A*(a + b*x)^11)/(11*a*x^11) + b^10*B*log(x)]

    @test_int [((a + b*x)^10*(A + B*x))/x^13, x, 2, -(A*(a + b*x)^11)/(12*a*x^12) + ((A*b - 12*a*B)*(a + b*x)^11)/(132*a^2*x^11)]
    @test_int [((a + b*x)^10*(A + B*x))/x^14, x, 3, -(A*(a + b*x)^11)/(13*a*x^13) + ((2*A*b - 13*a*B)*(a + b*x)^11)/(156*a^2*x^12) - (b*(2*A*b - 13*a*B)*(a + b*x)^11)/(1716*a^3*x^11)]
    @test_int [((a + b*x)^10*(A + B*x))/x^15, x, 4, -(A*(a + b*x)^11)/(14*a*x^14) + ((3*A*b - 14*a*B)*(a + b*x)^11)/(182*a^2*x^13) - (b*(3*A*b - 14*a*B)*(a + b*x)^11)/(1092*a^3*x^12) + (b^2*(3*A*b - 14*a*B)*(a + b*x)^11)/(12012*a^4*x^11)]
    @test_int [((a + b*x)^10*(A + B*x))/x^16, x, 5, -(A*(a + b*x)^11)/(15*a*x^15) + ((4*A*b - 15*a*B)*(a + b*x)^11)/(210*a^2*x^14) - (b*(4*A*b - 15*a*B)*(a + b*x)^11)/(910*a^3*x^13) + (b^2*(4*A*b - 15*a*B)*(a + b*x)^11)/(5460*a^4*x^12) - (b^3*(4*A*b - 15*a*B)*(a + b*x)^11)/(60060*a^5*x^11)]
    @test_int [((a + b*x)^10*(A + B*x))/x^17, x, 6, -(A*(a + b*x)^11)/(16*a*x^16) + ((5*A*b - 16*a*B)*(a + b*x)^11)/(240*a^2*x^15) - (b*(5*A*b - 16*a*B)*(a + b*x)^11)/(840*a^3*x^14) + (b^2*(5*A*b - 16*a*B)*(a + b*x)^11)/(3640*a^4*x^13) - (b^3*(5*A*b - 16*a*B)*(a + b*x)^11)/(21840*a^5*x^12) + (b^4*(5*A*b - 16*a*B)*(a + b*x)^11)/(240240*a^6*x^11)]
    @test_int [((a + b*x)^10*(A + B*x))/x^18, x, 7, -((A*(a + b*x)^11)/(17*a*x^17)) + ((6*A*b - 17*a*B)*(a + b*x)^11)/(272*a^2*x^16) - (b*(6*A*b - 17*a*B)*(a + b*x)^11)/(816*a^3*x^15) + (b^2*(6*A*b - 17*a*B)*(a + b*x)^11)/(2856*a^4*x^14) - (b^3*(6*A*b - 17*a*B)*(a + b*x)^11)/(12376*a^5*x^13) + (b^4*(6*A*b - 17*a*B)*(a + b*x)^11)/(74256*a^6*x^12) - (b^5*(6*A*b - 17*a*B)*(a + b*x)^11)/(816816*a^7*x^11)]

    @test_int [((a + b*x)^10*(A + B*x))/x^19, x, 2, -((a^10*A)/(18*x^18)) - (a^9*(10*A*b + a*B))/(17*x^17) - (5*a^8*b*(9*A*b + 2*a*B))/(16*x^16) - (a^7*b^2*(8*A*b + 3*a*B))/x^15 - (15*a^6*b^3*(7*A*b + 4*a*B))/(7*x^14) - (42*a^5*b^4*(6*A*b + 5*a*B))/(13*x^13) - (7*a^4*b^5*(5*A*b + 6*a*B))/(2*x^12) - (30*a^3*b^6*(4*A*b + 7*a*B))/(11*x^11) - (3*a^2*b^7*(3*A*b + 8*a*B))/(2*x^10) - (5*a*b^8*(2*A*b + 9*a*B))/(9*x^9) - (b^9*(A*b + 10*a*B))/(8*x^8) - (b^10*B)/(7*x^7)]
    @test_int [((a + b*x)^10*(A + B*x))/x^20, x, 2, -((a^10*A)/(19*x^19)) - (a^9*(10*A*b + a*B))/(18*x^18) - (5*a^8*b*(9*A*b + 2*a*B))/(17*x^17) - (15*a^7*b^2*(8*A*b + 3*a*B))/(16*x^16) - (2*a^6*b^3*(7*A*b + 4*a*B))/x^15 - (3*a^5*b^4*(6*A*b + 5*a*B))/x^14 - (42*a^4*b^5*(5*A*b + 6*a*B))/(13*x^13) - (5*a^3*b^6*(4*A*b + 7*a*B))/(2*x^12) - (15*a^2*b^7*(3*A*b + 8*a*B))/(11*x^11) - (a*b^8*(2*A*b + 9*a*B))/(2*x^10) - (b^9*(A*b + 10*a*B))/(9*x^9) - (b^10*B)/(8*x^8)]
    @test_int [((a + b*x)^10*(A + B*x))/x^21, x, 2, -((a^10*A)/(20*x^20)) - (a^9*(10*A*b + a*B))/(19*x^19) - (5*a^8*b*(9*A*b + 2*a*B))/(18*x^18) - (15*a^7*b^2*(8*A*b + 3*a*B))/(17*x^17) - (15*a^6*b^3*(7*A*b + 4*a*B))/(8*x^16) - (14*a^5*b^4*(6*A*b + 5*a*B))/(5*x^15) - (3*a^4*b^5*(5*A*b + 6*a*B))/x^14 - (30*a^3*b^6*(4*A*b + 7*a*B))/(13*x^13) - (5*a^2*b^7*(3*A*b + 8*a*B))/(4*x^12) - (5*a*b^8*(2*A*b + 9*a*B))/(11*x^11) - (b^9*(A*b + 10*a*B))/(10*x^10) - (b^10*B)/(9*x^9)]

    #= [x^14*(a + b*x)^15*(A + B*x), x, 2, (1/15)*a^15*A*x^15 + (1/16)*a^14*(15*A*b + a*B)*x^16 + (15/17)*a^13*b*(7*A*b + a*B)*x^17 + (35/18)*a^12*b^2*(13*A*b + 3*a*B)*x^18 + (455/19)*a^11*b^3*(3*A*b + a*B)*x^19 + (273/20)*a^10*b^4*(11*A*b + 5*a*B)*x^20 + (143/3)*a^9*b^5*(5*A*b + 3*a*B)*x^21 + (65/2)*a^8*b^6*(9*A*b + 7*a*B)*x^22 + (6435/23)*a^7*b^7*(A*b + a*B)*x^23 + (715/24)*a^6*b^8*(7*A*b + 9*a*B)*x^24 + (1001/25)*a^5*b^9*(3*A*b + 5*a*B)*x^25 + (21/2)*a^4*b^10*(5*A*b + 11*a*B)*x^26 + (455/27)*a^3*b^11*(A*b + 3*a*B)*x^27 + (5/4)*a^2*b^12*(3*A*b + 13*a*B)*x^28 + (15/29)*a*b^13*(A*b + 7*a*B)*x^29 + (1/30)*b^14*(A*b + 15*a*B)*x^30 + (1/31)*b^15*B*x^31]
    @test_int [x^13*(a + b*x)^15*(A + B*x), x, 2, (1/14)*a^15*A*x^14 + (1/15)*a^14*(15*A*b + a*B)*x^15 + (15/16)*a^13*b*(7*A*b + a*B)*x^16 + (35/17)*a^12*b^2*(13*A*b + 3*a*B)*x^17 + (455/18)*a^11*b^3*(3*A*b + a*B)*x^18 + (273/19)*a^10*b^4*(11*A*b + 5*a*B)*x^19 + (1001/20)*a^9*b^5*(5*A*b + 3*a*B)*x^20 + (715/21)*a^8*b^6*(9*A*b + 7*a*B)*x^21 + (585/2)*a^7*b^7*(A*b + a*B)*x^22 + (715/23)*a^6*b^8*(7*A*b + 9*a*B)*x^23 + (1001/24)*a^5*b^9*(3*A*b + 5*a*B)*x^24 + (273/25)*a^4*b^10*(5*A*b + 11*a*B)*x^25 + (35/2)*a^3*b^11*(A*b + 3*a*B)*x^26 + (35/27)*a^2*b^12*(3*A*b + 13*a*B)*x^27 + (15/28)*a*b^13*(A*b + 7*a*B)*x^28 + (1/29)*b^14*(A*b + 15*a*B)*x^29 + (1/30)*b^15*B*x^30]
    @test_int [x^12*(a + b*x)^15*(A + B*x), x, 2, (1/13)*a^15*A*x^13 + (1/14)*a^14*(15*A*b + a*B)*x^14 + a^13*b*(7*A*b + a*B)*x^15 + (35/16)*a^12*b^2*(13*A*b + 3*a*B)*x^16 + (455/17)*a^11*b^3*(3*A*b + a*B)*x^17 + (91/6)*a^10*b^4*(11*A*b + 5*a*B)*x^18 + (1001/19)*a^9*b^5*(5*A*b + 3*a*B)*x^19 + (143/4)*a^8*b^6*(9*A*b + 7*a*B)*x^20 + (2145/7)*a^7*b^7*(A*b + a*B)*x^21 + (65/2)*a^6*b^8*(7*A*b + 9*a*B)*x^22 + (1001/23)*a^5*b^9*(3*A*b + 5*a*B)*x^23 + (91/8)*a^4*b^10*(5*A*b + 11*a*B)*x^24 + (91/5)*a^3*b^11*(A*b + 3*a*B)*x^25 + (35/26)*a^2*b^12*(3*A*b + 13*a*B)*x^26 + (5/9)*a*b^13*(A*b + 7*a*B)*x^27 + (1/28)*b^14*(A*b + 15*a*B)*x^28 + (1/29)*b^15*B*x^29]

    @test_int [x^11*(a + b*x)^15*(A + B*x), x, 2, -((a^11*(A*b - a*B)*(a + b*x)^16)/(16*b^13)) + (a^10*(11*A*b - 12*a*B)*(a + b*x)^17)/(17*b^13) - (11*a^9*(5*A*b - 6*a*B)*(a + b*x)^18)/(18*b^13) + (55*a^8*(3*A*b - 4*a*B)*(a + b*x)^19)/(19*b^13) - (33*a^7*(2*A*b - 3*a*B)*(a + b*x)^20)/(4*b^13) + (22*a^6*(7*A*b - 12*a*B)*(a + b*x)^21)/(7*b^13) - (21*a^5*(A*b - 2*a*B)*(a + b*x)^22)/b^13 + (66*a^4*(5*A*b - 12*a*B)*(a + b*x)^23)/(23*b^13) - (55*a^3*(A*b - 3*a*B)*(a + b*x)^24)/(8*b^13) + (11*a^2*(A*b - 4*a*B)*(a + b*x)^25)/(5*b^13) - (11*a*(A*b - 6*a*B)*(a + b*x)^26)/(26*b^13) + ((A*b - 12*a*B)*(a + b*x)^27)/(27*b^13) + (B*(a + b*x)^28)/(28*b^13)]
    @test_int [x^10*(a + b*x)^15*(A + B*x), x, 2, (a^10*(A*b - a*B)*(a + b*x)^16)/(16*b^12) - (a^9*(10*A*b - 11*a*B)*(a + b*x)^17)/(17*b^12) + (5*a^8*(9*A*b - 11*a*B)*(a + b*x)^18)/(18*b^12) - (15*a^7*(8*A*b - 11*a*B)*(a + b*x)^19)/(19*b^12) + (3*a^6*(7*A*b - 11*a*B)*(a + b*x)^20)/(2*b^12) - (2*a^5*(6*A*b - 11*a*B)*(a + b*x)^21)/b^12 + (21*a^4*(5*A*b - 11*a*B)*(a + b*x)^22)/(11*b^12) - (30*a^3*(4*A*b - 11*a*B)*(a + b*x)^23)/(23*b^12) + (5*a^2*(3*A*b - 11*a*B)*(a + b*x)^24)/(8*b^12) - (a*(2*A*b - 11*a*B)*(a + b*x)^25)/(5*b^12) + ((A*b - 11*a*B)*(a + b*x)^26)/(26*b^12) + (B*(a + b*x)^27)/(27*b^12)]
    @test_int [x^9*(a + b*x)^15*(A + B*x), x, 2, -(a^9*(A*b - a*B)*(a + b*x)^16)/(16*b^11) + (a^8*(9*A*b - 10*a*B)*(a + b*x)^17)/(17*b^11) - (a^7*(4*A*b - 5*a*B)*(a + b*x)^18)/(2*b^11) + (12*a^6*(7*A*b - 10*a*B)*(a + b*x)^19)/(19*b^11) - (21*a^5*(3*A*b - 5*a*B)*(a + b*x)^20)/(10*b^11) + (6*a^4*(A*b - 2*a*B)*(a + b*x)^21)/b^11 - (21*a^3*(2*A*b - 5*a*B)*(a + b*x)^22)/(11*b^11) + (12*a^2*(3*A*b - 10*a*B)*(a + b*x)^23)/(23*b^11) - (3*a*(A*b - 5*a*B)*(a + b*x)^24)/(8*b^11) + ((A*b - 10*a*B)*(a + b*x)^25)/(25*b^11) + (B*(a + b*x)^26)/(26*b^11)]
    @test_int [x^8*(a + b*x)^15*(A + B*x), x, 2, (a^8*(A*b - a*B)*(a + b*x)^16)/(16*b^10) - (a^7*(8*A*b - 9*a*B)*(a + b*x)^17)/(17*b^10) + (2*a^6*(7*A*b - 9*a*B)*(a + b*x)^18)/(9*b^10) - (28*a^5*(2*A*b - 3*a*B)*(a + b*x)^19)/(19*b^10) + (7*a^4*(5*A*b - 9*a*B)*(a + b*x)^20)/(10*b^10) - (2*a^3*(4*A*b - 9*a*B)*(a + b*x)^21)/(3*b^10) + (14*a^2*(A*b - 3*a*B)*(a + b*x)^22)/(11*b^10) - (4*a*(2*A*b - 9*a*B)*(a + b*x)^23)/(23*b^10) + ((A*b - 9*a*B)*(a + b*x)^24)/(24*b^10) + (B*(a + b*x)^25)/(25*b^10)]
    @test_int [x^7*(a + b*x)^15*(A + B*x), x, 2, -(a^7*(A*b - a*B)*(a + b*x)^16)/(16*b^9) + (a^6*(7*A*b - 8*a*B)*(a + b*x)^17)/(17*b^9) - (7*a^5*(3*A*b - 4*a*B)*(a + b*x)^18)/(18*b^9) + (7*a^4*(5*A*b - 8*a*B)*(a + b*x)^19)/(19*b^9) - (7*a^3*(A*b - 2*a*B)*(a + b*x)^20)/(4*b^9) + (a^2*(3*A*b - 8*a*B)*(a + b*x)^21)/(3*b^9) - (7*a*(A*b - 4*a*B)*(a + b*x)^22)/(22*b^9) + ((A*b - 8*a*B)*(a + b*x)^23)/(23*b^9) + (B*(a + b*x)^24)/(24*b^9)]
    @test_int [x^6*(a + b*x)^15*(A + B*x), x, 2, (a^6*(A*b - a*B)*(a + b*x)^16)/(16*b^8) - (a^5*(6*A*b - 7*a*B)*(a + b*x)^17)/(17*b^8) + (a^4*(5*A*b - 7*a*B)*(a + b*x)^18)/(6*b^8) - (5*a^3*(4*A*b - 7*a*B)*(a + b*x)^19)/(19*b^8) + (a^2*(3*A*b - 7*a*B)*(a + b*x)^20)/(4*b^8) - (a*(2*A*b - 7*a*B)*(a + b*x)^21)/(7*b^8) + ((A*b - 7*a*B)*(a + b*x)^22)/(22*b^8) + (B*(a + b*x)^23)/(23*b^8)]
    @test_int [x^5*(a + b*x)^15*(A + B*x), x, 2, -(a^5*(A*b - a*B)*(a + b*x)^16)/(16*b^7) + (a^4*(5*A*b - 6*a*B)*(a + b*x)^17)/(17*b^7) - (5*a^3*(2*A*b - 3*a*B)*(a + b*x)^18)/(18*b^7) + (10*a^2*(A*b - 2*a*B)*(a + b*x)^19)/(19*b^7) - (a*(A*b - 3*a*B)*(a + b*x)^20)/(4*b^7) + ((A*b - 6*a*B)*(a + b*x)^21)/(21*b^7) + (B*(a + b*x)^22)/(22*b^7)]
    @test_int [x^4*(a + b*x)^15*(A + B*x), x, 2, (a^4*(A*b - a*B)*(a + b*x)^16)/(16*b^6) - (a^3*(4*A*b - 5*a*B)*(a + b*x)^17)/(17*b^6) + (a^2*(3*A*b - 5*a*B)*(a + b*x)^18)/(9*b^6) - (2*a*(2*A*b - 5*a*B)*(a + b*x)^19)/(19*b^6) + ((A*b - 5*a*B)*(a + b*x)^20)/(20*b^6) + (B*(a + b*x)^21)/(21*b^6)]
    @test_int [x^3*(a + b*x)^15*(A + B*x), x, 2, -(a^3*(A*b - a*B)*(a + b*x)^16)/(16*b^5) + (a^2*(3*A*b - 4*a*B)*(a + b*x)^17)/(17*b^5) - (a*(A*b - 2*a*B)*(a + b*x)^18)/(6*b^5) + ((A*b - 4*a*B)*(a + b*x)^19)/(19*b^5) + (B*(a + b*x)^20)/(20*b^5)]
    @test_int [x^2*(a + b*x)^15*(A + B*x), x, 2, (a^2*(A*b - a*B)*(a + b*x)^16)/(16*b^4) - (a*(2*A*b - 3*a*B)*(a + b*x)^17)/(17*b^4) + ((A*b - 3*a*B)*(a + b*x)^18)/(18*b^4) + (B*(a + b*x)^19)/(19*b^4)]
    @test_int [x*(a + b*x)^15*(A + B*x), x, 2, -(a*(A*b - a*B)*(a + b*x)^16)/(16*b^3) + ((A*b - 2*a*B)*(a + b*x)^17)/(17*b^3) + (B*(a + b*x)^18)/(18*b^3)]
    @test_int [(a + b*x)^15*(A + B*x), x, 2, ((A*b - a*B)*(a + b*x)^16)/(16*b^2) + (B*(a + b*x)^17)/(17*b^2)]

    @test_int [((a + b*x)^15*(A + B*x))/x, x, 3, 15*a^14*A*b*x + (105/2)*a^13*A*b^2*x^2 + (455/3)*a^12*A*b^3*x^3 + (1365/4)*a^11*A*b^4*x^4 + (3003/5)*a^10*A*b^5*x^5 + (5005/6)*a^9*A*b^6*x^6 + (6435/7)*a^8*A*b^7*x^7 + (6435/8)*a^7*A*b^8*x^8 + (5005/9)*a^6*A*b^9*x^9 + (3003/10)*a^5*A*b^10*x^10 + (1365/11)*a^4*A*b^11*x^11 + (455/12)*a^3*A*b^12*x^12 + (105/13)*a^2*A*b^13*x^13 + (15/14)*a*A*b^14*x^14 + (1/15)*A*b^15*x^15 + (B*(a + b*x)^16)/(16*b) + a^15*A*log(x)]
    @test_int [((a + b*x)^15*(A + B*x))/x^2, x, 2, -((a^15*A)/x) + 15*a^13*b*(7*A*b + a*B)*x + (35*a^12*b^2*(13*A*b + 3*a*B)*x^2)/2 + (455*a^11*b^3*(3*A*b + a*B)*x^3)/3 + (273*a^10*b^4*(11*A*b + 5*a*B)*x^4)/4 + (1001*a^9*b^5*(5*A*b + 3*a*B)*x^5)/5 + (715*a^8*b^6*(9*A*b + 7*a*B)*x^6)/6 + (6435*a^7*b^7*(A*b + a*B)*x^7)/7 + (715*a^6*b^8*(7*A*b + 9*a*B)*x^8)/8 + (1001*a^5*b^9*(3*A*b + 5*a*B)*x^9)/9 + (273*a^4*b^10*(5*A*b + 11*a*B)*x^10)/10 + (455*a^3*b^11*(A*b + 3*a*B)*x^11)/11 + (35*a^2*b^12*(3*A*b + 13*a*B)*x^12)/12 + (15*a*b^13*(A*b + 7*a*B)*x^13)/13 + (b^14*(A*b + 15*a*B)*x^14)/14 + (b^15*B*x^15)/15 + a^14*(15*A*b + a*B)*log(x)]
    @test_int [((a + b*x)^15*(A + B*x))/x^3, x, 2, -(a^15*A)/(2*x^2) - (a^14*(15*A*b + a*B))/x + 35*a^12*b^2*(13*A*b + 3*a*B)*x + (455*a^11*b^3*(3*A*b + a*B)*x^2)/2 + 91*a^10*b^4*(11*A*b + 5*a*B)*x^3 + (1001*a^9*b^5*(5*A*b + 3*a*B)*x^4)/4 + 143*a^8*b^6*(9*A*b + 7*a*B)*x^5 + (2145*a^7*b^7*(A*b + a*B)*x^6)/2 + (715*a^6*b^8*(7*A*b + 9*a*B)*x^7)/7 + (1001*a^5*b^9*(3*A*b + 5*a*B)*x^8)/8 + (91*a^4*b^10*(5*A*b + 11*a*B)*x^9)/3 + (91*a^3*b^11*(A*b + 3*a*B)*x^10)/2 + (35*a^2*b^12*(3*A*b + 13*a*B)*x^11)/11 + (5*a*b^13*(A*b + 7*a*B)*x^12)/4 + (b^14*(A*b + 15*a*B)*x^13)/13 + (b^15*B*x^14)/14 + 15*a^13*b*(7*A*b + a*B)*log(x)]
    @test_int [((a + b*x)^15*(A + B*x))/x^4, x, 2, -(a^15*A)/(3*x^3) - (a^14*(15*A*b + a*B))/(2*x^2) - (15*a^13*b*(7*A*b + a*B))/x + 455*a^11*b^3*(3*A*b + a*B)*x + (273*a^10*b^4*(11*A*b + 5*a*B)*x^2)/2 + (1001*a^9*b^5*(5*A*b + 3*a*B)*x^3)/3 + (715*a^8*b^6*(9*A*b + 7*a*B)*x^4)/4 + 1287*a^7*b^7*(A*b + a*B)*x^5 + (715*a^6*b^8*(7*A*b + 9*a*B)*x^6)/6 + 143*a^5*b^9*(3*A*b + 5*a*B)*x^7 + (273*a^4*b^10*(5*A*b + 11*a*B)*x^8)/8 + (455*a^3*b^11*(A*b + 3*a*B)*x^9)/9 + (7*a^2*b^12*(3*A*b + 13*a*B)*x^10)/2 + (15*a*b^13*(A*b + 7*a*B)*x^11)/11 + (b^14*(A*b + 15*a*B)*x^12)/12 + (b^15*B*x^13)/13 + 35*a^12*b^2*(13*A*b + 3*a*B)*log(x)]
    @test_int [((a + b*x)^15*(A + B*x))/x^5, x, 2, -(a^15*A)/(4*x^4) - (a^14*(15*A*b + a*B))/(3*x^3) - (15*a^13*b*(7*A*b + a*B))/(2*x^2) - (35*a^12*b^2*(13*A*b + 3*a*B))/x + 273*a^10*b^4*(11*A*b + 5*a*B)*x + (1001*a^9*b^5*(5*A*b + 3*a*B)*x^2)/2 + (715*a^8*b^6*(9*A*b + 7*a*B)*x^3)/3 + (6435*a^7*b^7*(A*b + a*B)*x^4)/4 + 143*a^6*b^8*(7*A*b + 9*a*B)*x^5 + (1001*a^5*b^9*(3*A*b + 5*a*B)*x^6)/6 + 39*a^4*b^10*(5*A*b + 11*a*B)*x^7 + (455*a^3*b^11*(A*b + 3*a*B)*x^8)/8 + (35*a^2*b^12*(3*A*b + 13*a*B)*x^9)/9 + (3*a*b^13*(A*b + 7*a*B)*x^10)/2 + (b^14*(A*b + 15*a*B)*x^11)/11 + (b^15*B*x^12)/12 + 455*a^11*b^3*(3*A*b + a*B)*log(x)]
    @test_int [((a + b*x)^15*(A + B*x))/x^6, x, 2, -(a^15*A)/(5*x^5) - (a^14*(15*A*b + a*B))/(4*x^4) - (5*a^13*b*(7*A*b + a*B))/x^3 - (35*a^12*b^2*(13*A*b + 3*a*B))/(2*x^2) - (455*a^11*b^3*(3*A*b + a*B))/x + 1001*a^9*b^5*(5*A*b + 3*a*B)*x + (715*a^8*b^6*(9*A*b + 7*a*B)*x^2)/2 + 2145*a^7*b^7*(A*b + a*B)*x^3 + (715*a^6*b^8*(7*A*b + 9*a*B)*x^4)/4 + (1001*a^5*b^9*(3*A*b + 5*a*B)*x^5)/5 + (91*a^4*b^10*(5*A*b + 11*a*B)*x^6)/2 + 65*a^3*b^11*(A*b + 3*a*B)*x^7 + (35*a^2*b^12*(3*A*b + 13*a*B)*x^8)/8 + (5*a*b^13*(A*b + 7*a*B)*x^9)/3 + (b^14*(A*b + 15*a*B)*x^10)/10 + (b^15*B*x^11)/11 + 273*a^10*b^4*(11*A*b + 5*a*B)*log(x)]
    @test_int [((a + b*x)^15*(A + B*x))/x^7, x, 2, -(a^15*A)/(6*x^6) - (a^14*(15*A*b + a*B))/(5*x^5) - (15*a^13*b*(7*A*b + a*B))/(4*x^4) - (35*a^12*b^2*(13*A*b + 3*a*B))/(3*x^3) - (455*a^11*b^3*(3*A*b + a*B))/(2*x^2) - (273*a^10*b^4*(11*A*b + 5*a*B))/x + 715*a^8*b^6*(9*A*b + 7*a*B)*x + (6435*a^7*b^7*(A*b + a*B)*x^2)/2 + (715*a^6*b^8*(7*A*b + 9*a*B)*x^3)/3 + (1001*a^5*b^9*(3*A*b + 5*a*B)*x^4)/4 + (273*a^4*b^10*(5*A*b + 11*a*B)*x^5)/5 + (455*a^3*b^11*(A*b + 3*a*B)*x^6)/6 + 5*a^2*b^12*(3*A*b + 13*a*B)*x^7 + (15*a*b^13*(A*b + 7*a*B)*x^8)/8 + (b^14*(A*b + 15*a*B)*x^9)/9 + (b^15*B*x^10)/10 + 1001*a^9*b^5*(5*A*b + 3*a*B)*log(x)]
    @test_int [((a + b*x)^15*(A + B*x))/x^8, x, 2, -(a^15*A)/(7*x^7) - (a^14*(15*A*b + a*B))/(6*x^6) - (3*a^13*b*(7*A*b + a*B))/x^5 - (35*a^12*b^2*(13*A*b + 3*a*B))/(4*x^4) - (455*a^11*b^3*(3*A*b + a*B))/(3*x^3) - (273*a^10*b^4*(11*A*b + 5*a*B))/(2*x^2) - (1001*a^9*b^5*(5*A*b + 3*a*B))/x + 6435*a^7*b^7*(A*b + a*B)*x + (715*a^6*b^8*(7*A*b + 9*a*B)*x^2)/2 + (1001*a^5*b^9*(3*A*b + 5*a*B)*x^3)/3 + (273*a^4*b^10*(5*A*b + 11*a*B)*x^4)/4 + 91*a^3*b^11*(A*b + 3*a*B)*x^5 + (35*a^2*b^12*(3*A*b + 13*a*B)*x^6)/6 + (15*a*b^13*(A*b + 7*a*B)*x^7)/7 + (b^14*(A*b + 15*a*B)*x^8)/8 + (b^15*B*x^9)/9 + 715*a^8*b^6*(9*A*b + 7*a*B)*log(x)]
    @test_int [((a + b*x)^15*(A + B*x))/x^9, x, 2, -(a^15*A)/(8*x^8) - (a^14*(15*A*b + a*B))/(7*x^7) - (5*a^13*b*(7*A*b + a*B))/(2*x^6) - (7*a^12*b^2*(13*A*b + 3*a*B))/x^5 - (455*a^11*b^3*(3*A*b + a*B))/(4*x^4) - (91*a^10*b^4*(11*A*b + 5*a*B))/x^3 - (1001*a^9*b^5*(5*A*b + 3*a*B))/(2*x^2) - (715*a^8*b^6*(9*A*b + 7*a*B))/x + 715*a^6*b^8*(7*A*b + 9*a*B)*x + (1001*a^5*b^9*(3*A*b + 5*a*B)*x^2)/2 + 91*a^4*b^10*(5*A*b + 11*a*B)*x^3 + (455*a^3*b^11*(A*b + 3*a*B)*x^4)/4 + 7*a^2*b^12*(3*A*b + 13*a*B)*x^5 + (5*a*b^13*(A*b + 7*a*B)*x^6)/2 + (b^14*(A*b + 15*a*B)*x^7)/7 + (b^15*B*x^8)/8 + 6435*a^7*b^7*(A*b + a*B)*log(x)]
    @test_int [((a + b*x)^15*(A + B*x))/x^10, x, 2, -(a^15*A)/(9*x^9) - (a^14*(15*A*b + a*B))/(8*x^8) - (15*a^13*b*(7*A*b + a*B))/(7*x^7) - (35*a^12*b^2*(13*A*b + 3*a*B))/(6*x^6) - (91*a^11*b^3*(3*A*b + a*B))/x^5 - (273*a^10*b^4*(11*A*b + 5*a*B))/(4*x^4) - (1001*a^9*b^5*(5*A*b + 3*a*B))/(3*x^3) - (715*a^8*b^6*(9*A*b + 7*a*B))/(2*x^2) - (6435*a^7*b^7*(A*b + a*B))/x + 1001*a^5*b^9*(3*A*b + 5*a*B)*x + (273*a^4*b^10*(5*A*b + 11*a*B)*x^2)/2 + (455*a^3*b^11*(A*b + 3*a*B)*x^3)/3 + (35*a^2*b^12*(3*A*b + 13*a*B)*x^4)/4 + 3*a*b^13*(A*b + 7*a*B)*x^5 + (b^14*(A*b + 15*a*B)*x^6)/6 + (b^15*B*x^7)/7 + 715*a^6*b^8*(7*A*b + 9*a*B)*log(x)]
    @test_int [((a + b*x)^15*(A + B*x))/x^11, x, 2, -(a^15*A)/(10*x^10) - (a^14*(15*A*b + a*B))/(9*x^9) - (15*a^13*b*(7*A*b + a*B))/(8*x^8) - (5*a^12*b^2*(13*A*b + 3*a*B))/x^7 - (455*a^11*b^3*(3*A*b + a*B))/(6*x^6) - (273*a^10*b^4*(11*A*b + 5*a*B))/(5*x^5) - (1001*a^9*b^5*(5*A*b + 3*a*B))/(4*x^4) - (715*a^8*b^6*(9*A*b + 7*a*B))/(3*x^3) - (6435*a^7*b^7*(A*b + a*B))/(2*x^2) - (715*a^6*b^8*(7*A*b + 9*a*B))/x + 273*a^4*b^10*(5*A*b + 11*a*B)*x + (455*a^3*b^11*(A*b + 3*a*B)*x^2)/2 + (35*a^2*b^12*(3*A*b + 13*a*B)*x^3)/3 + (15*a*b^13*(A*b + 7*a*B)*x^4)/4 + (b^14*(A*b + 15*a*B)*x^5)/5 + (b^15*B*x^6)/6 + 1001*a^5*b^9*(3*A*b + 5*a*B)*log(x)]
    @test_int [((a + b*x)^15*(A + B*x))/x^12, x, 2, -(a^15*A)/(11*x^11) - (a^14*(15*A*b + a*B))/(10*x^10) - (5*a^13*b*(7*A*b + a*B))/(3*x^9) - (35*a^12*b^2*(13*A*b + 3*a*B))/(8*x^8) - (65*a^11*b^3*(3*A*b + a*B))/x^7 - (91*a^10*b^4*(11*A*b + 5*a*B))/(2*x^6) - (1001*a^9*b^5*(5*A*b + 3*a*B))/(5*x^5) - (715*a^8*b^6*(9*A*b + 7*a*B))/(4*x^4) - (2145*a^7*b^7*(A*b + a*B))/x^3 - (715*a^6*b^8*(7*A*b + 9*a*B))/(2*x^2) - (1001*a^5*b^9*(3*A*b + 5*a*B))/x + 455*a^3*b^11*(A*b + 3*a*B)*x + (35*a^2*b^12*(3*A*b + 13*a*B)*x^2)/2 + 5*a*b^13*(A*b + 7*a*B)*x^3 + (b^14*(A*b + 15*a*B)*x^4)/4 + (b^15*B*x^5)/5 + 273*a^4*b^10*(5*A*b + 11*a*B)*log(x)]
    @test_int [((a + b*x)^15*(A + B*x))/x^13, x, 2, -(a^15*A)/(12*x^12) - (a^14*(15*A*b + a*B))/(11*x^11) - (3*a^13*b*(7*A*b + a*B))/(2*x^10) - (35*a^12*b^2*(13*A*b + 3*a*B))/(9*x^9) - (455*a^11*b^3*(3*A*b + a*B))/(8*x^8) - (39*a^10*b^4*(11*A*b + 5*a*B))/x^7 - (1001*a^9*b^5*(5*A*b + 3*a*B))/(6*x^6) - (143*a^8*b^6*(9*A*b + 7*a*B))/x^5 - (6435*a^7*b^7*(A*b + a*B))/(4*x^4) - (715*a^6*b^8*(7*A*b + 9*a*B))/(3*x^3) - (1001*a^5*b^9*(3*A*b + 5*a*B))/(2*x^2) - (273*a^4*b^10*(5*A*b + 11*a*B))/x + 35*a^2*b^12*(3*A*b + 13*a*B)*x + (15*a*b^13*(A*b + 7*a*B)*x^2)/2 + (b^14*(A*b + 15*a*B)*x^3)/3 + (b^15*B*x^4)/4 + 455*a^3*b^11*(A*b + 3*a*B)*log(x)]
    @test_int [((a + b*x)^15*(A + B*x))/x^14, x, 2, -(a^15*A)/(13*x^13) - (a^14*(15*A*b + a*B))/(12*x^12) - (15*a^13*b*(7*A*b + a*B))/(11*x^11) - (7*a^12*b^2*(13*A*b + 3*a*B))/(2*x^10) - (455*a^11*b^3*(3*A*b + a*B))/(9*x^9) - (273*a^10*b^4*(11*A*b + 5*a*B))/(8*x^8) - (143*a^9*b^5*(5*A*b + 3*a*B))/x^7 - (715*a^8*b^6*(9*A*b + 7*a*B))/(6*x^6) - (1287*a^7*b^7*(A*b + a*B))/x^5 - (715*a^6*b^8*(7*A*b + 9*a*B))/(4*x^4) - (1001*a^5*b^9*(3*A*b + 5*a*B))/(3*x^3) - (273*a^4*b^10*(5*A*b + 11*a*B))/(2*x^2) - (455*a^3*b^11*(A*b + 3*a*B))/x + 15*a*b^13*(A*b + 7*a*B)*x + (b^14*(A*b + 15*a*B)*x^2)/2 + (b^15*B*x^3)/3 + 35*a^2*b^12*(3*A*b + 13*a*B)*log(x)]
    @test_int [((a + b*x)^15*(A + B*x))/x^15, x, 2, -(a^15*A)/(14*x^14) - (a^14*(15*A*b + a*B))/(13*x^13) - (5*a^13*b*(7*A*b + a*B))/(4*x^12) - (35*a^12*b^2*(13*A*b + 3*a*B))/(11*x^11) - (91*a^11*b^3*(3*A*b + a*B))/(2*x^10) - (91*a^10*b^4*(11*A*b + 5*a*B))/(3*x^9) - (1001*a^9*b^5*(5*A*b + 3*a*B))/(8*x^8) - (715*a^8*b^6*(9*A*b + 7*a*B))/(7*x^7) - (2145*a^7*b^7*(A*b + a*B))/(2*x^6) - (143*a^6*b^8*(7*A*b + 9*a*B))/x^5 - (1001*a^5*b^9*(3*A*b + 5*a*B))/(4*x^4) - (91*a^4*b^10*(5*A*b + 11*a*B))/x^3 - (455*a^3*b^11*(A*b + 3*a*B))/(2*x^2) - (35*a^2*b^12*(3*A*b + 13*a*B))/x + b^14*(A*b + 15*a*B)*x + (b^15*B*x^2)/2 + 15*a*b^13*(A*b + 7*a*B)*log(x)]
    @test_int [((a + b*x)^15*(A + B*x))/x^16, x, 2, -(a^15*A)/(15*x^15) - (a^14*(15*A*b + a*B))/(14*x^14) - (15*a^13*b*(7*A*b + a*B))/(13*x^13) - (35*a^12*b^2*(13*A*b + 3*a*B))/(12*x^12) - (455*a^11*b^3*(3*A*b + a*B))/(11*x^11) - (273*a^10*b^4*(11*A*b + 5*a*B))/(10*x^10) - (1001*a^9*b^5*(5*A*b + 3*a*B))/(9*x^9) - (715*a^8*b^6*(9*A*b + 7*a*B))/(8*x^8) - (6435*a^7*b^7*(A*b + a*B))/(7*x^7) - (715*a^6*b^8*(7*A*b + 9*a*B))/(6*x^6) - (1001*a^5*b^9*(3*A*b + 5*a*B))/(5*x^5) - (273*a^4*b^10*(5*A*b + 11*a*B))/(4*x^4) - (455*a^3*b^11*(A*b + 3*a*B))/(3*x^3) - (35*a^2*b^12*(3*A*b + 13*a*B))/(2*x^2) - (15*a*b^13*(A*b + 7*a*B))/x + b^15*B*x + b^14*(A*b + 15*a*B)*log(x)]
    @test_int [((a + b*x)^15*(A + B*x))/x^17, x, 3, -(a^15*B)/(15*x^15) - (15*a^14*b*B)/(14*x^14) - (105*a^13*b^2*B)/(13*x^13) - (455*a^12*b^3*B)/(12*x^12) - (1365*a^11*b^4*B)/(11*x^11) - (3003*a^10*b^5*B)/(10*x^10) - (5005*a^9*b^6*B)/(9*x^9) - (6435*a^8*b^7*B)/(8*x^8) - (6435*a^7*b^8*B)/(7*x^7) - (5005*a^6*b^9*B)/(6*x^6) - (3003*a^5*b^10*B)/(5*x^5) - (1365*a^4*b^11*B)/(4*x^4) - (455*a^3*b^12*B)/(3*x^3) - (105*a^2*b^13*B)/(2*x^2) - (15*a*b^14*B)/x - (A*(a + b*x)^16)/(16*a*x^16) + b^15*B*log(x)]

    @test_int [((a + b*x)^15*(A + B*x))/x^18, x, 2, -(A*(a + b*x)^16)/(17*a*x^17) + ((A*b - 17*a*B)*(a + b*x)^16)/(272*a^2*x^16)]
    @test_int [((a + b*x)^15*(A + B*x))/x^19, x, 3, -(A*(a + b*x)^16)/(18*a*x^18) + ((A*b - 9*a*B)*(a + b*x)^16)/(153*a^2*x^17) - (b*(A*b - 9*a*B)*(a + b*x)^16)/(2448*a^3*x^16)]
    @test_int [((a + b*x)^15*(A + B*x))/x^20, x, 4, -(A*(a + b*x)^16)/(19*a*x^19) + ((3*A*b - 19*a*B)*(a + b*x)^16)/(342*a^2*x^18) - (b*(3*A*b - 19*a*B)*(a + b*x)^16)/(2907*a^3*x^17) + (b^2*(3*A*b - 19*a*B)*(a + b*x)^16)/(46512*a^4*x^16)]
    @test_int [((a + b*x)^15*(A + B*x))/x^21, x, 5, -(A*(a + b*x)^16)/(20*a*x^20) + ((A*b - 5*a*B)*(a + b*x)^16)/(95*a^2*x^19) - (b*(A*b - 5*a*B)*(a + b*x)^16)/(570*a^3*x^18) + (b^2*(A*b - 5*a*B)*(a + b*x)^16)/(4845*a^4*x^17) - (b^3*(A*b - 5*a*B)*(a + b*x)^16)/(77520*a^5*x^16)]
    @test_int [((a + b*x)^15*(A + B*x))/x^22, x, 6, -(A*(a + b*x)^16)/(21*a*x^21) + ((5*A*b - 21*a*B)*(a + b*x)^16)/(420*a^2*x^20) - (b*(5*A*b - 21*a*B)*(a + b*x)^16)/(1995*a^3*x^19) + (b^2*(5*A*b - 21*a*B)*(a + b*x)^16)/(11970*a^4*x^18) - (b^3*(5*A*b - 21*a*B)*(a + b*x)^16)/(101745*a^5*x^17) + (b^4*(5*A*b - 21*a*B)*(a + b*x)^16)/(1627920*a^6*x^16)]
    @test_int [((a + b*x)^15*(A + B*x))/x^23, x, 7, -(A*(a + b*x)^16)/(22*a*x^22) + ((3*A*b - 11*a*B)*(a + b*x)^16)/(231*a^2*x^21) - (b*(3*A*b - 11*a*B)*(a + b*x)^16)/(924*a^3*x^20) + (b^2*(3*A*b - 11*a*B)*(a + b*x)^16)/(4389*a^4*x^19) - (b^3*(3*A*b - 11*a*B)*(a + b*x)^16)/(26334*a^5*x^18) + (b^4*(3*A*b - 11*a*B)*(a + b*x)^16)/(223839*a^6*x^17) - (b^5*(3*A*b - 11*a*B)*(a + b*x)^16)/(3581424*a^7*x^16)]
    @test_int [((a + b*x)^15*(A + B*x))/x^24, x, 8, -(A*(a + b*x)^16)/(23*a*x^23) + ((7*A*b - 23*a*B)*(a + b*x)^16)/(506*a^2*x^22) - (b*(7*A*b - 23*a*B)*(a + b*x)^16)/(1771*a^3*x^21) + (b^2*(7*A*b - 23*a*B)*(a + b*x)^16)/(7084*a^4*x^20) - (b^3*(7*A*b - 23*a*B)*(a + b*x)^16)/(33649*a^5*x^19) + (b^4*(7*A*b - 23*a*B)*(a + b*x)^16)/(201894*a^6*x^18) - (b^5*(7*A*b - 23*a*B)*(a + b*x)^16)/(1716099*a^7*x^17) + (b^6*(7*A*b - 23*a*B)*(a + b*x)^16)/(27457584*a^8*x^16)]
    @test_int [((a + b*x)^15*(A + B*x))/x^25, x, 9, -(A*(a + b*x)^16)/(24*a*x^24) + ((A*b - 3*a*B)*(a + b*x)^16)/(69*a^2*x^23) - (7*b*(A*b - 3*a*B)*(a + b*x)^16)/(1518*a^3*x^22) + (b^2*(A*b - 3*a*B)*(a + b*x)^16)/(759*a^4*x^21) - (b^3*(A*b - 3*a*B)*(a + b*x)^16)/(3036*a^5*x^20) + (b^4*(A*b - 3*a*B)*(a + b*x)^16)/(14421*a^6*x^19) - (b^5*(A*b - 3*a*B)*(a + b*x)^16)/(86526*a^7*x^18) + (b^6*(A*b - 3*a*B)*(a + b*x)^16)/(735471*a^8*x^17) - (b^7*(A*b - 3*a*B)*(a + b*x)^16)/(11767536*a^9*x^16)]
    @test_int [((a + b*x)^15*(A + B*x))/x^26, x, 10, -(A*(a + b*x)^16)/(25*a*x^25) + ((9*A*b - 25*a*B)*(a + b*x)^16)/(600*a^2*x^24) - (b*(9*A*b - 25*a*B)*(a + b*x)^16)/(1725*a^3*x^23) + (7*b^2*(9*A*b - 25*a*B)*(a + b*x)^16)/(37950*a^4*x^22) - (b^3*(9*A*b - 25*a*B)*(a + b*x)^16)/(18975*a^5*x^21) + (b^4*(9*A*b - 25*a*B)*(a + b*x)^16)/(75900*a^6*x^20) - (b^5*(9*A*b - 25*a*B)*(a + b*x)^16)/(360525*a^7*x^19) + (b^6*(9*A*b - 25*a*B)*(a + b*x)^16)/(2163150*a^8*x^18) - (b^7*(9*A*b - 25*a*B)*(a + b*x)^16)/(18386775*a^9*x^17) + (b^8*(9*A*b - 25*a*B)*(a + b*x)^16)/(294188400*a^10*x^16)]
    @test_int [((a + b*x)^15*(A + B*x))/x^27, x, 11, -(A*(a + b*x)^16)/(26*a*x^26) + ((5*A*b - 13*a*B)*(a + b*x)^16)/(325*a^2*x^25) - (3*b*(5*A*b - 13*a*B)*(a + b*x)^16)/(2600*a^3*x^24) + (3*b^2*(5*A*b - 13*a*B)*(a + b*x)^16)/(7475*a^4*x^23) - (21*b^3*(5*A*b - 13*a*B)*(a + b*x)^16)/(164450*a^5*x^22) + (3*b^4*(5*A*b - 13*a*B)*(a + b*x)^16)/(82225*a^6*x^21) - (3*b^5*(5*A*b - 13*a*B)*(a + b*x)^16)/(328900*a^7*x^20) + (3*b^6*(5*A*b - 13*a*B)*(a + b*x)^16)/(1562275*a^8*x^19) - (b^7*(5*A*b - 13*a*B)*(a + b*x)^16)/(3124550*a^9*x^18) + (b^8*(5*A*b - 13*a*B)*(a + b*x)^16)/(26558675*a^10*x^17) - (b^9*(5*A*b - 13*a*B)*(a + b*x)^16)/(424938800*a^11*x^16)]

    @test_int [((a + b*x)^15*(A + B*x))/x^28, x, 2, -(a^15*A)/(27*x^27) - (a^14*(15*A*b + a*B))/(26*x^26) - (3*a^13*b*(7*A*b + a*B))/(5*x^25) - (35*a^12*b^2*(13*A*b + 3*a*B))/(24*x^24) - (455*a^11*b^3*(3*A*b + a*B))/(23*x^23) - (273*a^10*b^4*(11*A*b + 5*a*B))/(22*x^22) - (143*a^9*b^5*(5*A*b + 3*a*B))/(3*x^21) - (143*a^8*b^6*(9*A*b + 7*a*B))/(4*x^20) - (6435*a^7*b^7*(A*b + a*B))/(19*x^19) - (715*a^6*b^8*(7*A*b + 9*a*B))/(18*x^18) - (1001*a^5*b^9*(3*A*b + 5*a*B))/(17*x^17) - (273*a^4*b^10*(5*A*b + 11*a*B))/(16*x^16) - (91*a^3*b^11*(A*b + 3*a*B))/(3*x^15) - (5*a^2*b^12*(3*A*b + 13*a*B))/(2*x^14) - (15*a*b^13*(A*b + 7*a*B))/(13*x^13) - (b^14*(A*b + 15*a*B))/(12*x^12) - (b^15*B)/(11*x^11)]
    @test_int [((a + b*x)^15*(A + B*x))/x^29, x, 2, -(a^15*A)/(28*x^28) - (a^14*(15*A*b + a*B))/(27*x^27) - (15*a^13*b*(7*A*b + a*B))/(26*x^26) - (7*a^12*b^2*(13*A*b + 3*a*B))/(5*x^25) - (455*a^11*b^3*(3*A*b + a*B))/(24*x^24) - (273*a^10*b^4*(11*A*b + 5*a*B))/(23*x^23) - (91*a^9*b^5*(5*A*b + 3*a*B))/(2*x^22) - (715*a^8*b^6*(9*A*b + 7*a*B))/(21*x^21) - (1287*a^7*b^7*(A*b + a*B))/(4*x^20) - (715*a^6*b^8*(7*A*b + 9*a*B))/(19*x^19) - (1001*a^5*b^9*(3*A*b + 5*a*B))/(18*x^18) - (273*a^4*b^10*(5*A*b + 11*a*B))/(17*x^17) - (455*a^3*b^11*(A*b + 3*a*B))/(16*x^16) - (7*a^2*b^12*(3*A*b + 13*a*B))/(3*x^15) - (15*a*b^13*(A*b + 7*a*B))/(14*x^14) - (b^14*(A*b + 15*a*B))/(13*x^13) - (b^15*B)/(12*x^12)]
    @test_int [((a + b*x)^15*(A + B*x))/x^30, x, 2, -(a^15*A)/(29*x^29) - (a^14*(15*A*b + a*B))/(28*x^28) - (5*a^13*b*(7*A*b + a*B))/(9*x^27) - (35*a^12*b^2*(13*A*b + 3*a*B))/(26*x^26) - (91*a^11*b^3*(3*A*b + a*B))/(5*x^25) - (91*a^10*b^4*(11*A*b + 5*a*B))/(8*x^24) - (1001*a^9*b^5*(5*A*b + 3*a*B))/(23*x^23) - (65*a^8*b^6*(9*A*b + 7*a*B))/(2*x^22) - (2145*a^7*b^7*(A*b + a*B))/(7*x^21) - (143*a^6*b^8*(7*A*b + 9*a*B))/(4*x^20) - (1001*a^5*b^9*(3*A*b + 5*a*B))/(19*x^19) - (91*a^4*b^10*(5*A*b + 11*a*B))/(6*x^18) - (455*a^3*b^11*(A*b + 3*a*B))/(17*x^17) - (35*a^2*b^12*(3*A*b + 13*a*B))/(16*x^16) - (a*b^13*(A*b + 7*a*B))/x^15 - (b^14*(A*b + 15*a*B))/(14*x^14) - (b^15*B)/(13*x^13)] =#

    @test_int [x^3*(a + b*x)*(c + d*x)^16, x, 2, (c^3*(b*c - a*d)*(c + d*x)^17)/(17*d^5) - (c^2*(4*b*c - 3*a*d)*(c + d*x)^18)/(18*d^5) + (3*c*(2*b*c - a*d)*(c + d*x)^19)/(19*d^5) - ((4*b*c - a*d)*(c + d*x)^20)/(20*d^5) + (b*(c + d*x)^21)/(21*d^5)]
    @test_int [x^2*(a + b*x)*(c + d*x)^16, x, 2, -((c^2*(b*c - a*d)*(c + d*x)^17)/(17*d^4)) + (c*(3*b*c - 2*a*d)*(c + d*x)^18)/(18*d^4) - ((3*b*c - a*d)*(c + d*x)^19)/(19*d^4) + (b*(c + d*x)^20)/(20*d^4)]
    @test_int [x^1*(a + b*x)*(c + d*x)^16, x, 2, (c*(b*c - a*d)*(c + d*x)^17)/(17*d^3) - ((2*b*c - a*d)*(c + d*x)^18)/(18*d^3) + (b*(c + d*x)^19)/(19*d^3)]
    @test_int [x^0*(a + b*x)*(c + d*x)^16, x, 2, -(((b*c - a*d)*(c + d*x)^17)/(17*d^2)) + (b*(c + d*x)^18)/(18*d^2)]

    @test_int [x^2*(2 + x)^5*(2 + 3*x), x, 1, (1/3)*x^3*(2 + x)^6]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^4*(A + B*x)/(a + b*x), x, 2, -((a^3*(A*b - a*B)*x)/b^5) + (a^2*(A*b - a*B)*x^2)/(2*b^4) - (a*(A*b - a*B)*x^3)/(3*b^3) + ((A*b - a*B)*x^4)/(4*b^2) + (B*x^5)/(5*b) + (a^4*(A*b - a*B)*log(a + b*x))/b^6]
    @test_int [x^3*(A + B*x)/(a + b*x), x, 2, (a^2*(A*b - a*B)*x)/b^4 - (a*(A*b - a*B)*x^2)/(2*b^3) + ((A*b - a*B)*x^3)/(3*b^2) + (B*x^4)/(4*b) - (a^3*(A*b - a*B)*log(a + b*x))/b^5]
    @test_int [x^2*(A + B*x)/(a + b*x), x, 2, -((a*(A*b - a*B)*x)/b^3) + ((A*b - a*B)*x^2)/(2*b^2) + (B*x^3)/(3*b) + (a^2*(A*b - a*B)*log(a + b*x))/b^4]
    @test_int [x^1*(A + B*x)/(a + b*x), x, 2, ((A*b - a*B)*x)/b^2 + (B*x^2)/(2*b) - (a*(A*b - a*B)*log(a + b*x))/b^3]
    @test_int [x^0*(A + B*x)/(a + b*x), x, 2, (B*x)/b + ((A*b - a*B)*log(a + b*x))/b^2]
    @test_int [(A + B*x)/(x^1*(a + b*x)), x, 2, (A*log(x))/a - ((A*b - a*B)*log(a + b*x))/(a*b)]
    @test_int [(A + B*x)/(x^2*(a + b*x)), x, 2, -(A/(a*x)) - ((A*b - a*B)*log(x))/a^2 + ((A*b - a*B)*log(a + b*x))/a^2]
    @test_int [(A + B*x)/(x^3*(a + b*x)), x, 2, -A/(2*a*x^2) + (A*b - a*B)/(a^2*x) + (b*(A*b - a*B)*log(x))/a^3 - (b*(A*b - a*B)*log(a + b*x))/a^3]
    @test_int [(A + B*x)/(x^4*(a + b*x)), x, 2, -A/(3*a*x^3) + (A*b - a*B)/(2*a^2*x^2) - (b*(A*b - a*B))/(a^3*x) - (b^2*(A*b - a*B)*log(x))/a^4 + (b^2*(A*b - a*B)*log(a + b*x))/a^4]
    @test_int [(A + B*x)/(x^5*(a + b*x)), x, 2, -A/(4*a*x^4) + (A*b - a*B)/(3*a^2*x^3) - (b*(A*b - a*B))/(2*a^3*x^2) + (b^2*(A*b - a*B))/(a^4*x) + (b^3*(A*b - a*B)*log(x))/a^5 - (b^3*(A*b - a*B)*log(a + b*x))/a^5]

    @test_int [x^4*(A + B*x)/(a + b*x)^2, x, 2, (a^2*(3*A*b - 4*a*B)*x)/b^5 - (a*(2*A*b - 3*a*B)*x^2)/(2*b^4) + ((A*b - 2*a*B)*x^3)/(3*b^3) + (B*x^4)/(4*b^2) - (a^4*(A*b - a*B))/(b^6*(a + b*x)) - (a^3*(4*A*b - 5*a*B)*log(a + b*x))/b^6]
    @test_int [x^3*(A + B*x)/(a + b*x)^2, x, 2, -((a*(2*A*b - 3*a*B)*x)/b^4) + ((A*b - 2*a*B)*x^2)/(2*b^3) + (B*x^3)/(3*b^2) + (a^3*(A*b - a*B))/(b^5*(a + b*x)) + (a^2*(3*A*b - 4*a*B)*log(a + b*x))/b^5]
    @test_int [x^2*(A + B*x)/(a + b*x)^2, x, 2, ((A*b - 2*a*B)*x)/b^3 + (B*x^2)/(2*b^2) - (a^2*(A*b - a*B))/(b^4*(a + b*x)) - (a*(2*A*b - 3*a*B)*log(a + b*x))/b^4]
    @test_int [x^1*(A + B*x)/(a + b*x)^2, x, 2, (B*x)/b^2 + (a*(A*b - a*B))/(b^3*(a + b*x)) + ((A*b - 2*a*B)*log(a + b*x))/b^3]
    @test_int [x^0*(A + B*x)/(a + b*x)^2, x, 2, -((A*b - a*B)/(b^2*(a + b*x))) + (B*log(a + b*x))/b^2]
    @test_int [(A + B*x)/(x^1*(a + b*x)^2), x, 2, (A*b - a*B)/(a*b*(a + b*x)) + (A*log(x))/a^2 - (A*log(a + b*x))/a^2]
    @test_int [(A + B*x)/(x^2*(a + b*x)^2), x, 2, -(A/(a^2*x)) - (A*b - a*B)/(a^2*(a + b*x)) - ((2*A*b - a*B)*log(x))/a^3 + ((2*A*b - a*B)*log(a + b*x))/a^3]
    @test_int [(A + B*x)/(x^3*(a + b*x)^2), x, 2, -(A/(2*a^2*x^2)) + (2*A*b - a*B)/(a^3*x) + (b*(A*b - a*B))/(a^3*(a + b*x)) + (b*(3*A*b - 2*a*B)*log(x))/a^4 - (b*(3*A*b - 2*a*B)*log(a + b*x))/a^4]
    @test_int [(A + B*x)/(x^4*(a + b*x)^2), x, 2, -(A/(3*a^2*x^3)) + (2*A*b - a*B)/(2*a^3*x^2) - (b*(3*A*b - 2*a*B))/(a^4*x) - (b^2*(A*b - a*B))/(a^4*(a + b*x)) - (b^2*(4*A*b - 3*a*B)*log(x))/a^5 + (b^2*(4*A*b - 3*a*B)*log(a + b*x))/a^5]

    @test_int [x^4*(A + B*x)/(a + b*x)^3, x, 2, -((3*a*(A*b - 2*a*B)*x)/b^5) + ((A*b - 3*a*B)*x^2)/(2*b^4) + (B*x^3)/(3*b^3) - (a^4*(A*b - a*B))/(2*b^6*(a + b*x)^2) + (a^3*(4*A*b - 5*a*B))/(b^6*(a + b*x)) + (2*a^2*(3*A*b - 5*a*B)*log(a + b*x))/b^6]
    @test_int [x^3*(A + B*x)/(a + b*x)^3, x, 2, ((A*b - 3*a*B)*x)/b^4 + (B*x^2)/(2*b^3) + (a^3*(A*b - a*B))/(2*b^5*(a + b*x)^2) - (a^2*(3*A*b - 4*a*B))/(b^5*(a + b*x)) - (3*a*(A*b - 2*a*B)*log(a + b*x))/b^5]
    @test_int [x^2*(A + B*x)/(a + b*x)^3, x, 2, (B*x)/b^3 - (a^2*(A*b - a*B))/(2*b^4*(a + b*x)^2) + (a*(2*A*b - 3*a*B))/(b^4*(a + b*x)) + ((A*b - 3*a*B)*log(a + b*x))/b^4]
    @test_int [x^1*(A + B*x)/(a + b*x)^3, x, 2, (a*(A*b - a*B))/(2*b^3*(a + b*x)^2) - (A*b - 2*a*B)/(b^3*(a + b*x)) + (B*log(a + b*x))/b^3]
    @test_int [x^0*(A + B*x)/(a + b*x)^3, x, 1, -((A + B*x)^2/(2*(A*b - a*B)*(a + b*x)^2))]
    @test_int [(A + B*x)/(x^1*(a + b*x)^3), x, 2, (A*b - a*B)/(2*a*b*(a + b*x)^2) + A/(a^2*(a + b*x)) + (A*log(x))/a^3 - (A*log(a + b*x))/a^3]
    @test_int [(A + B*x)/(x^2*(a + b*x)^3), x, 2, -(A/(a^3*x)) - (A*b - a*B)/(2*a^2*(a + b*x)^2) - (2*A*b - a*B)/(a^3*(a + b*x)) - ((3*A*b - a*B)*log(x))/a^4 + ((3*A*b - a*B)*log(a + b*x))/a^4]
    @test_int [(A + B*x)/(x^3*(a + b*x)^3), x, 2, -(A/(2*a^3*x^2)) + (3*A*b - a*B)/(a^4*x) + (b*(A*b - a*B))/(2*a^3*(a + b*x)^2) + (b*(3*A*b - 2*a*B))/(a^4*(a + b*x)) + (3*b*(2*A*b - a*B)*log(x))/a^5 - (3*b*(2*A*b - a*B)*log(a + b*x))/a^5]
    @test_int [(A + B*x)/(x^4*(a + b*x)^3), x, 2, -(A/(3*a^3*x^3)) + (3*A*b - a*B)/(2*a^4*x^2) - (3*b*(2*A*b - a*B))/(a^5*x) - (b^2*(A*b - a*B))/(2*a^4*(a + b*x)^2) - (b^2*(4*A*b - 3*a*B))/(a^5*(a + b*x)) - (2*b^2*(5*A*b - 3*a*B)*log(x))/a^6 + (2*b^2*(5*A*b - 3*a*B)*log(a + b*x))/a^6]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x)^2*(c+d*x)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^3*(a + b*x)^2*(c + d*x)^16, x, 2, -((c^3*(b*c - a*d)^2*(c + d*x)^17)/(17*d^6)) + (c^2*(5*b*c - 3*a*d)*(b*c - a*d)*(c + d*x)^18)/(18*d^6) - (c*(10*b^2*c^2 - 12*a*b*c*d + 3*a^2*d^2)*(c + d*x)^19)/(19*d^6) + ((10*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*(c + d*x)^20)/(20*d^6) - (b*(5*b*c - 2*a*d)*(c + d*x)^21)/(21*d^6) + (b^2*(c + d*x)^22)/(22*d^6)]
    @test_int [x^2*(a + b*x)^2*(c + d*x)^16, x, 2, (c^2*(b*c - a*d)^2*(c + d*x)^17)/(17*d^5) - (c*(b*c - a*d)*(2*b*c - a*d)*(c + d*x)^18)/(9*d^5) + ((6*b^2*c^2 - 6*a*b*c*d + a^2*d^2)*(c + d*x)^19)/(19*d^5) - (b*(2*b*c - a*d)*(c + d*x)^20)/(10*d^5) + (b^2*(c + d*x)^21)/(21*d^5)]
    @test_int [x^1*(a + b*x)^2*(c + d*x)^16, x, 2, -((c*(b*c - a*d)^2*(c + d*x)^17)/(17*d^4)) + ((b*c - a*d)*(3*b*c - a*d)*(c + d*x)^18)/(18*d^4) - (b*(3*b*c - 2*a*d)*(c + d*x)^19)/(19*d^4) + (b^2*(c + d*x)^20)/(20*d^4)]

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x)^p / (a+b*x)^1=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^3*(c + d*x)/(a + b*x), x, 2, (a^2*(b*c - a*d)*x)/b^4 - (a*(b*c - a*d)*x^2)/(2*b^3) + ((b*c - a*d)*x^3)/(3*b^2) + (d*x^4)/(4*b) - (a^3*(b*c - a*d)*log(a + b*x))/b^5]
    @test_int [x^2*(c + d*x)/(a + b*x), x, 2, -((a*(b*c - a*d)*x)/b^3) + ((b*c - a*d)*x^2)/(2*b^2) + (d*x^3)/(3*b) + (a^2*(b*c - a*d)*log(a + b*x))/b^4]
    @test_int [x^1*(c + d*x)/(a + b*x), x, 2, ((b*c - a*d)*x)/b^2 + (d*x^2)/(2*b) - (a*(b*c - a*d)*log(a + b*x))/b^3]
    @test_int [x^0*(c + d*x)/(a + b*x), x, 2, (d*x)/b + ((b*c - a*d)*log(a + b*x))/b^2]
    @test_int [(c + d*x)/(x^1*(a + b*x)), x, 2, (c*log(x))/a - ((b*c - a*d)*log(a + b*x))/(a*b)]
    @test_int [(c + d*x)/(x^2*(a + b*x)), x, 2, -(c/(a*x)) - ((b*c - a*d)*log(x))/a^2 + ((b*c - a*d)*log(a + b*x))/a^2]
    @test_int [(c + d*x)/(x^3*(a + b*x)), x, 2, -c/(2*a*x^2) + (b*c - a*d)/(a^2*x) + (b*(b*c - a*d)*log(x))/a^3 - (b*(b*c - a*d)*log(a + b*x))/a^3]
    @test_int [(c + d*x)/(x^4*(a + b*x)), x, 2, -c/(3*a*x^3) + (b*c - a*d)/(2*a^2*x^2) - (b*(b*c - a*d))/(a^3*x) - (b^2*(b*c - a*d)*log(x))/a^4 + (b^2*(b*c - a*d)*log(a + b*x))/a^4]

    @test_int [x^3*(c + d*x)^2/(a + b*x), x, 2, (a^2*(b*c - a*d)^2*x)/b^5 - (a*(b*c - a*d)^2*x^2)/(2*b^4) + ((b*c - a*d)^2*x^3)/(3*b^3) + (d*(2*b*c - a*d)*x^4)/(4*b^2) + (d^2*x^5)/(5*b) - (a^3*(b*c - a*d)^2*log(a + b*x))/b^6]
    @test_int [x^2*(c + d*x)^2/(a + b*x), x, 2, -((a*(b*c - a*d)^2*x)/b^4) + ((b*c - a*d)^2*x^2)/(2*b^3) + (d*(2*b*c - a*d)*x^3)/(3*b^2) + (d^2*x^4)/(4*b) + (a^2*(b*c - a*d)^2*log(a + b*x))/b^5]
    @test_int [x^1*(c + d*x)^2/(a + b*x), x, 2, ((b*c - a*d)^2*x)/b^3 + (d*(2*b*c - a*d)*x^2)/(2*b^2) + (d^2*x^3)/(3*b) - (a*(b*c - a*d)^2*log(a + b*x))/b^4]
    @test_int [x^0*(c + d*x)^2/(a + b*x), x, 2, (d*(b*c - a*d)*x)/b^2 + (c + d*x)^2/(2*b) + ((b*c - a*d)^2*log(a + b*x))/b^3]
    @test_int [(c + d*x)^2/(x^1*(a + b*x)), x, 2, (d^2*x)/b + (c^2*log(x))/a - ((b*c - a*d)^2*log(a + b*x))/(a*b^2)]
    @test_int [(c + d*x)^2/(x^2*(a + b*x)), x, 2, -(c^2/(a*x)) - (c*(b*c - 2*a*d)*log(x))/a^2 + ((b*c - a*d)^2*log(a + b*x))/(a^2*b)]
    @test_int [(c + d*x)^2/(x^3*(a + b*x)), x, 2, -c^2/(2*a*x^2) + (c*(b*c - 2*a*d))/(a^2*x) + ((b*c - a*d)^2*log(x))/a^3 - ((b*c - a*d)^2*log(a + b*x))/a^3]
    @test_int [(c + d*x)^2/(x^4*(a + b*x)), x, 2, -c^2/(3*a*x^3) + (c*(b*c - 2*a*d))/(2*a^2*x^2) - (b*c - a*d)^2/(a^3*x) - (b*(b*c - a*d)^2*log(x))/a^4 + (b*(b*c - a*d)^2*log(a + b*x))/a^4]
    @test_int [(c + d*x)^2/(x^5*(a + b*x)), x, 2, -c^2/(4*a*x^4) + (c*(b*c - 2*a*d))/(3*a^2*x^3) - (b*c - a*d)^2/(2*a^3*x^2) + (b*(b*c - a*d)^2)/(a^4*x) + (b^2*(b*c - a*d)^2*log(x))/a^5 - (b^2*(b*c - a*d)^2*log(a + b*x))/a^5]

    @test_int [x^3*(c + d*x)^3/(a + b*x), x, 2, (a^2*(b*c - a*d)^3*x)/b^6 - (a*(b*c - a*d)^3*x^2)/(2*b^5) + ((b*c - a*d)^3*x^3)/(3*b^4) + (d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x^4)/(4*b^3) + (d^2*(3*b*c - a*d)*x^5)/(5*b^2) + (d^3*x^6)/(6*b) - (a^3*(b*c - a*d)^3*log(a + b*x))/b^7]
    @test_int [x^2*(c + d*x)^3/(a + b*x), x, 2, -((a*(b*c - a*d)^3*x)/b^5) + ((b*c - a*d)^3*x^2)/(2*b^4) + (d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x^3)/(3*b^3) + (d^2*(3*b*c - a*d)*x^4)/(4*b^2) + (d^3*x^5)/(5*b) + (a^2*(b*c - a*d)^3*log(a + b*x))/b^6]
    @test_int [x^1*(c + d*x)^3/(a + b*x), x, 2, ((b*c - a*d)^3*x)/b^4 + (d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x^2)/(2*b^3) + (d^2*(3*b*c - a*d)*x^3)/(3*b^2) + (d^3*x^4)/(4*b) - (a*(b*c - a*d)^3*log(a + b*x))/b^5]
    @test_int [x^0*(c + d*x)^3/(a + b*x), x, 2, (d*(b*c - a*d)^2*x)/b^3 + ((b*c - a*d)*(c + d*x)^2)/(2*b^2) + (c + d*x)^3/(3*b) + ((b*c - a*d)^3*log(a + b*x))/b^4]
    @test_int [(c + d*x)^3/(x^1*(a + b*x)), x, 2, (d^2*(3*b*c - a*d)*x)/b^2 + (d^3*x^2)/(2*b) + (c^3*log(x))/a - ((b*c - a*d)^3*log(a + b*x))/(a*b^3)]
    @test_int [(c + d*x)^3/(x^2*(a + b*x)), x, 2, -(c^3/(a*x)) + (d^3*x)/b - (c^2*(b*c - 3*a*d)*log(x))/a^2 + ((b*c - a*d)^3*log(a + b*x))/(a^2*b^2)]
    @test_int [(c + d*x)^3/(x^3*(a + b*x)), x, 2, -c^3/(2*a*x^2) + (c^2*(b*c - 3*a*d))/(a^2*x) + (c*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2)*log(x))/a^3 - ((b*c - a*d)^3*log(a + b*x))/(a^3*b)]
    @test_int [(c + d*x)^3/(x^4*(a + b*x)), x, 2, -c^3/(3*a*x^3) + (c^2*(b*c - 3*a*d))/(2*a^2*x^2) - (c*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2))/(a^3*x) - ((b*c - a*d)^3*log(x))/a^4 + ((b*c - a*d)^3*log(a + b*x))/a^4]
    @test_int [(c + d*x)^3/(x^5*(a + b*x)), x, 2, -c^3/(4*a*x^4) + (c^2*(b*c - 3*a*d))/(3*a^2*x^3) - (c*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2))/(2*a^3*x^2) + (b*c - a*d)^3/(a^4*x) + (b*(b*c - a*d)^3*log(x))/a^5 - (b*(b*c - a*d)^3*log(a + b*x))/a^5]
    @test_int [(c + d*x)^3/(x^6*(a + b*x)), x, 2, -c^3/(5*a*x^5) + (c^2*(b*c - 3*a*d))/(4*a^2*x^4) - (c*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2))/(3*a^3*x^3) + (b*c - a*d)^3/(2*a^4*x^2) - (b*(b*c - a*d)^3)/(a^5*x) - (b^2*(b*c - a*d)^3*log(x))/a^6 + (b^2*(b*c - a*d)^3*log(a + b*x))/a^6]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^5/((a + b*x)*(c + d*x)), x, 2, -(((b*c + a*d)*(b^2*c^2 + a^2*d^2)*x)/(b^4*d^4)) + ((b^2*c^2 + a*b*c*d + a^2*d^2)*x^2)/(2*b^3*d^3) - ((b*c + a*d)*x^3)/(3*b^2*d^2) + x^4/(4*b*d) - (a^5*log(a + b*x))/(b^5*(b*c - a*d)) + (c^5*log(c + d*x))/(d^5*(b*c - a*d))]
    @test_int [x^4/((a + b*x)*(c + d*x)), x, 2, ((b^2*c^2 + a*b*c*d + a^2*d^2)*x)/(b^3*d^3) - ((b*c + a*d)*x^2)/(2*b^2*d^2) + x^3/(3*b*d) + (a^4*log(a + b*x))/(b^4*(b*c - a*d)) - (c^4*log(c + d*x))/(d^4*(b*c - a*d))]
    @test_int [x^3/((a + b*x)*(c + d*x)), x, 2, -(((b*c + a*d)*x)/(b^2*d^2)) + x^2/(2*b*d) - (a^3*log(a + b*x))/(b^3*(b*c - a*d)) + (c^3*log(c + d*x))/(d^3*(b*c - a*d))]
    @test_int [x^2/((a + b*x)*(c + d*x)), x, 2, x/(b*d) + (a^2*log(a + b*x))/(b^2*(b*c - a*d)) - (c^2*log(c + d*x))/(d^2*(b*c - a*d))]
    @test_int [x^1/((a + b*x)*(c + d*x)), x, 2, -((a*log(a + b*x))/(b*(b*c - a*d))) + (c*log(c + d*x))/(d*(b*c - a*d))]
    @test_int [x^0/((a + b*x)*(c + d*x)), x, 3, log(a + b*x)/(b*c - a*d) - log(c + d*x)/(b*c - a*d)]
    @test_int [1/(x^1*(a + b*x)*(c + d*x)), x, 2, log(x)/(a*c) - (b*log(a + b*x))/(a*(b*c - a*d)) + (d*log(c + d*x))/(c*(b*c - a*d))]
    @test_int [1/(x^2*(a + b*x)*(c + d*x)), x, 2, -(1/(a*c*x)) - ((b*c + a*d)*log(x))/(a^2*c^2) + (b^2*log(a + b*x))/(a^2*(b*c - a*d)) - (d^2*log(c + d*x))/(c^2*(b*c - a*d))]
    @test_int [1/(x^3*(a + b*x)*(c + d*x)), x, 2, -(1/(2*a*c*x^2)) + (b*c + a*d)/(a^2*c^2*x) + ((b^2*c^2 + a*b*c*d + a^2*d^2)*log(x))/(a^3*c^3) - (b^3*log(a + b*x))/(a^3*(b*c - a*d)) + (d^3*log(c + d*x))/(c^3*(b*c - a*d))]
    @test_int [1/(x^4*(a + b*x)*(c + d*x)), x, 2, -(1/(3*a*c*x^3)) + (b*c + a*d)/(2*a^2*c^2*x^2) - (b^2*c^2 + a*b*c*d + a^2*d^2)/(a^3*c^3*x) - ((b*c + a*d)*(b^2*c^2 + a^2*d^2)*log(x))/(a^4*c^4) + (b^4*log(a + b*x))/(a^4*(b*c - a*d)) - (d^4*log(c + d*x))/(c^4*(b*c - a*d))]

    @test_int [x^5/((a + b*x)*(c + d*x)^2), x, 2, ((3*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*x)/(b^3*d^4) - ((2*b*c + a*d)*x^2)/(2*b^2*d^3) + x^3/(3*b*d^2) - c^5/(d^5*(b*c - a*d)*(c + d*x)) - (a^5*log(a + b*x))/(b^4*(b*c - a*d)^2) - (c^4*(4*b*c - 5*a*d)*log(c + d*x))/(d^5*(b*c - a*d)^2)]
    @test_int [x^4/((a + b*x)*(c + d*x)^2), x, 2, -(((2*b*c + a*d)*x)/(b^2*d^3)) + x^2/(2*b*d^2) + c^4/(d^4*(b*c - a*d)*(c + d*x)) + (a^4*log(a + b*x))/(b^3*(b*c - a*d)^2) + (c^3*(3*b*c - 4*a*d)*log(c + d*x))/(d^4*(b*c - a*d)^2)]
    @test_int [x^3/((a + b*x)*(c + d*x)^2), x, 2, x/(b*d^2) - c^3/(d^3*(b*c - a*d)*(c + d*x)) - (a^3*log(a + b*x))/(b^2*(b*c - a*d)^2) - (c^2*(2*b*c - 3*a*d)*log(c + d*x))/(d^3*(b*c - a*d)^2)]
    @test_int [x^2/((a + b*x)*(c + d*x)^2), x, 2, c^2/(d^2*(b*c - a*d)*(c + d*x)) + (a^2*log(a + b*x))/(b*(b*c - a*d)^2) + (c*(b*c - 2*a*d)*log(c + d*x))/(d^2*(b*c - a*d)^2)]
    @test_int [x^1/((a + b*x)*(c + d*x)^2), x, 2, -(c/(d*(b*c - a*d)*(c + d*x))) - (a*log(a + b*x))/(b*c - a*d)^2 + (a*log(c + d*x))/(b*c - a*d)^2]
    @test_int [x^0/((a + b*x)*(c + d*x)^2), x, 2, 1/((b*c - a*d)*(c + d*x)) + (b*log(a + b*x))/(b*c - a*d)^2 - (b*log(c + d*x))/(b*c - a*d)^2]
    @test_int [1/(x^1*(a + b*x)*(c + d*x)^2), x, 2, -(d/(c*(b*c - a*d)*(c + d*x))) + log(x)/(a*c^2) - (b^2*log(a + b*x))/(a*(b*c - a*d)^2) + (d*(2*b*c - a*d)*log(c + d*x))/(c^2*(b*c - a*d)^2)]
    @test_int [1/(x^2*(a + b*x)*(c + d*x)^2), x, 2, -(1/(a*c^2*x)) + d^2/(c^2*(b*c - a*d)*(c + d*x)) - ((b*c + 2*a*d)*log(x))/(a^2*c^3) + (b^3*log(a + b*x))/(a^2*(b*c - a*d)^2) - (d^2*(3*b*c - 2*a*d)*log(c + d*x))/(c^3*(b*c - a*d)^2)]
    @test_int [1/(x^3*(a + b*x)*(c + d*x)^2), x, 2, -(1/(2*a*c^2*x^2)) + (b*c + 2*a*d)/(a^2*c^3*x) - d^3/(c^3*(b*c - a*d)*(c + d*x)) + ((b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*log(x))/(a^3*c^4) - (b^4*log(a + b*x))/(a^3*(b*c - a*d)^2) + (d^3*(4*b*c - 3*a*d)*log(c + d*x))/(c^4*(b*c - a*d)^2)]

    @test_int [x^5/((a + b*x)*(c + d*x)^3), x, 2, -(((3*b*c + a*d)*x)/(b^2*d^4)) + x^2/(2*b*d^3) - c^5/(2*d^5*(b*c - a*d)*(c + d*x)^2) + (c^4*(4*b*c - 5*a*d))/(d^5*(b*c - a*d)^2*(c + d*x)) - (a^5*log(a + b*x))/(b^3*(b*c - a*d)^3) + (c^3*(6*b^2*c^2 - 15*a*b*c*d + 10*a^2*d^2)*log(c + d*x))/(d^5*(b*c - a*d)^3)]
    @test_int [x^4/((a + b*x)*(c + d*x)^3), x, 2, x/(b*d^3) + c^4/(2*d^4*(b*c - a*d)*(c + d*x)^2) - (c^3*(3*b*c - 4*a*d))/(d^4*(b*c - a*d)^2*(c + d*x)) + (a^4*log(a + b*x))/(b^2*(b*c - a*d)^3) - (c^2*(3*b^2*c^2 - 8*a*b*c*d + 6*a^2*d^2)*log(c + d*x))/(d^4*(b*c - a*d)^3)]
    @test_int [x^3/((a + b*x)*(c + d*x)^3), x, 2, -(c^3/(2*d^3*(b*c - a*d)*(c + d*x)^2)) + (c^2*(2*b*c - 3*a*d))/(d^3*(b*c - a*d)^2*(c + d*x)) - (a^3*log(a + b*x))/(b*(b*c - a*d)^3) + (c*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2)*log(c + d*x))/(d^3*(b*c - a*d)^3)]
    @test_int [x^2/((a + b*x)*(c + d*x)^3), x, 2, c^2/(2*d^2*(b*c - a*d)*(c + d*x)^2) - (c*(b*c - 2*a*d))/(d^2*(b*c - a*d)^2*(c + d*x)) + (a^2*log(a + b*x))/(b*c - a*d)^3 - (a^2*log(c + d*x))/(b*c - a*d)^3]
    @test_int [x^1/((a + b*x)*(c + d*x)^3), x, 2, -(c/(2*d*(b*c - a*d)*(c + d*x)^2)) - a/((b*c - a*d)^2*(c + d*x)) - (a*b*log(a + b*x))/(b*c - a*d)^3 + (a*b*log(c + d*x))/(b*c - a*d)^3]
    @test_int [x^0/((a + b*x)*(c + d*x)^3), x, 2, 1/(2*(b*c - a*d)*(c + d*x)^2) + b/((b*c - a*d)^2*(c + d*x)) + (b^2*log(a + b*x))/(b*c - a*d)^3 - (b^2*log(c + d*x))/(b*c - a*d)^3]
    @test_int [1/(x^1*(a + b*x)*(c + d*x)^3), x, 2, -(d/(2*c*(b*c - a*d)*(c + d*x)^2)) - (d*(2*b*c - a*d))/(c^2*(b*c - a*d)^2*(c + d*x)) + log(x)/(a*c^3) - (b^3*log(a + b*x))/(a*(b*c - a*d)^3) + (d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*log(c + d*x))/(c^3*(b*c - a*d)^3)]
    @test_int [1/(x^2*(a + b*x)*(c + d*x)^3), x, 2, -(1/(a*c^3*x)) + d^2/(2*c^2*(b*c - a*d)*(c + d*x)^2) + (d^2*(3*b*c - 2*a*d))/(c^3*(b*c - a*d)^2*(c + d*x)) - ((b*c + 3*a*d)*log(x))/(a^2*c^4) + (b^4*log(a + b*x))/(a^2*(b*c - a*d)^3) - (d^2*(6*b^2*c^2 - 8*a*b*c*d + 3*a^2*d^2)*log(c + d*x))/(c^4*(b*c - a*d)^3)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x)^p / (a+b*x)^2=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [x^4*(c + d*x)^2/(a + b*x)^2, x, 2, (a^2*(3*b*c - 5*a*d)*(b*c - a*d)*x)/b^6 - (a*(b*c - 2*a*d)*(b*c - a*d)*x^2)/b^5 + ((b*c - 3*a*d)*(b*c - a*d)*x^3)/(3*b^4) + (d*(b*c - a*d)*x^4)/(2*b^3) + (d^2*x^5)/(5*b^2) - (a^4*(b*c - a*d)^2)/(b^7*(a + b*x)) - (2*a^3*(2*b*c - 3*a*d)*(b*c - a*d)*log(a + b*x))/b^7]
    @test_int [x^3*(c + d*x)^2/(a + b*x)^2, x, 2, -((2*a*(b*c - 2*a*d)*(b*c - a*d)*x)/b^5) + ((b*c - 3*a*d)*(b*c - a*d)*x^2)/(2*b^4) + (2*d*(b*c - a*d)*x^3)/(3*b^3) + (d^2*x^4)/(4*b^2) + (a^3*(b*c - a*d)^2)/(b^6*(a + b*x)) + (a^2*(3*b*c - 5*a*d)*(b*c - a*d)*log(a + b*x))/b^6]
    @test_int [x^2*(c + d*x)^2/(a + b*x)^2, x, 2, ((b*c - 3*a*d)*(b*c - a*d)*x)/b^4 + (d*(b*c - a*d)*x^2)/b^3 + (d^2*x^3)/(3*b^2) - (a^2*(b*c - a*d)^2)/(b^5*(a + b*x)) - (2*a*(b*c - 2*a*d)*(b*c - a*d)*log(a + b*x))/b^5]
    @test_int [x^1*(c + d*x)^2/(a + b*x)^2, x, 2, (2*d*(b*c - a*d)*x)/b^3 + (d^2*x^2)/(2*b^2) + (a*(b*c - a*d)^2)/(b^4*(a + b*x)) + ((b*c - 3*a*d)*(b*c - a*d)*log(a + b*x))/b^4]
    @test_int [x^0*(c + d*x)^2/(a + b*x)^2, x, 2, (d^2*x)/b^2 - (b*c - a*d)^2/(b^3*(a + b*x)) + (2*d*(b*c - a*d)*log(a + b*x))/b^3]
    @test_int [(c + d*x)^2/(x^1*(a + b*x)^2), x, 2, (b*c - a*d)^2/(a*b^2*(a + b*x)) + (c^2*log(x))/a^2 - (c^2/a^2 - d^2/b^2)*log(a + b*x)]
    @test_int [(c + d*x)^2/(x^2*(a + b*x)^2), x, 2, -(c^2/(a^2*x)) - (b*c - a*d)^2/(a^2*b*(a + b*x)) - (2*c*(b*c - a*d)*log(x))/a^3 + (2*c*(b*c - a*d)*log(a + b*x))/a^3]
    @test_int [(c + d*x)^2/(x^3*(a + b*x)^2), x, 2, -(c^2/(2*a^2*x^2)) + (2*c*(b*c - a*d))/(a^3*x) + (b*c - a*d)^2/(a^3*(a + b*x)) + ((b*c - a*d)*(3*b*c - a*d)*log(x))/a^4 - ((b*c - a*d)*(3*b*c - a*d)*log(a + b*x))/a^4]
    @test_int [(c + d*x)^2/(x^4*(a + b*x)^2), x, 2, -(c^2/(3*a^2*x^3)) + (c*(b*c - a*d))/(a^3*x^2) - ((b*c - a*d)*(3*b*c - a*d))/(a^4*x) - (b*(b*c - a*d)^2)/(a^4*(a + b*x)) - (2*b*(b*c - a*d)*(2*b*c - a*d)*log(x))/a^5 + (2*b*(b*c - a*d)*(2*b*c - a*d)*log(a + b*x))/a^5]
    @test_int [(c + d*x)^2/(x^5*(a + b*x)^2), x, 2, -(c^2/(4*a^2*x^4)) + (2*c*(b*c - a*d))/(3*a^3*x^3) - ((b*c - a*d)*(3*b*c - a*d))/(2*a^4*x^2) + (2*b*(b*c - a*d)*(2*b*c - a*d))/(a^5*x) + (b^2*(b*c - a*d)^2)/(a^5*(a + b*x)) + (b^2*(5*b*c - 3*a*d)*(b*c - a*d)*log(x))/a^6 - (b^2*(5*b*c - 3*a*d)*(b*c - a*d)*log(a + b*x))/a^6]

    @test_int [x^4*(c + d*x)^3/(a + b*x)^2, x, 2, (3*a^2*(b*c - 2*a*d)*(b*c - a*d)^2*x)/b^7 - (a*(2*b*c - 5*a*d)*(b*c - a*d)^2*x^2)/(2*b^6) + ((b*c - 4*a*d)*(b*c - a*d)^2*x^3)/(3*b^5) + (3*d*(b*c - a*d)^2*x^4)/(4*b^4) + (d^2*(3*b*c - 2*a*d)*x^5)/(5*b^3) + (d^3*x^6)/(6*b^2) - (a^4*(b*c - a*d)^3)/(b^8*(a + b*x)) - (a^3*(4*b*c - 7*a*d)*(b*c - a*d)^2*log(a + b*x))/b^8]
    @test_int [x^3*(c + d*x)^3/(a + b*x)^2, x, 2, -((a*(2*b*c - 5*a*d)*(b*c - a*d)^2*x)/b^6) + ((b*c - 4*a*d)*(b*c - a*d)^2*x^2)/(2*b^5) + (d*(b*c - a*d)^2*x^3)/b^4 + (d^2*(3*b*c - 2*a*d)*x^4)/(4*b^3) + (d^3*x^5)/(5*b^2) + (a^3*(b*c - a*d)^3)/(b^7*(a + b*x)) + (3*a^2*(b*c - 2*a*d)*(b*c - a*d)^2*log(a + b*x))/b^7]
    @test_int [x^2*(c + d*x)^3/(a + b*x)^2, x, 2, ((b*c - 4*a*d)*(b*c - a*d)^2*x)/b^5 + (3*d*(b*c - a*d)^2*x^2)/(2*b^4) + (d^2*(3*b*c - 2*a*d)*x^3)/(3*b^3) + (d^3*x^4)/(4*b^2) - (a^2*(b*c - a*d)^3)/(b^6*(a + b*x)) - (a*(2*b*c - 5*a*d)*(b*c - a*d)^2*log(a + b*x))/b^6]
    @test_int [x^1*(c + d*x)^3/(a + b*x)^2, x, 2, (3*d*(b*c - a*d)^2*x)/b^4 + (d^2*(3*b*c - 2*a*d)*x^2)/(2*b^3) + (d^3*x^3)/(3*b^2) + (a*(b*c - a*d)^3)/(b^5*(a + b*x)) + ((b*c - 4*a*d)*(b*c - a*d)^2*log(a + b*x))/b^5]
    @test_int [x^0*(c + d*x)^3/(a + b*x)^2, x, 2, (d^2*(3*b*c - 2*a*d)*x)/b^3 + (d^3*x^2)/(2*b^2) - (b*c - a*d)^3/(b^4*(a + b*x)) + (3*d*(b*c - a*d)^2*log(a + b*x))/b^4]
    @test_int [(c + d*x)^3/(x^1*(a + b*x)^2), x, 2, (d^3*x)/b^2 + (b*c - a*d)^3/(a*b^3*(a + b*x)) + (c^3*log(x))/a^2 - ((b*c - a*d)^2*(b*c + 2*a*d)*log(a + b*x))/(a^2*b^3)]
    @test_int [(c + d*x)^3/(x^2*(a + b*x)^2), x, 2, -(c^3/(a^2*x)) - (b*c - a*d)^3/(a^2*b^2*(a + b*x)) - (c^2*(2*b*c - 3*a*d)*log(x))/a^3 + ((b*c - a*d)^2*(2*b*c + a*d)*log(a + b*x))/(a^3*b^2)]
    @test_int [(c + d*x)^3/(x^3*(a + b*x)^2), x, 2, -c^3/(2*a^2*x^2) + (c^2*(2*b*c - 3*a*d))/(a^3*x) + (b*c - a*d)^3/(a^3*b*(a + b*x)) + (3*c*(b*c - a*d)^2*log(x))/a^4 - (3*c*(b*c - a*d)^2*log(a + b*x))/a^4]
    @test_int [(c + d*x)^3/(x^4*(a + b*x)^2), x, 2, -c^3/(3*a^2*x^3) + (c^2*(2*b*c - 3*a*d))/(2*a^3*x^2) - (3*c*(b*c - a*d)^2)/(a^4*x) - (b*c - a*d)^3/(a^4*(a + b*x)) - ((b*c - a*d)^2*(4*b*c - a*d)*log(x))/a^5 + ((b*c - a*d)^2*(4*b*c - a*d)*log(a + b*x))/a^5]
    @test_int [(c + d*x)^3/(x^5*(a + b*x)^2), x, 2, -c^3/(4*a^2*x^4) + (c^2*(2*b*c - 3*a*d))/(3*a^3*x^3) - (3*c*(b*c - a*d)^2)/(2*a^4*x^2) + ((b*c - a*d)^2*(4*b*c - a*d))/(a^5*x) + (b*(b*c - a*d)^3)/(a^5*(a + b*x)) + (b*(5*b*c - 2*a*d)*(b*c - a*d)^2*log(x))/a^6 - (b*(5*b*c - 2*a*d)*(b*c - a*d)^2*log(a + b*x))/a^6]
    @test_int [(c + d*x)^3/(x^6*(a + b*x)^2), x, 2, -c^3/(5*a^2*x^5) + (c^2*(2*b*c - 3*a*d))/(4*a^3*x^4) - (c*(b*c - a*d)^2)/(a^4*x^3) + ((b*c - a*d)^2*(4*b*c - a*d))/(2*a^5*x^2) - (b*(5*b*c - 2*a*d)*(b*c - a*d)^2)/(a^6*x) - (b^2*(b*c - a*d)^3)/(a^6*(a + b*x)) - (3*b^2*(b*c - a*d)^2*(2*b*c - a*d)*log(x))/a^7 + (3*b^2*(b*c - a*d)^2*(2*b*c - a*d)*log(a + b*x))/a^7]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [x^6/((a + b*x)^2*(c + d*x)^2), x, 2, ((3*b^2*c^2 + 4*a*b*c*d + 3*a^2*d^2)*x)/(b^4*d^4) - ((b*c + a*d)*x^2)/(b^3*d^3) + x^3/(3*b^2*d^2) - a^6/(b^5*(b*c - a*d)^2*(a + b*x)) - c^6/(d^5*(b*c - a*d)^2*(c + d*x)) - (2*a^5*(3*b*c - 2*a*d)*log(a + b*x))/(b^5*(b*c - a*d)^3) - (2*c^5*(2*b*c - 3*a*d)*log(c + d*x))/(d^5*(b*c - a*d)^3)]
    @test_int [x^5/((a + b*x)^2*(c + d*x)^2), x, 2, -((2*(b*c + a*d)*x)/(b^3*d^3)) + x^2/(2*b^2*d^2) + a^5/(b^4*(b*c - a*d)^2*(a + b*x)) + c^5/(d^4*(b*c - a*d)^2*(c + d*x)) + (a^4*(5*b*c - 3*a*d)*log(a + b*x))/(b^4*(b*c - a*d)^3) + (c^4*(3*b*c - 5*a*d)*log(c + d*x))/(d^4*(b*c - a*d)^3)]
    @test_int [x^4/((a + b*x)^2*(c + d*x)^2), x, 2, x/(b^2*d^2) - a^4/(b^3*(b*c - a*d)^2*(a + b*x)) - c^4/(d^3*(b*c - a*d)^2*(c + d*x)) - (2*a^3*(2*b*c - a*d)*log(a + b*x))/(b^3*(b*c - a*d)^3) - (2*c^3*(b*c - 2*a*d)*log(c + d*x))/(d^3*(b*c - a*d)^3)]
    @test_int [x^3/((a + b*x)^2*(c + d*x)^2), x, 2, a^3/(b^2*(b*c - a*d)^2*(a + b*x)) + c^3/(d^2*(b*c - a*d)^2*(c + d*x)) + (a^2*(3*b*c - a*d)*log(a + b*x))/(b^2*(b*c - a*d)^3) + (c^2*(b*c - 3*a*d)*log(c + d*x))/(d^2*(b*c - a*d)^3)]
    @test_int [x^2/((a + b*x)^2*(c + d*x)^2), x, 2, -(a^2/(b*(b*c - a*d)^2*(a + b*x))) - c^2/(d*(b*c - a*d)^2*(c + d*x)) - (2*a*c*log(a + b*x))/(b*c - a*d)^3 + (2*a*c*log(c + d*x))/(b*c - a*d)^3]
    @test_int [x^1/((a + b*x)^2*(c + d*x)^2), x, 2, a/((b*c - a*d)^2*(a + b*x)) + c/((b*c - a*d)^2*(c + d*x)) + ((b*c + a*d)*log(a + b*x))/(b*c - a*d)^3 - ((b*c + a*d)*log(c + d*x))/(b*c - a*d)^3]
    @test_int [x^0/((a + b*x)^2*(c + d*x)^2), x, 2, -(b/((b*c - a*d)^2*(a + b*x))) - d/((b*c - a*d)^2*(c + d*x)) - (2*b*d*log(a + b*x))/(b*c - a*d)^3 + (2*b*d*log(c + d*x))/(b*c - a*d)^3]
    @test_int [1/(x^1*(a + b*x)^2*(c + d*x)^2), x, 2, b^2/(a*(b*c - a*d)^2*(a + b*x)) + d^2/(c*(b*c - a*d)^2*(c + d*x)) + log(x)/(a^2*c^2) - (b^2*(b*c - 3*a*d)*log(a + b*x))/(a^2*(b*c - a*d)^3) - (d^2*(3*b*c - a*d)*log(c + d*x))/(c^2*(b*c - a*d)^3)]
    @test_int [1/(x^2*(a + b*x)^2*(c + d*x)^2), x, 2, -(1/(a^2*c^2*x)) - b^3/(a^2*(b*c - a*d)^2*(a + b*x)) - d^3/(c^2*(b*c - a*d)^2*(c + d*x)) - (2*(b*c + a*d)*log(x))/(a^3*c^3) + (2*b^3*(b*c - 2*a*d)*log(a + b*x))/(a^3*(b*c - a*d)^3) + (2*d^3*(2*b*c - a*d)*log(c + d*x))/(c^3*(b*c - a*d)^3)]
    @test_int [1/(x^3*(a + b*x)^2*(c + d*x)^2), x, 2, -(1/(2*a^2*c^2*x^2)) + (2*(b*c + a*d))/(a^3*c^3*x) + b^4/(a^3*(b*c - a*d)^2*(a + b*x)) + d^4/(c^3*(b*c - a*d)^2*(c + d*x)) + ((3*b^2*c^2 + 4*a*b*c*d + 3*a^2*d^2)*log(x))/(a^4*c^4) - (b^4*(3*b*c - 5*a*d)*log(a + b*x))/(a^4*(b*c - a*d)^3) - (d^4*(5*b*c - 3*a*d)*log(c + d*x))/(c^4*(b*c - a*d)^3)]

    @test_int [x^7/((a + b*x)^2*(c + d*x)^3), x, 2, (3*(2*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*x)/(b^4*d^5) - ((3*b*c + 2*a*d)*x^2)/(2*b^3*d^4) + x^3/(3*b^2*d^3) + a^7/(b^5*(b*c - a*d)^3*(a + b*x)) + c^7/(2*d^6*(b*c - a*d)^2*(c + d*x)^2) - (c^6*(5*b*c - 7*a*d))/(d^6*(b*c - a*d)^3*(c + d*x)) + (a^6*(7*b*c - 4*a*d)*log(a + b*x))/(b^5*(b*c - a*d)^4) - (c^5*(10*b^2*c^2 - 28*a*b*c*d + 21*a^2*d^2)*log(c + d*x))/(d^6*(b*c - a*d)^4)]
    @test_int [x^6/((a + b*x)^2*(c + d*x)^3), x, 2, -(((3*b*c + 2*a*d)*x)/(b^3*d^4)) + x^2/(2*b^2*d^3) - a^6/(b^4*(b*c - a*d)^3*(a + b*x)) - c^6/(2*d^5*(b*c - a*d)^2*(c + d*x)^2) + (2*c^5*(2*b*c - 3*a*d))/(d^5*(b*c - a*d)^3*(c + d*x)) - (3*a^5*(2*b*c - a*d)*log(a + b*x))/(b^4*(b*c - a*d)^4) + (3*c^4*(2*b^2*c^2 - 6*a*b*c*d + 5*a^2*d^2)*log(c + d*x))/(d^5*(b*c - a*d)^4)]
    @test_int [x^5/((a + b*x)^2*(c + d*x)^3), x, 2, x/(b^2*d^3) + a^5/(b^3*(b*c - a*d)^3*(a + b*x)) + c^5/(2*d^4*(b*c - a*d)^2*(c + d*x)^2) - (c^4*(3*b*c - 5*a*d))/(d^4*(b*c - a*d)^3*(c + d*x)) + (a^4*(5*b*c - 2*a*d)*log(a + b*x))/(b^3*(b*c - a*d)^4) - (c^3*(3*b^2*c^2 - 10*a*b*c*d + 10*a^2*d^2)*log(c + d*x))/(d^4*(b*c - a*d)^4)]
    @test_int [x^4/((a + b*x)^2*(c + d*x)^3), x, 2, -(a^4/(b^2*(b*c - a*d)^3*(a + b*x))) - c^4/(2*d^3*(b*c - a*d)^2*(c + d*x)^2) + (2*c^3*(b*c - 2*a*d))/(d^3*(b*c - a*d)^3*(c + d*x)) - (a^3*(4*b*c - a*d)*log(a + b*x))/(b^2*(b*c - a*d)^4) + (c^2*(b^2*c^2 - 4*a*b*c*d + 6*a^2*d^2)*log(c + d*x))/(d^3*(b*c - a*d)^4)]
    @test_int [x^3/((a + b*x)^2*(c + d*x)^3), x, 2, a^3/(b*(b*c - a*d)^3*(a + b*x)) + c^3/(2*d^2*(b*c - a*d)^2*(c + d*x)^2) - (c^2*(b*c - 3*a*d))/(d^2*(b*c - a*d)^3*(c + d*x)) + (3*a^2*c*log(a + b*x))/(b*c - a*d)^4 - (3*a^2*c*log(c + d*x))/(b*c - a*d)^4]
    @test_int [x^2/((a + b*x)^2*(c + d*x)^3), x, 2, -(a^2/((b*c - a*d)^3*(a + b*x))) - c^2/(2*d*(b*c - a*d)^2*(c + d*x)^2) - (2*a*c)/((b*c - a*d)^3*(c + d*x)) - (a*(2*b*c + a*d)*log(a + b*x))/(b*c - a*d)^4 + (a*(2*b*c + a*d)*log(c + d*x))/(b*c - a*d)^4]
    @test_int [x^1/((a + b*x)^2*(c + d*x)^3), x, 2, (a*b)/((b*c - a*d)^3*(a + b*x)) + c/(2*(b*c - a*d)^2*(c + d*x)^2) + (b*c + a*d)/((b*c - a*d)^3*(c + d*x)) + (b*(b*c + 2*a*d)*log(a + b*x))/(b*c - a*d)^4 - (b*(b*c + 2*a*d)*log(c + d*x))/(b*c - a*d)^4]
    @test_int [x^0/((a + b*x)^2*(c + d*x)^3), x, 2, -(b^2/((b*c - a*d)^3*(a + b*x))) - d/(2*(b*c - a*d)^2*(c + d*x)^2) - (2*b*d)/((b*c - a*d)^3*(c + d*x)) - (3*b^2*d*log(a + b*x))/(b*c - a*d)^4 + (3*b^2*d*log(c + d*x))/(b*c - a*d)^4]
    @test_int [1/(x^1*(a + b*x)^2*(c + d*x)^3), x, 2, b^3/(a*(b*c - a*d)^3*(a + b*x)) + d^2/(2*c*(b*c - a*d)^2*(c + d*x)^2) + (d^2*(3*b*c - a*d))/(c^2*(b*c - a*d)^3*(c + d*x)) + log(x)/(a^2*c^3) - (b^3*(b*c - 4*a*d)*log(a + b*x))/(a^2*(b*c - a*d)^4) - (d^2*(6*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*log(c + d*x))/(c^3*(b*c - a*d)^4)]
    @test_int [1/(x^2*(a + b*x)^2*(c + d*x)^3), x, 2, -(1/(a^2*c^3*x)) - b^4/(a^2*(b*c - a*d)^3*(a + b*x)) - d^3/(2*c^2*(b*c - a*d)^2*(c + d*x)^2) - (2*d^3*(2*b*c - a*d))/(c^3*(b*c - a*d)^3*(c + d*x)) - ((2*b*c + 3*a*d)*log(x))/(a^3*c^4) + (b^4*(2*b*c - 5*a*d)*log(a + b*x))/(a^3*(b*c - a*d)^4) + (d^3*(10*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*log(c + d*x))/(c^4*(b*c - a*d)^4)]
    @test_int [1/(x^3*(a + b*x)^2*(c + d*x)^3), x, 2, -(1/(2*a^2*c^3*x^2)) + (2*b*c + 3*a*d)/(a^3*c^4*x) + b^5/(a^3*(b*c - a*d)^3*(a + b*x)) + d^4/(2*c^3*(b*c - a*d)^2*(c + d*x)^2) + (d^4*(5*b*c - 3*a*d))/(c^4*(b*c - a*d)^3*(c + d*x)) + (3*(b^2*c^2 + 2*a*b*c*d + 2*a^2*d^2)*log(x))/(a^4*c^5) - (3*b^5*(b*c - 2*a*d)*log(a + b*x))/(a^4*(b*c - a*d)^4) - (3*d^4*(5*b^2*c^2 - 6*a*b*c*d + 2*a^2*d^2)*log(c + d*x))/(c^5*(b*c - a*d)^4)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x)^p / (a+b*x)^3=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [x^3*(c + d*x)^3/(a + b*x)^3, x, 2, ((b*c - a*d)*(b^2*c^2 - 8*a*b*c*d + 10*a^2*d^2)*x)/b^6 + (3*d*(b*c - 2*a*d)*(b*c - a*d)*x^2)/(2*b^5) + (d^2*(b*c - a*d)*x^3)/b^4 + (d^3*x^4)/(4*b^3) + (a^3*(b*c - a*d)^3)/(2*b^7*(a + b*x)^2) - (3*a^2*(b*c - 2*a*d)*(b*c - a*d)^2)/(b^7*(a + b*x)) - (3*a*(b*c - a*d)*(b^2*c^2 - 5*a*b*c*d + 5*a^2*d^2)*log(a + b*x))/b^7]
    @test_int [x^2*(c + d*x)^3/(a + b*x)^3, x, 2, (3*d*(b*c - 2*a*d)*(b*c - a*d)*x)/b^5 + (3*d^2*(b*c - a*d)*x^2)/(2*b^4) + (d^3*x^3)/(3*b^3) - (a^2*(b*c - a*d)^3)/(2*b^6*(a + b*x)^2) + (a*(2*b*c - 5*a*d)*(b*c - a*d)^2)/(b^6*(a + b*x)) + ((b*c - a*d)*(b^2*c^2 - 8*a*b*c*d + 10*a^2*d^2)*log(a + b*x))/b^6]
    @test_int [x^1*(c + d*x)^3/(a + b*x)^3, x, 2, (3*d^2*(b*c - a*d)*x)/b^4 + (d^3*x^2)/(2*b^3) + (a*(b*c - a*d)^3)/(2*b^5*(a + b*x)^2) - ((b*c - 4*a*d)*(b*c - a*d)^2)/(b^5*(a + b*x)) + (3*d*(b*c - 2*a*d)*(b*c - a*d)*log(a + b*x))/b^5]
    @test_int [x^0*(c + d*x)^3/(a + b*x)^3, x, 2, (d^3*x)/b^3 - (b*c - a*d)^3/(2*b^4*(a + b*x)^2) - (3*d*(b*c - a*d)^2)/(b^4*(a + b*x)) + (3*d^2*(b*c - a*d)*log(a + b*x))/b^4]
    @test_int [(c + d*x)^3/(x^1*(a + b*x)^3), x, 2, (b*c - a*d)^3/(2*a*b^3*(a + b*x)^2) + ((b*c - a*d)^2*(b*c + 2*a*d))/(a^2*b^3*(a + b*x)) + (c^3*log(x))/a^3 - (c^3/a^3 - d^3/b^3)*log(a + b*x)]
    @test_int [(c + d*x)^3/(x^2*(a + b*x)^3), x, 2, -(c^3/(a^3*x)) - (b*c - a*d)^3/(2*a^2*b^2*(a + b*x)^2) - ((b*c - a*d)^2*(2*b*c + a*d))/(a^3*b^2*(a + b*x)) - (3*c^2*(b*c - a*d)*log(x))/a^4 + (3*c^2*(b*c - a*d)*log(a + b*x))/a^4]
    @test_int [(c + d*x)^3/(x^3*(a + b*x)^3), x, 2, -(c^3/(2*a^3*x^2)) + (3*c^2*(b*c - a*d))/(a^4*x) + (b*c - a*d)^3/(2*a^3*b*(a + b*x)^2) + (3*c*(b*c - a*d)^2)/(a^4*(a + b*x)) + (3*c*(b*c - a*d)*(2*b*c - a*d)*log(x))/a^5 - (3*c*(b*c - a*d)*(2*b*c - a*d)*log(a + b*x))/a^5]
    @test_int [(c + d*x)^3/(x^4*(a + b*x)^3), x, 2, -(c^3/(3*a^3*x^3)) + (3*c^2*(b*c - a*d))/(2*a^4*x^2) - (3*c*(b*c - a*d)*(2*b*c - a*d))/(a^5*x) - (b*c - a*d)^3/(2*a^4*(a + b*x)^2) - ((b*c - a*d)^2*(4*b*c - a*d))/(a^5*(a + b*x)) - ((b*c - a*d)*(10*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*log(x))/a^6 + ((b*c - a*d)*(10*b^2*c^2 - 8*a*b*c*d + a^2*d^2)*log(a + b*x))/a^6]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [x^7/((a + b*x)^3*(c + d*x)^3), x, 2, -((3*(b*c + a*d)*x)/(b^4*d^4)) + x^2/(2*b^3*d^3) + a^7/(2*b^5*(b*c - a*d)^3*(a + b*x)^2) - (a^6*(7*b*c - 4*a*d))/(b^5*(b*c - a*d)^4*(a + b*x)) - c^7/(2*d^5*(b*c - a*d)^3*(c + d*x)^2) + (c^6*(4*b*c - 7*a*d))/(d^5*(b*c - a*d)^4*(c + d*x)) - (3*a^5*(7*b^2*c^2 - 7*a*b*c*d + 2*a^2*d^2)*log(a + b*x))/(b^5*(b*c - a*d)^5) + (3*c^5*(2*b^2*c^2 - 7*a*b*c*d + 7*a^2*d^2)*log(c + d*x))/(d^5*(b*c - a*d)^5)]
    @test_int [x^6/((a + b*x)^3*(c + d*x)^3), x, 2, x/(b^3*d^3) - a^6/(2*b^4*(b*c - a*d)^3*(a + b*x)^2) + (3*a^5*(2*b*c - a*d))/(b^4*(b*c - a*d)^4*(a + b*x)) + c^6/(2*d^4*(b*c - a*d)^3*(c + d*x)^2) - (3*c^5*(b*c - 2*a*d))/(d^4*(b*c - a*d)^4*(c + d*x)) + (3*a^4*(5*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*log(a + b*x))/(b^4*(b*c - a*d)^5) - (3*c^4*(b^2*c^2 - 4*a*b*c*d + 5*a^2*d^2)*log(c + d*x))/(d^4*(b*c - a*d)^5)]
    @test_int [x^5/((a + b*x)^3*(c + d*x)^3), x, 2, a^5/(2*b^3*(b*c - a*d)^3*(a + b*x)^2) - (a^4*(5*b*c - 2*a*d))/(b^3*(b*c - a*d)^4*(a + b*x)) - c^5/(2*d^3*(b*c - a*d)^3*(c + d*x)^2) + (c^4*(2*b*c - 5*a*d))/(d^3*(b*c - a*d)^4*(c + d*x)) - (a^3*(10*b^2*c^2 - 5*a*b*c*d + a^2*d^2)*log(a + b*x))/(b^3*(b*c - a*d)^5) + (c^3*(b^2*c^2 - 5*a*b*c*d + 10*a^2*d^2)*log(c + d*x))/(d^3*(b*c - a*d)^5)]
    @test_int [x^4/((a + b*x)^3*(c + d*x)^3), x, 2, -(a^4/(2*b^2*(b*c - a*d)^3*(a + b*x)^2)) + (a^3*(4*b*c - a*d))/(b^2*(b*c - a*d)^4*(a + b*x)) + c^4/(2*d^2*(b*c - a*d)^3*(c + d*x)^2) - (c^3*(b*c - 4*a*d))/(d^2*(b*c - a*d)^4*(c + d*x)) + (6*a^2*c^2*log(a + b*x))/(b*c - a*d)^5 - (6*a^2*c^2*log(c + d*x))/(b*c - a*d)^5]
    @test_int [x^3/((a + b*x)^3*(c + d*x)^3), x, 2, a^3/(2*b*(b*c - a*d)^3*(a + b*x)^2) - (3*a^2*c)/((b*c - a*d)^4*(a + b*x)) - c^3/(2*d*(b*c - a*d)^3*(c + d*x)^2) - (3*a*c^2)/((b*c - a*d)^4*(c + d*x)) - (3*a*c*(b*c + a*d)*log(a + b*x))/(b*c - a*d)^5 + (3*a*c*(b*c + a*d)*log(c + d*x))/(b*c - a*d)^5]
    @test_int [x^2/((a + b*x)^3*(c + d*x)^3), x, 2, -(a^2/(2*(b*c - a*d)^3*(a + b*x)^2)) + (a*(2*b*c + a*d))/((b*c - a*d)^4*(a + b*x)) + c^2/(2*(b*c - a*d)^3*(c + d*x)^2) + (c*(b*c + 2*a*d))/((b*c - a*d)^4*(c + d*x)) + ((b^2*c^2 + 4*a*b*c*d + a^2*d^2)*log(a + b*x))/(b*c - a*d)^5 - ((b^2*c^2 + 4*a*b*c*d + a^2*d^2)*log(c + d*x))/(b*c - a*d)^5]
    @test_int [x^1/((a + b*x)^3*(c + d*x)^3), x, 2, (a*b)/(2*(b*c - a*d)^3*(a + b*x)^2) - (b*(b*c + 2*a*d))/((b*c - a*d)^4*(a + b*x)) - (c*d)/(2*(b*c - a*d)^3*(c + d*x)^2) - (d*(2*b*c + a*d))/((b*c - a*d)^4*(c + d*x)) - (3*b*d*(b*c + a*d)*log(a + b*x))/(b*c - a*d)^5 + (3*b*d*(b*c + a*d)*log(c + d*x))/(b*c - a*d)^5]
    @test_int [x^0/((a + b*x)^3*(c + d*x)^3), x, 2, -(b^2/(2*(b*c - a*d)^3*(a + b*x)^2)) + (3*b^2*d)/((b*c - a*d)^4*(a + b*x)) + d^2/(2*(b*c - a*d)^3*(c + d*x)^2) + (3*b*d^2)/((b*c - a*d)^4*(c + d*x)) + (6*b^2*d^2*log(a + b*x))/(b*c - a*d)^5 - (6*b^2*d^2*log(c + d*x))/(b*c - a*d)^5]
    @test_int [1/(x^1*(a + b*x)^3*(c + d*x)^3), x, 2, b^3/(2*a*(b*c - a*d)^3*(a + b*x)^2) + (b^3*(b*c - 4*a*d))/(a^2*(b*c - a*d)^4*(a + b*x)) - d^3/(2*c*(b*c - a*d)^3*(c + d*x)^2) - (d^3*(4*b*c - a*d))/(c^2*(b*c - a*d)^4*(c + d*x)) + log(x)/(a^3*c^3) - (b^3*(b^2*c^2 - 5*a*b*c*d + 10*a^2*d^2)*log(a + b*x))/(a^3*(b*c - a*d)^5) + (d^3*(10*b^2*c^2 - 5*a*b*c*d + a^2*d^2)*log(c + d*x))/(c^3*(b*c - a*d)^5)]
    @test_int [1/(x^2*(a + b*x)^3*(c + d*x)^3), x, 2, -(1/(a^3*c^3*x)) - b^4/(2*a^2*(b*c - a*d)^3*(a + b*x)^2) - (b^4*(2*b*c - 5*a*d))/(a^3*(b*c - a*d)^4*(a + b*x)) + d^4/(2*c^2*(b*c - a*d)^3*(c + d*x)^2) + (d^4*(5*b*c - 2*a*d))/(c^3*(b*c - a*d)^4*(c + d*x)) - (3*(b*c + a*d)*log(x))/(a^4*c^4) + (3*b^4*(b^2*c^2 - 4*a*b*c*d + 5*a^2*d^2)*log(a + b*x))/(a^4*(b*c - a*d)^5) - (3*d^4*(5*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*log(c + d*x))/(c^4*(b*c - a*d)^5)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^(m/2)*(a+b*x)^1*(c+d*x)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^(7/2)*(a + b*x)*(A + B*x), x, 2, (2*a*A*x^(9/2))/9 + (2*(A*b + a*B)*x^(11/2))/11 + (2*b*B*x^(13/2))/13]
    @test_int [x^(5/2)*(a + b*x)*(A + B*x), x, 2, (2*a*A*x^(7/2))/7 + (2*(A*b + a*B)*x^(9/2))/9 + (2*b*B*x^(11/2))/11]
    @test_int [x^(3/2)*(a + b*x)*(A + B*x), x, 2, (2*a*A*x^(5/2))/5 + (2*(A*b + a*B)*x^(7/2))/7 + (2*b*B*x^(9/2))/9]
    @test_int [sqrt(x)*(a + b*x)*(A + B*x), x, 2, (2*a*A*x^(3/2))/3 + (2*(A*b + a*B)*x^(5/2))/5 + (2*b*B*x^(7/2))/7]
    @test_int [((a + b*x)*(A + B*x))/sqrt(x), x, 2, 2*a*A*sqrt(x) + (2*(A*b + a*B)*x^(3/2))/3 + (2*b*B*x^(5/2))/5]
    @test_int [((a + b*x)*(A + B*x))/x^(3/2), x, 2, (-2*a*A)/sqrt(x) + 2*(A*b + a*B)*sqrt(x) + (2*b*B*x^(3/2))/3]
    @test_int [((a + b*x)*(A + B*x))/x^(5/2), x, 2, (-2*a*A)/(3*x^(3/2)) - (2*(A*b + a*B))/sqrt(x) + 2*b*B*sqrt(x)]
    @test_int [((a + b*x)*(A + B*x))/x^(7/2), x, 2, (-2*a*A)/(5*x^(5/2)) - (2*(A*b + a*B))/(3*x^(3/2)) - (2*b*B)/sqrt(x)]

    @test_int [x^(7/2)*(a + b*x)^2*(A + B*x), x, 2, (2*a^2*A*x^(9/2))/9 + (2*a*(2*A*b + a*B)*x^(11/2))/11 + (2*b*(A*b + 2*a*B)*x^(13/2))/13 + (2*b^2*B*x^(15/2))/15]
    @test_int [x^(5/2)*(a + b*x)^2*(A + B*x), x, 2, (2*a^2*A*x^(7/2))/7 + (2*a*(2*A*b + a*B)*x^(9/2))/9 + (2*b*(A*b + 2*a*B)*x^(11/2))/11 + (2*b^2*B*x^(13/2))/13]
    @test_int [x^(3/2)*(a + b*x)^2*(A + B*x), x, 2, (2*a^2*A*x^(5/2))/5 + (2*a*(2*A*b + a*B)*x^(7/2))/7 + (2*b*(A*b + 2*a*B)*x^(9/2))/9 + (2*b^2*B*x^(11/2))/11]
    @test_int [sqrt(x)*(a + b*x)^2*(A + B*x), x, 2, (2*a^2*A*x^(3/2))/3 + (2*a*(2*A*b + a*B)*x^(5/2))/5 + (2*b*(A*b + 2*a*B)*x^(7/2))/7 + (2*b^2*B*x^(9/2))/9]
    @test_int [((a + b*x)^2*(A + B*x))/sqrt(x), x, 2, 2*a^2*A*sqrt(x) + (2*a*(2*A*b + a*B)*x^(3/2))/3 + (2*b*(A*b + 2*a*B)*x^(5/2))/5 + (2*b^2*B*x^(7/2))/7]
    @test_int [((a + b*x)^2*(A + B*x))/x^(3/2), x, 2, -((2*a^2*A)/sqrt(x)) + 2*a*(2*A*b + a*B)*sqrt(x) + (2/3)*b*(A*b + 2*a*B)*x^(3/2) + (2/5)*b^2*B*x^(5/2)]
    @test_int [((a + b*x)^2*(A + B*x))/x^(5/2), x, 2, -((2*a^2*A)/(3*x^(3/2))) - (2*a*(2*A*b + a*B))/sqrt(x) + 2*b*(A*b + 2*a*B)*sqrt(x) + (2/3)*b^2*B*x^(3/2)]
    @test_int [((a + b*x)^2*(A + B*x))/x^(7/2), x, 2, -((2*a^2*A)/(5*x^(5/2))) - (2*a*(2*A*b + a*B))/(3*x^(3/2)) - (2*b*(A*b + 2*a*B))/sqrt(x) + 2*b^2*B*sqrt(x)]

    @test_int [x^(7/2)*(a + b*x)^3*(A + B*x), x, 2, (2*a^3*A*x^(9/2))/9 + (2*a^2*(3*A*b + a*B)*x^(11/2))/11 + (6*a*b*(A*b + a*B)*x^(13/2))/13 + (2*b^2*(A*b + 3*a*B)*x^(15/2))/15 + (2*b^3*B*x^(17/2))/17]
    @test_int [x^(5/2)*(a + b*x)^3*(A + B*x), x, 2, (2*a^3*A*x^(7/2))/7 + (2*a^2*(3*A*b + a*B)*x^(9/2))/9 + (6*a*b*(A*b + a*B)*x^(11/2))/11 + (2*b^2*(A*b + 3*a*B)*x^(13/2))/13 + (2*b^3*B*x^(15/2))/15]
    @test_int [x^(3/2)*(a + b*x)^3*(A + B*x), x, 2, (2*a^3*A*x^(5/2))/5 + (2*a^2*(3*A*b + a*B)*x^(7/2))/7 + (2*a*b*(A*b + a*B)*x^(9/2))/3 + (2*b^2*(A*b + 3*a*B)*x^(11/2))/11 + (2*b^3*B*x^(13/2))/13]
    @test_int [sqrt(x)*(a + b*x)^3*(A + B*x), x, 2, (2*a^3*A*x^(3/2))/3 + (2*a^2*(3*A*b + a*B)*x^(5/2))/5 + (6*a*b*(A*b + a*B)*x^(7/2))/7 + (2*b^2*(A*b + 3*a*B)*x^(9/2))/9 + (2*b^3*B*x^(11/2))/11]
    @test_int [((a + b*x)^3*(A + B*x))/sqrt(x), x, 2, 2*a^3*A*sqrt(x) + (2*a^2*(3*A*b + a*B)*x^(3/2))/3 + (6*a*b*(A*b + a*B)*x^(5/2))/5 + (2*b^2*(A*b + 3*a*B)*x^(7/2))/7 + (2*b^3*B*x^(9/2))/9]
    @test_int [((a + b*x)^3*(A + B*x))/x^(3/2), x, 2, -((2*a^3*A)/sqrt(x)) + 2*a^2*(3*A*b + a*B)*sqrt(x) + 2*a*b*(A*b + a*B)*x^(3/2) + (2/5)*b^2*(A*b + 3*a*B)*x^(5/2) + (2/7)*b^3*B*x^(7/2)]
    @test_int [((a + b*x)^3*(A + B*x))/x^(5/2), x, 2, -((2*a^3*A)/(3*x^(3/2))) - (2*a^2*(3*A*b + a*B))/sqrt(x) + 6*a*b*(A*b + a*B)*sqrt(x) + (2/3)*b^2*(A*b + 3*a*B)*x^(3/2) + (2/5)*b^3*B*x^(5/2)]
    @test_int [((a + b*x)^3*(A + B*x))/x^(7/2), x, 2, -((2*a^3*A)/(5*x^(5/2))) - (2*a^2*(3*A*b + a*B))/(3*x^(3/2)) - (6*a*b*(A*b + a*B))/sqrt(x) + 2*b^2*(A*b + 3*a*B)*sqrt(x) + (2/3)*b^3*B*x^(3/2)]

    @test_int [((2 - 3*x)^3*sqrt(x))/(1 + x)^2, x, 5, -450*sqrt(x) + 72*x^(3/2) - (54*x^(5/2))/5 - (125*sqrt(x))/(1 + x) + 575*atan(sqrt(x)), (-(3/5))*(917 - 171*x)*sqrt(x) - (21/5)*(2 - 3*x)^2*sqrt(x) - ((2 - 3*x)^3*sqrt(x))/(1 + x) + 575*atan(sqrt(x))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(x^(7/2)*(A + B*x))/(a + b*x), x, 7, (-2*a^3*(A*b - a*B)*sqrt(x))/b^5 + (2*a^2*(A*b - a*B)*x^(3/2))/(3*b^4) - (2*a*(A*b - a*B)*x^(5/2))/(5*b^3) + (2*(A*b - a*B)*x^(7/2))/(7*b^2) + (2*B*x^(9/2))/(9*b) + (2*a^(7/2)*(A*b - a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/b^(11/2)]
    @test_int [(x^(5/2)*(A + B*x))/(a + b*x), x, 6, (2*a^2*(A*b - a*B)*sqrt(x))/b^4 - (2*a*(A*b - a*B)*x^(3/2))/(3*b^3) + (2*(A*b - a*B)*x^(5/2))/(5*b^2) + (2*B*x^(7/2))/(7*b) - (2*a^(5/2)*(A*b - a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/b^(9/2)]
    @test_int [(x^(3/2)*(A + B*x))/(a + b*x), x, 5, (-2*a*(A*b - a*B)*sqrt(x))/b^3 + (2*(A*b - a*B)*x^(3/2))/(3*b^2) + (2*B*x^(5/2))/(5*b) + (2*a^(3/2)*(A*b - a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/b^(7/2)]
    @test_int [(sqrt(x)*(A + B*x))/(a + b*x), x, 4, (2*(A*b - a*B)*sqrt(x))/b^2 + (2*B*x^(3/2))/(3*b) - (2*sqrt(a)*(A*b - a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/b^(5/2)]
    @test_int [(A + B*x)/(sqrt(x)*(a + b*x)), x, 3, (2*B*sqrt(x))/b + (2*(A*b - a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/(sqrt(a)*b^(3/2))]
    @test_int [(A + B*x)/(x^(3/2)*(a + b*x)), x, 3, (-2*A)/(a*sqrt(x)) - (2*(A*b - a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/(a^(3/2)*sqrt(b))]
    @test_int [(A + B*x)/(x^(5/2)*(a + b*x)), x, 4, (-2*A)/(3*a*x^(3/2)) + (2*(A*b - a*B))/(a^2*sqrt(x)) + (2*sqrt(b)*(A*b - a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/a^(5/2)]
    @test_int [(A + B*x)/(x^(7/2)*(a + b*x)), x, 5, (-2*A)/(5*a*x^(5/2)) + (2*(A*b - a*B))/(3*a^2*x^(3/2)) - (2*b*(A*b - a*B))/(a^3*sqrt(x)) - (2*b^(3/2)*(A*b - a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/a^(7/2)]
    @test_int [(A + B*x)/(x^(9/2)*(a + b*x)), x, 6, (-2*A)/(7*a*x^(7/2)) + (2*(A*b - a*B))/(5*a^2*x^(5/2)) - (2*b*(A*b - a*B))/(3*a^3*x^(3/2)) + (2*b^2*(A*b - a*B))/(a^4*sqrt(x)) + (2*b^(5/2)*(A*b - a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/a^(9/2)]
    @test_int [(A + B*x)/(x^(11/2)*(a + b*x)), x, 7, (-2*A)/(9*a*x^(9/2)) + (2*(A*b - a*B))/(7*a^2*x^(7/2)) - (2*b*(A*b - a*B))/(5*a^3*x^(5/2)) + (2*b^2*(A*b - a*B))/(3*a^4*x^(3/2)) - (2*b^3*(A*b - a*B))/(a^5*sqrt(x)) - (2*b^(7/2)*(A*b - a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/a^(11/2)]

    @test_int [(x^(7/2)*(A + B*x))/(a + b*x)^2, x, 7, (a^2*(7*A*b - 9*a*B)*sqrt(x))/b^5 - (a*(7*A*b - 9*a*B)*x^(3/2))/(3*b^4) + ((7*A*b - 9*a*B)*x^(5/2))/(5*b^3) - ((7*A*b - 9*a*B)*x^(7/2))/(7*a*b^2) + ((A*b - a*B)*x^(9/2))/(a*b*(a + b*x)) - (a^(5/2)*(7*A*b - 9*a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/b^(11/2)]
    @test_int [(x^(5/2)*(A + B*x))/(a + b*x)^2, x, 6, -((a*(5*A*b - 7*a*B)*sqrt(x))/b^4) + ((5*A*b - 7*a*B)*x^(3/2))/(3*b^3) - ((5*A*b - 7*a*B)*x^(5/2))/(5*a*b^2) + ((A*b - a*B)*x^(7/2))/(a*b*(a + b*x)) + (a^(3/2)*(5*A*b - 7*a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/b^(9/2)]
    @test_int [(x^(3/2)*(A + B*x))/(a + b*x)^2, x, 5, ((3*A*b - 5*a*B)*sqrt(x))/b^3 - ((3*A*b - 5*a*B)*x^(3/2))/(3*a*b^2) + ((A*b - a*B)*x^(5/2))/(a*b*(a + b*x)) - (sqrt(a)*(3*A*b - 5*a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/b^(7/2)]
    @test_int [(sqrt(x)*(A + B*x))/(a + b*x)^2, x, 4, -(((A*b - 3*a*B)*sqrt(x))/(a*b^2)) + ((A*b - a*B)*x^(3/2))/(a*b*(a + b*x)) + ((A*b - 3*a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/(sqrt(a)*b^(5/2))]
    @test_int [(A + B*x)/(sqrt(x)*(a + b*x)^2), x, 3, ((A*b - a*B)*sqrt(x))/(a*b*(a + b*x)) + ((A*b + a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/(a^(3/2)*b^(3/2))]
    @test_int [(A + B*x)/(x^(3/2)*(a + b*x)^2), x, 4, -((3*A*b - a*B)/(a^2*b*sqrt(x))) + (A*b - a*B)/(a*b*sqrt(x)*(a + b*x)) - ((3*A*b - a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/(a^(5/2)*sqrt(b))]
    @test_int [(A + B*x)/(x^(5/2)*(a + b*x)^2), x, 5, -((5*A*b - 3*a*B)/(3*a^2*b*x^(3/2))) + (5*A*b - 3*a*B)/(a^3*sqrt(x)) + (A*b - a*B)/(a*b*x^(3/2)*(a + b*x)) + (sqrt(b)*(5*A*b - 3*a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/a^(7/2)]
    @test_int [(A + B*x)/(x^(7/2)*(a + b*x)^2), x, 6, -((7*A*b - 5*a*B)/(5*a^2*b*x^(5/2))) + (7*A*b - 5*a*B)/(3*a^3*x^(3/2)) - (b*(7*A*b - 5*a*B))/(a^4*sqrt(x)) + (A*b - a*B)/(a*b*x^(5/2)*(a + b*x)) - (b^(3/2)*(7*A*b - 5*a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/a^(9/2)]
    @test_int [(A + B*x)/(x^(9/2)*(a + b*x)^2), x, 7, -((9*A*b - 7*a*B)/(7*a^2*b*x^(7/2))) + (9*A*b - 7*a*B)/(5*a^3*x^(5/2)) - (b*(9*A*b - 7*a*B))/(3*a^4*x^(3/2)) + (b^2*(9*A*b - 7*a*B))/(a^5*sqrt(x)) + (A*b - a*B)/(a*b*x^(7/2)*(a + b*x)) + (b^(5/2)*(9*A*b - 7*a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/a^(11/2)]

    @test_int [(x^(7/2)*(A + B*x))/(a + b*x)^3, x, 7, (-7*a*(5*A*b - 9*a*B)*sqrt(x))/(4*b^5) + (7*(5*A*b - 9*a*B)*x^(3/2))/(12*b^4) - (7*(5*A*b - 9*a*B)*x^(5/2))/(20*a*b^3) + ((A*b - a*B)*x^(9/2))/(2*a*b*(a + b*x)^2) + ((5*A*b - 9*a*B)*x^(7/2))/(4*a*b^2*(a + b*x)) + (7*a^(3/2)*(5*A*b - 9*a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/(4*b^(11/2))]
    @test_int [(x^(5/2)*(A + B*x))/(a + b*x)^3, x, 6, (5*(3*A*b - 7*a*B)*sqrt(x))/(4*b^4) - (5*(3*A*b - 7*a*B)*x^(3/2))/(12*a*b^3) + ((A*b - a*B)*x^(7/2))/(2*a*b*(a + b*x)^2) + ((3*A*b - 7*a*B)*x^(5/2))/(4*a*b^2*(a + b*x)) - (5*sqrt(a)*(3*A*b - 7*a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/(4*b^(9/2))]
    @test_int [(x^(3/2)*(A + B*x))/(a + b*x)^3, x, 5, (-3*(A*b - 5*a*B)*sqrt(x))/(4*a*b^3) + ((A*b - a*B)*x^(5/2))/(2*a*b*(a + b*x)^2) + ((A*b - 5*a*B)*x^(3/2))/(4*a*b^2*(a + b*x)) + (3*(A*b - 5*a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/(4*sqrt(a)*b^(7/2))]
    @test_int [(sqrt(x)*(A + B*x))/(a + b*x)^3, x, 4, ((A*b - a*B)*x^(3/2))/(2*a*b*(a + b*x)^2) - ((A*b + 3*a*B)*sqrt(x))/(4*a*b^2*(a + b*x)) + ((A*b + 3*a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/(4*a^(3/2)*b^(5/2))]
    @test_int [(A + B*x)/(sqrt(x)*(a + b*x)^3), x, 4, ((A*b - a*B)*sqrt(x))/(2*a*b*(a + b*x)^2) + ((3*A*b + a*B)*sqrt(x))/(4*a^2*b*(a + b*x)) + ((3*A*b + a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/(4*a^(5/2)*b^(3/2))]
    @test_int [(A + B*x)/(x^(3/2)*(a + b*x)^3), x, 5, -((3*(5*A*b - a*B))/(4*a^3*b*sqrt(x))) + (A*b - a*B)/(2*a*b*sqrt(x)*(a + b*x)^2) + (5*A*b - a*B)/(4*a^2*b*sqrt(x)*(a + b*x)) - (3*(5*A*b - a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/(4*a^(7/2)*sqrt(b))]
    @test_int [(A + B*x)/(x^(5/2)*(a + b*x)^3), x, 6, -((5*(7*A*b - 3*a*B))/(12*a^3*b*x^(3/2))) + (5*(7*A*b - 3*a*B))/(4*a^4*sqrt(x)) + (A*b - a*B)/(2*a*b*x^(3/2)*(a + b*x)^2) + (7*A*b - 3*a*B)/(4*a^2*b*x^(3/2)*(a + b*x)) + (5*sqrt(b)*(7*A*b - 3*a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/(4*a^(9/2))]
    @test_int [(A + B*x)/(x^(7/2)*(a + b*x)^3), x, 7, -((7*(9*A*b - 5*a*B))/(20*a^3*b*x^(5/2))) + (7*(9*A*b - 5*a*B))/(12*a^4*x^(3/2)) - (7*b*(9*A*b - 5*a*B))/(4*a^5*sqrt(x)) + (A*b - a*B)/(2*a*b*x^(5/2)*(a + b*x)^2) + (9*A*b - 5*a*B)/(4*a^2*b*x^(5/2)*(a + b*x)) - (7*b^(3/2)*(9*A*b - 5*a*B)*atan((sqrt(b)*sqrt(x))/sqrt(a)))/(4*a^(11/2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x)^n*(c+d*x)^p*with*m*symbolic=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^m*(a + b*x)^4*(A + B*x), x, 2, (a^4*A*x^(1 + m))/(1 + m) + (a^3*(4*A*b + a*B)*x^(2 + m))/(2 + m) + (2*a^2*b*(3*A*b + 2*a*B)*x^(3 + m))/(3 + m) + (2*a*b^2*(2*A*b + 3*a*B)*x^(4 + m))/(4 + m) + (b^3*(A*b + 4*a*B)*x^(5 + m))/(5 + m) + (b^4*B*x^(6 + m))/(6 + m)]
    @test_int [x^m*(a + b*x)^3*(A + B*x), x, 2, (a^3*A*x^(1 + m))/(1 + m) + (a^2*(3*A*b + a*B)*x^(2 + m))/(2 + m) + (3*a*b*(A*b + a*B)*x^(3 + m))/(3 + m) + (b^2*(A*b + 3*a*B)*x^(4 + m))/(4 + m) + (b^3*B*x^(5 + m))/(5 + m)]
    @test_int [x^m*(a + b*x)^2*(A + B*x), x, 2, (a^2*A*x^(1 + m))/(1 + m) + (a*(2*A*b + a*B)*x^(2 + m))/(2 + m) + (b*(A*b + 2*a*B)*x^(3 + m))/(3 + m) + (b^2*B*x^(4 + m))/(4 + m)]
    @test_int [x^m*(a + b*x)^1*(A + B*x), x, 2, (a*A*x^(1 + m))/(1 + m) + ((A*b + a*B)*x^(2 + m))/(2 + m) + (b*B*x^(3 + m))/(3 + m)]
    @test_int [x^m/(a + b*x)^1*(A + B*x), x, 2, (B*x^(1 + m))/(b*(1 + m)) + ((A*b - a*B)*x^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((b*x)/a)))/(a*b*(1 + m))]
    @test_int [x^m/(a + b*x)^2*(A + B*x), x, 2, ((A*b - a*B)*x^(1 + m))/(a*b*(a + b*x)) - ((A*b*m - a*B*(1 + m))*x^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((b*x)/a)))/(a^2*b*(1 + m))]
    @test_int [x^m/(a + b*x)^3*(A + B*x), x, 2, ((A*b - a*B)*x^(1 + m))/(2*a*b*(a + b*x)^2) + ((A*b*(1 - m) + a*B*(1 + m))*x^(1 + m)*HypergeometricFunctions._₂F₁(2, 1 + m, 2 + m, -((b*x)/a)))/(2*a^3*b*(1 + m))]

    @test_int [x^m*(a + b*x)^2*(c + d*x)^5, x, 2, (a^2*c^5*x^(1 + m))/(1 + m) + (a*c^4*(2*b*c + 5*a*d)*x^(2 + m))/(2 + m) + (c^3*(b^2*c^2 + 10*a*b*c*d + 10*a^2*d^2)*x^(3 + m))/(3 + m) + (5*c^2*d*(b^2*c^2 + 4*a*b*c*d + 2*a^2*d^2)*x^(4 + m))/(4 + m) + (5*c*d^2*(2*b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(5 + m))/(5 + m) + (d^3*(10*b^2*c^2 + 10*a*b*c*d + a^2*d^2)*x^(6 + m))/(6 + m) + (b*d^4*(5*b*c + 2*a*d)*x^(7 + m))/(7 + m) + (b^2*d^5*x^(8 + m))/(8 + m)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^m*(c + d*x)^3/(a + b*x), x, 7, (d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x^(1 + m))/(b^3*(1 + m)) + (d^2*(3*b*c - a*d)*x^(2 + m))/(b^2*(2 + m)) + (d^3*x^(3 + m))/(b*(3 + m)) + ((b*c - a*d)^3*x^(1 + m)*HypergeometricFunctions._₂F₁(1, 1, 1 - m, a/(a + b*x)))/(b^3*m*(a + b*x)), (c^2*d*x^(1 + m))/(b*(1 + m)) + (c*d*(b*c - a*d)*x^(1 + m))/(b^2*(1 + m)) + (d*(b*c - a*d)^2*x^(1 + m))/(b^3*(1 + m)) + (2*c*d^2*x^(2 + m))/(b*(2 + m)) + (d^2*(b*c - a*d)*x^(2 + m))/(b^2*(2 + m)) + (d^3*x^(3 + m))/(b*(3 + m)) + ((b*c - a*d)^3*x^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((b*x)/a)))/(a*b^3*(1 + m))]
    @test_int [x^m*(c + d*x)^2/(a + b*x), x, 5, (c*d*x^(1 + m))/(b*(1 + m)) + (d*(b*c - a*d)*x^(1 + m))/(b^2*(1 + m)) + (d^2*x^(2 + m))/(b*(2 + m)) + ((b*c - a*d)^2*x^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((b*x)/a)))/(a*b^2*(1 + m))]
    @test_int [x^m*(c + d*x)^1/(a + b*x), x, 2, (d*x^(1 + m))/(b*(1 + m)) + ((b*c - a*d)*x^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((b*x)/a)))/(a*b*(1 + m))]
    @test_int [x^m/((a + b*x)*(c + d*x)^1), x, 3, (b*x^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((b*x)/a)))/(a*(b*c - a*d)*(1 + m)) - (d*x^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((d*x)/c)))/(c*(b*c - a*d)*(1 + m))]
    @test_int [x^m/((a + b*x)*(c + d*x)^2), x, 4, -((d*x^(1 + m))/(c*(b*c - a*d)*(c + d*x))) + (b^2*x^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((b*x)/a)))/(a*(b*c - a*d)^2*(1 + m)) - (d*(b*c*(1 - m) + a*d*m)*x^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((d*x)/c)))/(c^2*(b*c - a*d)^2*(1 + m))]
    @test_int [x^m/((a + b*x)*(c + d*x)^3), x, 5, -((d*x^(1 + m))/(2*c*(b*c - a*d)*(c + d*x)^2)) + (d*(a*d*(1 - m) - b*c*(3 - m))*x^(1 + m))/(2*c^2*(b*c - a*d)^2*(c + d*x)) + (b^3*x^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((b*x)/a)))/(a*(b*c - a*d)^3*(1 + m)) + (d*(a^2*d^2*(1 - m)*m - 2*a*b*c*d*(2 - m)*m - b^2*c^2*(2 - 3*m + m^2))*x^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((d*x)/c)))/(2*c^3*(b*c - a*d)^3*(1 + m))]

    #= Following*integrands*are*equal: =#
    @test_int [(b^2*x^m)/(b + a*x^2)^2, x, 2, (x^(1 + m)*HypergeometricFunctions._₂F₁(2, (1 + m)/2, (3 + m)/2, -((a*x^2)/b)))/(1 + m)]
    @test_int [x^m/((1 - (sqrt(a)*x)/sqrt(-b))^2*(1 + (sqrt(a)*x)/sqrt(-b))^2), x, 2, (x^(1 + m)*HypergeometricFunctions._₂F₁(2, (1 + m)/2, (3 + m)/2, -((a*x^2)/b)))/(1 + m)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x)^n*(c+d*x)^(p/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x)^1*(c+d*x)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^4*sqrt(a + b*x)*(A + B*x), x, 2, (2*a^4*(A*b - a*B)*(a + b*x)^(3/2))/(3*b^6) - (2*a^3*(4*A*b - 5*a*B)*(a + b*x)^(5/2))/(5*b^6) + (4*a^2*(3*A*b - 5*a*B)*(a + b*x)^(7/2))/(7*b^6) - (4*a*(2*A*b - 5*a*B)*(a + b*x)^(9/2))/(9*b^6) + (2*(A*b - 5*a*B)*(a + b*x)^(11/2))/(11*b^6) + (2*B*(a + b*x)^(13/2))/(13*b^6)]
    @test_int [x^3*sqrt(a + b*x)*(A + B*x), x, 2, -((2*a^3*(A*b - a*B)*(a + b*x)^(3/2))/(3*b^5)) + (2*a^2*(3*A*b - 4*a*B)*(a + b*x)^(5/2))/(5*b^5) - (6*a*(A*b - 2*a*B)*(a + b*x)^(7/2))/(7*b^5) + (2*(A*b - 4*a*B)*(a + b*x)^(9/2))/(9*b^5) + (2*B*(a + b*x)^(11/2))/(11*b^5)]
    @test_int [x^2*sqrt(a + b*x)*(A + B*x), x, 2, (2*a^2*(A*b - a*B)*(a + b*x)^(3/2))/(3*b^4) - (2*a*(2*A*b - 3*a*B)*(a + b*x)^(5/2))/(5*b^4) + (2*(A*b - 3*a*B)*(a + b*x)^(7/2))/(7*b^4) + (2*B*(a + b*x)^(9/2))/(9*b^4)]
    @test_int [x*sqrt(a + b*x)*(A + B*x), x, 2, -((2*a*(A*b - a*B)*(a + b*x)^(3/2))/(3*b^3)) + (2*(A*b - 2*a*B)*(a + b*x)^(5/2))/(5*b^3) + (2*B*(a + b*x)^(7/2))/(7*b^3)]
    @test_int [sqrt(a + b*x)*(A + B*x), x, 2, (2*(A*b - a*B)*(a + b*x)^(3/2))/(3*b^2) + (2*B*(a + b*x)^(5/2))/(5*b^2)]
    @test_int [(sqrt(a + b*x)*(A + B*x))/x, x, 4, 2*A*sqrt(a + b*x) + (2*B*(a + b*x)^(3/2))/(3*b) - 2*sqrt(a)*A*atanh(sqrt(a + b*x)/sqrt(a))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/x^2, x, 4, ((A*b + 2*a*B)*sqrt(a + b*x))/a - (A*(a + b*x)^(3/2))/(a*x) - ((A*b + 2*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/sqrt(a)]
    @test_int [(sqrt(a + b*x)*(A + B*x))/x^3, x, 4, ((A*b - 4*a*B)*sqrt(a + b*x))/(4*a*x) - (A*(a + b*x)^(3/2))/(2*a*x^2) + (b*(A*b - 4*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(4*a^(3/2))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/x^4, x, 5, ((A*b - 2*a*B)*sqrt(a + b*x))/(4*a*x^2) + (b*(A*b - 2*a*B)*sqrt(a + b*x))/(8*a^2*x) - (A*(a + b*x)^(3/2))/(3*a*x^3) - (b^2*(A*b - 2*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(8*a^(5/2))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/x^5, x, 6, ((5*A*b - 8*a*B)*sqrt(a + b*x))/(24*a*x^3) + (b*(5*A*b - 8*a*B)*sqrt(a + b*x))/(96*a^2*x^2) - (b^2*(5*A*b - 8*a*B)*sqrt(a + b*x))/(64*a^3*x) - (A*(a + b*x)^(3/2))/(4*a*x^4) + (b^3*(5*A*b - 8*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(64*a^(7/2))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/x^6, x, 7, ((7*A*b - 10*a*B)*sqrt(a + b*x))/(40*a*x^4) + (b*(7*A*b - 10*a*B)*sqrt(a + b*x))/(240*a^2*x^3) - (b^2*(7*A*b - 10*a*B)*sqrt(a + b*x))/(192*a^3*x^2) + (b^3*(7*A*b - 10*a*B)*sqrt(a + b*x))/(128*a^4*x) - (A*(a + b*x)^(3/2))/(5*a*x^5) - (b^4*(7*A*b - 10*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(128*a^(9/2))]

    @test_int [x^4*(a + b*x)^(3/2)*(A + B*x), x, 2, (2*a^4*(A*b - a*B)*(a + b*x)^(5/2))/(5*b^6) - (2*a^3*(4*A*b - 5*a*B)*(a + b*x)^(7/2))/(7*b^6) + (4*a^2*(3*A*b - 5*a*B)*(a + b*x)^(9/2))/(9*b^6) - (4*a*(2*A*b - 5*a*B)*(a + b*x)^(11/2))/(11*b^6) + (2*(A*b - 5*a*B)*(a + b*x)^(13/2))/(13*b^6) + (2*B*(a + b*x)^(15/2))/(15*b^6)]
    @test_int [x^3*(a + b*x)^(3/2)*(A + B*x), x, 2, -((2*a^3*(A*b - a*B)*(a + b*x)^(5/2))/(5*b^5)) + (2*a^2*(3*A*b - 4*a*B)*(a + b*x)^(7/2))/(7*b^5) - (2*a*(A*b - 2*a*B)*(a + b*x)^(9/2))/(3*b^5) + (2*(A*b - 4*a*B)*(a + b*x)^(11/2))/(11*b^5) + (2*B*(a + b*x)^(13/2))/(13*b^5)]
    @test_int [x^2*(a + b*x)^(3/2)*(A + B*x), x, 2, (2*a^2*(A*b - a*B)*(a + b*x)^(5/2))/(5*b^4) - (2*a*(2*A*b - 3*a*B)*(a + b*x)^(7/2))/(7*b^4) + (2*(A*b - 3*a*B)*(a + b*x)^(9/2))/(9*b^4) + (2*B*(a + b*x)^(11/2))/(11*b^4)]
    @test_int [x*(a + b*x)^(3/2)*(A + B*x), x, 2, -((2*a*(A*b - a*B)*(a + b*x)^(5/2))/(5*b^3)) + (2*(A*b - 2*a*B)*(a + b*x)^(7/2))/(7*b^3) + (2*B*(a + b*x)^(9/2))/(9*b^3)]
    @test_int [(a + b*x)^(3/2)*(A + B*x), x, 2, (2*(A*b - a*B)*(a + b*x)^(5/2))/(5*b^2) + (2*B*(a + b*x)^(7/2))/(7*b^2)]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/x, x, 5, 2*a*A*sqrt(a + b*x) + (2*A*(a + b*x)^(3/2))/3 + (2*B*(a + b*x)^(5/2))/(5*b) - 2*a^(3/2)*A*atanh(sqrt(a + b*x)/sqrt(a))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/x^2, x, 5, (3*A*b + 2*a*B)*sqrt(a + b*x) + ((3*A*b + 2*a*B)*(a + b*x)^(3/2))/(3*a) - (A*(a + b*x)^(5/2))/(a*x) - sqrt(a)*(3*A*b + 2*a*B)*atanh(sqrt(a + b*x)/sqrt(a))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/x^3, x, 5, (3*b*(A*b + 4*a*B)*sqrt(a + b*x))/(4*a) - ((A*b + 4*a*B)*(a + b*x)^(3/2))/(4*a*x) - (A*(a + b*x)^(5/2))/(2*a*x^2) - (3*b*(A*b + 4*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(4*sqrt(a))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/x^4, x, 5, (b*(A*b - 6*a*B)*sqrt(a + b*x))/(8*a*x) + ((A*b - 6*a*B)*(a + b*x)^(3/2))/(12*a*x^2) - (A*(a + b*x)^(5/2))/(3*a*x^3) + (b^2*(A*b - 6*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(8*a^(3/2))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/x^5, x, 6, (b*(3*A*b - 8*a*B)*sqrt(a + b*x))/(32*a*x^2) + (b^2*(3*A*b - 8*a*B)*sqrt(a + b*x))/(64*a^2*x) + ((3*A*b - 8*a*B)*(a + b*x)^(3/2))/(24*a*x^3) - (A*(a + b*x)^(5/2))/(4*a*x^4) - (b^3*(3*A*b - 8*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(64*a^(5/2))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/x^6, x, 7, (b*(A*b - 2*a*B)*sqrt(a + b*x))/(16*a*x^3) + (b^2*(A*b - 2*a*B)*sqrt(a + b*x))/(64*a^2*x^2) - (3*b^3*(A*b - 2*a*B)*sqrt(a + b*x))/(128*a^3*x) + ((A*b - 2*a*B)*(a + b*x)^(3/2))/(8*a*x^4) - (A*(a + b*x)^(5/2))/(5*a*x^5) + (3*b^4*(A*b - 2*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(128*a^(7/2))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/x^7, x, 8, (b*(7*A*b - 12*a*B)*sqrt(a + b*x))/(160*a*x^4) + (b^2*(7*A*b - 12*a*B)*sqrt(a + b*x))/(960*a^2*x^3) - (b^3*(7*A*b - 12*a*B)*sqrt(a + b*x))/(768*a^3*x^2) + (b^4*(7*A*b - 12*a*B)*sqrt(a + b*x))/(512*a^4*x) + ((7*A*b - 12*a*B)*(a + b*x)^(3/2))/(60*a*x^5) - (A*(a + b*x)^(5/2))/(6*a*x^6) - (b^5*(7*A*b - 12*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(512*a^(9/2))]

    @test_int [x^4*(a + b*x)^(5/2)*(A + B*x), x, 2, (2*a^4*(A*b - a*B)*(a + b*x)^(7/2))/(7*b^6) - (2*a^3*(4*A*b - 5*a*B)*(a + b*x)^(9/2))/(9*b^6) + (4*a^2*(3*A*b - 5*a*B)*(a + b*x)^(11/2))/(11*b^6) - (4*a*(2*A*b - 5*a*B)*(a + b*x)^(13/2))/(13*b^6) + (2*(A*b - 5*a*B)*(a + b*x)^(15/2))/(15*b^6) + (2*B*(a + b*x)^(17/2))/(17*b^6)]
    @test_int [x^3*(a + b*x)^(5/2)*(A + B*x), x, 2, -((2*a^3*(A*b - a*B)*(a + b*x)^(7/2))/(7*b^5)) + (2*a^2*(3*A*b - 4*a*B)*(a + b*x)^(9/2))/(9*b^5) - (6*a*(A*b - 2*a*B)*(a + b*x)^(11/2))/(11*b^5) + (2*(A*b - 4*a*B)*(a + b*x)^(13/2))/(13*b^5) + (2*B*(a + b*x)^(15/2))/(15*b^5)]
    @test_int [x^2*(a + b*x)^(5/2)*(A + B*x), x, 2, (2*a^2*(A*b - a*B)*(a + b*x)^(7/2))/(7*b^4) - (2*a*(2*A*b - 3*a*B)*(a + b*x)^(9/2))/(9*b^4) + (2*(A*b - 3*a*B)*(a + b*x)^(11/2))/(11*b^4) + (2*B*(a + b*x)^(13/2))/(13*b^4)]
    @test_int [x*(a + b*x)^(5/2)*(A + B*x), x, 2, -((2*a*(A*b - a*B)*(a + b*x)^(7/2))/(7*b^3)) + (2*(A*b - 2*a*B)*(a + b*x)^(9/2))/(9*b^3) + (2*B*(a + b*x)^(11/2))/(11*b^3)]
    @test_int [(a + b*x)^(5/2)*(A + B*x), x, 2, (2*(A*b - a*B)*(a + b*x)^(7/2))/(7*b^2) + (2*B*(a + b*x)^(9/2))/(9*b^2)]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/x, x, 6, 2*a^2*A*sqrt(a + b*x) + (2*a*A*(a + b*x)^(3/2))/3 + (2*A*(a + b*x)^(5/2))/5 + (2*B*(a + b*x)^(7/2))/(7*b) - 2*a^(5/2)*A*atanh(sqrt(a + b*x)/sqrt(a))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/x^2, x, 6, a*(5*A*b + 2*a*B)*sqrt(a + b*x) + ((5*A*b + 2*a*B)*(a + b*x)^(3/2))/3 + ((5*A*b + 2*a*B)*(a + b*x)^(5/2))/(5*a) - (A*(a + b*x)^(7/2))/(a*x) - a^(3/2)*(5*A*b + 2*a*B)*atanh(sqrt(a + b*x)/sqrt(a))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/x^3, x, 6, (5*b*(3*A*b + 4*a*B)*sqrt(a + b*x))/4 + (5*b*(3*A*b + 4*a*B)*(a + b*x)^(3/2))/(12*a) - ((3*A*b + 4*a*B)*(a + b*x)^(5/2))/(4*a*x) - (A*(a + b*x)^(7/2))/(2*a*x^2) - (5*sqrt(a)*b*(3*A*b + 4*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/4]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/x^4, x, 6, (5*b^2*(A*b + 6*a*B)*sqrt(a + b*x))/(8*a) - (5*b*(A*b + 6*a*B)*(a + b*x)^(3/2))/(24*a*x) - ((A*b + 6*a*B)*(a + b*x)^(5/2))/(12*a*x^2) - (A*(a + b*x)^(7/2))/(3*a*x^3) - (5*b^2*(A*b + 6*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(8*sqrt(a))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/x^5, x, 6, (5*b^2*(A*b - 8*a*B)*sqrt(a + b*x))/(64*a*x) + (5*b*(A*b - 8*a*B)*(a + b*x)^(3/2))/(96*a*x^2) + ((A*b - 8*a*B)*(a + b*x)^(5/2))/(24*a*x^3) - (A*(a + b*x)^(7/2))/(4*a*x^4) + (5*b^3*(A*b - 8*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(64*a^(3/2))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/x^6, x, 7, (b^2*(3*A*b - 10*a*B)*sqrt(a + b*x))/(64*a*x^2) + (b^3*(3*A*b - 10*a*B)*sqrt(a + b*x))/(128*a^2*x) + (b*(3*A*b - 10*a*B)*(a + b*x)^(3/2))/(48*a*x^3) + ((3*A*b - 10*a*B)*(a + b*x)^(5/2))/(40*a*x^4) - (A*(a + b*x)^(7/2))/(5*a*x^5) - (b^4*(3*A*b - 10*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(128*a^(5/2))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/x^7, x, 8, (b^2*(5*A*b - 12*a*B)*sqrt(a + b*x))/(192*a*x^3) + (b^3*(5*A*b - 12*a*B)*sqrt(a + b*x))/(768*a^2*x^2) - (b^4*(5*A*b - 12*a*B)*sqrt(a + b*x))/(512*a^3*x) + (b*(5*A*b - 12*a*B)*(a + b*x)^(3/2))/(96*a*x^4) + ((5*A*b - 12*a*B)*(a + b*x)^(5/2))/(60*a*x^5) - (A*(a + b*x)^(7/2))/(6*a*x^6) + (b^5*(5*A*b - 12*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(512*a^(7/2))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/x^8, x, 9, (b^2*(A*b - 2*a*B)*sqrt(a + b*x))/(64*a*x^4) + (b^3*(A*b - 2*a*B)*sqrt(a + b*x))/(384*a^2*x^3) - (5*b^4*(A*b - 2*a*B)*sqrt(a + b*x))/(1536*a^3*x^2) + (5*b^5*(A*b - 2*a*B)*sqrt(a + b*x))/(1024*a^4*x) + (b*(A*b - 2*a*B)*(a + b*x)^(3/2))/(24*a*x^5) + ((A*b - 2*a*B)*(a + b*x)^(5/2))/(12*a*x^6) - (A*(a + b*x)^(7/2))/(7*a*x^7) - (5*b^6*(A*b - 2*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(1024*a^(9/2))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(x^4*(A + B*x))/sqrt(a + b*x), x, 2, (2*a^4*(A*b - a*B)*sqrt(a + b*x))/b^6 - (2*a^3*(4*A*b - 5*a*B)*(a + b*x)^(3/2))/(3*b^6) + (4*a^2*(3*A*b - 5*a*B)*(a + b*x)^(5/2))/(5*b^6) - (4*a*(2*A*b - 5*a*B)*(a + b*x)^(7/2))/(7*b^6) + (2*(A*b - 5*a*B)*(a + b*x)^(9/2))/(9*b^6) + (2*B*(a + b*x)^(11/2))/(11*b^6)]
    @test_int [(x^3*(A + B*x))/sqrt(a + b*x), x, 2, -((2*a^3*(A*b - a*B)*sqrt(a + b*x))/b^5) + (2*a^2*(3*A*b - 4*a*B)*(a + b*x)^(3/2))/(3*b^5) - (6*a*(A*b - 2*a*B)*(a + b*x)^(5/2))/(5*b^5) + (2*(A*b - 4*a*B)*(a + b*x)^(7/2))/(7*b^5) + (2*B*(a + b*x)^(9/2))/(9*b^5)]
    @test_int [(x^2*(A + B*x))/sqrt(a + b*x), x, 2, (2*a^2*(A*b - a*B)*sqrt(a + b*x))/b^4 - (2*a*(2*A*b - 3*a*B)*(a + b*x)^(3/2))/(3*b^4) + (2*(A*b - 3*a*B)*(a + b*x)^(5/2))/(5*b^4) + (2*B*(a + b*x)^(7/2))/(7*b^4)]
    @test_int [(x*(A + B*x))/sqrt(a + b*x), x, 2, -((2*a*(A*b - a*B)*sqrt(a + b*x))/b^3) + (2*(A*b - 2*a*B)*(a + b*x)^(3/2))/(3*b^3) + (2*B*(a + b*x)^(5/2))/(5*b^3)]
    @test_int [(A + B*x)/sqrt(a + b*x), x, 2, (2*(A*b - a*B)*sqrt(a + b*x))/b^2 + (2*B*(a + b*x)^(3/2))/(3*b^2)]
    @test_int [(A + B*x)/(x*sqrt(a + b*x)), x, 3, (2*B*sqrt(a + b*x))/b - (2*A*atanh(sqrt(a + b*x)/sqrt(a)))/sqrt(a)]
    @test_int [(A + B*x)/(x^2*sqrt(a + b*x)), x, 3, -((A*sqrt(a + b*x))/(a*x)) + ((A*b - 2*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/a^(3/2)]
    @test_int [(A + B*x)/(x^3*sqrt(a + b*x)), x, 4, -(A*sqrt(a + b*x))/(2*a*x^2) + ((3*A*b - 4*a*B)*sqrt(a + b*x))/(4*a^2*x) - (b*(3*A*b - 4*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(4*a^(5/2))]
    @test_int [(A + B*x)/(x^4*sqrt(a + b*x)), x, 5, -(A*sqrt(a + b*x))/(3*a*x^3) + ((5*A*b - 6*a*B)*sqrt(a + b*x))/(12*a^2*x^2) - (b*(5*A*b - 6*a*B)*sqrt(a + b*x))/(8*a^3*x) + (b^2*(5*A*b - 6*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(8*a^(7/2))]
    @test_int [(A + B*x)/(x^5*sqrt(a + b*x)), x, 6, -(A*sqrt(a + b*x))/(4*a*x^4) + ((7*A*b - 8*a*B)*sqrt(a + b*x))/(24*a^2*x^3) - (5*b*(7*A*b - 8*a*B)*sqrt(a + b*x))/(96*a^3*x^2) + (5*b^2*(7*A*b - 8*a*B)*sqrt(a + b*x))/(64*a^4*x) - (5*b^3*(7*A*b - 8*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(64*a^(9/2))]
    @test_int [(A + B*x)/(x^6*sqrt(a + b*x)), x, 7, -(A*sqrt(a + b*x))/(5*a*x^5) + ((9*A*b - 10*a*B)*sqrt(a + b*x))/(40*a^2*x^4) - (7*b*(9*A*b - 10*a*B)*sqrt(a + b*x))/(240*a^3*x^3) + (7*b^2*(9*A*b - 10*a*B)*sqrt(a + b*x))/(192*a^4*x^2) - (7*b^3*(9*A*b - 10*a*B)*sqrt(a + b*x))/(128*a^5*x) + (7*b^4*(9*A*b - 10*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(128*a^(11/2))]

    @test_int [(x^4*(A + B*x))/(a + b*x)^(3/2), x, 2, -((2*a^4*(A*b - a*B))/(b^6*sqrt(a + b*x))) - (2*a^3*(4*A*b - 5*a*B)*sqrt(a + b*x))/b^6 + (4*a^2*(3*A*b - 5*a*B)*(a + b*x)^(3/2))/(3*b^6) - (4*a*(2*A*b - 5*a*B)*(a + b*x)^(5/2))/(5*b^6) + (2*(A*b - 5*a*B)*(a + b*x)^(7/2))/(7*b^6) + (2*B*(a + b*x)^(9/2))/(9*b^6)]
    @test_int [(x^3*(A + B*x))/(a + b*x)^(3/2), x, 2, (2*a^3*(A*b - a*B))/(b^5*sqrt(a + b*x)) + (2*a^2*(3*A*b - 4*a*B)*sqrt(a + b*x))/b^5 - (2*a*(A*b - 2*a*B)*(a + b*x)^(3/2))/b^5 + (2*(A*b - 4*a*B)*(a + b*x)^(5/2))/(5*b^5) + (2*B*(a + b*x)^(7/2))/(7*b^5)]
    @test_int [(x^2*(A + B*x))/(a + b*x)^(3/2), x, 2, -((2*a^2*(A*b - a*B))/(b^4*sqrt(a + b*x))) - (2*a*(2*A*b - 3*a*B)*sqrt(a + b*x))/b^4 + (2*(A*b - 3*a*B)*(a + b*x)^(3/2))/(3*b^4) + (2*B*(a + b*x)^(5/2))/(5*b^4)]
    @test_int [(x*(A + B*x))/(a + b*x)^(3/2), x, 2, (2*a*(A*b - a*B))/(b^3*sqrt(a + b*x)) + (2*(A*b - 2*a*B)*sqrt(a + b*x))/b^3 + (2*B*(a + b*x)^(3/2))/(3*b^3)]
    @test_int [(A + B*x)/(a + b*x)^(3/2), x, 2, (-2*(A*b - a*B))/(b^2*sqrt(a + b*x)) + (2*B*sqrt(a + b*x))/b^2]
    @test_int [(A + B*x)/(x^1*(a + b*x)^(3/2)), x, 3, (2*(A*b - a*B))/(a*b*sqrt(a + b*x)) - (2*A*atanh(sqrt(a + b*x)/sqrt(a)))/a^(3/2)]
    @test_int [(A + B*x)/(x^2*(a + b*x)^(3/2)), x, 4, -((3*A*b - 2*a*B)/(a^2*sqrt(a + b*x))) - A/(a*x*sqrt(a + b*x)) + ((3*A*b - 2*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/a^(5/2)]
    @test_int [(A + B*x)/(x^3*(a + b*x)^(3/2)), x, 5, (3*b*(5*A*b - 4*a*B))/(4*a^3*sqrt(a + b*x)) - A/(2*a*x^2*sqrt(a + b*x)) + (5*A*b - 4*a*B)/(4*a^2*x*sqrt(a + b*x)) - (3*b*(5*A*b - 4*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(4*a^(7/2))]
    @test_int [(A + B*x)/(x^4*(a + b*x)^(3/2)), x, 6, -((5*b^2*(7*A*b - 6*a*B))/(8*a^4*sqrt(a + b*x))) - A/(3*a*x^3*sqrt(a + b*x)) + (7*A*b - 6*a*B)/(12*a^2*x^2*sqrt(a + b*x)) - (5*b*(7*A*b - 6*a*B))/(24*a^3*x*sqrt(a + b*x)) + (5*b^2*(7*A*b - 6*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(8*a^(9/2))]
    @test_int [(A + B*x)/(x^5*(a + b*x)^(3/2)), x, 7, (35*b^3*(9*A*b - 8*a*B))/(64*a^5*sqrt(a + b*x)) - A/(4*a*x^4*sqrt(a + b*x)) + (9*A*b - 8*a*B)/(24*a^2*x^3*sqrt(a + b*x)) - (7*b*(9*A*b - 8*a*B))/(96*a^3*x^2*sqrt(a + b*x)) + (35*b^2*(9*A*b - 8*a*B))/(192*a^4*x*sqrt(a + b*x)) - (35*b^3*(9*A*b - 8*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(64*a^(11/2))]

    @test_int [(x^4*(A + B*x))/(a + b*x)^(5/2), x, 2, -((2*a^4*(A*b - a*B))/(3*b^6*(a + b*x)^(3/2))) + (2*a^3*(4*A*b - 5*a*B))/(b^6*sqrt(a + b*x)) + (4*a^2*(3*A*b - 5*a*B)*sqrt(a + b*x))/b^6 - (4*a*(2*A*b - 5*a*B)*(a + b*x)^(3/2))/(3*b^6) + (2*(A*b - 5*a*B)*(a + b*x)^(5/2))/(5*b^6) + (2*B*(a + b*x)^(7/2))/(7*b^6)]
    @test_int [(x^3*(A + B*x))/(a + b*x)^(5/2), x, 2, (2*a^3*(A*b - a*B))/(3*b^5*(a + b*x)^(3/2)) - (2*a^2*(3*A*b - 4*a*B))/(b^5*sqrt(a + b*x)) - (6*a*(A*b - 2*a*B)*sqrt(a + b*x))/b^5 + (2*(A*b - 4*a*B)*(a + b*x)^(3/2))/(3*b^5) + (2*B*(a + b*x)^(5/2))/(5*b^5)]
    @test_int [(x^2*(A + B*x))/(a + b*x)^(5/2), x, 2, -((2*a^2*(A*b - a*B))/(3*b^4*(a + b*x)^(3/2))) + (2*a*(2*A*b - 3*a*B))/(b^4*sqrt(a + b*x)) + (2*(A*b - 3*a*B)*sqrt(a + b*x))/b^4 + (2*B*(a + b*x)^(3/2))/(3*b^4)]
    @test_int [(x*(A + B*x))/(a + b*x)^(5/2), x, 2, (2*a*(A*b - a*B))/(3*b^3*(a + b*x)^(3/2)) - (2*(A*b - 2*a*B))/(b^3*sqrt(a + b*x)) + (2*B*sqrt(a + b*x))/b^3]
    @test_int [(A + B*x)/(a + b*x)^(5/2), x, 2, (-2*(A*b - a*B))/(3*b^2*(a + b*x)^(3/2)) - (2*B)/(b^2*sqrt(a + b*x))]
    @test_int [(A + B*x)/(x*(a + b*x)^(5/2)), x, 4, (2*(A*b - a*B))/(3*a*b*(a + b*x)^(3/2)) + (2*A)/(a^2*sqrt(a + b*x)) - (2*A*atanh(sqrt(a + b*x)/sqrt(a)))/a^(5/2)]
    @test_int [(A + B*x)/(x^2*(a + b*x)^(5/2)), x, 5, -(5*A*b - 2*a*B)/(3*a^2*(a + b*x)^(3/2)) - A/(a*x*(a + b*x)^(3/2)) - (5*A*b - 2*a*B)/(a^3*sqrt(a + b*x)) + ((5*A*b - 2*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/a^(7/2)]
    @test_int [(A + B*x)/(x^3*(a + b*x)^(5/2)), x, 6, (5*b*(7*A*b - 4*a*B))/(12*a^3*(a + b*x)^(3/2)) - A/(2*a*x^2*(a + b*x)^(3/2)) + (7*A*b - 4*a*B)/(4*a^2*x*(a + b*x)^(3/2)) + (5*b*(7*A*b - 4*a*B))/(4*a^4*sqrt(a + b*x)) - (5*b*(7*A*b - 4*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(4*a^(9/2))]
    @test_int [(A + B*x)/(x^4*(a + b*x)^(5/2)), x, 7, -((35*b^2*(3*A*b - 2*a*B))/(24*a^4*(a + b*x)^(3/2))) - A/(3*a*x^3*(a + b*x)^(3/2)) + (3*A*b - 2*a*B)/(4*a^2*x^2*(a + b*x)^(3/2)) - (7*b*(3*A*b - 2*a*B))/(8*a^3*x*(a + b*x)^(3/2)) - (35*b^2*(3*A*b - 2*a*B))/(8*a^5*sqrt(a + b*x)) + (35*b^2*(3*A*b - 2*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(8*a^(11/2))]
    @test_int [(A + B*x)/(x^5*(a + b*x)^(5/2)), x, 8, (35*b^3*(11*A*b - 8*a*B))/(64*a^5*(a + b*x)^(3/2)) - A/(4*a*x^4*(a + b*x)^(3/2)) + (11*A*b - 8*a*B)/(24*a^2*x^3*(a + b*x)^(3/2)) - (3*b*(11*A*b - 8*a*B))/(32*a^3*x^2*(a + b*x)^(3/2)) + (21*b^2*(11*A*b - 8*a*B))/(64*a^4*x*(a + b*x)^(3/2)) + (105*b^3*(11*A*b - 8*a*B))/(64*a^6*sqrt(a + b*x)) - (105*b^3*(11*A*b - 8*a*B)*atanh(sqrt(a + b*x)/sqrt(a)))/(64*a^(13/2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x)^2*(c+d*x)^(p/2)=#

    @test_int [(a + b*x)^2/(x^2*sqrt(c + d*x)), x, 4, (2*b^2*sqrt(c + d*x))/d - (a^2*sqrt(c + d*x))/(c*x) - (a*(4*b*c - a*d)*atanh(sqrt(c + d*x)/sqrt(c)))/c^(3/2)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x)^(p/2) / (a+b*x)^1=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^3*(c + d*x)^(5/2)/(a + b*x), x, 7, -((2*a^3*(b*c - a*d)^2*sqrt(c + d*x))/b^6) - (2*a^3*(b*c - a*d)*(c + d*x)^(3/2))/(3*b^5) - (2*a^3*(c + d*x)^(5/2))/(5*b^4) + (2*(b^2*c^2 + a*b*c*d + a^2*d^2)*(c + d*x)^(7/2))/(7*b^3*d^3) - (2*(2*b*c + a*d)*(c + d*x)^(9/2))/(9*b^2*d^3) + (2*(c + d*x)^(11/2))/(11*b*d^3) + (2*a^3*(b*c - a*d)^(5/2)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/b^(13/2)]
    @test_int [x^2*(c + d*x)^(5/2)/(a + b*x), x, 7, (2*a^2*(b*c - a*d)^2*sqrt(c + d*x))/b^5 + (2*a^2*(b*c - a*d)*(c + d*x)^(3/2))/(3*b^4) + (2*a^2*(c + d*x)^(5/2))/(5*b^3) - (2*(b*c + a*d)*(c + d*x)^(7/2))/(7*b^2*d^2) + (2*(c + d*x)^(9/2))/(9*b*d^2) - (2*a^2*(b*c - a*d)^(5/2)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/b^(11/2)]
    @test_int [x^1*(c + d*x)^(5/2)/(a + b*x), x, 6, -((2*a*(b*c - a*d)^2*sqrt(c + d*x))/b^4) - (2*a*(b*c - a*d)*(c + d*x)^(3/2))/(3*b^3) - (2*a*(c + d*x)^(5/2))/(5*b^2) + (2*(c + d*x)^(7/2))/(7*b*d) + (2*a*(b*c - a*d)^(5/2)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/b^(9/2)]
    @test_int [x^0*(c + d*x)^(5/2)/(a + b*x), x, 5, (2*(b*c - a*d)^2*sqrt(c + d*x))/b^3 + (2*(b*c - a*d)*(c + d*x)^(3/2))/(3*b^2) + (2*(c + d*x)^(5/2))/(5*b) - (2*(b*c - a*d)^(5/2)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/b^(7/2)]
    @test_int [(c + d*x)^(5/2)/(x^1*(a + b*x)), x, 7, (2*d*(2*b*c - a*d)*sqrt(c + d*x))/b^2 + (2*d*(c + d*x)^(3/2))/(3*b) - (2*c^(5/2)*atanh(sqrt(c + d*x)/sqrt(c)))/a + (2*(b*c - a*d)^(5/2)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/(a*b^(5/2))]
    @test_int [(c + d*x)^(5/2)/(x^2*(a + b*x)), x, 7, (d*(b*c + 2*a*d)*sqrt(c + d*x))/(a*b) - (c*(c + d*x)^(3/2))/(a*x) + (c^(3/2)*(2*b*c - 5*a*d)*atanh(sqrt(c + d*x)/sqrt(c)))/a^2 - (2*(b*c - a*d)^(5/2)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/(a^2*b^(3/2))]
    @test_int [(c + d*x)^(5/2)/(x^3*(a + b*x)), x, 7, (c*(4*b*c - 7*a*d)*sqrt(c + d*x))/(4*a^2*x) - (c*(c + d*x)^(3/2))/(2*a*x^2) - (sqrt(c)*(8*b^2*c^2 - 20*a*b*c*d + 15*a^2*d^2)*atanh(sqrt(c + d*x)/sqrt(c)))/(4*a^3) + (2*(b*c - a*d)^(5/2)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/(a^3*sqrt(b))]
    @test_int [(c + d*x)^(5/2)/(x^4*(a + b*x)), x, 8, (c*(2*b*c - 3*a*d)*sqrt(c + d*x))/(4*a^2*x^2) - ((8*b^2*c^2 - 18*a*b*c*d + 11*a^2*d^2)*sqrt(c + d*x))/(8*a^3*x) - (c*(c + d*x)^(3/2))/(3*a*x^3) + ((16*b^3*c^3 - 40*a*b^2*c^2*d + 30*a^2*b*c*d^2 - 5*a^3*d^3)*atanh(sqrt(c + d*x)/sqrt(c)))/(8*a^4*sqrt(c)) - (2*sqrt(b)*(b*c - a*d)^(5/2)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/a^4]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/(x^(1/3)*sqrt(c + d*x)*(4*c + d*x)), x, 2, -(atan((sqrt(3)*c^(1/6)*(c^(1/3) + 2^(1/3)*d^(1/3)*x^(1/3)))/sqrt(c + d*x))/(2^(2/3)*sqrt(3)*c^(5/6)*d^(2/3))) + atan(sqrt(c + d*x)/(sqrt(3)*sqrt(c)))/(2^(2/3)*sqrt(3)*c^(5/6)*d^(2/3)) - atanh((c^(1/6)*(c^(1/3) - 2^(1/3)*d^(1/3)*x^(1/3)))/sqrt(c + d*x))/(2^(2/3)*c^(5/6)*d^(2/3)) + atanh(sqrt(c + d*x)/sqrt(c))/(3*2^(2/3)*c^(5/6)*d^(2/3))]

    @test_int [1/(x^(1/3)*(8*c - d*x)*sqrt(c + d*x)), x, 9, -(atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x^(1/3)))/sqrt(c + d*x))/(2*sqrt(3)*c^(5/6)*d^(2/3))) + atanh((c^(1/3) + d^(1/3)*x^(1/3))^2/(3*c^(1/6)*sqrt(c + d*x)))/(6*c^(5/6)*d^(2/3)) - atanh(sqrt(c + d*x)/(3*sqrt(c)))/(6*c^(5/6)*d^(2/3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x)^(p/2) / (a+b*x)^2=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(c + d*x)^(1/2)/(x^2*(a + b*x)^2), x, 7, -((2*b*sqrt(c + d*x))/(a^2*(a + b*x))) - sqrt(c + d*x)/(a*x*(a + b*x)) + ((4*b*c - a*d)*atanh(sqrt(c + d*x)/sqrt(c)))/(a^3*sqrt(c)) - (sqrt(b)*(4*b*c - 3*a*d)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/(a^3*sqrt(b*c - a*d))]

    @test_int [(c + d*x)^(3/2)/(x^1*(a + b*x)^2), x, 6, ((b*c - a*d)*sqrt(c + d*x))/(a*b*(a + b*x)) - (2*c^(3/2)*atanh(sqrt(c + d*x)/sqrt(c)))/a^2 + (sqrt(b*c - a*d)*(2*b*c + a*d)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/(a^2*b^(3/2))]
    @test_int [(c + d*x)^(3/2)/(x^2*(a + b*x)^2), x, 7, -(((2*b*c - a*d)*sqrt(c + d*x))/(a^2*(a + b*x))) - (c*sqrt(c + d*x))/(a*x*(a + b*x)) + (sqrt(c)*(4*b*c - 3*a*d)*atanh(sqrt(c + d*x)/sqrt(c)))/a^3 - (sqrt(b*c - a*d)*(4*b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/(a^3*sqrt(b))]

    @test_int [x^3*(c + d*x)^(5/2)/(a + b*x)^2, x, 7, (a^2*(6*b*c - 11*a*d)*(b*c - a*d)*sqrt(c + d*x))/b^6 + (a^2*(6*b*c - 11*a*d)*(c + d*x)^(3/2))/(3*b^5) + (11*x^2*(c + d*x)^(5/2))/(9*b^2) - (x^3*(c + d*x)^(5/2))/(b*(a + b*x)) - ((c + d*x)^(5/2)*(20*b^2*c^2 + 180*a*b*c*d - 693*a^2*d^2 - 5*b*d*(10*b*c - 99*a*d)*x))/(315*b^4*d^2) - (a^2*(6*b*c - 11*a*d)*(b*c - a*d)^(3/2)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/b^(13/2)]
    @test_int [x^2*(c + d*x)^(5/2)/(a + b*x)^2, x, 7, -((a*(4*b*c - 9*a*d)*(b*c - a*d)*sqrt(c + d*x))/b^5) - (a*(4*b*c - 9*a*d)*(c + d*x)^(3/2))/(3*b^4) - (a*(4*b*c - 9*a*d)*(c + d*x)^(5/2))/(5*b^3*(b*c - a*d)) + (2*(c + d*x)^(7/2))/(7*b^2*d) - (a^2*(c + d*x)^(7/2))/(b^2*(b*c - a*d)*(a + b*x)) + (a*(4*b*c - 9*a*d)*(b*c - a*d)^(3/2)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/b^(11/2)]
    @test_int [x^1*(c + d*x)^(5/2)/(a + b*x)^2, x, 6, ((2*b*c - 7*a*d)*(b*c - a*d)*sqrt(c + d*x))/b^4 + ((2*b*c - 7*a*d)*(c + d*x)^(3/2))/(3*b^3) + ((2*b*c - 7*a*d)*(c + d*x)^(5/2))/(5*b^2*(b*c - a*d)) + (a*(c + d*x)^(7/2))/(b*(b*c - a*d)*(a + b*x)) - ((2*b*c - 7*a*d)*(b*c - a*d)^(3/2)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/b^(9/2)]
    @test_int [x^0*(c + d*x)^(5/2)/(a + b*x)^2, x, 5, (5*d*(b*c - a*d)*sqrt(c + d*x))/b^3 + (5*d*(c + d*x)^(3/2))/(3*b^2) - (c + d*x)^(5/2)/(b*(a + b*x)) - (5*d*(b*c - a*d)^(3/2)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/b^(7/2)]
    @test_int [(c + d*x)^(5/2)/(x^1*(a + b*x)^2), x, 7, -((d*(b*c - 3*a*d)*sqrt(c + d*x))/(a*b^2)) + ((b*c - a*d)*(c + d*x)^(3/2))/(a*b*(a + b*x)) - (2*c^(5/2)*atanh(sqrt(c + d*x)/sqrt(c)))/a^2 + ((b*c - a*d)^(3/2)*(2*b*c + 3*a*d)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/(a^2*b^(5/2))]
    @test_int [(c + d*x)^(5/2)/(x^2*(a + b*x)^2), x, 7, -((c^2*sqrt(c + d*x))/(a^2*x)) - ((b*c - a*d)^2*sqrt(c + d*x))/(a^2*b*(a + b*x)) + (c^(3/2)*(4*b*c - 5*a*d)*atanh(sqrt(c + d*x)/sqrt(c)))/a^3 - ((b*c - a*d)^(3/2)*(4*b*c + a*d)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/(a^3*b^(3/2)), -(((b*c - a*d)*(2*b*c - a*d)*sqrt(c + d*x))/(a^2*b*(a + b*x))) - (c*(c + d*x)^(3/2))/(a*x*(a + b*x)) + (c^(3/2)*(4*b*c - 5*a*d)*atanh(sqrt(c + d*x)/sqrt(c)))/a^3 - ((b*c - a*d)^(3/2)*(4*b*c + a*d)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/(a^3*b^(3/2))]
    @test_int [(c + d*x)^(5/2)/(x^3*(a + b*x)^2), x, 8, ((12*b^2*c^2 - 17*a*b*c*d + 4*a^2*d^2)*sqrt(c + d*x))/(4*a^3*(a + b*x)) + (c*(6*b*c - 7*a*d)*sqrt(c + d*x))/(4*a^2*x*(a + b*x)) - (c*(c + d*x)^(3/2))/(2*a*x^2*(a + b*x)) - (sqrt(c)*(24*b^2*c^2 - 40*a*b*c*d + 15*a^2*d^2)*atanh(sqrt(c + d*x)/sqrt(c)))/(4*a^4) + ((b*c - a*d)^(3/2)*(6*b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/(a^4*sqrt(b))]
    @test_int [(c + d*x)^(5/2)/(x^4*(a + b*x)^2), x, 9, -((b*(32*b^2*c^2 - 52*a*b*c*d + 19*a^2*d^2)*sqrt(c + d*x))/(8*a^4*(a + b*x))) + (c*(8*b*c - 9*a*d)*sqrt(c + d*x))/(12*a^2*x^2*(a + b*x)) - ((48*b^2*c^2 - 82*a*b*c*d + 33*a^2*d^2)*sqrt(c + d*x))/(24*a^3*x*(a + b*x)) - (c*(c + d*x)^(3/2))/(3*a*x^3*(a + b*x)) + ((64*b^3*c^3 - 120*a*b^2*c^2*d + 60*a^2*b*c*d^2 - 5*a^3*d^3)*atanh(sqrt(c + d*x)/sqrt(c)))/(8*a^5*sqrt(c)) - (sqrt(b)*(8*b*c - 3*a*d)*(b*c - a*d)^(3/2)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/a^5]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [1/(x^2*(a + b*x)^2*(c + d*x)^(1/2)), x, 7, -((b*(2*b*c - a*d)*sqrt(c + d*x))/(a^2*c*(b*c - a*d)*(a + b*x))) - sqrt(c + d*x)/(a*c*x*(a + b*x)) + ((4*b*c + a*d)*atanh(sqrt(c + d*x)/sqrt(c)))/(a^3*c^(3/2)) - (b^(3/2)*(4*b*c - 5*a*d)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/(a^3*(b*c - a*d)^(3/2))]

    @test_int [1/(x^2*(a + b*x)^2*(c + d*x)^(3/2)), x, 8, -((d*(2*b^2*c^2 - 2*a*b*c*d + 3*a^2*d^2))/(a^2*c^2*(b*c - a*d)^2*sqrt(c + d*x))) - (b*(2*b*c - a*d))/(a^2*c*(b*c - a*d)*(a + b*x)*sqrt(c + d*x)) - 1/(a*c*x*(a + b*x)*sqrt(c + d*x)) + ((4*b*c + 3*a*d)*atanh(sqrt(c + d*x)/sqrt(c)))/(a^3*c^(5/2)) - (b^(5/2)*(4*b*c - 7*a*d)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/(a^3*(b*c - a*d)^(5/2))]

    @test_int [1/(x^2*(a + b*x)^2*(c + d*x)^(5/2)), x, 9, -((d*(6*b^2*c^2 - 6*a*b*c*d + 5*a^2*d^2))/(3*a^2*c^2*(b*c - a*d)^2*(c + d*x)^(3/2))) - (b*(2*b*c - a*d))/(a^2*c*(b*c - a*d)*(a + b*x)*(c + d*x)^(3/2)) - 1/(a*c*x*(a + b*x)*(c + d*x)^(3/2)) - (d*(2*b*c - a*d)*(b^2*c^2 - a*b*c*d + 5*a^2*d^2))/(a^2*c^3*(b*c - a*d)^3*sqrt(c + d*x)) + ((4*b*c + 5*a*d)*atanh(sqrt(c + d*x)/sqrt(c)))/(a^3*c^(7/2)) - (b^(7/2)*(4*b*c - 9*a*d)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/(a^3*(b*c - a*d)^(7/2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^(m/2)*(a+b*x)^n*(c+d*x)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^(5/2)*sqrt(a + b*x)*(A + B*x), x, 8, (a^3*(10*A*b - 7*a*B)*sqrt(x)*sqrt(a + b*x))/(128*b^4) - (a^2*(10*A*b - 7*a*B)*x^(3/2)*sqrt(a + b*x))/(192*b^3) + (a*(10*A*b - 7*a*B)*x^(5/2)*sqrt(a + b*x))/(240*b^2) + ((10*A*b - 7*a*B)*x^(7/2)*sqrt(a + b*x))/(40*b) + (B*x^(7/2)*(a + b*x)^(3/2))/(5*b) - (a^4*(10*A*b - 7*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(128*b^(9/2))]
    @test_int [x^(3/2)*sqrt(a + b*x)*(A + B*x), x, 7, -(a^2*(8*A*b - 5*a*B)*sqrt(x)*sqrt(a + b*x))/(64*b^3) + (a*(8*A*b - 5*a*B)*x^(3/2)*sqrt(a + b*x))/(96*b^2) + ((8*A*b - 5*a*B)*x^(5/2)*sqrt(a + b*x))/(24*b) + (B*x^(5/2)*(a + b*x)^(3/2))/(4*b) + (a^3*(8*A*b - 5*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(64*b^(7/2))]
    @test_int [sqrt(x)*sqrt(a + b*x)*(A + B*x), x, 6, (a*(2*A*b - a*B)*sqrt(x)*sqrt(a + b*x))/(8*b^2) + ((2*A*b - a*B)*x^(3/2)*sqrt(a + b*x))/(4*b) + (B*x^(3/2)*(a + b*x)^(3/2))/(3*b) - (a^2*(2*A*b - a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(8*b^(5/2))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/sqrt(x), x, 5, ((4*A*b - a*B)*sqrt(x)*sqrt(a + b*x))/(4*b) + (B*sqrt(x)*(a + b*x)^(3/2))/(2*b) + (a*(4*A*b - a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(4*b^(3/2))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/x^(3/2), x, 5, ((2*A*b + a*B)*sqrt(x)*sqrt(a + b*x))/a - (2*A*(a + b*x)^(3/2))/(a*sqrt(x)) + ((2*A*b + a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/sqrt(b)]
    @test_int [(sqrt(a + b*x)*(A + B*x))/x^(5/2), x, 5, (-2*B*sqrt(a + b*x))/sqrt(x) - (2*A*(a + b*x)^(3/2))/(3*a*x^(3/2)) + 2*sqrt(b)*B*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/x^(7/2), x, 2, (-2*A*(a + b*x)^(3/2))/(5*a*x^(5/2)) + (2*(2*A*b - 5*a*B)*(a + b*x)^(3/2))/(15*a^2*x^(3/2))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/x^(9/2), x, 3, (-2*A*(a + b*x)^(3/2))/(7*a*x^(7/2)) + (2*(4*A*b - 7*a*B)*(a + b*x)^(3/2))/(35*a^2*x^(5/2)) - (4*b*(4*A*b - 7*a*B)*(a + b*x)^(3/2))/(105*a^3*x^(3/2))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/x^(11/2), x, 4, (-2*A*(a + b*x)^(3/2))/(9*a*x^(9/2)) + (2*(2*A*b - 3*a*B)*(a + b*x)^(3/2))/(21*a^2*x^(7/2)) - (8*b*(2*A*b - 3*a*B)*(a + b*x)^(3/2))/(105*a^3*x^(5/2)) + (16*b^2*(2*A*b - 3*a*B)*(a + b*x)^(3/2))/(315*a^4*x^(3/2))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/x^(13/2), x, 5, (-2*A*(a + b*x)^(3/2))/(11*a*x^(11/2)) + (2*(8*A*b - 11*a*B)*(a + b*x)^(3/2))/(99*a^2*x^(9/2)) - (4*b*(8*A*b - 11*a*B)*(a + b*x)^(3/2))/(231*a^3*x^(7/2)) + (16*b^2*(8*A*b - 11*a*B)*(a + b*x)^(3/2))/(1155*a^4*x^(5/2)) - (32*b^3*(8*A*b - 11*a*B)*(a + b*x)^(3/2))/(3465*a^5*x^(3/2))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/x^(15/2), x, 6, (-2*A*(a + b*x)^(3/2))/(13*a*x^(13/2)) + (2*(10*A*b - 13*a*B)*(a + b*x)^(3/2))/(143*a^2*x^(11/2)) - (16*b*(10*A*b - 13*a*B)*(a + b*x)^(3/2))/(1287*a^3*x^(9/2)) + (32*b^2*(10*A*b - 13*a*B)*(a + b*x)^(3/2))/(3003*a^4*x^(7/2)) - (128*b^3*(10*A*b - 13*a*B)*(a + b*x)^(3/2))/(15015*a^5*x^(5/2)) + (256*b^4*(10*A*b - 13*a*B)*(a + b*x)^(3/2))/(45045*a^6*x^(3/2))]

    @test_int [x^(5/2)*(a + b*x)^(3/2)*(A + B*x), x, 9, (a^4*(12*A*b - 7*a*B)*sqrt(x)*sqrt(a + b*x))/(512*b^4) - (a^3*(12*A*b - 7*a*B)*x^(3/2)*sqrt(a + b*x))/(768*b^3) + (a^2*(12*A*b - 7*a*B)*x^(5/2)*sqrt(a + b*x))/(960*b^2) + (a*(12*A*b - 7*a*B)*x^(7/2)*sqrt(a + b*x))/(160*b) + ((12*A*b - 7*a*B)*x^(7/2)*(a + b*x)^(3/2))/(60*b) + (B*x^(7/2)*(a + b*x)^(5/2))/(6*b) - (a^5*(12*A*b - 7*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(512*b^(9/2))]
    @test_int [x^(3/2)*(a + b*x)^(3/2)*(A + B*x), x, 8, (-3*a^3*(2*A*b - a*B)*sqrt(x)*sqrt(a + b*x))/(128*b^3) + (a^2*(2*A*b - a*B)*x^(3/2)*sqrt(a + b*x))/(64*b^2) + (a*(2*A*b - a*B)*x^(5/2)*sqrt(a + b*x))/(16*b) + ((2*A*b - a*B)*x^(5/2)*(a + b*x)^(3/2))/(8*b) + (B*x^(5/2)*(a + b*x)^(5/2))/(5*b) + (3*a^4*(2*A*b - a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(128*b^(7/2))]
    @test_int [sqrt(x)*(a + b*x)^(3/2)*(A + B*x), x, 7, (a^2*(8*A*b - 3*a*B)*sqrt(x)*sqrt(a + b*x))/(64*b^2) + (a*(8*A*b - 3*a*B)*x^(3/2)*sqrt(a + b*x))/(32*b) + ((8*A*b - 3*a*B)*x^(3/2)*(a + b*x)^(3/2))/(24*b) + (B*x^(3/2)*(a + b*x)^(5/2))/(4*b) - (a^3*(8*A*b - 3*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(64*b^(5/2))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/sqrt(x), x, 6, (a*(6*A*b - a*B)*sqrt(x)*sqrt(a + b*x))/(8*b) + ((6*A*b - a*B)*sqrt(x)*(a + b*x)^(3/2))/(12*b) + (B*sqrt(x)*(a + b*x)^(5/2))/(3*b) + (a^2*(6*A*b - a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(8*b^(3/2))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/x^(3/2), x, 6, (3*(4*A*b + a*B)*sqrt(x)*sqrt(a + b*x))/4 + ((4*A*b + a*B)*sqrt(x)*(a + b*x)^(3/2))/(2*a) - (2*A*(a + b*x)^(5/2))/(a*sqrt(x)) + (3*a*(4*A*b + a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(4*sqrt(b))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/x^(5/2), x, 6, (b*(2*A*b + 3*a*B)*sqrt(x)*sqrt(a + b*x))/a - (2*(2*A*b + 3*a*B)*(a + b*x)^(3/2))/(3*a*sqrt(x)) - (2*A*(a + b*x)^(5/2))/(3*a*x^(3/2)) + sqrt(b)*(2*A*b + 3*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/x^(7/2), x, 6, (-2*b*B*sqrt(a + b*x))/sqrt(x) - (2*B*(a + b*x)^(3/2))/(3*x^(3/2)) - (2*A*(a + b*x)^(5/2))/(5*a*x^(5/2)) + 2*b^(3/2)*B*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/x^(9/2), x, 2, (-2*A*(a + b*x)^(5/2))/(7*a*x^(7/2)) + (2*(2*A*b - 7*a*B)*(a + b*x)^(5/2))/(35*a^2*x^(5/2))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/x^(11/2), x, 3, (-2*A*(a + b*x)^(5/2))/(9*a*x^(9/2)) + (2*(4*A*b - 9*a*B)*(a + b*x)^(5/2))/(63*a^2*x^(7/2)) - (4*b*(4*A*b - 9*a*B)*(a + b*x)^(5/2))/(315*a^3*x^(5/2))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/x^(13/2), x, 4, (-2*A*(a + b*x)^(5/2))/(11*a*x^(11/2)) + (2*(6*A*b - 11*a*B)*(a + b*x)^(5/2))/(99*a^2*x^(9/2)) - (8*b*(6*A*b - 11*a*B)*(a + b*x)^(5/2))/(693*a^3*x^(7/2)) + (16*b^2*(6*A*b - 11*a*B)*(a + b*x)^(5/2))/(3465*a^4*x^(5/2))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/x^(15/2), x, 5, -((2*A*(a + b*x)^(5/2))/(13*a*x^(13/2))) + (2*(8*A*b - 13*a*B)*(a + b*x)^(5/2))/(143*a^2*x^(11/2)) - (4*b*(8*A*b - 13*a*B)*(a + b*x)^(5/2))/(429*a^3*x^(9/2)) + (16*b^2*(8*A*b - 13*a*B)*(a + b*x)^(5/2))/(3003*a^4*x^(7/2)) - (32*b^3*(8*A*b - 13*a*B)*(a + b*x)^(5/2))/(15015*a^5*x^(5/2))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/x^(17/2), x, 6, -((2*A*(a + b*x)^(5/2))/(15*a*x^(15/2))) + (2*(2*A*b - 3*a*B)*(a + b*x)^(5/2))/(39*a^2*x^(13/2)) - (16*b*(2*A*b - 3*a*B)*(a + b*x)^(5/2))/(429*a^3*x^(11/2)) + (32*b^2*(2*A*b - 3*a*B)*(a + b*x)^(5/2))/(1287*a^4*x^(9/2)) - (128*b^3*(2*A*b - 3*a*B)*(a + b*x)^(5/2))/(9009*a^5*x^(7/2)) + (256*b^4*(2*A*b - 3*a*B)*(a + b*x)^(5/2))/(45045*a^6*x^(5/2))]

    @test_int [x^(3/2)*(a + b*x)^(5/2)*(A + B*x), x, 9, -(a^4*(12*A*b - 5*a*B)*sqrt(x)*sqrt(a + b*x))/(512*b^3) + (a^3*(12*A*b - 5*a*B)*x^(3/2)*sqrt(a + b*x))/(768*b^2) + (a^2*(12*A*b - 5*a*B)*x^(5/2)*sqrt(a + b*x))/(192*b) + (a*(12*A*b - 5*a*B)*x^(5/2)*(a + b*x)^(3/2))/(96*b) + ((12*A*b - 5*a*B)*x^(5/2)*(a + b*x)^(5/2))/(60*b) + (B*x^(5/2)*(a + b*x)^(7/2))/(6*b) + (a^5*(12*A*b - 5*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(512*b^(7/2))]
    @test_int [sqrt(x)*(a + b*x)^(5/2)*(A + B*x), x, 8, (a^3*(10*A*b - 3*a*B)*sqrt(x)*sqrt(a + b*x))/(128*b^2) + (a^2*(10*A*b - 3*a*B)*x^(3/2)*sqrt(a + b*x))/(64*b) + (a*(10*A*b - 3*a*B)*x^(3/2)*(a + b*x)^(3/2))/(48*b) + ((10*A*b - 3*a*B)*x^(3/2)*(a + b*x)^(5/2))/(40*b) + (B*x^(3/2)*(a + b*x)^(7/2))/(5*b) - (a^4*(10*A*b - 3*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(128*b^(5/2))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/sqrt(x), x, 7, (5*a^2*(8*A*b - a*B)*sqrt(x)*sqrt(a + b*x))/(64*b) + (5*a*(8*A*b - a*B)*sqrt(x)*(a + b*x)^(3/2))/(96*b) + ((8*A*b - a*B)*sqrt(x)*(a + b*x)^(5/2))/(24*b) + (B*sqrt(x)*(a + b*x)^(7/2))/(4*b) + (5*a^3*(8*A*b - a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(64*b^(3/2))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/x^(3/2), x, 7, (5*a*(6*A*b + a*B)*sqrt(x)*sqrt(a + b*x))/8 + (5*(6*A*b + a*B)*sqrt(x)*(a + b*x)^(3/2))/12 + ((6*A*b + a*B)*sqrt(x)*(a + b*x)^(5/2))/(3*a) - (2*A*(a + b*x)^(7/2))/(a*sqrt(x)) + (5*a^2*(6*A*b + a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(8*sqrt(b))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/x^(5/2), x, 7, (5*b*(4*A*b + 3*a*B)*sqrt(x)*sqrt(a + b*x))/4 + (5*b*(4*A*b + 3*a*B)*sqrt(x)*(a + b*x)^(3/2))/(6*a) - (2*(4*A*b + 3*a*B)*(a + b*x)^(5/2))/(3*a*sqrt(x)) - (2*A*(a + b*x)^(7/2))/(3*a*x^(3/2)) + (5*a*sqrt(b)*(4*A*b + 3*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/4]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/x^(7/2), x, 7, (b^2*(2*A*b + 5*a*B)*sqrt(x)*sqrt(a + b*x))/a - (2*b*(2*A*b + 5*a*B)*(a + b*x)^(3/2))/(3*a*sqrt(x)) - (2*(2*A*b + 5*a*B)*(a + b*x)^(5/2))/(15*a*x^(3/2)) - (2*A*(a + b*x)^(7/2))/(5*a*x^(5/2)) + b^(3/2)*(2*A*b + 5*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/x^(9/2), x, 7, (-2*b^2*B*sqrt(a + b*x))/sqrt(x) - (2*b*B*(a + b*x)^(3/2))/(3*x^(3/2)) - (2*B*(a + b*x)^(5/2))/(5*x^(5/2)) - (2*A*(a + b*x)^(7/2))/(7*a*x^(7/2)) + 2*b^(5/2)*B*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/x^(11/2), x, 2, (-2*A*(a + b*x)^(7/2))/(9*a*x^(9/2)) + (2*(2*A*b - 9*a*B)*(a + b*x)^(7/2))/(63*a^2*x^(7/2))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/x^(13/2), x, 3, (-2*A*(a + b*x)^(7/2))/(11*a*x^(11/2)) + (2*(4*A*b - 11*a*B)*(a + b*x)^(7/2))/(99*a^2*x^(9/2)) - (4*b*(4*A*b - 11*a*B)*(a + b*x)^(7/2))/(693*a^3*x^(7/2))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/x^(15/2), x, 4, (-2*A*(a + b*x)^(7/2))/(13*a*x^(13/2)) + (2*(6*A*b - 13*a*B)*(a + b*x)^(7/2))/(143*a^2*x^(11/2)) - (8*b*(6*A*b - 13*a*B)*(a + b*x)^(7/2))/(1287*a^3*x^(9/2)) + (16*b^2*(6*A*b - 13*a*B)*(a + b*x)^(7/2))/(9009*a^4*x^(7/2))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/x^(17/2), x, 5, -((2*A*(a + b*x)^(7/2))/(15*a*x^(15/2))) + (2*(8*A*b - 15*a*B)*(a + b*x)^(7/2))/(195*a^2*x^(13/2)) - (4*b*(8*A*b - 15*a*B)*(a + b*x)^(7/2))/(715*a^3*x^(11/2)) + (16*b^2*(8*A*b - 15*a*B)*(a + b*x)^(7/2))/(6435*a^4*x^(9/2)) - (32*b^3*(8*A*b - 15*a*B)*(a + b*x)^(7/2))/(45045*a^5*x^(7/2))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/x^(19/2), x, 6, -((2*A*(a + b*x)^(7/2))/(17*a*x^(17/2))) + (2*(10*A*b - 17*a*B)*(a + b*x)^(7/2))/(255*a^2*x^(15/2)) - (16*b*(10*A*b - 17*a*B)*(a + b*x)^(7/2))/(3315*a^3*x^(13/2)) + (32*b^2*(10*A*b - 17*a*B)*(a + b*x)^(7/2))/(12155*a^4*x^(11/2)) - (128*b^3*(10*A*b - 17*a*B)*(a + b*x)^(7/2))/(109395*a^5*x^(9/2)) + (256*b^4*(10*A*b - 17*a*B)*(a + b*x)^(7/2))/(765765*a^6*x^(7/2))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(x^(7/2)*(A + B*x))/sqrt(a + b*x), x, 8, (-7*a^3*(10*A*b - 9*a*B)*sqrt(x)*sqrt(a + b*x))/(128*b^5) + (7*a^2*(10*A*b - 9*a*B)*x^(3/2)*sqrt(a + b*x))/(192*b^4) - (7*a*(10*A*b - 9*a*B)*x^(5/2)*sqrt(a + b*x))/(240*b^3) + ((10*A*b - 9*a*B)*x^(7/2)*sqrt(a + b*x))/(40*b^2) + (B*x^(9/2)*sqrt(a + b*x))/(5*b) + (7*a^4*(10*A*b - 9*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(128*b^(11/2))]
    @test_int [(x^(5/2)*(A + B*x))/sqrt(a + b*x), x, 7, (5*a^2*(8*A*b - 7*a*B)*sqrt(x)*sqrt(a + b*x))/(64*b^4) - (5*a*(8*A*b - 7*a*B)*x^(3/2)*sqrt(a + b*x))/(96*b^3) + ((8*A*b - 7*a*B)*x^(5/2)*sqrt(a + b*x))/(24*b^2) + (B*x^(7/2)*sqrt(a + b*x))/(4*b) - (5*a^3*(8*A*b - 7*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(64*b^(9/2))]
    @test_int [(x^(3/2)*(A + B*x))/sqrt(a + b*x), x, 6, -(a*(6*A*b - 5*a*B)*sqrt(x)*sqrt(a + b*x))/(8*b^3) + ((6*A*b - 5*a*B)*x^(3/2)*sqrt(a + b*x))/(12*b^2) + (B*x^(5/2)*sqrt(a + b*x))/(3*b) + (a^2*(6*A*b - 5*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(8*b^(7/2))]
    @test_int [(sqrt(x)*(A + B*x))/sqrt(a + b*x), x, 5, ((4*A*b - 3*a*B)*sqrt(x)*sqrt(a + b*x))/(4*b^2) + (B*x^(3/2)*sqrt(a + b*x))/(2*b) - (a*(4*A*b - 3*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(4*b^(5/2))]
    @test_int [(A + B*x)/(sqrt(x)*sqrt(a + b*x)), x, 4, (B*sqrt(x)*sqrt(a + b*x))/b + ((2*A*b - a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/b^(3/2)]
    @test_int [(A + B*x)/(x^(3/2)*sqrt(a + b*x)), x, 4, (-2*A*sqrt(a + b*x))/(a*sqrt(x)) + (2*B*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/sqrt(b)]
    @test_int [(A + B*x)/(x^(5/2)*sqrt(a + b*x)), x, 2, (-2*A*sqrt(a + b*x))/(3*a*x^(3/2)) + (2*(2*A*b - 3*a*B)*sqrt(a + b*x))/(3*a^2*sqrt(x))]
    @test_int [(A + B*x)/(x^(7/2)*sqrt(a + b*x)), x, 3, (-2*A*sqrt(a + b*x))/(5*a*x^(5/2)) + (2*(4*A*b - 5*a*B)*sqrt(a + b*x))/(15*a^2*x^(3/2)) - (4*b*(4*A*b - 5*a*B)*sqrt(a + b*x))/(15*a^3*sqrt(x))]
    @test_int [(A + B*x)/(x^(9/2)*sqrt(a + b*x)), x, 4, (-2*A*sqrt(a + b*x))/(7*a*x^(7/2)) + (2*(6*A*b - 7*a*B)*sqrt(a + b*x))/(35*a^2*x^(5/2)) - (8*b*(6*A*b - 7*a*B)*sqrt(a + b*x))/(105*a^3*x^(3/2)) + (16*b^2*(6*A*b - 7*a*B)*sqrt(a + b*x))/(105*a^4*sqrt(x))]
    @test_int [(A + B*x)/(x^(11/2)*sqrt(a + b*x)), x, 5, (-2*A*sqrt(a + b*x))/(9*a*x^(9/2)) + (2*(8*A*b - 9*a*B)*sqrt(a + b*x))/(63*a^2*x^(7/2)) - (4*b*(8*A*b - 9*a*B)*sqrt(a + b*x))/(105*a^3*x^(5/2)) + (16*b^2*(8*A*b - 9*a*B)*sqrt(a + b*x))/(315*a^4*x^(3/2)) - (32*b^3*(8*A*b - 9*a*B)*sqrt(a + b*x))/(315*a^5*sqrt(x))]
    @test_int [(A + B*x)/(x^(13/2)*sqrt(a + b*x)), x, 6, (-2*A*sqrt(a + b*x))/(11*a*x^(11/2)) + (2*(10*A*b - 11*a*B)*sqrt(a + b*x))/(99*a^2*x^(9/2)) - (16*b*(10*A*b - 11*a*B)*sqrt(a + b*x))/(693*a^3*x^(7/2)) + (32*b^2*(10*A*b - 11*a*B)*sqrt(a + b*x))/(1155*a^4*x^(5/2)) - (128*b^3*(10*A*b - 11*a*B)*sqrt(a + b*x))/(3465*a^5*x^(3/2)) + (256*b^4*(10*A*b - 11*a*B)*sqrt(a + b*x))/(3465*a^6*sqrt(x))]
    @test_int [(A + B*x)/(x^(15/2)*sqrt(a + b*x)), x, 7, (-2*A*sqrt(a + b*x))/(13*a*x^(13/2)) + (2*(12*A*b - 13*a*B)*sqrt(a + b*x))/(143*a^2*x^(11/2)) - (20*b*(12*A*b - 13*a*B)*sqrt(a + b*x))/(1287*a^3*x^(9/2)) + (160*b^2*(12*A*b - 13*a*B)*sqrt(a + b*x))/(9009*a^4*x^(7/2)) - (64*b^3*(12*A*b - 13*a*B)*sqrt(a + b*x))/(3003*a^5*x^(5/2)) + (256*b^4*(12*A*b - 13*a*B)*sqrt(a + b*x))/(9009*a^6*x^(3/2)) - (512*b^5*(12*A*b - 13*a*B)*sqrt(a + b*x))/(9009*a^7*sqrt(x))]

    @test_int [(x^(7/2)*(A + B*x))/(a + b*x)^(3/2), x, 8, (2*(A*b - a*B)*x^(9/2))/(a*b*sqrt(a + b*x)) + (35*a^2*(8*A*b - 9*a*B)*sqrt(x)*sqrt(a + b*x))/(64*b^5) - (35*a*(8*A*b - 9*a*B)*x^(3/2)*sqrt(a + b*x))/(96*b^4) + (7*(8*A*b - 9*a*B)*x^(5/2)*sqrt(a + b*x))/(24*b^3) - ((8*A*b - 9*a*B)*x^(7/2)*sqrt(a + b*x))/(4*a*b^2) - (35*a^3*(8*A*b - 9*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(64*b^(11/2))]
    @test_int [(x^(5/2)*(A + B*x))/(a + b*x)^(3/2), x, 7, (2*(A*b - a*B)*x^(7/2))/(a*b*sqrt(a + b*x)) - (5*a*(6*A*b - 7*a*B)*sqrt(x)*sqrt(a + b*x))/(8*b^4) + (5*(6*A*b - 7*a*B)*x^(3/2)*sqrt(a + b*x))/(12*b^3) - ((6*A*b - 7*a*B)*x^(5/2)*sqrt(a + b*x))/(3*a*b^2) + (5*a^2*(6*A*b - 7*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(8*b^(9/2))]
    @test_int [(x^(3/2)*(A + B*x))/(a + b*x)^(3/2), x, 6, (2*(A*b - a*B)*x^(5/2))/(a*b*sqrt(a + b*x)) + (3*(4*A*b - 5*a*B)*sqrt(x)*sqrt(a + b*x))/(4*b^3) - ((4*A*b - 5*a*B)*x^(3/2)*sqrt(a + b*x))/(2*a*b^2) - (3*a*(4*A*b - 5*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(4*b^(7/2))]
    @test_int [(sqrt(x)*(A + B*x))/(a + b*x)^(3/2), x, 5, (2*(A*b - a*B)*x^(3/2))/(a*b*sqrt(a + b*x)) - ((2*A*b - 3*a*B)*sqrt(x)*sqrt(a + b*x))/(a*b^2) + ((2*A*b - 3*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/b^(5/2)]
    @test_int [(A + B*x)/(sqrt(x)*(a + b*x)^(3/2)), x, 4, (2*(A*b - a*B)*sqrt(x))/(a*b*sqrt(a + b*x)) + (2*B*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/b^(3/2)]
    @test_int [(A + B*x)/(x^(3/2)*(a + b*x)^(3/2)), x, 2, (-2*A)/(a*sqrt(x)*sqrt(a + b*x)) - (2*(2*A*b - a*B)*sqrt(x))/(a^2*sqrt(a + b*x))]
    @test_int [(A + B*x)/(x^(5/2)*(a + b*x)^(3/2)), x, 3, (-2*A)/(3*a*x^(3/2)*sqrt(a + b*x)) - (2*(4*A*b - 3*a*B))/(3*a^2*sqrt(x)*sqrt(a + b*x)) + (4*(4*A*b - 3*a*B)*sqrt(a + b*x))/(3*a^3*sqrt(x))]
    @test_int [(A + B*x)/(x^(7/2)*(a + b*x)^(3/2)), x, 4, (-2*A)/(5*a*x^(5/2)*sqrt(a + b*x)) - (2*(6*A*b - 5*a*B))/(5*a^2*x^(3/2)*sqrt(a + b*x)) + (8*(6*A*b - 5*a*B)*sqrt(a + b*x))/(15*a^3*x^(3/2)) - (16*b*(6*A*b - 5*a*B)*sqrt(a + b*x))/(15*a^4*sqrt(x))]
    @test_int [(A + B*x)/(x^(9/2)*(a + b*x)^(3/2)), x, 5, (-2*A)/(7*a*x^(7/2)*sqrt(a + b*x)) - (2*(8*A*b - 7*a*B))/(7*a^2*x^(5/2)*sqrt(a + b*x)) + (12*(8*A*b - 7*a*B)*sqrt(a + b*x))/(35*a^3*x^(5/2)) - (16*b*(8*A*b - 7*a*B)*sqrt(a + b*x))/(35*a^4*x^(3/2)) + (32*b^2*(8*A*b - 7*a*B)*sqrt(a + b*x))/(35*a^5*sqrt(x))]
    @test_int [(A + B*x)/(x^(11/2)*(a + b*x)^(3/2)), x, 6, (-2*A)/(9*a*x^(9/2)*sqrt(a + b*x)) - (2*(10*A*b - 9*a*B))/(9*a^2*x^(7/2)*sqrt(a + b*x)) + (16*(10*A*b - 9*a*B)*sqrt(a + b*x))/(63*a^3*x^(7/2)) - (32*b*(10*A*b - 9*a*B)*sqrt(a + b*x))/(105*a^4*x^(5/2)) + (128*b^2*(10*A*b - 9*a*B)*sqrt(a + b*x))/(315*a^5*x^(3/2)) - (256*b^3*(10*A*b - 9*a*B)*sqrt(a + b*x))/(315*a^6*sqrt(x))]
    @test_int [(A + B*x)/(x^(13/2)*(a + b*x)^(3/2)), x, 7, (-2*A)/(11*a*x^(11/2)*sqrt(a + b*x)) - (2*(12*A*b - 11*a*B))/(11*a^2*x^(9/2)*sqrt(a + b*x)) + (20*(12*A*b - 11*a*B)*sqrt(a + b*x))/(99*a^3*x^(9/2)) - (160*b*(12*A*b - 11*a*B)*sqrt(a + b*x))/(693*a^4*x^(7/2)) + (64*b^2*(12*A*b - 11*a*B)*sqrt(a + b*x))/(231*a^5*x^(5/2)) - (256*b^3*(12*A*b - 11*a*B)*sqrt(a + b*x))/(693*a^6*x^(3/2)) + (512*b^4*(12*A*b - 11*a*B)*sqrt(a + b*x))/(693*a^7*sqrt(x))]

    @test_int [(x^(7/2)*(A + B*x))/(a + b*x)^(5/2), x, 8, (2*(A*b - a*B)*x^(9/2))/(3*a*b*(a + b*x)^(3/2)) + (2*(2*A*b - 3*a*B)*x^(7/2))/(a*b^2*sqrt(a + b*x)) - (35*a*(2*A*b - 3*a*B)*sqrt(x)*sqrt(a + b*x))/(8*b^5) + (35*(2*A*b - 3*a*B)*x^(3/2)*sqrt(a + b*x))/(12*b^4) - (7*(2*A*b - 3*a*B)*x^(5/2)*sqrt(a + b*x))/(3*a*b^3) + (35*a^2*(2*A*b - 3*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(8*b^(11/2))]
    @test_int [(x^(5/2)*(A + B*x))/(a + b*x)^(5/2), x, 7, (2*(A*b - a*B)*x^(7/2))/(3*a*b*(a + b*x)^(3/2)) + (2*(4*A*b - 7*a*B)*x^(5/2))/(3*a*b^2*sqrt(a + b*x)) + (5*(4*A*b - 7*a*B)*sqrt(x)*sqrt(a + b*x))/(4*b^4) - (5*(4*A*b - 7*a*B)*x^(3/2)*sqrt(a + b*x))/(6*a*b^3) - (5*a*(4*A*b - 7*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/(4*b^(9/2))]
    @test_int [(x^(3/2)*(A + B*x))/(a + b*x)^(5/2), x, 6, (2*(A*b - a*B)*x^(5/2))/(3*a*b*(a + b*x)^(3/2)) + (2*(2*A*b - 5*a*B)*x^(3/2))/(3*a*b^2*sqrt(a + b*x)) - ((2*A*b - 5*a*B)*sqrt(x)*sqrt(a + b*x))/(a*b^3) + ((2*A*b - 5*a*B)*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/b^(7/2)]
    @test_int [(sqrt(x)*(A + B*x))/(a + b*x)^(5/2), x, 5, (2*(A*b - a*B)*x^(3/2))/(3*a*b*(a + b*x)^(3/2)) - (2*B*sqrt(x))/(b^2*sqrt(a + b*x)) + (2*B*atanh((sqrt(b)*sqrt(x))/sqrt(a + b*x)))/b^(5/2)]
    @test_int [(A + B*x)/(sqrt(x)*(a + b*x)^(5/2)), x, 2, (2*(A*b - a*B)*sqrt(x))/(3*a*b*(a + b*x)^(3/2)) + (2*(2*A*b + a*B)*sqrt(x))/(3*a^2*b*sqrt(a + b*x))]
    @test_int [(A + B*x)/(x^(3/2)*(a + b*x)^(5/2)), x, 3, (-2*A)/(a*sqrt(x)*(a + b*x)^(3/2)) - (2*(4*A*b - a*B)*sqrt(x))/(3*a^2*(a + b*x)^(3/2)) - (4*(4*A*b - a*B)*sqrt(x))/(3*a^3*sqrt(a + b*x))]
    @test_int [(A + B*x)/(x^(5/2)*(a + b*x)^(5/2)), x, 4, (-2*A)/(3*a*x^(3/2)*(a + b*x)^(3/2)) - (2*(2*A*b - a*B))/(3*a^2*sqrt(x)*(a + b*x)^(3/2)) - (8*(2*A*b - a*B))/(3*a^3*sqrt(x)*sqrt(a + b*x)) + (16*(2*A*b - a*B)*sqrt(a + b*x))/(3*a^4*sqrt(x))]
    @test_int [(A + B*x)/(x^(7/2)*(a + b*x)^(5/2)), x, 5, (-2*A)/(5*a*x^(5/2)*(a + b*x)^(3/2)) - (2*(8*A*b - 5*a*B))/(15*a^2*x^(3/2)*(a + b*x)^(3/2)) - (4*(8*A*b - 5*a*B))/(5*a^3*x^(3/2)*sqrt(a + b*x)) + (16*(8*A*b - 5*a*B)*sqrt(a + b*x))/(15*a^4*x^(3/2)) - (32*b*(8*A*b - 5*a*B)*sqrt(a + b*x))/(15*a^5*sqrt(x))]
    @test_int [(A + B*x)/(x^(9/2)*(a + b*x)^(5/2)), x, 6, (-2*A)/(7*a*x^(7/2)*(a + b*x)^(3/2)) - (2*(10*A*b - 7*a*B))/(21*a^2*x^(5/2)*(a + b*x)^(3/2)) - (16*(10*A*b - 7*a*B))/(21*a^3*x^(5/2)*sqrt(a + b*x)) + (32*(10*A*b - 7*a*B)*sqrt(a + b*x))/(35*a^4*x^(5/2)) - (128*b*(10*A*b - 7*a*B)*sqrt(a + b*x))/(105*a^5*x^(3/2)) + (256*b^2*(10*A*b - 7*a*B)*sqrt(a + b*x))/(105*a^6*sqrt(x))]
    @test_int [(A + B*x)/(x^(11/2)*(a + b*x)^(5/2)), x, 7, (-2*A)/(9*a*x^(9/2)*(a + b*x)^(3/2)) - (2*(4*A*b - 3*a*B))/(9*a^2*x^(7/2)*(a + b*x)^(3/2)) - (20*(4*A*b - 3*a*B))/(9*a^3*x^(7/2)*sqrt(a + b*x)) + (160*(4*A*b - 3*a*B)*sqrt(a + b*x))/(63*a^4*x^(7/2)) - (64*b*(4*A*b - 3*a*B)*sqrt(a + b*x))/(21*a^5*x^(5/2)) + (256*b^2*(4*A*b - 3*a*B)*sqrt(a + b*x))/(63*a^6*x^(3/2)) - (512*b^3*(4*A*b - 3*a*B)*sqrt(a + b*x))/(63*a^7*sqrt(x))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x)^(n/2)*(c+d*x)^(p/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x)^(n/2)*(a+b*x)^(1/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [x^3*sqrt(a + b*x)*sqrt(c + d*x), x, 7, -(((7*b^4*c^4 + 2*a*b^3*c^3*d - 2*a^3*b*c*d^3 - 7*a^4*d^4)*sqrt(a + b*x)*sqrt(c + d*x))/(128*b^4*d^4)) - ((b*c + a*d)*(7*b^2*c^2 + 2*a*b*c*d + 7*a^2*d^2)*(a + b*x)^(3/2)*sqrt(c + d*x))/(64*b^4*d^3) + (x^2*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(5*b*d) + ((a + b*x)^(3/2)*(c + d*x)^(3/2)*(35*b^2*c^2 + 38*a*b*c*d + 35*a^2*d^2 - 42*b*d*(b*c + a*d)*x))/(240*b^3*d^3) + ((b*c - a*d)^2*(b*c + a*d)*(7*b^2*c^2 + 2*a*b*c*d + 7*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(128*b^(9/2)*d^(9/2))]
    @test_int [x^2*sqrt(a + b*x)*sqrt(c + d*x), x, 7, -(((b*c - a*d)*(4*a*b*c*d - 5*(b*c + a*d)^2)*sqrt(a + b*x)*sqrt(c + d*x))/(64*b^3*d^3)) - ((4*a*b*c*d - 5*(b*c + a*d)^2)*(a + b*x)^(3/2)*sqrt(c + d*x))/(32*b^3*d^2) - (5*(b*c + a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(24*b^2*d^2) + (x*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(4*b*d) + ((b*c - a*d)^2*(4*a*b*c*d - 5*(b*c + a*d)^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(7/2)*d^(7/2))]
    @test_int [x*sqrt(a + b*x)*sqrt(c + d*x), x, 6, (1/8)*(a^2/b^2 - c^2/d^2)*sqrt(a + b*x)*sqrt(c + d*x) - ((b*c + a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(4*b^2*d) + ((a + b*x)^(3/2)*(c + d*x)^(3/2))/(3*b*d) + ((b*c - a*d)^2*(b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*b^(5/2)*d^(5/2))]
    @test_int [sqrt(a + b*x)*sqrt(c + d*x), x, 5, ((b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*b*d) + ((a + b*x)^(3/2)*sqrt(c + d*x))/(2*b) - ((b*c - a*d)^2*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(3/2)*d^(3/2))]
    @test_int [(sqrt(a + b*x)*sqrt(c + d*x))/x, x, 7, sqrt(a + b*x)*sqrt(c + d*x) - 2*sqrt(a)*sqrt(c)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))) + ((b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(sqrt(b)*sqrt(d))]
    @test_int [(sqrt(a + b*x)*sqrt(c + d*x))/x^2, x, 7, -((sqrt(a + b*x)*sqrt(c + d*x))/x) - ((b*c + a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(sqrt(a)*sqrt(c)) + 2*sqrt(b)*sqrt(d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x)))]
    @test_int [(sqrt(a + b*x)*sqrt(c + d*x))/x^3, x, 4, -((b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*a*c*x) - (sqrt(a + b*x)*(c + d*x)^(3/2))/(2*c*x^2) + ((b*c - a*d)^2*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(3/2)*c^(3/2))]
    @test_int [(sqrt(a + b*x)*sqrt(c + d*x))/x^4, x, 5, ((b^2/a^2 - d^2/c^2)*sqrt(a + b*x)*sqrt(c + d*x))/(8*x) + ((b*c + a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(4*a*c^2*x^2) - ((a + b*x)^(3/2)*(c + d*x)^(3/2))/(3*a*c*x^3) - ((b*c - a*d)^2*(b*c + a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*a^(5/2)*c^(5/2))]
    @test_int [(sqrt(a + b*x)*sqrt(c + d*x))/x^5, x, 7, -((sqrt(a + b*x)*sqrt(c + d*x))/(4*x^4)) - ((b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(24*a*c*x^3) + ((5*b^2*c^2 - 2*a*b*c*d + 5*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(96*a^2*c^2*x^2) - ((b*c + a*d)*(15*b^2*c^2 - 22*a*b*c*d + 15*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(192*a^3*c^3*x) + ((b*c - a*d)^2*(5*b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(7/2)*c^(7/2))]
    @test_int [(sqrt(a + b*x)*sqrt(c + d*x))/x^6, x, 8, -((sqrt(a + b*x)*sqrt(c + d*x))/(5*x^5)) - ((b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(40*a*c*x^4) + ((7*b^2*c^2 - 2*a*b*c*d + 7*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(240*a^2*c^2*x^3) - ((b*c + a*d)*(35*b^2*c^2 - 46*a*b*c*d + 35*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(960*a^3*c^3*x^2) + ((105*b^4*c^4 - 40*a*b^3*c^3*d - 34*a^2*b^2*c^2*d^2 - 40*a^3*b*c*d^3 + 105*a^4*d^4)*sqrt(a + b*x)*sqrt(c + d*x))/(1920*a^4*c^4*x) - ((b*c - a*d)^2*(b*c + a*d)*(7*b^2*c^2 + 2*a*b*c*d + 7*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(128*a^(9/2)*c^(9/2))]

    @test_int [x^2*sqrt(a + b*x)*(c + d*x)^(3/2), x, 8, ((b*c - a*d)^2*(3*b^2*c^2 + 6*a*b*c*d + 7*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(128*b^4*d^3) + ((b*c - a*d)*(3*b^2*c^2 + 6*a*b*c*d + 7*a^2*d^2)*(a + b*x)^(3/2)*sqrt(c + d*x))/(64*b^4*d^2) + ((3*b^2*c^2 + 6*a*b*c*d + 7*a^2*d^2)*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(48*b^3*d^2) - ((5*b*c + 7*a*d)*(a + b*x)^(3/2)*(c + d*x)^(5/2))/(40*b^2*d^2) + (x*(a + b*x)^(3/2)*(c + d*x)^(5/2))/(5*b*d) - ((b*c - a*d)^3*(3*b^2*c^2 + 6*a*b*c*d + 7*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(128*b^(9/2)*d^(7/2))]
    @test_int [x*sqrt(a + b*x)*(c + d*x)^(3/2), x, 7, -((b*c - a*d)^2*(3*b*c + 5*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(64*b^3*d^2) - ((b*c - a*d)*(3*b*c + 5*a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(32*b^3*d) - ((3*b*c + 5*a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(24*b^2*d) + ((a + b*x)^(3/2)*(c + d*x)^(5/2))/(4*b*d) + ((b*c - a*d)^3*(3*b*c + 5*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(7/2)*d^(5/2))]
    @test_int [sqrt(a + b*x)*(c + d*x)^(3/2), x, 6, ((b*c - a*d)^2*sqrt(a + b*x)*sqrt(c + d*x))/(8*b^2*d) + ((b*c - a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(4*b^2) + ((a + b*x)^(3/2)*(c + d*x)^(3/2))/(3*b) - ((b*c - a*d)^3*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*b^(5/2)*d^(3/2))]
    @test_int [(sqrt(a + b*x)*(c + d*x)^(3/2))/x, x, 8, ((3*b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*b) + (sqrt(a + b*x)*(c + d*x)^(3/2))/2 - 2*sqrt(a)*c^(3/2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))) + ((3*b^2*c^2 + 6*a*b*c*d - a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(3/2)*sqrt(d))]
    @test_int [(sqrt(a + b*x)*(c + d*x)^(3/2))/x^2, x, 8, 2*d*sqrt(a + b*x)*sqrt(c + d*x) - (sqrt(a + b*x)*(c + d*x)^(3/2))/x - (sqrt(c)*(b*c + 3*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/sqrt(a) + (sqrt(d)*(3*b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/sqrt(b)]
    @test_int [(sqrt(a + b*x)*(c + d*x)^(3/2))/x^3, x, 8, -((b*c + 3*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*a*x) - (sqrt(a + b*x)*(c + d*x)^(3/2))/(2*x^2) + ((b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(3/2)*sqrt(c)) + 2*sqrt(b)*d^(3/2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x)))]
    @test_int [(sqrt(a + b*x)*(c + d*x)^(3/2))/x^4, x, 5, ((b*c - a*d)^2*sqrt(a + b*x)*sqrt(c + d*x))/(8*a^2*c*x) - ((b*c - a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(12*a*c*x^2) - (sqrt(a + b*x)*(c + d*x)^(5/2))/(3*c*x^3) - ((b*c - a*d)^3*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*a^(5/2)*c^(3/2))]
    @test_int [(sqrt(a + b*x)*(c + d*x)^(3/2))/x^5, x, 6, -(((b*c - a*d)^2*(5*b*c + 3*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(64*a^3*c^2*x)) + ((b*c - a*d)*(5*b*c + 3*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(96*a^2*c^2*x^2) + ((5*b*c + 3*a*d)*sqrt(a + b*x)*(c + d*x)^(5/2))/(24*a*c^2*x^3) - ((a + b*x)^(3/2)*(c + d*x)^(5/2))/(4*a*c*x^4) + ((b*c - a*d)^3*(5*b*c + 3*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(7/2)*c^(5/2))]
    @test_int [(sqrt(a + b*x)*(c + d*x)^(3/2))/x^6, x, 8, -(((b*c + 3*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(40*a*x^4)) + (((7*b^2*c)/a - 12*b*d - (3*a*d^2)/c)*sqrt(a + b*x)*sqrt(c + d*x))/(240*a*x^3) - ((35*b^3*c^3 - 61*a*b^2*c^2*d + 9*a^2*b*c*d^2 - 15*a^3*d^3)*sqrt(a + b*x)*sqrt(c + d*x))/(960*a^3*c^2*x^2) + ((105*b^4*c^4 - 190*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 + 30*a^3*b*c*d^3 - 45*a^4*d^4)*sqrt(a + b*x)*sqrt(c + d*x))/(1920*a^4*c^3*x) - (sqrt(a + b*x)*(c + d*x)^(3/2))/(5*x^5) - ((b*c - a*d)^3*(7*b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(128*a^(9/2)*c^(7/2))]

    @test_int [x^2*sqrt(a + b*x)*(c + d*x)^(5/2), x, 9, ((b*c - a*d)^3*(5*b^2*c^2 + 14*a*b*c*d + 21*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(512*b^5*d^3) + ((b*c - a*d)^2*(5*b^2*c^2 + 14*a*b*c*d + 21*a^2*d^2)*(a + b*x)^(3/2)*sqrt(c + d*x))/(256*b^5*d^2) + ((b*c - a*d)*(5*b^2*c^2 + 14*a*b*c*d + 21*a^2*d^2)*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(192*b^4*d^2) + ((5*b^2*c^2 + 14*a*b*c*d + 21*a^2*d^2)*(a + b*x)^(3/2)*(c + d*x)^(5/2))/(160*b^3*d^2) - ((5*b*c + 9*a*d)*(a + b*x)^(3/2)*(c + d*x)^(7/2))/(60*b^2*d^2) + (x*(a + b*x)^(3/2)*(c + d*x)^(7/2))/(6*b*d) - ((b*c - a*d)^4*(5*b^2*c^2 + 14*a*b*c*d + 21*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(512*b^(11/2)*d^(7/2))]
    @test_int [x^1*sqrt(a + b*x)*(c + d*x)^(5/2), x, 8, -(((b*c - a*d)^3*(3*b*c + 7*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(128*b^4*d^2)) - ((b*c - a*d)^2*(3*b*c + 7*a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(64*b^4*d) - ((b*c - a*d)*(3*b*c + 7*a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(48*b^3*d) - ((3*b*c + 7*a*d)*(a + b*x)^(3/2)*(c + d*x)^(5/2))/(40*b^2*d) + ((a + b*x)^(3/2)*(c + d*x)^(7/2))/(5*b*d) + ((b*c - a*d)^4*(3*b*c + 7*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(128*b^(9/2)*d^(5/2))]
    @test_int [x^0*sqrt(a + b*x)*(c + d*x)^(5/2), x, 7, (5*(b*c - a*d)^3*sqrt(a + b*x)*sqrt(c + d*x))/(64*b^3*d) + (5*(b*c - a*d)^2*(a + b*x)^(3/2)*sqrt(c + d*x))/(32*b^3) + (5*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(24*b^2) + ((a + b*x)^(3/2)*(c + d*x)^(5/2))/(4*b) - (5*(b*c - a*d)^4*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(7/2)*d^(3/2))]
    @test_int [sqrt(a + b*x)*(c + d*x)^(5/2)/x^1, x, 9, ((5*b*c - a*d)*(b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(8*b^2) + ((5*b*c + a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(12*b) + (1/3)*sqrt(a + b*x)*(c + d*x)^(5/2) - 2*sqrt(a)*c^(5/2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))) + ((5*b^3*c^3 + 15*a*b^2*c^2*d - 5*a^2*b*c*d^2 + a^3*d^3)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*b^(5/2)*sqrt(d))]
    @test_int [sqrt(a + b*x)*(c + d*x)^(5/2)/x^2, x, 9, (d*(11*b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*b) + (3/2)*d*sqrt(a + b*x)*(c + d*x)^(3/2) - (sqrt(a + b*x)*(c + d*x)^(5/2))/x - (c^(3/2)*(b*c + 5*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/sqrt(a) + (sqrt(d)*(15*b^2*c^2 + 10*a*b*c*d - a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(3/2))]
    @test_int [sqrt(a + b*x)*(c + d*x)^(5/2)/x^3, x, 9, (d*(b*c + 11*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*a) - ((b*c + 5*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(4*a*x) - (sqrt(a + b*x)*(c + d*x)^(5/2))/(2*x^2) + (sqrt(c)*(b^2*c^2 - 10*a*b*c*d - 15*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(3/2)) + (d^(3/2)*(5*b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/sqrt(b)]
    @test_int [sqrt(a + b*x)*(c + d*x)^(5/2)/x^4, x, 9, ((b*c - 5*a*d)*(b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(8*a^2*x) - ((b*c + 5*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(12*a*x^2) - (sqrt(a + b*x)*(c + d*x)^(5/2))/(3*x^3) - ((b^3*c^3 - 5*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 5*a^3*d^3)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*a^(5/2)*sqrt(c)) + 2*sqrt(b)*d^(5/2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x)))]
    @test_int [sqrt(a + b*x)*(c + d*x)^(5/2)/x^5, x, 6, -((5*(b*c - a*d)^3*sqrt(a + b*x)*sqrt(c + d*x))/(64*a^3*c*x)) + (5*(b*c - a*d)^2*sqrt(a + b*x)*(c + d*x)^(3/2))/(96*a^2*c*x^2) - ((b*c - a*d)*sqrt(a + b*x)*(c + d*x)^(5/2))/(24*a*c*x^3) - (sqrt(a + b*x)*(c + d*x)^(7/2))/(4*c*x^4) + (5*(b*c - a*d)^4*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(7/2)*c^(3/2))]
    @test_int [sqrt(a + b*x)*(c + d*x)^(5/2)/x^6, x, 7, ((b*c - a*d)^3*(7*b*c + 3*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(128*a^4*c^2*x) - ((b*c - a*d)^2*(7*b*c + 3*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(192*a^3*c^2*x^2) + ((b*c - a*d)*(7*b*c + 3*a*d)*sqrt(a + b*x)*(c + d*x)^(5/2))/(240*a^2*c^2*x^3) + ((7*b*c + 3*a*d)*sqrt(a + b*x)*(c + d*x)^(7/2))/(40*a*c^2*x^4) - ((a + b*x)^(3/2)*(c + d*x)^(7/2))/(5*a*c*x^5) - ((b*c - a*d)^4*(7*b*c + 3*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(128*a^(9/2)*c^(5/2))]
    @test_int [sqrt(a + b*x)*(c + d*x)^(5/2)/x^7, x, 9, ((3*b^2*c^2 - 6*a*b*c*d - 5*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(160*a^2*x^4) - ((21*b^3*c^3 - 61*a*b^2*c^2*d + 51*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(a + b*x)*sqrt(c + d*x))/(960*a^3*c*x^3) + ((105*b^4*c^4 - 308*a*b^3*c^3*d + 262*a^2*b^2*c^2*d^2 - 20*a^3*b*c*d^3 + 25*a^4*d^4)*sqrt(a + b*x)*sqrt(c + d*x))/(3840*a^4*c^2*x^2) - ((315*b^5*c^5 - 945*a*b^4*c^4*d + 838*a^2*b^3*c^3*d^2 - 90*a^3*b^2*c^2*d^3 - 65*a^4*b*c*d^4 + 75*a^5*d^5)*sqrt(a + b*x)*sqrt(c + d*x))/(7680*a^5*c^3*x) - ((b*c + 5*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(60*a*x^5) - (sqrt(a + b*x)*(c + d*x)^(5/2))/(6*x^6) + ((b*c - a*d)^4*(21*b^2*c^2 + 14*a*b*c*d + 5*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(512*a^(11/2)*c^(7/2))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [x^3*sqrt(a + b*x)/sqrt(c + d*x), x, 6, -(((35*b^3*c^3 + 15*a*b^2*c^2*d + 9*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(a + b*x)*sqrt(c + d*x))/(64*b^3*d^4)) + (x^2*(a + b*x)^(3/2)*sqrt(c + d*x))/(4*b*d) + ((a + b*x)^(3/2)*sqrt(c + d*x)*(35*b^2*c^2 + 22*a*b*c*d + 15*a^2*d^2 - 4*b*d*(7*b*c + 5*a*d)*x))/(96*b^3*d^3) + ((b*c - a*d)*(35*b^3*c^3 + 15*a*b^2*c^2*d + 9*a^2*b*c*d^2 + 5*a^3*d^3)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(7/2)*d^(9/2))]
    @test_int [x^2*sqrt(a + b*x)/sqrt(c + d*x), x, 6, ((5*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(8*b^2*d^3) - ((5*b*c + 3*a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(12*b^2*d^2) + (x*(a + b*x)^(3/2)*sqrt(c + d*x))/(3*b*d) - ((b*c - a*d)*(5*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*b^(5/2)*d^(7/2))]
    @test_int [x^1*sqrt(a + b*x)/sqrt(c + d*x), x, 5, -((3*b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*b*d^2) + ((a + b*x)^(3/2)*sqrt(c + d*x))/(2*b*d) + ((b*c - a*d)*(3*b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(3/2)*d^(5/2))]
    @test_int [x^0*sqrt(a + b*x)/sqrt(c + d*x), x, 4, (sqrt(a + b*x)*sqrt(c + d*x))/d - ((b*c - a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(sqrt(b)*d^(3/2))]
    @test_int [sqrt(a + b*x)/(x^1*sqrt(c + d*x)), x, 7, (-2*sqrt(a)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/sqrt(c) + (2*sqrt(b)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/sqrt(d)]
    @test_int [sqrt(a + b*x)/(x^2*sqrt(c + d*x)), x, 3, -((sqrt(a + b*x)*sqrt(c + d*x))/(c*x)) - ((b*c - a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(sqrt(a)*c^(3/2))]
    @test_int [sqrt(a + b*x)/(x^3*sqrt(c + d*x)), x, 4, ((b*c + 3*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*a*c^2*x) - ((a + b*x)^(3/2)*sqrt(c + d*x))/(2*a*c*x^2) + ((b*c - a*d)*(b*c + 3*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(3/2)*c^(5/2))]
    @test_int [sqrt(a + b*x)/(x^4*sqrt(c + d*x)), x, 6, -((sqrt(a + b*x)*sqrt(c + d*x))/(3*c*x^3)) - ((b*c - 5*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(12*a*c^2*x^2) + ((3*b*c - 5*a*d)*(b*c + 3*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(24*a^2*c^3*x) - ((b*c - a*d)*(b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*a^(5/2)*c^(7/2))]
    @test_int [sqrt(a + b*x)/(x^5*sqrt(c + d*x)), x, 7, -((sqrt(a + b*x)*sqrt(c + d*x))/(4*c*x^4)) - ((b*c - 7*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(24*a*c^2*x^3) + ((5*b^2*c^2 + 6*a*b*c*d - 35*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(96*a^2*c^3*x^2) - ((15*b^3*c^3 + 17*a*b^2*c^2*d + 25*a^2*b*c*d^2 - 105*a^3*d^3)*sqrt(a + b*x)*sqrt(c + d*x))/(192*a^3*c^4*x) + ((b*c - a*d)*(5*b^3*c^3 + 9*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 35*a^3*d^3)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(7/2)*c^(9/2))]

    @test_int [(x^2*sqrt(a + b*x))/(c + d*x)^(3/2), x, 6, (2*c^2*(a + b*x)^(3/2))/(d^2*(b*c - a*d)*sqrt(c + d*x)) + ((6*a*c - (15*b*c^2)/d + (a^2*d)/b)*sqrt(a + b*x)*sqrt(c + d*x))/(4*d^2*(b*c - a*d)) + ((a + b*x)^(3/2)*sqrt(c + d*x))/(2*b*d^2) + ((15*b^2*c^2 - 6*a*b*c*d - a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(3/2)*d^(7/2))]
    @test_int [(x*sqrt(a + b*x))/(c + d*x)^(3/2), x, 5, (-2*c*(a + b*x)^(3/2))/(d*(b*c - a*d)*sqrt(c + d*x)) + ((3*b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(d^2*(b*c - a*d)) - ((3*b*c - a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(sqrt(b)*d^(5/2))]
    @test_int [sqrt(a + b*x)/(c + d*x)^(3/2), x, 4, (-2*sqrt(a + b*x))/(d*sqrt(c + d*x)) + (2*sqrt(b)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/d^(3/2)]
    @test_int [sqrt(a + b*x)/(x*(c + d*x)^(3/2)), x, 3, (2*sqrt(a + b*x))/(c*sqrt(c + d*x)) - (2*sqrt(a)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/c^(3/2)]
    @test_int [sqrt(a + b*x)/(x^2*(c + d*x)^(3/2)), x, 4, ((b*c - 3*a*d)*sqrt(a + b*x))/(a*c^2*sqrt(c + d*x)) - (a + b*x)^(3/2)/(a*c*x*sqrt(c + d*x)) - ((b*c - 3*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(sqrt(a)*c^(5/2))]
    @test_int [sqrt(a + b*x)/(x^3*(c + d*x)^(3/2)), x, 6, -(d*(b*c - 15*a*d)*sqrt(a + b*x))/(4*a*c^3*sqrt(c + d*x)) - sqrt(a + b*x)/(2*c*x^2*sqrt(c + d*x)) - ((b*c - 5*a*d)*sqrt(a + b*x))/(4*a*c^2*x*sqrt(c + d*x)) + ((b^2*c^2 + 6*a*b*c*d - 15*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(3/2)*c^(7/2))]

    @test_int [(x^3*sqrt(a + b*x))/(c + d*x)^(5/2), x, 6, -((2*x^3*sqrt(a + b*x))/(3*d*(c + d*x)^(3/2))) - (2*(7*b*c - 6*a*d)*x^2*sqrt(a + b*x))/(3*d^2*(b*c - a*d)*sqrt(c + d*x)) - (sqrt(a + b*x)*sqrt(c + d*x)*(105*b^2*c^2 - 100*a*b*c*d + 3*a^2*d^2 - 2*b*d*(35*b*c - 31*a*d)*x))/(12*b*d^4*(b*c - a*d)) + ((35*b^2*c^2 - 10*a*b*c*d - a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(3/2)*d^(9/2))]
    @test_int [(x^2*sqrt(a + b*x))/(c + d*x)^(5/2), x, 6, (2*c^2*(a + b*x)^(3/2))/(3*d^2*(b*c - a*d)*(c + d*x)^(3/2)) - (4*c*(a + b*x)^(3/2))/(d^2*(b*c - a*d)*sqrt(c + d*x)) + ((5*b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(d^3*(b*c - a*d)) - ((5*b*c - a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(sqrt(b)*d^(7/2))]
    @test_int [(x*sqrt(a + b*x))/(c + d*x)^(5/2), x, 5, (-2*c*(a + b*x)^(3/2))/(3*d*(b*c - a*d)*(c + d*x)^(3/2)) - (2*sqrt(a + b*x))/(d^2*sqrt(c + d*x)) + (2*sqrt(b)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/d^(5/2)]
    @test_int [sqrt(a + b*x)/(c + d*x)^(5/2), x, 1, (2*(a + b*x)^(3/2))/(3*(b*c - a*d)*(c + d*x)^(3/2))]
    @test_int [sqrt(a + b*x)/(x*(c + d*x)^(5/2)), x, 4, -((2*d*(a + b*x)^(3/2))/(3*c*(b*c - a*d)*(c + d*x)^(3/2))) + (2*sqrt(a + b*x))/(c^2*sqrt(c + d*x)) - (2*sqrt(a)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/c^(5/2)]
    @test_int [sqrt(a + b*x)/(x^2*(c + d*x)^(5/2)), x, 6, (-5*d*sqrt(a + b*x))/(3*c^2*(c + d*x)^(3/2)) - sqrt(a + b*x)/(c*x*(c + d*x)^(3/2)) - (d*(13*b*c - 15*a*d)*sqrt(a + b*x))/(3*c^3*(b*c - a*d)*sqrt(c + d*x)) - ((b*c - 5*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(sqrt(a)*c^(7/2))]
    @test_int [sqrt(a + b*x)/(x^3*(c + d*x)^(5/2)), x, 7, -(d*(3*b*c - 35*a*d)*sqrt(a + b*x))/(12*a*c^3*(c + d*x)^(3/2)) - sqrt(a + b*x)/(2*c*x^2*(c + d*x)^(3/2)) - ((b*c - 7*a*d)*sqrt(a + b*x))/(4*a*c^2*x*(c + d*x)^(3/2)) - (d*(3*b^2*c^2 - 100*a*b*c*d + 105*a^2*d^2)*sqrt(a + b*x))/(12*a*c^4*(b*c - a*d)*sqrt(c + d*x)) + ((b^2*c^2 + 10*a*b*c*d - 35*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(3/2)*c^(9/2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x)^(n/2)*(a+b*x)^(3/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [x^2*(a + b*x)^(3/2)*sqrt(c + d*x), x, 8, -(((b*c - a*d)^2*(7*b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(128*b^3*d^4)) + ((b*c - a*d)*(7*b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*(a + b*x)^(3/2)*sqrt(c + d*x))/(192*b^3*d^3) + ((7*b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*(a + b*x)^(5/2)*sqrt(c + d*x))/(48*b^3*d^2) - ((7*b*c + 5*a*d)*(a + b*x)^(5/2)*(c + d*x)^(3/2))/(40*b^2*d^2) + (x*(a + b*x)^(5/2)*(c + d*x)^(3/2))/(5*b*d) + ((b*c - a*d)^3*(7*b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(128*b^(7/2)*d^(9/2))]
    @test_int [x^1*(a + b*x)^(3/2)*sqrt(c + d*x), x, 7, ((b*c - a*d)^2*(5*b*c + 3*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(64*b^2*d^3) - ((b*c - a*d)*(5*b*c + 3*a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(96*b^2*d^2) - ((5*b*c + 3*a*d)*(a + b*x)^(5/2)*sqrt(c + d*x))/(24*b^2*d) + ((a + b*x)^(5/2)*(c + d*x)^(3/2))/(4*b*d) - ((b*c - a*d)^3*(5*b*c + 3*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(5/2)*d^(7/2))]
    @test_int [x^0*(a + b*x)^(3/2)*sqrt(c + d*x), x, 6, -((b*c - a*d)^2*sqrt(a + b*x)*sqrt(c + d*x))/(8*b*d^2) + ((b*c - a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(12*b*d) + ((a + b*x)^(5/2)*sqrt(c + d*x))/(3*b) + ((b*c - a*d)^3*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*b^(3/2)*d^(5/2))]
    @test_int [((a + b*x)^(3/2)*sqrt(c + d*x))/x^1, x, 8, ((b*c + 3*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*d) + ((a + b*x)^(3/2)*sqrt(c + d*x))/2 - 2*a^(3/2)*sqrt(c)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))) - ((b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*sqrt(b)*d^(3/2))]
    @test_int [((a + b*x)^(3/2)*sqrt(c + d*x))/x^2, x, 8, 2*b*sqrt(a + b*x)*sqrt(c + d*x) - ((a + b*x)^(3/2)*sqrt(c + d*x))/x - (sqrt(a)*(3*b*c + a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/sqrt(c) + (sqrt(b)*(b*c + 3*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/sqrt(d)]
    @test_int [((a + b*x)^(3/2)*sqrt(c + d*x))/x^3, x, 8, -((3*b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*c*x) - ((a + b*x)^(3/2)*sqrt(c + d*x))/(2*x^2) - ((3*b^2*c^2 + 6*a*b*c*d - a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*sqrt(a)*c^(3/2)) + 2*b^(3/2)*sqrt(d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x)))]
    @test_int [((a + b*x)^(3/2)*sqrt(c + d*x))/x^4, x, 5, -((b*c - a*d)^2*sqrt(a + b*x)*sqrt(c + d*x))/(8*a*c^2*x) - ((b*c - a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(4*c^2*x^2) - ((a + b*x)^(3/2)*(c + d*x)^(3/2))/(3*c*x^3) + ((b*c - a*d)^3*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*a^(3/2)*c^(5/2))]
    @test_int [((a + b*x)^(3/2)*sqrt(c + d*x))/x^5, x, 6, ((b*c - a*d)^2*(3*b*c + 5*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(64*a^2*c^3*x) + ((b*c - a*d)*(3*b*c + 5*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(32*a*c^3*x^2) + ((3*b*c + 5*a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(24*a*c^2*x^3) - ((a + b*x)^(5/2)*(c + d*x)^(3/2))/(4*a*c*x^4) - ((b*c - a*d)^3*(3*b*c + 5*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(5/2)*c^(7/2))]
    @test_int [((a + b*x)^(3/2)*sqrt(c + d*x))/x^6, x, 8, -(((3*b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(40*c*x^4)) - (((3*b^2*c)/a + 12*b*d - (7*a*d^2)/c)*sqrt(a + b*x)*sqrt(c + d*x))/(240*c*x^3) + ((15*b^3*c^3 - 9*a*b^2*c^2*d + 61*a^2*b*c*d^2 - 35*a^3*d^3)*sqrt(a + b*x)*sqrt(c + d*x))/(960*a^2*c^3*x^2) - ((45*b^4*c^4 - 30*a*b^3*c^3*d - 36*a^2*b^2*c^2*d^2 + 190*a^3*b*c*d^3 - 105*a^4*d^4)*sqrt(a + b*x)*sqrt(c + d*x))/(1920*a^3*c^4*x) - ((a + b*x)^(3/2)*sqrt(c + d*x))/(5*x^5) + ((b*c - a*d)^3*(3*b^2*c^2 + 6*a*b*c*d + 7*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(128*a^(7/2)*c^(9/2))]

    @test_int [x^2*(a + b*x)^(3/2)*(c + d*x)^(3/2), x, 9, ((b*c - a*d)^3*(4*a*b*c*d - 7*(b*c + a*d)^2)*sqrt(a + b*x)*sqrt(c + d*x))/(512*b^4*d^4) - ((b*c - a*d)^2*(4*a*b*c*d - 7*(b*c + a*d)^2)*(a + b*x)^(3/2)*sqrt(c + d*x))/(768*b^4*d^3) - ((b*c - a*d)*(4*a*b*c*d - 7*(b*c + a*d)^2)*(a + b*x)^(5/2)*sqrt(c + d*x))/(192*b^4*d^2) - ((4*a*b*c*d - 7*(b*c + a*d)^2)*(a + b*x)^(5/2)*(c + d*x)^(3/2))/(96*b^3*d^2) - (7*(b*c + a*d)*(a + b*x)^(5/2)*(c + d*x)^(5/2))/(60*b^2*d^2) + (x*(a + b*x)^(5/2)*(c + d*x)^(5/2))/(6*b*d) - ((b*c - a*d)^4*(4*a*b*c*d - 7*(b*c + a*d)^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(512*b^(9/2)*d^(9/2))]
    @test_int [x*(a + b*x)^(3/2)*(c + d*x)^(3/2), x, 8, (3*(b*c - a*d)^3*(b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(128*b^3*d^3) - ((b*c - a*d)^2*(b*c + a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(64*b^3*d^2) - ((b*c - a*d)*(b*c + a*d)*(a + b*x)^(5/2)*sqrt(c + d*x))/(16*b^3*d) - ((b*c + a*d)*(a + b*x)^(5/2)*(c + d*x)^(3/2))/(8*b^2*d) + ((a + b*x)^(5/2)*(c + d*x)^(5/2))/(5*b*d) - (3*(b*c - a*d)^4*(b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(128*b^(7/2)*d^(7/2))]
    @test_int [(a + b*x)^(3/2)*(c + d*x)^(3/2), x, 7, (-3*(b*c - a*d)^3*sqrt(a + b*x)*sqrt(c + d*x))/(64*b^2*d^2) + ((b*c - a*d)^2*(a + b*x)^(3/2)*sqrt(c + d*x))/(32*b^2*d) + ((b*c - a*d)*(a + b*x)^(5/2)*sqrt(c + d*x))/(8*b^2) + ((a + b*x)^(5/2)*(c + d*x)^(3/2))/(4*b) + (3*(b*c - a*d)^4*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(5/2)*d^(5/2))]
    @test_int [((a + b*x)^(3/2)*(c + d*x)^(3/2))/x, x, 9, (1/8)*(8*a*c - (b*c^2)/d + (a^2*d)/b)*sqrt(a + b*x)*sqrt(c + d*x) + ((b*c + a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(4*d) + (1/3)*(a + b*x)^(3/2)*(c + d*x)^(3/2) - 2*a^(3/2)*c^(3/2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))) - ((b*c + a*d)*(b^2*c^2 - 10*a*b*c*d + a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*b^(3/2)*d^(3/2))]
    @test_int [((a + b*x)^(3/2)*(c + d*x)^(3/2))/x^2, x, 9, (3*(b*c + 3*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/4 + (3*b*sqrt(a + b*x)*(c + d*x)^(3/2))/2 - ((a + b*x)^(3/2)*(c + d*x)^(3/2))/x - 3*sqrt(a)*sqrt(c)*(b*c + a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))) + (3*(b^2*c^2 + 6*a*b*c*d + a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*sqrt(b)*sqrt(d))]
    @test_int [((a + b*x)^(3/2)*(c + d*x)^(3/2))/x^3, x, 9, (3*d*(3*b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*c) - (3*(b*c + a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(4*c*x) - ((a + b*x)^(3/2)*(c + d*x)^(3/2))/(2*x^2) - (3*(b^2*c^2 + 6*a*b*c*d + a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*sqrt(a)*sqrt(c)) + 3*sqrt(b)*sqrt(d)*(b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x)))]
    @test_int [((a + b*x)^(3/2)*(c + d*x)^(3/2))/x^4, x, 9, -((((b^2*c)/a + 8*b*d - (a*d^2)/c)*sqrt(a + b*x)*sqrt(c + d*x))/(8*x)) - ((b*c + a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(4*c*x^2) - ((a + b*x)^(3/2)*(c + d*x)^(3/2))/(3*x^3) + ((b*c + a*d)*(b^2*c^2 - 10*a*b*c*d + a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*a^(3/2)*c^(3/2)) + 2*b^(3/2)*d^(3/2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x)))]
    @test_int [((a + b*x)^(3/2)*(c + d*x)^(3/2))/x^5, x, 6, (3*(b*c - a*d)^3*sqrt(a + b*x)*sqrt(c + d*x))/(64*a^2*c^2*x) - ((b*c - a*d)^2*sqrt(a + b*x)*(c + d*x)^(3/2))/(32*a*c^2*x^2) - ((b*c - a*d)*sqrt(a + b*x)*(c + d*x)^(5/2))/(8*c^2*x^3) - ((a + b*x)^(3/2)*(c + d*x)^(5/2))/(4*c*x^4) - (3*(b*c - a*d)^4*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(5/2)*c^(5/2))]
    @test_int [((a + b*x)^(3/2)*(c + d*x)^(3/2))/x^6, x, 7, -((3*(b*c - a*d)^3*(b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(128*a^3*c^3*x)) + ((b*c - a*d)^2*(b*c + a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(64*a^2*c^3*x^2) + ((b*c - a*d)*(b*c + a*d)*sqrt(a + b*x)*(c + d*x)^(5/2))/(16*a*c^3*x^3) + ((b*c + a*d)*(a + b*x)^(3/2)*(c + d*x)^(5/2))/(8*a*c^2*x^4) - ((a + b*x)^(5/2)*(c + d*x)^(5/2))/(5*a*c*x^5) + (3*(b*c - a*d)^4*(b*c + a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(128*a^(7/2)*c^(7/2))]

    @test_int [x^2*(a + b*x)^(3/2)*(c + d*x)^(5/2), x, 10, -(((b*c - a*d)^4*(5*b^2*c^2 + 10*a*b*c*d + 9*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(1024*b^5*d^4)) + ((b*c - a*d)^3*(5*b^2*c^2 + 10*a*b*c*d + 9*a^2*d^2)*(a + b*x)^(3/2)*sqrt(c + d*x))/(1536*b^5*d^3) + ((b*c - a*d)^2*(5*b^2*c^2 + 10*a*b*c*d + 9*a^2*d^2)*(a + b*x)^(5/2)*sqrt(c + d*x))/(384*b^5*d^2) + ((b*c - a*d)*(5*b^2*c^2 + 10*a*b*c*d + 9*a^2*d^2)*(a + b*x)^(5/2)*(c + d*x)^(3/2))/(192*b^4*d^2) + ((5*b^2*c^2 + 10*a*b*c*d + 9*a^2*d^2)*(a + b*x)^(5/2)*(c + d*x)^(5/2))/(120*b^3*d^2) - ((7*b*c + 9*a*d)*(a + b*x)^(5/2)*(c + d*x)^(7/2))/(84*b^2*d^2) + (x*(a + b*x)^(5/2)*(c + d*x)^(7/2))/(7*b*d) + ((b*c - a*d)^5*(5*b^2*c^2 + 10*a*b*c*d + 9*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(1024*b^(11/2)*d^(9/2))]
    @test_int [x*(a + b*x)^(3/2)*(c + d*x)^(5/2), x, 9, ((b*c - a*d)^4*(5*b*c + 7*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(512*b^4*d^3) - ((b*c - a*d)^3*(5*b*c + 7*a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(768*b^4*d^2) - ((b*c - a*d)^2*(5*b*c + 7*a*d)*(a + b*x)^(5/2)*sqrt(c + d*x))/(192*b^4*d) - ((b*c - a*d)*(5*b*c + 7*a*d)*(a + b*x)^(5/2)*(c + d*x)^(3/2))/(96*b^3*d) - ((5*b*c + 7*a*d)*(a + b*x)^(5/2)*(c + d*x)^(5/2))/(60*b^2*d) + ((a + b*x)^(5/2)*(c + d*x)^(7/2))/(6*b*d) - ((b*c - a*d)^5*(5*b*c + 7*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(512*b^(9/2)*d^(7/2))]
    @test_int [(a + b*x)^(3/2)*(c + d*x)^(5/2), x, 8, (-3*(b*c - a*d)^4*sqrt(a + b*x)*sqrt(c + d*x))/(128*b^3*d^2) + ((b*c - a*d)^3*(a + b*x)^(3/2)*sqrt(c + d*x))/(64*b^3*d) + ((b*c - a*d)^2*(a + b*x)^(5/2)*sqrt(c + d*x))/(16*b^3) + ((b*c - a*d)*(a + b*x)^(5/2)*(c + d*x)^(3/2))/(8*b^2) + ((a + b*x)^(5/2)*(c + d*x)^(5/2))/(5*b) + (3*(b*c - a*d)^5*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(128*b^(7/2)*d^(5/2))]
    @test_int [((a + b*x)^(3/2)*(c + d*x)^(5/2))/x, x, 10, -(((5*b^3*c^3 - 55*a*b^2*c^2*d - 17*a^2*b*c*d^2 + 3*a^3*d^3)*sqrt(a + b*x)*sqrt(c + d*x))/(64*b^2*d)) + (1/96)*(50*a*c - (5*b*c^2)/d + (3*a^2*d)/b)*sqrt(a + b*x)*(c + d*x)^(3/2) + ((5*b*c + 3*a*d)*sqrt(a + b*x)*(c + d*x)^(5/2))/(24*d) + (1/4)*(a + b*x)^(3/2)*(c + d*x)^(5/2) - 2*a^(3/2)*c^(5/2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))) - ((5*b^4*c^4 - 60*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 3*a^4*d^4)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(5/2)*d^(3/2))]
    @test_int [((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^2, x, 10, ((5*b^2*c^2 + 26*a*b*c*d + a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(8*b) + ((5*b*c + 19*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/12 + (4*b*sqrt(a + b*x)*(c + d*x)^(5/2))/3 - ((a + b*x)^(3/2)*(c + d*x)^(5/2))/x - sqrt(a)*c^(3/2)*(3*b*c + 5*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))) + ((5*b^3*c^3 + 45*a*b^2*c^2*d + 15*a^2*b*c*d^2 - a^3*d^3)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*b^(3/2)*sqrt(d))]
    @test_int [((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^3, x, 10, 3*d*(b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x) + (d*(7*b*c + 5*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(4*c) - ((3*b*c + 5*a*d)*sqrt(a + b*x)*(c + d*x)^(5/2))/(4*c*x) - ((a + b*x)^(3/2)*(c + d*x)^(5/2))/(2*x^2) - (3*sqrt(c)*(b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*sqrt(a)) + (3*sqrt(d)*(5*b^2*c^2 + 10*a*b*c*d + a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*sqrt(b))]
    @test_int [((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^4, x, 10, (d*(b^2*c^2 + 26*a*b*c*d + 5*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(8*a*c) - (((3*b^2*c)/a + 40*b*d + (5*a*d^2)/c)*sqrt(a + b*x)*(c + d*x)^(3/2))/(24*x) - ((3*b*c + 5*a*d)*sqrt(a + b*x)*(c + d*x)^(5/2))/(12*c*x^2) - ((a + b*x)^(3/2)*(c + d*x)^(5/2))/(3*x^3) + ((b^3*c^3 - 15*a*b^2*c^2*d - 45*a^2*b*c*d^2 - 5*a^3*d^3)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*a^(3/2)*sqrt(c)) + sqrt(b)*d^(3/2)*(5*b*c + 3*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x)))]
    @test_int [((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^5, x, 10, ((3*b^3*c^3 - 17*a*b^2*c^2*d - 55*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(a + b*x)*sqrt(c + d*x))/(64*a^2*c*x) - (((3*b^2*c)/a + 50*b*d - (5*a*d^2)/c)*sqrt(a + b*x)*(c + d*x)^(3/2))/(96*x^2) - ((3*b*c + 5*a*d)*sqrt(a + b*x)*(c + d*x)^(5/2))/(24*c*x^3) - ((a + b*x)^(3/2)*(c + d*x)^(5/2))/(4*x^4) - ((3*b^4*c^4 - 20*a*b^3*c^3*d + 90*a^2*b^2*c^2*d^2 + 60*a^3*b*c*d^3 - 5*a^4*d^4)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(5/2)*c^(3/2)) + 2*b^(3/2)*d^(5/2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x)))]
    @test_int [((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^6, x, 7, (-3*(b*c - a*d)^4*sqrt(a + b*x)*sqrt(c + d*x))/(128*a^3*c^2*x) + ((b*c - a*d)^3*sqrt(a + b*x)*(c + d*x)^(3/2))/(64*a^2*c^2*x^2) - ((b*c - a*d)^2*sqrt(a + b*x)*(c + d*x)^(5/2))/(80*a*c^2*x^3) - (3*(b*c - a*d)*sqrt(a + b*x)*(c + d*x)^(7/2))/(40*c^2*x^4) - ((a + b*x)^(3/2)*(c + d*x)^(7/2))/(5*c*x^5) + (3*(b*c - a*d)^5*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(128*a^(7/2)*c^(5/2))]
    @test_int [((a + b*x)^(3/2)*(c + d*x)^(5/2))/x^7, x, 8, ((b*c - a*d)^4*(7*b*c + 5*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(512*a^4*c^3*x) - ((b*c - a*d)^3*(7*b*c + 5*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(768*a^3*c^3*x^2) + ((b*c - a*d)^2*(7*b*c + 5*a*d)*sqrt(a + b*x)*(c + d*x)^(5/2))/(960*a^2*c^3*x^3) + ((b*c - a*d)*(7*b*c + 5*a*d)*sqrt(a + b*x)*(c + d*x)^(7/2))/(160*a*c^3*x^4) + ((7*b*c + 5*a*d)*(a + b*x)^(3/2)*(c + d*x)^(7/2))/(60*a*c^2*x^5) - ((a + b*x)^(5/2)*(c + d*x)^(7/2))/(6*a*c*x^6) - ((b*c - a*d)^5*(7*b*c + 5*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(512*a^(9/2)*c^(7/2))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(x^2*(a + b*x)^(3/2))/sqrt(c + d*x), x, 7, -(((b*c - a*d)*(35*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(64*b^2*d^4)) + ((35*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*(a + b*x)^(3/2)*sqrt(c + d*x))/(96*b^2*d^3) - ((7*b*c + 3*a*d)*(a + b*x)^(5/2)*sqrt(c + d*x))/(24*b^2*d^2) + (x*(a + b*x)^(5/2)*sqrt(c + d*x))/(4*b*d) + ((b*c - a*d)^2*(35*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(5/2)*d^(9/2))]
    @test_int [(x*(a + b*x)^(3/2))/sqrt(c + d*x), x, 6, ((b*c - a*d)*(5*b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(8*b*d^3) - ((5*b*c + a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(12*b*d^2) + ((a + b*x)^(5/2)*sqrt(c + d*x))/(3*b*d) - ((b*c - a*d)^2*(5*b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*b^(3/2)*d^(7/2))]
    @test_int [(a + b*x)^(3/2)/sqrt(c + d*x), x, 5, (-3*(b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*d^2) + ((a + b*x)^(3/2)*sqrt(c + d*x))/(2*d) + (3*(b*c - a*d)^2*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*sqrt(b)*d^(5/2))]
    @test_int [(a + b*x)^(3/2)/(x*sqrt(c + d*x)), x, 7, (b*sqrt(a + b*x)*sqrt(c + d*x))/d - (2*a^(3/2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/sqrt(c) - (sqrt(b)*(b*c - 3*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/d^(3/2)]
    @test_int [(a + b*x)^(3/2)/(x^2*sqrt(c + d*x)), x, 7, -((a*sqrt(a + b*x)*sqrt(c + d*x))/(c*x)) - (sqrt(a)*(3*b*c - a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/c^(3/2) + (2*b^(3/2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/sqrt(d)]
    @test_int [(a + b*x)^(3/2)/(x^3*sqrt(c + d*x)), x, 4, (-3*(b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*c^2*x) - ((a + b*x)^(3/2)*sqrt(c + d*x))/(2*c*x^2) - (3*(b*c - a*d)^2*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*sqrt(a)*c^(5/2))]
    @test_int [(a + b*x)^(3/2)/(x^4*sqrt(c + d*x)), x, 5, ((b*c - a*d)*(b*c + 5*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(8*a*c^3*x) + ((b*c + 5*a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(12*a*c^2*x^2) - ((a + b*x)^(5/2)*sqrt(c + d*x))/(3*a*c*x^3) + ((b*c - a*d)^2*(b*c + 5*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*a^(3/2)*c^(7/2))]
    @test_int [(a + b*x)^(3/2)/(x^5*sqrt(c + d*x)), x, 7, -((a*sqrt(a + b*x)*sqrt(c + d*x))/(4*c*x^4)) - ((9*b*c - 7*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(24*c^2*x^3) - ((3*b^2*c^2 - 46*a*b*c*d + 35*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(96*a*c^3*x^2) + ((9*b^3*c^3 + 15*a*b^2*c^2*d - 145*a^2*b*c*d^2 + 105*a^3*d^3)*sqrt(a + b*x)*sqrt(c + d*x))/(192*a^2*c^4*x) - ((b*c - a*d)^2*(3*b^2*c^2 + 10*a*b*c*d + 35*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(5/2)*c^(9/2))]

    @test_int [(x^2*(a + b*x)^(3/2))/(c + d*x)^(3/2), x, 7, (2*c^2*(a + b*x)^(5/2))/(d^2*(b*c - a*d)*sqrt(c + d*x)) + ((35*b^2*c^2 - 10*a*b*c*d - a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(8*b*d^4) + ((10*a*c - (35*b*c^2)/d + (a^2*d)/b)*(a + b*x)^(3/2)*sqrt(c + d*x))/(12*d^2*(b*c - a*d)) + ((a + b*x)^(5/2)*sqrt(c + d*x))/(3*b*d^2) - ((b*c - a*d)*(35*b^2*c^2 - 10*a*b*c*d - a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*b^(3/2)*d^(9/2))]
    @test_int [(x*(a + b*x)^(3/2))/(c + d*x)^(3/2), x, 6, (-2*c*(a + b*x)^(5/2))/(d*(b*c - a*d)*sqrt(c + d*x)) - (3*(5*b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*d^3) + ((5*b*c - a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(2*d^2*(b*c - a*d)) + (3*(b*c - a*d)*(5*b*c - a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*sqrt(b)*d^(7/2))]
    @test_int [(a + b*x)^(3/2)/(c + d*x)^(3/2), x, 5, (-2*(a + b*x)^(3/2))/(d*sqrt(c + d*x)) + (3*b*sqrt(a + b*x)*sqrt(c + d*x))/d^2 - (3*sqrt(b)*(b*c - a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/d^(5/2)]
    @test_int [(a + b*x)^(3/2)/(x*(c + d*x)^(3/2)), x, 7, -((2*(b*c - a*d)*sqrt(a + b*x))/(c*d*sqrt(c + d*x))) - (2*a^(3/2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/c^(3/2) + (2*b^(3/2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/d^(3/2)]
    @test_int [(a + b*x)^(3/2)/(x^2*(c + d*x)^(3/2)), x, 4, (3*(b*c - a*d)*sqrt(a + b*x))/(c^2*sqrt(c + d*x)) - (a + b*x)^(3/2)/(c*x*sqrt(c + d*x)) - (3*sqrt(a)*(b*c - a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/c^(5/2)]
    @test_int [(a + b*x)^(3/2)/(x^3*(c + d*x)^(3/2)), x, 5, (3*(b*c - 5*a*d)*(b*c - a*d)*sqrt(a + b*x))/(4*a*c^3*sqrt(c + d*x)) - ((b*c - 5*a*d)*(a + b*x)^(3/2))/(4*a*c^2*x*sqrt(c + d*x)) - (a + b*x)^(5/2)/(2*a*c*x^2*sqrt(c + d*x)) - (3*(b*c - 5*a*d)*(b*c - a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*sqrt(a)*c^(7/2))]
    @test_int [(a + b*x)^(3/2)/(x^4*(c + d*x)^(3/2)), x, 7, -((d*(3*b^2*c^2 - 100*a*b*c*d + 105*a^2*d^2)*sqrt(a + b*x))/(24*a*c^4*sqrt(c + d*x))) - (a*sqrt(a + b*x))/(3*c*x^3*sqrt(c + d*x)) - (7*(b*c - a*d)*sqrt(a + b*x))/(12*c^2*x^2*sqrt(c + d*x)) - ((3*b*c - 35*a*d)*(b*c - a*d)*sqrt(a + b*x))/(24*a*c^3*x*sqrt(c + d*x)) + ((b*c - a*d)*(b^2*c^2 + 10*a*b*c*d - 35*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*a^(3/2)*c^(9/2))]

    @test_int [(x^2*(a + b*x)^(3/2))/(c + d*x)^(5/2), x, 7, (2*c^2*(a + b*x)^(5/2))/(3*d^2*(b*c - a*d)*(c + d*x)^(3/2)) - (4*c*(4*b*c - 3*a*d)*(a + b*x)^(5/2))/(3*d^2*(b*c - a*d)^2*sqrt(c + d*x)) - ((35*b^2*c^2 - 30*a*b*c*d + 3*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(4*d^4*(b*c - a*d)) + ((35*b^2*c^2 - 30*a*b*c*d + 3*a^2*d^2)*(a + b*x)^(3/2)*sqrt(c + d*x))/(6*d^3*(b*c - a*d)^2) + ((35*b^2*c^2 - 30*a*b*c*d + 3*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*sqrt(b)*d^(9/2))]
    @test_int [(x*(a + b*x)^(3/2))/(c + d*x)^(5/2), x, 6, (-2*c*(a + b*x)^(5/2))/(3*d*(b*c - a*d)*(c + d*x)^(3/2)) - (2*(5*b*c - 3*a*d)*(a + b*x)^(3/2))/(3*d^2*(b*c - a*d)*sqrt(c + d*x)) + (b*(5*b*c - 3*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(d^3*(b*c - a*d)) - (sqrt(b)*(5*b*c - 3*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/d^(7/2)]
    @test_int [(a + b*x)^(3/2)/(c + d*x)^(5/2), x, 5, (-2*(a + b*x)^(3/2))/(3*d*(c + d*x)^(3/2)) - (2*b*sqrt(a + b*x))/(d^2*sqrt(c + d*x)) + (2*b^(3/2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/d^(5/2)]
    @test_int [(a + b*x)^(3/2)/(x*(c + d*x)^(5/2)), x, 4, (2*(a + b*x)^(3/2))/(3*c*(c + d*x)^(3/2)) + (2*a*sqrt(a + b*x))/(c^2*sqrt(c + d*x)) - (2*a^(3/2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/c^(5/2)]
    @test_int [(a + b*x)^(3/2)/(x^2*(c + d*x)^(5/2)), x, 5, ((3*b*c - 5*a*d)*(a + b*x)^(3/2))/(3*a*c^2*(c + d*x)^(3/2)) - (a + b*x)^(5/2)/(a*c*x*(c + d*x)^(3/2)) + ((3*b*c - 5*a*d)*sqrt(a + b*x))/(c^3*sqrt(c + d*x)) - (sqrt(a)*(3*b*c - 5*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/c^(7/2)]
    @test_int [(a + b*x)^(3/2)/(x^3*(c + d*x)^(5/2)), x, 7, -((d*(23*b*c - 35*a*d)*sqrt(a + b*x))/(12*c^3*(c + d*x)^(3/2))) - (a*sqrt(a + b*x))/(2*c*x^2*(c + d*x)^(3/2)) - ((5*b*c - 7*a*d)*sqrt(a + b*x))/(4*c^2*x*(c + d*x)^(3/2)) - (5*d*(11*b*c - 21*a*d)*sqrt(a + b*x))/(12*c^4*sqrt(c + d*x)) - ((3*b^2*c^2 - 30*a*b*c*d + 35*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*sqrt(a)*c^(9/2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x)^(n/2)*(a+b*x)^(5/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [x^2*(a + b*x)^(5/2)*sqrt(c + d*x), x, 9, ((b*c - a*d)^3*(21*b^2*c^2 + 14*a*b*c*d + 5*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(512*b^3*d^5) - ((b*c - a*d)^2*(21*b^2*c^2 + 14*a*b*c*d + 5*a^2*d^2)*(a + b*x)^(3/2)*sqrt(c + d*x))/(768*b^3*d^4) + ((b*c - a*d)*(21*b^2*c^2 + 14*a*b*c*d + 5*a^2*d^2)*(a + b*x)^(5/2)*sqrt(c + d*x))/(960*b^3*d^3) + ((21*b^2*c^2 + 14*a*b*c*d + 5*a^2*d^2)*(a + b*x)^(7/2)*sqrt(c + d*x))/(160*b^3*d^2) - ((9*b*c + 5*a*d)*(a + b*x)^(7/2)*(c + d*x)^(3/2))/(60*b^2*d^2) + (x*(a + b*x)^(7/2)*(c + d*x)^(3/2))/(6*b*d) - ((b*c - a*d)^4*(21*b^2*c^2 + 14*a*b*c*d + 5*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(512*b^(7/2)*d^(11/2))]
    @test_int [x*(a + b*x)^(5/2)*sqrt(c + d*x), x, 8, -((b*c - a*d)^3*(7*b*c + 3*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(128*b^2*d^4) + ((b*c - a*d)^2*(7*b*c + 3*a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(192*b^2*d^3) - ((b*c - a*d)*(7*b*c + 3*a*d)*(a + b*x)^(5/2)*sqrt(c + d*x))/(240*b^2*d^2) - ((7*b*c + 3*a*d)*(a + b*x)^(7/2)*sqrt(c + d*x))/(40*b^2*d) + ((a + b*x)^(7/2)*(c + d*x)^(3/2))/(5*b*d) + ((b*c - a*d)^4*(7*b*c + 3*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(128*b^(5/2)*d^(9/2))]
    @test_int [(a + b*x)^(5/2)*sqrt(c + d*x), x, 7, (5*(b*c - a*d)^3*sqrt(a + b*x)*sqrt(c + d*x))/(64*b*d^3) - (5*(b*c - a*d)^2*(a + b*x)^(3/2)*sqrt(c + d*x))/(96*b*d^2) + ((b*c - a*d)*(a + b*x)^(5/2)*sqrt(c + d*x))/(24*b*d) + ((a + b*x)^(7/2)*sqrt(c + d*x))/(4*b) - (5*(b*c - a*d)^4*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(3/2)*d^(7/2))]
    @test_int [((a + b*x)^(5/2)*sqrt(c + d*x))/x, x, 9, -(((b*c - 5*a*d)*(b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(8*d^2)) + ((b*c + 5*a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(12*d) + (1/3)*(a + b*x)^(5/2)*sqrt(c + d*x) - 2*a^(5/2)*sqrt(c)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))) + ((b^3*c^3 - 5*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 5*a^3*d^3)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*sqrt(b)*d^(5/2))]
    @test_int [((a + b*x)^(5/2)*sqrt(c + d*x))/x^2, x, 9, (b*(b*c + 11*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*d) + (3*b*(a + b*x)^(3/2)*sqrt(c + d*x))/2 - ((a + b*x)^(5/2)*sqrt(c + d*x))/x - (a^(3/2)*(5*b*c + a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/sqrt(c) - (sqrt(b)*(b^2*c^2 - 10*a*b*c*d - 15*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*d^(3/2))]
    @test_int [((a + b*x)^(5/2)*sqrt(c + d*x))/x^3, x, 9, (b*(11*b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*c) - ((5*b*c + a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(4*c*x) - ((a + b*x)^(5/2)*sqrt(c + d*x))/(2*x^2) - (sqrt(a)*(15*b^2*c^2 + 10*a*b*c*d - a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*c^(3/2)) + (b^(3/2)*(b*c + 5*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/sqrt(d)]
    @test_int [((a + b*x)^(5/2)*sqrt(c + d*x))/x^4, x, 9, -(((5*b*c - a*d)*(b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(8*c^2*x)) - ((5*b*c + a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(12*c*x^2) - ((a + b*x)^(5/2)*sqrt(c + d*x))/(3*x^3) - ((5*b^3*c^3 + 15*a*b^2*c^2*d - 5*a^2*b*c*d^2 + a^3*d^3)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*sqrt(a)*c^(5/2)) + 2*b^(5/2)*sqrt(d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x)))]
    @test_int [((a + b*x)^(5/2)*sqrt(c + d*x))/x^5, x, 6, (-5*(b*c - a*d)^3*sqrt(a + b*x)*sqrt(c + d*x))/(64*a*c^3*x) - (5*(b*c - a*d)^2*sqrt(a + b*x)*(c + d*x)^(3/2))/(32*c^3*x^2) - (5*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(24*c^2*x^3) - ((a + b*x)^(5/2)*(c + d*x)^(3/2))/(4*c*x^4) + (5*(b*c - a*d)^4*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(3/2)*c^(7/2))]
    @test_int [((a + b*x)^(5/2)*sqrt(c + d*x))/x^6, x, 7, ((b*c - a*d)^3*(3*b*c + 7*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(128*a^2*c^4*x) + ((b*c - a*d)^2*(3*b*c + 7*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(64*a*c^4*x^2) + ((b*c - a*d)*(3*b*c + 7*a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(48*a*c^3*x^3) + ((3*b*c + 7*a*d)*(a + b*x)^(5/2)*(c + d*x)^(3/2))/(40*a*c^2*x^4) - ((a + b*x)^(7/2)*(c + d*x)^(3/2))/(5*a*c*x^5) - ((b*c - a*d)^4*(3*b*c + 7*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(128*a^(5/2)*c^(9/2))]

    @test_int [x^2*(a + b*x)^(5/2)*(c + d*x)^(3/2), x, 10, ((b*c - a*d)^4*(9*b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(1024*b^4*d^5) - ((b*c - a*d)^3*(9*b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*(a + b*x)^(3/2)*sqrt(c + d*x))/(1536*b^4*d^4) + ((b*c - a*d)^2*(9*b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*(a + b*x)^(5/2)*sqrt(c + d*x))/(1920*b^4*d^3) + ((b*c - a*d)*(9*b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*(a + b*x)^(7/2)*sqrt(c + d*x))/(320*b^4*d^2) + ((9*b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*(a + b*x)^(7/2)*(c + d*x)^(3/2))/(120*b^3*d^2) - ((9*b*c + 7*a*d)*(a + b*x)^(7/2)*(c + d*x)^(5/2))/(84*b^2*d^2) + (x*(a + b*x)^(7/2)*(c + d*x)^(5/2))/(7*b*d) - ((b*c - a*d)^5*(9*b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(1024*b^(9/2)*d^(11/2))]
    @test_int [x*(a + b*x)^(5/2)*(c + d*x)^(3/2), x, 9, -((b*c - a*d)^4*(7*b*c + 5*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(512*b^3*d^4) + ((b*c - a*d)^3*(7*b*c + 5*a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(768*b^3*d^3) - ((b*c - a*d)^2*(7*b*c + 5*a*d)*(a + b*x)^(5/2)*sqrt(c + d*x))/(960*b^3*d^2) - ((b*c - a*d)*(7*b*c + 5*a*d)*(a + b*x)^(7/2)*sqrt(c + d*x))/(160*b^3*d) - ((7*b*c + 5*a*d)*(a + b*x)^(7/2)*(c + d*x)^(3/2))/(60*b^2*d) + ((a + b*x)^(7/2)*(c + d*x)^(5/2))/(6*b*d) + ((b*c - a*d)^5*(7*b*c + 5*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(512*b^(7/2)*d^(9/2))]
    @test_int [(a + b*x)^(5/2)*(c + d*x)^(3/2), x, 8, (3*(b*c - a*d)^4*sqrt(a + b*x)*sqrt(c + d*x))/(128*b^2*d^3) - ((b*c - a*d)^3*(a + b*x)^(3/2)*sqrt(c + d*x))/(64*b^2*d^2) + ((b*c - a*d)^2*(a + b*x)^(5/2)*sqrt(c + d*x))/(80*b^2*d) + (3*(b*c - a*d)*(a + b*x)^(7/2)*sqrt(c + d*x))/(40*b^2) + ((a + b*x)^(7/2)*(c + d*x)^(3/2))/(5*b) - (3*(b*c - a*d)^5*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(128*b^(5/2)*d^(7/2))]
    @test_int [((a + b*x)^(5/2)*(c + d*x)^(3/2))/x, x, 10, ((64*a^2*b*c*d^2 + (b*c - 5*a*d)*(b*c - a*d)*(3*b*c + a*d))*sqrt(a + b*x)*sqrt(c + d*x))/(64*b*d^2) - ((b*c - 5*a*d)*(3*b*c + a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(32*d^2) + ((3*b*c + 5*a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(24*d) + (1/4)*(a + b*x)^(5/2)*(c + d*x)^(3/2) - 2*a^(5/2)*c^(3/2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))) + ((3*b^4*c^4 - 20*a*b^3*c^3*d + 90*a^2*b^2*c^2*d^2 + 60*a^3*b*c*d^3 - 5*a^4*d^4)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(3/2)*d^(5/2))]
    @test_int [((a + b*x)^(5/2)*(c + d*x)^(3/2))/x^2, x, 10, -((b^2*c^2 - 14*a*b*c*d - 19*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(8*d) + (b*(b*c + 7*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(4*d) + (4*b*(a + b*x)^(3/2)*(c + d*x)^(3/2))/3 - ((a + b*x)^(5/2)*(c + d*x)^(3/2))/x - a^(3/2)*sqrt(c)*(5*b*c + 3*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))) - ((b^3*c^3 - 15*a*b^2*c^2*d - 45*a^2*b*c*d^2 - 5*a^3*d^3)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*sqrt(b)*d^(3/2))]
    @test_int [((a + b*x)^(5/2)*(c + d*x)^(3/2))/x^3, x, 10, (3*(b^2*c^2 + 6*a*b*c*d + a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(4*c) + (3*b*(3*b*c + a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(4*c) - ((5*b*c + 3*a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(4*c*x) - ((a + b*x)^(5/2)*(c + d*x)^(3/2))/(2*x^2) - (3*sqrt(a)*(5*b^2*c^2 + 10*a*b*c*d + a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*sqrt(c)) + (3*sqrt(b)*(b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*sqrt(d))]
    @test_int [((a + b*x)^(5/2)*(c + d*x)^(3/2))/x^4, x, 10, (d*(19*b^2*c^2 + 14*a*b*c*d - a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(8*c^2) - ((5*b^2*c^2 + 12*a*b*c*d - a^2*d^2)*sqrt(a + b*x)*(c + d*x)^(3/2))/(8*c^2*x) - ((5*b*c + 3*a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(12*c*x^2) - ((a + b*x)^(5/2)*(c + d*x)^(3/2))/(3*x^3) - ((5*b^3*c^3 + 45*a*b^2*c^2*d + 15*a^2*b*c*d^2 - a^3*d^3)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*sqrt(a)*c^(3/2)) + b^(3/2)*sqrt(d)*(3*b*c + 5*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x)))]
    @test_int [((a + b*x)^(5/2)*(c + d*x)^(3/2))/x^5, x, 10, -(((5*b^3*c^3 + 73*a*b^2*c^2*d - 17*a^2*b*c*d^2 + 3*a^3*d^3)*sqrt(a + b*x)*sqrt(c + d*x))/(64*a*c^2*x)) - ((5*b*c - a*d)*(b*c + 3*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(32*c^2*x^2) - ((5*b*c + 3*a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2))/(24*c*x^3) - ((a + b*x)^(5/2)*(c + d*x)^(3/2))/(4*x^4) + ((5*b^4*c^4 - 60*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 3*a^4*d^4)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(3/2)*c^(5/2)) + 2*b^(5/2)*d^(3/2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x)))]
    @test_int [((a + b*x)^(5/2)*(c + d*x)^(3/2))/x^6, x, 7, (3*(b*c - a*d)^4*sqrt(a + b*x)*sqrt(c + d*x))/(128*a^2*c^3*x) - ((b*c - a*d)^3*sqrt(a + b*x)*(c + d*x)^(3/2))/(64*a*c^3*x^2) - ((b*c - a*d)^2*sqrt(a + b*x)*(c + d*x)^(5/2))/(16*c^3*x^3) - ((b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(5/2))/(8*c^2*x^4) - ((a + b*x)^(5/2)*(c + d*x)^(5/2))/(5*c*x^5) - (3*(b*c - a*d)^5*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(128*a^(5/2)*c^(7/2))]

    @test_int [x*(a + b*x)^(5/2)*(c + d*x)^(5/2), x, 10, (-5*(b*c - a*d)^5*(b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(1024*b^4*d^4) + (5*(b*c - a*d)^4*(b*c + a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(1536*b^4*d^3) - ((b*c - a*d)^3*(b*c + a*d)*(a + b*x)^(5/2)*sqrt(c + d*x))/(384*b^4*d^2) - ((b*c - a*d)^2*(b*c + a*d)*(a + b*x)^(7/2)*sqrt(c + d*x))/(64*b^4*d) - ((b*c - a*d)*(b*c + a*d)*(a + b*x)^(7/2)*(c + d*x)^(3/2))/(24*b^3*d) - ((b*c + a*d)*(a + b*x)^(7/2)*(c + d*x)^(5/2))/(12*b^2*d) + ((a + b*x)^(7/2)*(c + d*x)^(7/2))/(7*b*d) + (5*(b*c - a*d)^6*(b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(1024*b^(9/2)*d^(9/2))]
    @test_int [(a + b*x)^(5/2)*(c + d*x)^(5/2), x, 9, (5*(b*c - a*d)^5*sqrt(a + b*x)*sqrt(c + d*x))/(512*b^3*d^3) - (5*(b*c - a*d)^4*(a + b*x)^(3/2)*sqrt(c + d*x))/(768*b^3*d^2) + ((b*c - a*d)^3*(a + b*x)^(5/2)*sqrt(c + d*x))/(192*b^3*d) + ((b*c - a*d)^2*(a + b*x)^(7/2)*sqrt(c + d*x))/(32*b^3) + ((b*c - a*d)*(a + b*x)^(7/2)*(c + d*x)^(3/2))/(12*b^2) + ((a + b*x)^(7/2)*(c + d*x)^(5/2))/(6*b) - (5*(b*c - a*d)^6*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(512*b^(7/2)*d^(7/2))]
    @test_int [((a + b*x)^(5/2)*(c + d*x)^(5/2))/x, x, 11, ((3*b^4*c^4 - 22*a*b^3*c^3*d + 128*a^2*b^2*c^2*d^2 + 22*a^3*b*c*d^3 - 3*a^4*d^4)*sqrt(a + b*x)*sqrt(c + d*x))/(128*b^2*d^2) + ((3*b^3*c^3 - 19*a*b^2*c^2*d + 109*a^2*b*c*d^2 + 3*a^3*d^3)*sqrt(a + b*x)*(c + d*x)^(3/2))/(192*b*d^2) - ((3*b^2*c^2 - 16*a*b*c*d - 3*a^2*d^2)*sqrt(a + b*x)*(c + d*x)^(5/2))/(48*d^2) + ((b*c + a*d)*(a + b*x)^(3/2)*(c + d*x)^(5/2))/(8*d) + (1/5)*(a + b*x)^(5/2)*(c + d*x)^(5/2) - 2*a^(5/2)*c^(5/2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))) + ((b*c + a*d)*(3*b^4*c^4 - 28*a*b^3*c^3*d + 178*a^2*b^2*c^2*d^2 - 28*a^3*b*c*d^3 + 3*a^4*d^4)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(128*b^(5/2)*d^(5/2))]
    @test_int [((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^2, x, 11, (-5*(b^3*c^3 - 19*a*b^2*c^2*d - 45*a^2*b*c*d^2 - a^3*d^3)*sqrt(a + b*x)*sqrt(c + d*x))/(64*b*d) - (5*(b^2*c^2 - 18*a*b*c*d - 31*a^2*d^2)*sqrt(a + b*x)*(c + d*x)^(3/2))/(96*d) + (5*b*(b*c + 7*a*d)*sqrt(a + b*x)*(c + d*x)^(5/2))/(24*d) + (5*b*(a + b*x)^(3/2)*(c + d*x)^(5/2))/4 - ((a + b*x)^(5/2)*(c + d*x)^(5/2))/x - 5*a^(3/2)*c^(3/2)*(b*c + a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))) - (5*(b^4*c^4 - 20*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 - 20*a^3*b*c*d^3 + a^4*d^4)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(3/2)*d^(3/2))]
    @test_int [((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^3, x, 11, (5/8)*(b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x) + (5*(b^2*c^2 + 8*a*b*c*d + 3*a^2*d^2)*sqrt(a + b*x)*(c + d*x)^(3/2))/(12*c) + (5*b*(5*b*c + 3*a*d)*sqrt(a + b*x)*(c + d*x)^(5/2))/(12*c) - (5*(b*c + a*d)*(a + b*x)^(3/2)*(c + d*x)^(5/2))/(4*c*x) - ((a + b*x)^(5/2)*(c + d*x)^(5/2))/(2*x^2) - (5/4)*sqrt(a)*sqrt(c)*(3*b*c + a*d)*(b*c + 3*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))) + (5*(b*c + a*d)*(b^2*c^2 + 14*a*b*c*d + a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*sqrt(b)*sqrt(d))]
    @test_int [((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^4, x, 11, (5*d*(5*b^2*c^2 + 10*a*b*c*d + a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(8*c) + (5*d*(9*b^2*c^2 + 14*a*b*c*d + a^2*d^2)*sqrt(a + b*x)*(c + d*x)^(3/2))/(24*c^2) - (5*(3*b^2*c^2 + 12*a*b*c*d + a^2*d^2)*sqrt(a + b*x)*(c + d*x)^(5/2))/(24*c^2*x) - (5*(b*c + a*d)*(a + b*x)^(3/2)*(c + d*x)^(5/2))/(12*c*x^2) - ((a + b*x)^(5/2)*(c + d*x)^(5/2))/(3*x^3) - (5*(b*c + a*d)*(b^2*c^2 + 14*a*b*c*d + a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*sqrt(a)*sqrt(c)) + (5/4)*sqrt(b)*sqrt(d)*(3*b*c + a*d)*(b*c + 3*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x)))]
    @test_int [((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^5, x, 11, (5*d*(b^3*c^3 + 45*a*b^2*c^2*d + 19*a^2*b*c*d^2 - a^3*d^3)*sqrt(a + b*x)*sqrt(c + d*x))/(64*a*c^2) - (5*(3*b*c + a*d)*(b^2*c^2 + 24*a*b*c*d - a^2*d^2)*sqrt(a + b*x)*(c + d*x)^(3/2))/(192*a*c^2*x) - (5*(3*b^2*c^2 + 14*a*b*c*d - a^2*d^2)*sqrt(a + b*x)*(c + d*x)^(5/2))/(96*c^2*x^2) - (5*(b*c + a*d)*(a + b*x)^(3/2)*(c + d*x)^(5/2))/(24*c*x^3) - ((a + b*x)^(5/2)*(c + d*x)^(5/2))/(4*x^4) + (5*(b^4*c^4 - 20*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 - 20*a^3*b*c*d^3 + a^4*d^4)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(3/2)*c^(3/2)) + 5*b^(3/2)*d^(3/2)*(b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x)))]
    @test_int [((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^6, x, 11, ((3*b^4*c^4 - 22*a*b^3*c^3*d - 128*a^2*b^2*c^2*d^2 + 22*a^3*b*c*d^3 - 3*a^4*d^4)*sqrt(a + b*x)*sqrt(c + d*x))/(128*a^2*c^2*x) - ((3*b^3*c^3 + 109*a*b^2*c^2*d - 19*a^2*b*c*d^2 + 3*a^3*d^3)*sqrt(a + b*x)*(c + d*x)^(3/2))/(192*a*c^2*x^2) - ((3*b^2*c^2 + 16*a*b*c*d - 3*a^2*d^2)*sqrt(a + b*x)*(c + d*x)^(5/2))/(48*c^2*x^3) - ((b*c + a*d)*(a + b*x)^(3/2)*(c + d*x)^(5/2))/(8*c*x^4) - ((a + b*x)^(5/2)*(c + d*x)^(5/2))/(5*x^5) - ((b*c + a*d)*(3*b^4*c^4 - 28*a*b^3*c^3*d + 178*a^2*b^2*c^2*d^2 - 28*a^3*b*c*d^3 + 3*a^4*d^4)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(128*a^(5/2)*c^(5/2)) + 2*b^(5/2)*d^(5/2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x)))]
    @test_int [((a + b*x)^(5/2)*(c + d*x)^(5/2))/x^7, x, 8, (-5*(b*c - a*d)^5*sqrt(a + b*x)*sqrt(c + d*x))/(512*a^3*c^3*x) + (5*(b*c - a*d)^4*sqrt(a + b*x)*(c + d*x)^(3/2))/(768*a^2*c^3*x^2) - ((b*c - a*d)^3*sqrt(a + b*x)*(c + d*x)^(5/2))/(192*a*c^3*x^3) - ((b*c - a*d)^2*sqrt(a + b*x)*(c + d*x)^(7/2))/(32*c^3*x^4) - ((b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(7/2))/(12*c^2*x^5) - ((a + b*x)^(5/2)*(c + d*x)^(7/2))/(6*c*x^6) + (5*(b*c - a*d)^6*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(512*a^(7/2)*c^(7/2))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(x^2*(a + b*x)^(5/2))/sqrt(c + d*x), x, 8, ((b*c - a*d)^2*(63*b^2*c^2 + 14*a*b*c*d + 3*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(128*b^2*d^5) - ((b*c - a*d)*(63*b^2*c^2 + 14*a*b*c*d + 3*a^2*d^2)*(a + b*x)^(3/2)*sqrt(c + d*x))/(192*b^2*d^4) + ((63*b^2*c^2 + 14*a*b*c*d + 3*a^2*d^2)*(a + b*x)^(5/2)*sqrt(c + d*x))/(240*b^2*d^3) - (3*(3*b*c + a*d)*(a + b*x)^(7/2)*sqrt(c + d*x))/(40*b^2*d^2) + (x*(a + b*x)^(7/2)*sqrt(c + d*x))/(5*b*d) - ((b*c - a*d)^3*(63*b^2*c^2 + 14*a*b*c*d + 3*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(128*b^(5/2)*d^(11/2))]
    @test_int [(x*(a + b*x)^(5/2))/sqrt(c + d*x), x, 7, (-5*(b*c - a*d)^2*(7*b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(64*b*d^4) + (5*(b*c - a*d)*(7*b*c + a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(96*b*d^3) - ((7*b*c + a*d)*(a + b*x)^(5/2)*sqrt(c + d*x))/(24*b*d^2) + ((a + b*x)^(7/2)*sqrt(c + d*x))/(4*b*d) + (5*(b*c - a*d)^3*(7*b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(3/2)*d^(9/2))]
    @test_int [(a + b*x)^(5/2)/sqrt(c + d*x), x, 6, (5*(b*c - a*d)^2*sqrt(a + b*x)*sqrt(c + d*x))/(8*d^3) - (5*(b*c - a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(12*d^2) + ((a + b*x)^(5/2)*sqrt(c + d*x))/(3*d) - (5*(b*c - a*d)^3*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*sqrt(b)*d^(7/2))]
    @test_int [(a + b*x)^(5/2)/(x*sqrt(c + d*x)), x, 8, -(b*(3*b*c - 7*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*d^2) + (b*(a + b*x)^(3/2)*sqrt(c + d*x))/(2*d) - (2*a^(5/2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/sqrt(c) + (sqrt(b)*(3*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*d^(5/2))]
    @test_int [(a + b*x)^(5/2)/(x^2*sqrt(c + d*x)), x, 8, (b*(b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(c*d) - (a*(a + b*x)^(3/2)*sqrt(c + d*x))/(c*x) - (a^(3/2)*(5*b*c - a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/c^(3/2) - (b^(3/2)*(b*c - 5*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/d^(3/2)]
    @test_int [(a + b*x)^(5/2)/(x^3*sqrt(c + d*x)), x, 8, -((a*(7*b*c - 3*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*c^2*x)) - (a*(a + b*x)^(3/2)*sqrt(c + d*x))/(2*c*x^2) - (sqrt(a)*(15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*c^(5/2)) + (2*b^(5/2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/sqrt(d)]
    @test_int [(a + b*x)^(5/2)/(x^4*sqrt(c + d*x)), x, 5, (-5*(b*c - a*d)^2*sqrt(a + b*x)*sqrt(c + d*x))/(8*c^3*x) - (5*(b*c - a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(12*c^2*x^2) - ((a + b*x)^(5/2)*sqrt(c + d*x))/(3*c*x^3) - (5*(b*c - a*d)^3*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*sqrt(a)*c^(7/2))]
    @test_int [(a + b*x)^(5/2)/(x^5*sqrt(c + d*x)), x, 6, (5*(b*c - a*d)^2*(b*c + 7*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(64*a*c^4*x) + (5*(b*c - a*d)*(b*c + 7*a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(96*a*c^3*x^2) + ((b*c + 7*a*d)*(a + b*x)^(5/2)*sqrt(c + d*x))/(24*a*c^2*x^3) - ((a + b*x)^(7/2)*sqrt(c + d*x))/(4*a*c*x^4) + (5*(b*c - a*d)^3*(b*c + 7*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(3/2)*c^(9/2))]

    @test_int [(x^2*(a + b*x)^(5/2))/(c + d*x)^(3/2), x, 8, (2*c^2*(a + b*x)^(7/2))/(d^2*(b*c - a*d)*sqrt(c + d*x)) - (5*(b*c - a*d)*(63*b^2*c^2 - 14*a*b*c*d - a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(64*b*d^5) + (5*(63*b^2*c^2 - 14*a*b*c*d - a^2*d^2)*(a + b*x)^(3/2)*sqrt(c + d*x))/(96*b*d^4) + ((14*a*c - (63*b*c^2)/d + (a^2*d)/b)*(a + b*x)^(5/2)*sqrt(c + d*x))/(24*d^2*(b*c - a*d)) + ((a + b*x)^(7/2)*sqrt(c + d*x))/(4*b*d^2) + (5*(b*c - a*d)^2*(63*b^2*c^2 - 14*a*b*c*d - a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(3/2)*d^(11/2))]
    @test_int [(x*(a + b*x)^(5/2))/(c + d*x)^(3/2), x, 7, (-2*c*(a + b*x)^(7/2))/(d*(b*c - a*d)*sqrt(c + d*x)) + (5*(b*c - a*d)*(7*b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(8*d^4) - (5*(7*b*c - a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(12*d^3) + ((7*b*c - a*d)*(a + b*x)^(5/2)*sqrt(c + d*x))/(3*d^2*(b*c - a*d)) - (5*(b*c - a*d)^2*(7*b*c - a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*sqrt(b)*d^(9/2))]
    @test_int [(a + b*x)^(5/2)/(c + d*x)^(3/2), x, 6, (-2*(a + b*x)^(5/2))/(d*sqrt(c + d*x)) - (15*b*(b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*d^3) + (5*b*(a + b*x)^(3/2)*sqrt(c + d*x))/(2*d^2) + (15*sqrt(b)*(b*c - a*d)^2*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*d^(7/2))]
    @test_int [(a + b*x)^(5/2)/(x*(c + d*x)^(3/2)), x, 8, -((2*(b*c - a*d)*(a + b*x)^(3/2))/(c*d*sqrt(c + d*x))) + (b*(3*b*c - 2*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(c*d^2) - (2*a^(5/2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/c^(3/2) - (b^(3/2)*(3*b*c - 5*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/d^(5/2)]
    @test_int [(a + b*x)^(5/2)/(x^2*(c + d*x)^(3/2)), x, 8, -(((2*b*c - 3*a*d)*(b*c - a*d)*sqrt(a + b*x))/(c^2*d*sqrt(c + d*x))) - (a*(a + b*x)^(3/2))/(c*x*sqrt(c + d*x)) - (a^(3/2)*(5*b*c - 3*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/c^(5/2) + (2*b^(5/2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/d^(3/2)]
    @test_int [(a + b*x)^(5/2)/(x^3*(c + d*x)^(3/2)), x, 5, (15*(b*c - a*d)^2*sqrt(a + b*x))/(4*c^3*sqrt(c + d*x)) - (5*(b*c - a*d)*(a + b*x)^(3/2))/(4*c^2*x*sqrt(c + d*x)) - (a + b*x)^(5/2)/(2*c*x^2*sqrt(c + d*x)) - (15*sqrt(a)*(b*c - a*d)^2*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*c^(7/2))]
    @test_int [(a + b*x)^(5/2)/(x^4*(c + d*x)^(3/2)), x, 6, (5*(b*c - 7*a*d)*(b*c - a*d)^2*sqrt(a + b*x))/(8*a*c^4*sqrt(c + d*x)) - (5*(b*c - 7*a*d)*(b*c - a*d)*(a + b*x)^(3/2))/(24*a*c^3*x*sqrt(c + d*x)) - ((b*c - 7*a*d)*(a + b*x)^(5/2))/(12*a*c^2*x^2*sqrt(c + d*x)) - (a + b*x)^(7/2)/(3*a*c*x^3*sqrt(c + d*x)) - (5*(b*c - 7*a*d)*(b*c - a*d)^2*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*sqrt(a)*c^(9/2))]
    @test_int [(a + b*x)^(5/2)/(x^5*(c + d*x)^(3/2)), x, 8, -((d*(15*b^3*c^3 - 839*a*b^2*c^2*d + 1785*a^2*b*c*d^2 - 945*a^3*d^3)*sqrt(a + b*x))/(192*a*c^5*sqrt(c + d*x))) - (a*(11*b*c - 9*a*d)*sqrt(a + b*x))/(24*c^2*x^3*sqrt(c + d*x)) - ((59*b*c - 63*a*d)*(b*c - a*d)*sqrt(a + b*x))/(96*c^3*x^2*sqrt(c + d*x)) - ((b*c - a*d)*(15*b^2*c^2 - 322*a*b*c*d + 315*a^2*d^2)*sqrt(a + b*x))/(192*a*c^4*x*sqrt(c + d*x)) - (a*(a + b*x)^(3/2))/(4*c*x^4*sqrt(c + d*x)) + (5*(b*c - a*d)^2*(b^2*c^2 + 14*a*b*c*d - 63*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(3/2)*c^(11/2))]

    @test_int [(x^3*(a + b*x)^(5/2))/(c + d*x)^(5/2), x, 8, -((2*x^3*(a + b*x)^(5/2))/(3*d*(c + d*x)^(3/2))) - (2*(11*b*c - 6*a*d)*x^2*(a + b*x)^(5/2))/(3*d^2*(b*c - a*d)*sqrt(c + d*x)) - (5*(231*b^3*c^3 - 189*a*b^2*c^2*d + 21*a^2*b*c*d^2 + a^3*d^3)*sqrt(a + b*x)*sqrt(c + d*x))/(64*b*d^6) + (5*(231*b^3*c^3 - 189*a*b^2*c^2*d + 21*a^2*b*c*d^2 + a^3*d^3)*(a + b*x)^(3/2)*sqrt(c + d*x))/(96*b*d^5*(b*c - a*d)) - ((a + b*x)^(5/2)*sqrt(c + d*x)*(231*b^2*c^2 - 156*a*b*c*d + 5*a^2*d^2 - 2*b*d*(99*b*c - 59*a*d)*x))/(24*b*d^4*(b*c - a*d)) + (5*(b*c - a*d)*(231*b^3*c^3 - 189*a*b^2*c^2*d + 21*a^2*b*c*d^2 + a^3*d^3)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(3/2)*d^(13/2))]
    @test_int [(x^2*(a + b*x)^(5/2))/(c + d*x)^(5/2), x, 8, (2*c^2*(a + b*x)^(7/2))/(3*d^2*(b*c - a*d)*(c + d*x)^(3/2)) - (4*c*(5*b*c - 3*a*d)*(a + b*x)^(7/2))/(3*d^2*(b*c - a*d)^2*sqrt(c + d*x)) + (5*(21*b^2*c^2 - 14*a*b*c*d + a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(8*d^5) - (5*(21*b^2*c^2 - 14*a*b*c*d + a^2*d^2)*(a + b*x)^(3/2)*sqrt(c + d*x))/(12*d^4*(b*c - a*d)) + ((21*b^2*c^2 - 14*a*b*c*d + a^2*d^2)*(a + b*x)^(5/2)*sqrt(c + d*x))/(3*d^3*(b*c - a*d)^2) - (5*(b*c - a*d)*(21*b^2*c^2 - 14*a*b*c*d + a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*sqrt(b)*d^(11/2))]
    @test_int [(x*(a + b*x)^(5/2))/(c + d*x)^(5/2), x, 7, (-2*c*(a + b*x)^(7/2))/(3*d*(b*c - a*d)*(c + d*x)^(3/2)) - (2*(7*b*c - 3*a*d)*(a + b*x)^(5/2))/(3*d^2*(b*c - a*d)*sqrt(c + d*x)) - (5*b*(7*b*c - 3*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*d^4) + (5*b*(7*b*c - 3*a*d)*(a + b*x)^(3/2)*sqrt(c + d*x))/(6*d^3*(b*c - a*d)) + (5*sqrt(b)*(7*b*c - 3*a*d)*(b*c - a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*d^(9/2))]
    @test_int [(a + b*x)^(5/2)/(c + d*x)^(5/2), x, 6, (-2*(a + b*x)^(5/2))/(3*d*(c + d*x)^(3/2)) - (10*b*(a + b*x)^(3/2))/(3*d^2*sqrt(c + d*x)) + (5*b^2*sqrt(a + b*x)*sqrt(c + d*x))/d^3 - (5*b^(3/2)*(b*c - a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/d^(7/2)]
    @test_int [(a + b*x)^(5/2)/(x*(c + d*x)^(5/2)), x, 8, -((2*(b*c - a*d)*(a + b*x)^(3/2))/(3*c*d*(c + d*x)^(3/2))) + (2*(a^2/c^2 - b^2/d^2)*sqrt(a + b*x))/sqrt(c + d*x) - (2*a^(5/2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/c^(5/2) + (2*b^(5/2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/d^(5/2)]
    @test_int [(a + b*x)^(5/2)/(x^2*(c + d*x)^(5/2)), x, 5, (5*(b*c - a*d)*(a + b*x)^(3/2))/(3*c^2*(c + d*x)^(3/2)) - (a + b*x)^(5/2)/(c*x*(c + d*x)^(3/2)) + (5*a*(b*c - a*d)*sqrt(a + b*x))/(c^3*sqrt(c + d*x)) - (5*a^(3/2)*(b*c - a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/c^(7/2)]
    @test_int [(a + b*x)^(5/2)/(x^3*(c + d*x)^(5/2)), x, 6, (5*(3*b*c - 7*a*d)*(b*c - a*d)*(a + b*x)^(3/2))/(12*a*c^3*(c + d*x)^(3/2)) - ((3*b*c - 7*a*d)*(a + b*x)^(5/2))/(4*a*c^2*x*(c + d*x)^(3/2)) - (a + b*x)^(7/2)/(2*a*c*x^2*(c + d*x)^(3/2)) + (5*(3*b*c - 7*a*d)*(b*c - a*d)*sqrt(a + b*x))/(4*c^4*sqrt(c + d*x)) - (5*sqrt(a)*(3*b*c - 7*a*d)*(b*c - a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*c^(9/2))]
    @test_int [(a + b*x)^(5/2)/(x^4*(c + d*x)^(5/2)), x, 8, -((7*d*(7*b*c - 15*a*d)*(b*c - a*d)*sqrt(a + b*x))/(24*c^4*(c + d*x)^(3/2))) - (3*a*(b*c - a*d)*sqrt(a + b*x))/(4*c^2*x^2*(c + d*x)^(3/2)) - ((11*b*c - 21*a*d)*(b*c - a*d)*sqrt(a + b*x))/(8*c^3*x*(c + d*x)^(3/2)) - (a*(a + b*x)^(3/2))/(3*c*x^3*(c + d*x)^(3/2)) - (d*(113*b^2*c^2 - 420*a*b*c*d + 315*a^2*d^2)*sqrt(a + b*x))/(24*c^5*sqrt(c + d*x)) - (5*(b*c - a*d)*(b^2*c^2 - 14*a*b*c*d + 21*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*sqrt(a)*c^(11/2))]
    @test_int [(a + b*x)^(5/2)/(x^5*(c + d*x)^(5/2)), x, 9, -((d*(b*c - a*d)*(5*b^2*c^2 - 238*a*b*c*d + 385*a^2*d^2)*sqrt(a + b*x))/(64*a*c^5*(c + d*x)^(3/2))) - (11*a*(b*c - a*d)*sqrt(a + b*x))/(24*c^2*x^3*(c + d*x)^(3/2)) - ((59*b*c - 99*a*d)*(b*c - a*d)*sqrt(a + b*x))/(96*c^3*x^2*(c + d*x)^(3/2)) - ((b*c - a*d)*(5*b^2*c^2 - 156*a*b*c*d + 231*a^2*d^2)*sqrt(a + b*x))/(64*a*c^4*x*(c + d*x)^(3/2)) - (a*(a + b*x)^(3/2))/(4*c*x^4*(c + d*x)^(3/2)) - (d*(5*b^3*c^3 - 581*a*b^2*c^2*d + 1715*a^2*b*c*d^2 - 1155*a^3*d^3)*sqrt(a + b*x))/(64*a*c^6*sqrt(c + d*x)) + (5*(b*c - a*d)*(b^3*c^3 + 21*a*b^2*c^2*d - 189*a^2*b*c*d^2 + 231*a^3*d^3)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(3/2)*c^(13/2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x)^(n/2) / (a+b*x)^(1/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [x^2*sqrt(c + d*x)/sqrt(a + b*x), x, 6, ((b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(8*b^3*d^2) - ((3*b*c + 5*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(12*b^2*d^2) + (x*sqrt(a + b*x)*(c + d*x)^(3/2))/(3*b*d) + ((b*c - a*d)*(b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*b^(7/2)*d^(5/2))]
    @test_int [x^1*sqrt(c + d*x)/sqrt(a + b*x), x, 5, -((b*c + 3*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*b^2*d) + (sqrt(a + b*x)*(c + d*x)^(3/2))/(2*b*d) - ((b*c - a*d)*(b*c + 3*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(5/2)*d^(3/2))]
    @test_int [x^0*sqrt(c + d*x)/sqrt(a + b*x), x, 4, (sqrt(a + b*x)*sqrt(c + d*x))/b + ((b*c - a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(b^(3/2)*sqrt(d))]
    @test_int [sqrt(c + d*x)/(x^1*sqrt(a + b*x)), x, 7, (-2*sqrt(c)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/sqrt(a) + (2*sqrt(d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/sqrt(b)]
    @test_int [sqrt(c + d*x)/(x^2*sqrt(a + b*x)), x, 3, -((sqrt(a + b*x)*sqrt(c + d*x))/(a*x)) + ((b*c - a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(a^(3/2)*sqrt(c))]
    @test_int [sqrt(c + d*x)/(x^3*sqrt(a + b*x)), x, 4, ((3*b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*a^2*c*x) - (sqrt(a + b*x)*(c + d*x)^(3/2))/(2*a*c*x^2) - ((b*c - a*d)*(3*b*c + a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(5/2)*c^(3/2))]
    @test_int [sqrt(c + d*x)/(x^4*sqrt(a + b*x)), x, 6, -((sqrt(a + b*x)*sqrt(c + d*x))/(3*a*x^3)) + ((5*b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(12*a^2*c*x^2) - ((5*b*c - 3*a*d)*(3*b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(24*a^3*c^2*x) + ((b*c - a*d)*(5*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*a^(7/2)*c^(5/2))]

    @test_int [(x^2*(c + d*x)^(3/2))/sqrt(a + b*x), x, 7, ((b*c - a*d)*(3*b^2*c^2 + 10*a*b*c*d + 35*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(64*b^4*d^2) + ((3*b^2*c^2 + 10*a*b*c*d + 35*a^2*d^2)*sqrt(a + b*x)*(c + d*x)^(3/2))/(96*b^3*d^2) - ((3*b*c + 7*a*d)*sqrt(a + b*x)*(c + d*x)^(5/2))/(24*b^2*d^2) + (x*sqrt(a + b*x)*(c + d*x)^(5/2))/(4*b*d) + ((b*c - a*d)^2*(3*b^2*c^2 + 10*a*b*c*d + 35*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(9/2)*d^(5/2))]
    @test_int [(x*(c + d*x)^(3/2))/sqrt(a + b*x), x, 6, -((b*c - a*d)*(b*c + 5*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(8*b^3*d) - ((b*c + 5*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(12*b^2*d) + (sqrt(a + b*x)*(c + d*x)^(5/2))/(3*b*d) - ((b*c - a*d)^2*(b*c + 5*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*b^(7/2)*d^(3/2))]
    @test_int [(c + d*x)^(3/2)/sqrt(a + b*x), x, 5, (3*(b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*b^2) + (sqrt(a + b*x)*(c + d*x)^(3/2))/(2*b) + (3*(b*c - a*d)^2*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(5/2)*sqrt(d))]
    @test_int [(c + d*x)^(3/2)/(x*sqrt(a + b*x)), x, 7, (d*sqrt(a + b*x)*sqrt(c + d*x))/b - (2*c^(3/2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/sqrt(a) + (sqrt(d)*(3*b*c - a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/b^(3/2)]
    @test_int [(c + d*x)^(3/2)/(x^2*sqrt(a + b*x)), x, 7, -((c*sqrt(a + b*x)*sqrt(c + d*x))/(a*x)) + (sqrt(c)*(b*c - 3*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/a^(3/2) + (2*d^(3/2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/sqrt(b)]
    @test_int [(c + d*x)^(3/2)/(x^3*sqrt(a + b*x)), x, 4, (3*(b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*a^2*x) - (sqrt(a + b*x)*(c + d*x)^(3/2))/(2*a*x^2) - (3*(b*c - a*d)^2*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(5/2)*sqrt(c))]
    @test_int [(c + d*x)^(3/2)/(x^4*sqrt(a + b*x)), x, 5, -(((b*c - a*d)*(5*b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(8*a^3*c*x)) + ((5*b*c + a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(12*a^2*c*x^2) - (sqrt(a + b*x)*(c + d*x)^(5/2))/(3*a*c*x^3) + ((b*c - a*d)^2*(5*b*c + a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*a^(7/2)*c^(3/2))]
    @test_int [(c + d*x)^(3/2)/(x^5*sqrt(a + b*x)), x, 7, -((c*sqrt(a + b*x)*sqrt(c + d*x))/(4*a*x^4)) + ((7*b*c - 9*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(24*a^2*x^3) - ((35*b^2*c^2 - 46*a*b*c*d + 3*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(96*a^3*c*x^2) + ((105*b^3*c^3 - 145*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 9*a^3*d^3)*sqrt(a + b*x)*sqrt(c + d*x))/(192*a^4*c^2*x) - ((b*c - a*d)^2*(35*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(9/2)*c^(5/2))]

    @test_int [(x^2*(c + d*x)^(5/2))/sqrt(a + b*x), x, 8, ((b*c - a*d)^2*(3*b^2*c^2 + 14*a*b*c*d + 63*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(128*b^5*d^2) + ((b*c - a*d)*(3*b^2*c^2 + 14*a*b*c*d + 63*a^2*d^2)*sqrt(a + b*x)*(c + d*x)^(3/2))/(192*b^4*d^2) + ((3*b^2*c^2 + 14*a*b*c*d + 63*a^2*d^2)*sqrt(a + b*x)*(c + d*x)^(5/2))/(240*b^3*d^2) - (3*(b*c + 3*a*d)*sqrt(a + b*x)*(c + d*x)^(7/2))/(40*b^2*d^2) + (x*sqrt(a + b*x)*(c + d*x)^(7/2))/(5*b*d) + ((b*c - a*d)^3*(3*b^2*c^2 + 14*a*b*c*d + 63*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(128*b^(11/2)*d^(5/2))]
    @test_int [(x*(c + d*x)^(5/2))/sqrt(a + b*x), x, 7, (-5*(b*c - a*d)^2*(b*c + 7*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(64*b^4*d) - (5*(b*c - a*d)*(b*c + 7*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(96*b^3*d) - ((b*c + 7*a*d)*sqrt(a + b*x)*(c + d*x)^(5/2))/(24*b^2*d) + (sqrt(a + b*x)*(c + d*x)^(7/2))/(4*b*d) - (5*(b*c - a*d)^3*(b*c + 7*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(9/2)*d^(3/2))]
    @test_int [(c + d*x)^(5/2)/sqrt(a + b*x), x, 6, (5*(b*c - a*d)^2*sqrt(a + b*x)*sqrt(c + d*x))/(8*b^3) + (5*(b*c - a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(12*b^2) + (sqrt(a + b*x)*(c + d*x)^(5/2))/(3*b) + (5*(b*c - a*d)^3*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*b^(7/2)*sqrt(d))]
    @test_int [(c + d*x)^(5/2)/(x*sqrt(a + b*x)), x, 8, (d*(7*b*c - 3*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*b^2) + (d*sqrt(a + b*x)*(c + d*x)^(3/2))/(2*b) - (2*c^(5/2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/sqrt(a) + (sqrt(d)*(15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(5/2))]
    @test_int [(c + d*x)^(5/2)/(x^2*sqrt(a + b*x)), x, 8, (d*(b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(a*b) - (c*sqrt(a + b*x)*(c + d*x)^(3/2))/(a*x) + (c^(3/2)*(b*c - 5*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/a^(3/2) + (d^(3/2)*(5*b*c - a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/b^(3/2)]
    @test_int [(c + d*x)^(5/2)/(x^3*sqrt(a + b*x)), x, 8, (c*(3*b*c - 7*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*a^2*x) - (c*sqrt(a + b*x)*(c + d*x)^(3/2))/(2*a*x^2) - (sqrt(c)*(3*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(5/2)) + (2*d^(5/2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/sqrt(b)]
    @test_int [(c + d*x)^(5/2)/(x^4*sqrt(a + b*x)), x, 5, -((5*(b*c - a*d)^2*sqrt(a + b*x)*sqrt(c + d*x))/(8*a^3*x)) + (5*(b*c - a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(12*a^2*x^2) - (sqrt(a + b*x)*(c + d*x)^(5/2))/(3*a*x^3) + (5*(b*c - a*d)^3*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*a^(7/2)*sqrt(c))]
    @test_int [(c + d*x)^(5/2)/(x^5*sqrt(a + b*x)), x, 6, (5*(b*c - a*d)^2*(7*b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(64*a^4*c*x) - (5*(b*c - a*d)*(7*b*c + a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(96*a^3*c*x^2) + ((7*b*c + a*d)*sqrt(a + b*x)*(c + d*x)^(5/2))/(24*a^2*c*x^3) - (sqrt(a + b*x)*(c + d*x)^(7/2))/(4*a*c*x^4) - (5*(b*c - a*d)^3*(7*b*c + a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(9/2)*c^(3/2))]
    @test_int [(c + d*x)^(5/2)/(x^6*sqrt(a + b*x)), x, 8, (c*(9*b*c - 13*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(40*a^2*x^4) - ((63*b^2*c^2 - 148*a*b*c*d + 93*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(240*a^3*x^3) + ((315*b^3*c^3 - 749*a*b^2*c^2*d + 481*a^2*b*c*d^2 - 15*a^3*d^3)*sqrt(a + b*x)*sqrt(c + d*x))/(960*a^4*c*x^2) - ((945*b^4*c^4 - 2310*a*b^3*c^3*d + 1564*a^2*b^2*c^2*d^2 - 90*a^3*b*c*d^3 - 45*a^4*d^4)*sqrt(a + b*x)*sqrt(c + d*x))/(1920*a^5*c^2*x) - (c*sqrt(a + b*x)*(c + d*x)^(3/2))/(5*a*x^5) + ((b*c - a*d)^3*(63*b^2*c^2 + 14*a*b*c*d + 3*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(128*a^(11/2)*c^(5/2))]

    @test_int [x^4*(1 + x)^(3/2)/sqrt(1 - x), x, 7, (-(11/16))*sqrt(1 - x)*sqrt(1 + x) - (11/48)*sqrt(1 - x)*(1 + x)^(3/2) - (1/15)*sqrt(1 - x)*x^2*(1 + x)^(5/2) - (1/6)*sqrt(1 - x)*x^3*(1 + x)^(5/2) - (1/120)*sqrt(1 - x)*(1 + x)^(5/2)*(18 + 19*x) + (11*asin(x))/16]
    @test_int [x^3*(1 + x)^(3/2)/sqrt(1 - x), x, 8, (-(3/4))*sqrt(1 - x)*sqrt(1 + x) - (1/4)*sqrt(1 - x)*(1 + x)^(3/2) - (1/10)*sqrt(1 - x)*(1 + x)^(5/2) - (1/5)*sqrt(1 - x)*x^2*(1 + x)^(5/2) - (1/10)*sqrt(1 - x)*(1 + x)^(7/2) + (3*asin(x))/4]
    @test_int [x^2*(1 + x)^(3/2)/sqrt(1 - x), x, 6, (-(7/8))*sqrt(1 - x)*sqrt(1 + x) - (7/24)*sqrt(1 - x)*(1 + x)^(3/2) - (1/6)*sqrt(1 - x)*(1 + x)^(5/2) - (1/4)*sqrt(1 - x)*x*(1 + x)^(5/2) + (7*asin(x))/8]
    @test_int [x^1*(1 + x)^(3/2)/sqrt(1 - x), x, 5, (-sqrt(1 - x))*sqrt(1 + x) - (1/3)*sqrt(1 - x)*(1 + x)^(3/2) - (1/3)*sqrt(1 - x)*(1 + x)^(5/2) + asin(x)]
    @test_int [x^0*(1 + x)^(3/2)/sqrt(1 - x), x, 4, (-(3/2))*sqrt(1 - x)*sqrt(1 + x) - (1/2)*sqrt(1 - x)*(1 + x)^(3/2) + (3*asin(x))/2]
    @test_int [(1 + x)^(3/2)/(x^1*sqrt(1 - x)), x, 6, (-sqrt(1 - x))*sqrt(1 + x) + 2*asin(x) - atanh(sqrt(1 - x)*sqrt(1 + x))]
    @test_int [(1 + x)^(3/2)/(x^2*sqrt(1 - x)), x, 6, -((sqrt(1 - x)*sqrt(1 + x))/x) + asin(x) - 2*atanh(sqrt(1 - x)*sqrt(1 + x))]
    @test_int [(1 + x)^(3/2)/(x^3*sqrt(1 - x)), x, 4, -((3*sqrt(1 - x)*sqrt(1 + x))/(2*x)) - (sqrt(1 - x)*(1 + x)^(3/2))/(2*x^2) - (3/2)*atanh(sqrt(1 - x)*sqrt(1 + x))]
    @test_int [(1 + x)^(3/2)/(x^4*sqrt(1 - x)), x, 5, -((sqrt(1 - x)*sqrt(1 + x))/x) - (sqrt(1 - x)*(1 + x)^(3/2))/(3*x^2) - (sqrt(1 - x)*(1 + x)^(5/2))/(3*x^3) - atanh(sqrt(1 - x)*sqrt(1 + x))]
    @test_int [(1 + x)^(3/2)/(x^5*sqrt(1 - x)), x, 7, -((sqrt(1 - x)*sqrt(1 + x))/(4*x^4)) - (2*sqrt(1 - x)*sqrt(1 + x))/(3*x^3) - (7*sqrt(1 - x)*sqrt(1 + x))/(8*x^2) - (4*sqrt(1 - x)*sqrt(1 + x))/(3*x) - (7/8)*atanh(sqrt(1 - x)*sqrt(1 + x))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [x^3/(sqrt(a + b*x)*sqrt(c + d*x)), x, 5, (x^2*sqrt(a + b*x)*sqrt(c + d*x))/(3*b*d) + (sqrt(a + b*x)*sqrt(c + d*x)*(15*b^2*c^2 + 14*a*b*c*d + 15*a^2*d^2 - 10*b*d*(b*c + a*d)*x))/(24*b^3*d^3) - ((b*c + a*d)*(5*b^2*c^2 - 2*a*b*c*d + 5*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*b^(7/2)*d^(7/2))]
    @test_int [x^2/(sqrt(a + b*x)*sqrt(c + d*x)), x, 5, -((3*(b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*b^2*d^2)) + (x*sqrt(a + b*x)*sqrt(c + d*x))/(2*b*d) - ((4*a*b*c*d - 3*(b*c + a*d)^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(5/2)*d^(5/2))]
    @test_int [x/(sqrt(a + b*x)*sqrt(c + d*x)), x, 4, (sqrt(a + b*x)*sqrt(c + d*x))/(b*d) - ((b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(b^(3/2)*d^(3/2))]
    @test_int [1/(sqrt(a + b*x)*sqrt(c + d*x)), x, 3, (2*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(sqrt(b)*sqrt(d))]
    @test_int [1/(x*sqrt(a + b*x)*sqrt(c + d*x)), x, 2, -((2*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(sqrt(a)*sqrt(c)))]
    @test_int [1/(x^2*sqrt(a + b*x)*sqrt(c + d*x)), x, 3, -((sqrt(a + b*x)*sqrt(c + d*x))/(a*c*x)) + ((b*c + a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(a^(3/2)*c^(3/2))]
    @test_int [1/(x^3*sqrt(a + b*x)*sqrt(c + d*x)), x, 5, -((sqrt(a + b*x)*sqrt(c + d*x))/(2*a*c*x^2)) + (3*(b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*a^2*c^2*x) - ((3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(5/2)*c^(5/2))]
    @test_int [1/(x^4*sqrt(a + b*x)*sqrt(c + d*x)), x, 6, -((sqrt(a + b*x)*sqrt(c + d*x))/(3*a*c*x^3)) + (5*(b*c + a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(12*a^2*c^2*x^2) - ((15*b^2*c^2 + 14*a*b*c*d + 15*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(24*a^3*c^3*x) + ((b*c + a*d)*(5*b^2*c^2 - 2*a*b*c*d + 5*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*a^(7/2)*c^(7/2))]

    @test_int [x^3/(sqrt(a + b*x)*(c + d*x)^(3/2)), x, 5, -((2*c*x^2*sqrt(a + b*x))/(d*(b*c - a*d)*sqrt(c + d*x))) - (sqrt(a + b*x)*sqrt(c + d*x)*((5*b*c - 3*a*d)*(3*b*c + a*d) - 2*b*d*(5*b*c - a*d)*x))/(4*b^2*d^3*(b*c - a*d)) + (3*(5*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(5/2)*d^(7/2))]
    @test_int [x^2/(sqrt(a + b*x)*(c + d*x)^(3/2)), x, 5, (2*c^2*sqrt(a + b*x))/(d^2*(b*c - a*d)*sqrt(c + d*x)) + (sqrt(a + b*x)*sqrt(c + d*x))/(b*d^2) - ((3*b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(b^(3/2)*d^(5/2))]
    @test_int [x/(sqrt(a + b*x)*(c + d*x)^(3/2)), x, 4, -((2*c*sqrt(a + b*x))/(d*(b*c - a*d)*sqrt(c + d*x))) + (2*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(sqrt(b)*d^(3/2))]
    @test_int [1/(sqrt(a + b*x)*(c + d*x)^(3/2)), x, 1, (2*sqrt(a + b*x))/((b*c - a*d)*sqrt(c + d*x))]
    @test_int [1/(x*sqrt(a + b*x)*(c + d*x)^(3/2)), x, 3, -((2*d*sqrt(a + b*x))/(c*(b*c - a*d)*sqrt(c + d*x))) - (2*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(sqrt(a)*c^(3/2))]
    @test_int [1/(x^2*sqrt(a + b*x)*(c + d*x)^(3/2)), x, 5, -((d*(b*c - 3*a*d)*sqrt(a + b*x))/(a*c^2*(b*c - a*d)*sqrt(c + d*x))) - sqrt(a + b*x)/(a*c*x*sqrt(c + d*x)) + ((b*c + 3*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(a^(3/2)*c^(5/2))]
    @test_int [1/(x^3*sqrt(a + b*x)*(c + d*x)^(3/2)), x, 6, (d*(3*b*c - 5*a*d)*(b*c + 3*a*d)*sqrt(a + b*x))/(4*a^2*c^3*(b*c - a*d)*sqrt(c + d*x)) - sqrt(a + b*x)/(2*a*c*x^2*sqrt(c + d*x)) + ((3*b*c + 5*a*d)*sqrt(a + b*x))/(4*a^2*c^2*x*sqrt(c + d*x)) - (3*(b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(5/2)*c^(7/2))]

    @test_int [x^4/(sqrt(a + b*x)*(c + d*x)^(5/2)), x, 6, -((2*c*x^3*sqrt(a + b*x))/(3*d*(b*c - a*d)*(c + d*x)^(3/2))) - (2*c*(7*b*c - 9*a*d)*x^2*sqrt(a + b*x))/(3*d^2*(b*c - a*d)^2*sqrt(c + d*x)) - (sqrt(a + b*x)*sqrt(c + d*x)*(105*b^3*c^3 - 145*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 9*a^3*d^3 - 2*b*d*(35*b^2*c^2 - 46*a*b*c*d + 3*a^2*d^2)*x))/(12*b^2*d^4*(b*c - a*d)^2) + ((35*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(5/2)*d^(9/2))]
    @test_int [x^3/(sqrt(a + b*x)*(c + d*x)^(5/2)), x, 5, -((2*c*x^2*sqrt(a + b*x))/(3*d*(b*c - a*d)*(c + d*x)^(3/2))) + (sqrt(a + b*x)*(c*(15*b^2*c^2 - 22*a*b*c*d + 3*a^2*d^2) + d*(5*b*c - 3*a*d)*(b*c - a*d)*x))/(3*b*d^3*(b*c - a*d)^2*sqrt(c + d*x)) - ((5*b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(b^(3/2)*d^(7/2))]
    @test_int [x^2/(sqrt(a + b*x)*(c + d*x)^(5/2)), x, 5, (2*c^2*sqrt(a + b*x))/(3*d^2*(b*c - a*d)*(c + d*x)^(3/2)) - (4*c*(2*b*c - 3*a*d)*sqrt(a + b*x))/(3*d^2*(b*c - a*d)^2*sqrt(c + d*x)) + (2*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(sqrt(b)*d^(5/2))]
    @test_int [x/(sqrt(a + b*x)*(c + d*x)^(5/2)), x, 2, -((2*c*sqrt(a + b*x))/(3*d*(b*c - a*d)*(c + d*x)^(3/2))) + (2*(b*c - 3*a*d)*sqrt(a + b*x))/(3*d*(b*c - a*d)^2*sqrt(c + d*x))]
    @test_int [1/(sqrt(a + b*x)*(c + d*x)^(5/2)), x, 2, (2*sqrt(a + b*x))/(3*(b*c - a*d)*(c + d*x)^(3/2)) + (4*b*sqrt(a + b*x))/(3*(b*c - a*d)^2*sqrt(c + d*x))]
    @test_int [1/(x*sqrt(a + b*x)*(c + d*x)^(5/2)), x, 5, -((2*d*sqrt(a + b*x))/(3*c*(b*c - a*d)*(c + d*x)^(3/2))) - (2*d*(5*b*c - 3*a*d)*sqrt(a + b*x))/(3*c^2*(b*c - a*d)^2*sqrt(c + d*x)) - (2*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(sqrt(a)*c^(5/2))]
    @test_int [1/(x^2*sqrt(a + b*x)*(c + d*x)^(5/2)), x, 6, -((d*(3*b*c - 5*a*d)*sqrt(a + b*x))/(3*a*c^2*(b*c - a*d)*(c + d*x)^(3/2))) - sqrt(a + b*x)/(a*c*x*(c + d*x)^(3/2)) - (d*(3*b^2*c^2 - 22*a*b*c*d + 15*a^2*d^2)*sqrt(a + b*x))/(3*a*c^3*(b*c - a*d)^2*sqrt(c + d*x)) + ((b*c + 5*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(a^(3/2)*c^(7/2))]
    @test_int [1/(x^3*sqrt(a + b*x)*(c + d*x)^(5/2)), x, 7, (d*(9*b^2*c^2 + 18*a*b*c*d - 35*a^2*d^2)*sqrt(a + b*x))/(12*a^2*c^3*(b*c - a*d)*(c + d*x)^(3/2)) - sqrt(a + b*x)/(2*a*c*x^2*(c + d*x)^(3/2)) + ((3*b*c + 7*a*d)*sqrt(a + b*x))/(4*a^2*c^2*x*(c + d*x)^(3/2)) + (d*(9*b^3*c^3 + 15*a*b^2*c^2*d - 145*a^2*b*c*d^2 + 105*a^3*d^3)*sqrt(a + b*x))/(12*a^2*c^4*(b*c - a*d)^2*sqrt(c + d*x)) - ((3*b^2*c^2 + 10*a*b*c*d + 35*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(5/2)*c^(9/2))]

    @test_int [1/(x*sqrt(c*x)*sqrt(a + b*x)), x, 2, -((2*sqrt(a + b*x))/(a*sqrt(c*x)))]

    @test_int [1/(x*sqrt(a*c - b*c*x)*sqrt(a + b*x)), x, 2, -(atanh((sqrt(a + b*x)*sqrt(a*c - b*c*x))/(a*sqrt(c)))/(a*sqrt(c)))]

    @test_int [1/(x*sqrt(1 - a - b*x)*sqrt(1 + a + b*x)), x, 2, -((2*atanh((sqrt(1 - a)*sqrt(1 + a + b*x))/(sqrt(1 + a)*sqrt(1 - a - b*x))))/sqrt(1 - a^2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x)^(n/2) / (a+b*x)^(3/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(x^3*(c + d*x)^(3/2))/(a + b*x)^(3/2), x, 7, (3*(b^3*c^3 + 5*a*b^2*c^2*d + 35*a^2*b*c*d^2 - 105*a^3*d^3)*sqrt(a + b*x)*sqrt(c + d*x))/(64*b^5*d^2) - (2*x^3*(c + d*x)^(3/2))/(b*sqrt(a + b*x)) + (9*x^2*sqrt(a + b*x)*(c + d*x)^(3/2))/(4*b^2) - (sqrt(a + b*x)*(c + d*x)^(3/2)*(3*b^2*c^2 + 14*a*b*c*d - 105*a^2*d^2 - 4*b*d*(b*c - 21*a*d)*x))/(32*b^4*d^2) + (3*(b*c - a*d)*(b^3*c^3 + 5*a*b^2*c^2*d + 35*a^2*b*c*d^2 - 105*a^3*d^3)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(11/2)*d^(5/2))]
    @test_int [(x^2*(c + d*x)^(3/2))/(a + b*x)^(3/2), x, 7, -(((b^2*c^2 + 10*a*b*c*d - 35*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(8*b^4*d)) - ((10*a*c + (b*c^2)/d - (35*a^2*d)/b)*sqrt(a + b*x)*(c + d*x)^(3/2))/(12*b^2*(b*c - a*d)) - (2*a^2*(c + d*x)^(5/2))/(b^2*(b*c - a*d)*sqrt(a + b*x)) + (sqrt(a + b*x)*(c + d*x)^(5/2))/(3*b^2*d) - ((b*c - a*d)*(b^2*c^2 + 10*a*b*c*d - 35*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*b^(9/2)*d^(3/2))]
    @test_int [(x*(c + d*x)^(3/2))/(a + b*x)^(3/2), x, 6, (3*(b*c - 5*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*b^3) + ((b*c - 5*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(2*b^2*(b*c - a*d)) + (2*a*(c + d*x)^(5/2))/(b*(b*c - a*d)*sqrt(a + b*x)) + (3*(b*c - 5*a*d)*(b*c - a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(7/2)*sqrt(d))]
    @test_int [(c + d*x)^(3/2)/(a + b*x)^(3/2), x, 5, (3*d*sqrt(a + b*x)*sqrt(c + d*x))/b^2 - (2*(c + d*x)^(3/2))/(b*sqrt(a + b*x)) + (3*sqrt(d)*(b*c - a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/b^(5/2)]
    @test_int [(c + d*x)^(3/2)/(x*(a + b*x)^(3/2)), x, 7, (2*(b*c - a*d)*sqrt(c + d*x))/(a*b*sqrt(a + b*x)) - (2*c^(3/2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/a^(3/2) + (2*d^(3/2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/b^(3/2)]
    @test_int [(c + d*x)^(3/2)/(x^2*(a + b*x)^(3/2)), x, 4, (-3*(b*c - a*d)*sqrt(c + d*x))/(a^2*sqrt(a + b*x)) - (c + d*x)^(3/2)/(a*x*sqrt(a + b*x)) + (3*sqrt(c)*(b*c - a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/a^(5/2)]
    @test_int [(c + d*x)^(3/2)/(x^3*(a + b*x)^(3/2)), x, 5, (3*(b*c - a*d)*(5*b*c - a*d)*sqrt(c + d*x))/(4*a^3*c*sqrt(a + b*x)) + ((5*b*c - a*d)*(c + d*x)^(3/2))/(4*a^2*c*x*sqrt(a + b*x)) - (c + d*x)^(5/2)/(2*a*c*x^2*sqrt(a + b*x)) - (3*(b*c - a*d)*(5*b*c - a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(7/2)*sqrt(c))]
    @test_int [(c + d*x)^(3/2)/(x^4*(a + b*x)^(3/2)), x, 7, -((b*(105*b^2*c^2 - 100*a*b*c*d + 3*a^2*d^2)*sqrt(c + d*x))/(24*a^4*c*sqrt(a + b*x))) - (c*sqrt(c + d*x))/(3*a*x^3*sqrt(a + b*x)) + (7*(b*c - a*d)*sqrt(c + d*x))/(12*a^2*x^2*sqrt(a + b*x)) - ((35*b*c - 3*a*d)*(b*c - a*d)*sqrt(c + d*x))/(24*a^3*c*x*sqrt(a + b*x)) + ((b*c - a*d)*(35*b^2*c^2 - 10*a*b*c*d - a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*a^(9/2)*c^(3/2))]

    @test_int [(x^3*(c + d*x)^(5/2))/(a + b*x)^(3/2), x, 8, (3*(b*c - a*d)*(b^3*c^3 + 7*a*b^2*c^2*d + 63*a^2*b*c*d^2 - 231*a^3*d^3)*sqrt(a + b*x)*sqrt(c + d*x))/(128*b^6*d^2) + ((b^3*c^3 + 7*a*b^2*c^2*d + 63*a^2*b*c*d^2 - 231*a^3*d^3)*sqrt(a + b*x)*(c + d*x)^(3/2))/(64*b^5*d^2) - (2*x^3*(c + d*x)^(5/2))/(b*sqrt(a + b*x)) + (11*x^2*sqrt(a + b*x)*(c + d*x)^(5/2))/(5*b^2) - (sqrt(a + b*x)*(c + d*x)^(5/2)*(5*b^2*c^2 + 30*a*b*c*d - 231*a^2*d^2 - 2*b*d*(5*b*c - 99*a*d)*x))/(80*b^4*d^2) + (3*(b*c - a*d)^2*(b^3*c^3 + 7*a*b^2*c^2*d + 63*a^2*b*c*d^2 - 231*a^3*d^3)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(128*b^(13/2)*d^(5/2))]
    @test_int [(x^2*(c + d*x)^(5/2))/(a + b*x)^(3/2), x, 8, -((5*(b*c - a*d)*(b^2*c^2 + 14*a*b*c*d - 63*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(64*b^5*d)) - (5*(b^2*c^2 + 14*a*b*c*d - 63*a^2*d^2)*sqrt(a + b*x)*(c + d*x)^(3/2))/(96*b^4*d) - ((14*a*c + (b*c^2)/d - (63*a^2*d)/b)*sqrt(a + b*x)*(c + d*x)^(5/2))/(24*b^2*(b*c - a*d)) - (2*a^2*(c + d*x)^(7/2))/(b^2*(b*c - a*d)*sqrt(a + b*x)) + (sqrt(a + b*x)*(c + d*x)^(7/2))/(4*b^2*d) - (5*(b*c - a*d)^2*(b^2*c^2 + 14*a*b*c*d - 63*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(11/2)*d^(3/2))]
    @test_int [(x*(c + d*x)^(5/2))/(a + b*x)^(3/2), x, 7, (5*(b*c - 7*a*d)*(b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(8*b^4) + (5*(b*c - 7*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(12*b^3) + ((b*c - 7*a*d)*sqrt(a + b*x)*(c + d*x)^(5/2))/(3*b^2*(b*c - a*d)) + (2*a*(c + d*x)^(7/2))/(b*(b*c - a*d)*sqrt(a + b*x)) + (5*(b*c - 7*a*d)*(b*c - a*d)^2*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*b^(9/2)*sqrt(d))]
    @test_int [(c + d*x)^(5/2)/(a + b*x)^(3/2), x, 6, (15*d*(b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*b^3) + (5*d*sqrt(a + b*x)*(c + d*x)^(3/2))/(2*b^2) - (2*(c + d*x)^(5/2))/(b*sqrt(a + b*x)) + (15*sqrt(d)*(b*c - a*d)^2*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(7/2))]
    @test_int [(c + d*x)^(5/2)/(x*(a + b*x)^(3/2)), x, 8, -((d*(2*b*c - 3*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(a*b^2)) + (2*(b*c - a*d)*(c + d*x)^(3/2))/(a*b*sqrt(a + b*x)) - (2*c^(5/2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/a^(3/2) + (d^(3/2)*(5*b*c - 3*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/b^(5/2)]
    @test_int [(c + d*x)^(5/2)/(x^2*(a + b*x)^(3/2)), x, 8, -(((3*b*c - 2*a*d)*(b*c - a*d)*sqrt(c + d*x))/(a^2*b*sqrt(a + b*x))) - (c*(c + d*x)^(3/2))/(a*x*sqrt(a + b*x)) + (c^(3/2)*(3*b*c - 5*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/a^(5/2) + (2*d^(5/2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/b^(3/2)]
    @test_int [(c + d*x)^(5/2)/(x^3*(a + b*x)^(3/2)), x, 5, (15*(b*c - a*d)^2*sqrt(c + d*x))/(4*a^3*sqrt(a + b*x)) + (5*(b*c - a*d)*(c + d*x)^(3/2))/(4*a^2*x*sqrt(a + b*x)) - (c + d*x)^(5/2)/(2*a*x^2*sqrt(a + b*x)) - (15*sqrt(c)*(b*c - a*d)^2*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(7/2))]
    @test_int [(c + d*x)^(5/2)/(x^4*(a + b*x)^(3/2)), x, 6, -((5*(b*c - a*d)^2*(7*b*c - a*d)*sqrt(c + d*x))/(8*a^4*c*sqrt(a + b*x))) - (5*(b*c - a*d)*(7*b*c - a*d)*(c + d*x)^(3/2))/(24*a^3*c*x*sqrt(a + b*x)) + ((7*b*c - a*d)*(c + d*x)^(5/2))/(12*a^2*c*x^2*sqrt(a + b*x)) - (c + d*x)^(7/2)/(3*a*c*x^3*sqrt(a + b*x)) + (5*(b*c - a*d)^2*(7*b*c - a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*a^(9/2)*sqrt(c))]
    @test_int [(c + d*x)^(5/2)/(x^5*(a + b*x)^(3/2)), x, 8, (b*(945*b^3*c^3 - 1785*a*b^2*c^2*d + 839*a^2*b*c*d^2 - 15*a^3*d^3)*sqrt(c + d*x))/(192*a^5*c*sqrt(a + b*x)) + (c*(9*b*c - 11*a*d)*sqrt(c + d*x))/(24*a^2*x^3*sqrt(a + b*x)) - ((63*b*c - 59*a*d)*(b*c - a*d)*sqrt(c + d*x))/(96*a^3*x^2*sqrt(a + b*x)) + ((b*c - a*d)*(315*b^2*c^2 - 322*a*b*c*d + 15*a^2*d^2)*sqrt(c + d*x))/(192*a^4*c*x*sqrt(a + b*x)) - (c*(c + d*x)^(3/2))/(4*a*x^4*sqrt(a + b*x)) - (5*(b*c - a*d)^2*(63*b^2*c^2 - 14*a*b*c*d - a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(11/2)*c^(3/2))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [x^4/((a + b*x)^(3/2)*(c + d*x)^(3/2)), x, 6, (2*a*x^3)/(b*(b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x)) - (2*c*(b*c + a*d)*x^2*sqrt(a + b*x))/(b*d*(b*c - a*d)^2*sqrt(c + d*x)) - (sqrt(a + b*x)*sqrt(c + d*x)*((b*c + a*d)*(15*b^2*c^2 - 22*a*b*c*d + 15*a^2*d^2) - 2*b*d*(5*b^2*c^2 - 2*a*b*c*d + 5*a^2*d^2)*x))/(4*b^3*d^3*(b*c - a*d)^2) + (3*(5*b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(7/2)*d^(7/2))]
    @test_int [x^3/((a + b*x)^(3/2)*(c + d*x)^(3/2)), x, 5, (2*a*x^2)/(b*(b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x)) + (sqrt(a + b*x)*(c*(3*b^2*c^2 - 2*a*b*c*d + 3*a^2*d^2) + d*(b*c - 3*a*d)*(b*c - a*d)*x))/(b^2*d^2*(b*c - a*d)^2*sqrt(c + d*x)) - (3*(b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(b^(5/2)*d^(5/2))]
    @test_int [x^2/((a + b*x)^(3/2)*(c + d*x)^(3/2)), x, 5, -((2*a^2)/(b^2*(b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))) - (2*(b^2*c^2 + a^2*d^2)*sqrt(a + b*x))/(b^2*d*(b*c - a*d)^2*sqrt(c + d*x)) + (2*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(b^(3/2)*d^(3/2))]
    @test_int [x/((a + b*x)^(3/2)*(c + d*x)^(3/2)), x, 2, -((2*c)/(d*(b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))) + (2*(b*c + a*d)*sqrt(c + d*x))/(d*(b*c - a*d)^2*sqrt(a + b*x))]
    @test_int [1/((a + b*x)^(3/2)*(c + d*x)^(3/2)), x, 2, -(2/((b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))) - (4*d*sqrt(a + b*x))/((b*c - a*d)^2*sqrt(c + d*x))]
    @test_int [1/(x*(a + b*x)^(3/2)*(c + d*x)^(3/2)), x, 5, (2*b)/(a*(b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x)) + (2*d*(b*c + a*d)*sqrt(a + b*x))/(a*c*(b*c - a*d)^2*sqrt(c + d*x)) - (2*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(a^(3/2)*c^(3/2))]
    @test_int [1/(x^2*(a + b*x)^(3/2)*(c + d*x)^(3/2)), x, 6, -((b*(3*b*c - a*d))/(a^2*c*(b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x))) - 1/(a*c*x*sqrt(a + b*x)*sqrt(c + d*x)) - (d*(3*b^2*c^2 - 2*a*b*c*d + 3*a^2*d^2)*sqrt(a + b*x))/(a^2*c^2*(b*c - a*d)^2*sqrt(c + d*x)) + (3*(b*c + a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(a^(5/2)*c^(5/2))]
    @test_int [1/(x^3*(a + b*x)^(3/2)*(c + d*x)^(3/2)), x, 7, (b*(15*b^2*c^2 - 2*a*b*c*d - 5*a^2*d^2))/(4*a^3*c^2*(b*c - a*d)*sqrt(a + b*x)*sqrt(c + d*x)) - 1/(2*a*c*x^2*sqrt(a + b*x)*sqrt(c + d*x)) + (5*(b*c + a*d))/(4*a^2*c^2*x*sqrt(a + b*x)*sqrt(c + d*x)) + (d*(b*c + a*d)*(15*b^2*c^2 - 22*a*b*c*d + 15*a^2*d^2)*sqrt(a + b*x))/(4*a^3*c^3*(b*c - a*d)^2*sqrt(c + d*x)) - (3*(5*b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(7/2)*c^(7/2))]

    @test_int [x^5/((a + b*x)^(3/2)*(c + d*x)^(5/2)), x, 7, (2*a*x^4)/(b*(b*c - a*d)*sqrt(a + b*x)*(c + d*x)^(3/2)) - (2*c*(b*c + 3*a*d)*x^3*sqrt(a + b*x))/(3*b*d*(b*c - a*d)^2*(c + d*x)^(3/2)) - (2*c*(7*b^2*c^2 - 12*a*b*c*d - 3*a^2*d^2)*x^2*sqrt(a + b*x))/(3*b*d^2*(b*c - a*d)^3*sqrt(c + d*x)) - (sqrt(a + b*x)*sqrt(c + d*x)*(105*b^4*c^4 - 190*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 + 30*a^3*b*c*d^3 - 45*a^4*d^4 - 2*b*d*(35*b^3*c^3 - 61*a*b^2*c^2*d + 9*a^2*b*c*d^2 - 15*a^3*d^3)*x))/(12*b^3*d^4*(b*c - a*d)^3) + (5*(7*b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(7/2)*d^(9/2))]
    @test_int [x^4/((a + b*x)^(3/2)*(c + d*x)^(5/2)), x, 6, (2*a*x^3)/(b*(b*c - a*d)*sqrt(a + b*x)*(c + d*x)^(3/2)) - (2*c*(b*c + 3*a*d)*x^2*sqrt(a + b*x))/(3*b*d*(b*c - a*d)^2*(c + d*x)^(3/2)) + (sqrt(a + b*x)*(c*(15*b^3*c^3 - 31*a*b^2*c^2*d + 9*a^2*b*c*d^2 - 9*a^3*d^3) + d*(b*c - a*d)*(5*b^2*c^2 - 6*a*b*c*d + 9*a^2*d^2)*x))/(3*b^2*d^3*(b*c - a*d)^3*sqrt(c + d*x)) - ((5*b*c + 3*a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(b^(5/2)*d^(7/2))]
    @test_int [x^3/((a + b*x)^(3/2)*(c + d*x)^(5/2)), x, 5, (2*a*x^2)/(b*(b*c - a*d)*sqrt(a + b*x)*(c + d*x)^(3/2)) - (2*c*sqrt(a + b*x)*(c*(b*c - 3*a*d)*(3*b*c + a*d) + 2*d*(2*b^2*c^2 - 3*a*b*c*d - 3*a^2*d^2)*x))/(3*b*d^2*(b*c - a*d)^3*(c + d*x)^(3/2)) + (2*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(b^(3/2)*d^(5/2))]
    @test_int [x^2/((a + b*x)^(3/2)*(c + d*x)^(5/2)), x, 3, -((2*a^2)/(b^2*(b*c - a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))) - (2*(b^2*c^2 + 3*a^2*d^2)*sqrt(a + b*x))/(3*b^2*d*(b*c - a*d)^2*(c + d*x)^(3/2)) + (2*(b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*sqrt(a + b*x))/(3*b*d*(b*c - a*d)^3*sqrt(c + d*x))]
    @test_int [x/((a + b*x)^(3/2)*(c + d*x)^(5/2)), x, 3, (2*a)/(b*(b*c - a*d)*sqrt(a + b*x)*(c + d*x)^(3/2)) + (2*(b*c + 3*a*d)*sqrt(a + b*x))/(3*b*(b*c - a*d)^2*(c + d*x)^(3/2)) + (4*(b*c + 3*a*d)*sqrt(a + b*x))/(3*(b*c - a*d)^3*sqrt(c + d*x))]
    @test_int [1/((a + b*x)^(3/2)*(c + d*x)^(5/2)), x, 3, -(2/((b*c - a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))) - (8*d*sqrt(a + b*x))/(3*(b*c - a*d)^2*(c + d*x)^(3/2)) - (16*b*d*sqrt(a + b*x))/(3*(b*c - a*d)^3*sqrt(c + d*x))]
    @test_int [1/(x*(a + b*x)^(3/2)*(c + d*x)^(5/2)), x, 6, (2*b)/(a*(b*c - a*d)*sqrt(a + b*x)*(c + d*x)^(3/2)) + (2*d*(3*b*c + a*d)*sqrt(a + b*x))/(3*a*c*(b*c - a*d)^2*(c + d*x)^(3/2)) + (2*d*(3*b*c - a*d)*(b*c + 3*a*d)*sqrt(a + b*x))/(3*a*c^2*(b*c - a*d)^3*sqrt(c + d*x)) - (2*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(a^(3/2)*c^(5/2))]
    @test_int [1/(x^2*(a + b*x)^(3/2)*(c + d*x)^(5/2)), x, 7, -((b*(3*b*c - a*d))/(a^2*c*(b*c - a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))) - 1/(a*c*x*sqrt(a + b*x)*(c + d*x)^(3/2)) - (d*(9*b^2*c^2 - 6*a*b*c*d + 5*a^2*d^2)*sqrt(a + b*x))/(3*a^2*c^2*(b*c - a*d)^2*(c + d*x)^(3/2)) - (d*(9*b^3*c^3 - 9*a*b^2*c^2*d + 31*a^2*b*c*d^2 - 15*a^3*d^3)*sqrt(a + b*x))/(3*a^2*c^3*(b*c - a*d)^3*sqrt(c + d*x)) + ((3*b*c + 5*a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(a^(5/2)*c^(7/2))]
    @test_int [1/(x^3*(a + b*x)^(3/2)*(c + d*x)^(5/2)), x, 8, (b*(15*b^2*c^2 - 7*a^2*d^2))/(4*a^3*c^2*(b*c - a*d)*sqrt(a + b*x)*(c + d*x)^(3/2)) - 1/(2*a*c*x^2*sqrt(a + b*x)*(c + d*x)^(3/2)) + (5*b*c + 7*a*d)/(4*a^2*c^2*x*sqrt(a + b*x)*(c + d*x)^(3/2)) + (d*(45*b^3*c^3 - 15*a*b^2*c^2*d - 33*a^2*b*c*d^2 + 35*a^3*d^3)*sqrt(a + b*x))/(12*a^3*c^3*(b*c - a*d)^2*(c + d*x)^(3/2)) + (d*(45*b^4*c^4 - 30*a*b^3*c^3*d - 36*a^2*b^2*c^2*d^2 + 190*a^3*b*c*d^3 - 105*a^4*d^4)*sqrt(a + b*x))/(12*a^3*c^4*(b*c - a*d)^3*sqrt(c + d*x)) - (5*(3*b^2*c^2 + 6*a*b*c*d + 7*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(7/2)*c^(9/2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x)^(n/2) / (a+b*x)^(5/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(x^4*(c + d*x)^(5/2))/(a + b*x)^(5/2), x, 9, ((3*b^4*c^4 + 28*a*b^3*c^3*d + 378*a^2*b^2*c^2*d^2 - 2772*a^3*b*c*d^3 + 3003*a^4*d^4)*sqrt(a + b*x)*sqrt(c + d*x))/(128*b^7*d^2) + ((3*b^4*c^4 + 28*a*b^3*c^3*d + 378*a^2*b^2*c^2*d^2 - 2772*a^3*b*c*d^3 + 3003*a^4*d^4)*sqrt(a + b*x)*(c + d*x)^(3/2))/(192*b^6*d^2*(b*c - a*d)) - (2*x^4*(c + d*x)^(5/2))/(3*b*(a + b*x)^(3/2)) - (2*(8*b*c - 13*a*d)*x^3*(c + d*x)^(5/2))/(3*b^2*(b*c - a*d)*sqrt(a + b*x)) + ((93*b*c - 143*a*d)*x^2*sqrt(a + b*x)*(c + d*x)^(5/2))/(15*b^3*(b*c - a*d)) - (sqrt(a + b*x)*(c + d*x)^(5/2)*(15*b^3*c^3 + 125*a*b^2*c^2*d - 2343*a^2*b*c*d^2 + 3003*a^3*d^3 - 2*b*d*(15*b^2*c^2 - 902*a*b*c*d + 1287*a^2*d^2)*x))/(240*b^5*d^2*(b*c - a*d)) + ((b*c - a*d)*(3*b^4*c^4 + 28*a*b^3*c^3*d + 378*a^2*b^2*c^2*d^2 - 2772*a^3*b*c*d^3 + 3003*a^4*d^4)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(128*b^(15/2)*d^(5/2))]
    @test_int [(x^3*(c + d*x)^(5/2))/(a + b*x)^(5/2), x, 8, -((5*(b^3*c^3 + 21*a*b^2*c^2*d - 189*a^2*b*c*d^2 + 231*a^3*d^3)*sqrt(a + b*x)*sqrt(c + d*x))/(64*b^6*d)) - (5*(b^3*c^3 + 21*a*b^2*c^2*d - 189*a^2*b*c*d^2 + 231*a^3*d^3)*sqrt(a + b*x)*(c + d*x)^(3/2))/(96*b^5*d*(b*c - a*d)) - (2*x^3*(c + d*x)^(5/2))/(3*b*(a + b*x)^(3/2)) - (2*(6*b*c - 11*a*d)*x^2*(c + d*x)^(5/2))/(3*b^2*(b*c - a*d)*sqrt(a + b*x)) + (sqrt(a + b*x)*(c + d*x)^(5/2)*(5*b^2*c^2 - 156*a*b*c*d + 231*a^2*d^2 + 2*b*d*(59*b*c - 99*a*d)*x))/(24*b^4*d*(b*c - a*d)) - (5*(b*c - a*d)*(b^3*c^3 + 21*a*b^2*c^2*d - 189*a^2*b*c*d^2 + 231*a^3*d^3)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(64*b^(13/2)*d^(3/2))]
    @test_int [(x^2*(c + d*x)^(5/2))/(a + b*x)^(5/2), x, 8, (5*(b^2*c^2 - 14*a*b*c*d + 21*a^2*d^2)*sqrt(a + b*x)*sqrt(c + d*x))/(8*b^5) + (5*(b^2*c^2 - 14*a*b*c*d + 21*a^2*d^2)*sqrt(a + b*x)*(c + d*x)^(3/2))/(12*b^4*(b*c - a*d)) + ((b^2*c^2 - 14*a*b*c*d + 21*a^2*d^2)*sqrt(a + b*x)*(c + d*x)^(5/2))/(3*b^3*(b*c - a*d)^2) - (2*a^2*(c + d*x)^(7/2))/(3*b^2*(b*c - a*d)*(a + b*x)^(3/2)) + (4*a*(3*b*c - 5*a*d)*(c + d*x)^(7/2))/(3*b^2*(b*c - a*d)^2*sqrt(a + b*x)) + (5*(b*c - a*d)*(b^2*c^2 - 14*a*b*c*d + 21*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(8*b^(11/2)*sqrt(d))]
    @test_int [(x*(c + d*x)^(5/2))/(a + b*x)^(5/2), x, 7, (5*d*(3*b*c - 7*a*d)*sqrt(a + b*x)*sqrt(c + d*x))/(4*b^4) + (5*d*(3*b*c - 7*a*d)*sqrt(a + b*x)*(c + d*x)^(3/2))/(6*b^3*(b*c - a*d)) - (2*(3*b*c - 7*a*d)*(c + d*x)^(5/2))/(3*b^2*(b*c - a*d)*sqrt(a + b*x)) + (2*a*(c + d*x)^(7/2))/(3*b*(b*c - a*d)*(a + b*x)^(3/2)) + (5*sqrt(d)*(3*b*c - 7*a*d)*(b*c - a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(9/2))]
    @test_int [(c + d*x)^(5/2)/(a + b*x)^(5/2), x, 6, (5*d^2*sqrt(a + b*x)*sqrt(c + d*x))/b^3 - (10*d*(c + d*x)^(3/2))/(3*b^2*sqrt(a + b*x)) - (2*(c + d*x)^(5/2))/(3*b*(a + b*x)^(3/2)) + (5*d^(3/2)*(b*c - a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/b^(7/2)]
    @test_int [(c + d*x)^(5/2)/(x*(a + b*x)^(5/2)), x, 8, (2*(c^2/a^2 - d^2/b^2)*sqrt(c + d*x))/sqrt(a + b*x) + (2*(b*c - a*d)*(c + d*x)^(3/2))/(3*a*b*(a + b*x)^(3/2)) - (2*c^(5/2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/a^(5/2) + (2*d^(5/2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/b^(5/2)]
    @test_int [(c + d*x)^(5/2)/(x^2*(a + b*x)^(5/2)), x, 5, (-5*c*(b*c - a*d)*sqrt(c + d*x))/(a^3*sqrt(a + b*x)) - (5*(b*c - a*d)*(c + d*x)^(3/2))/(3*a^2*(a + b*x)^(3/2)) - (c + d*x)^(5/2)/(a*x*(a + b*x)^(3/2)) + (5*c^(3/2)*(b*c - a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/a^(7/2)]
    @test_int [(c + d*x)^(5/2)/(x^3*(a + b*x)^(5/2)), x, 6, (5*(7*b*c - 3*a*d)*(b*c - a*d)*sqrt(c + d*x))/(4*a^4*sqrt(a + b*x)) + (5*(7*b*c - 3*a*d)*(b*c - a*d)*(c + d*x)^(3/2))/(12*a^3*c*(a + b*x)^(3/2)) + ((7*b*c - 3*a*d)*(c + d*x)^(5/2))/(4*a^2*c*x*(a + b*x)^(3/2)) - (c + d*x)^(7/2)/(2*a*c*x^2*(a + b*x)^(3/2)) - (5*sqrt(c)*(7*b*c - 3*a*d)*(b*c - a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(9/2))]
    @test_int [(c + d*x)^(5/2)/(x^4*(a + b*x)^(5/2)), x, 8, -((7*b*(15*b*c - 7*a*d)*(b*c - a*d)*sqrt(c + d*x))/(24*a^4*(a + b*x)^(3/2))) + (3*c*(b*c - a*d)*sqrt(c + d*x))/(4*a^2*x^2*(a + b*x)^(3/2)) - ((21*b*c - 11*a*d)*(b*c - a*d)*sqrt(c + d*x))/(8*a^3*x*(a + b*x)^(3/2)) - (b*(315*b^2*c^2 - 420*a*b*c*d + 113*a^2*d^2)*sqrt(c + d*x))/(24*a^5*sqrt(a + b*x)) - (c*(c + d*x)^(3/2))/(3*a*x^3*(a + b*x)^(3/2)) + (5*(b*c - a*d)*(21*b^2*c^2 - 14*a*b*c*d + a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(8*a^(11/2)*sqrt(c))]
    @test_int [(c + d*x)^(5/2)/(x^5*(a + b*x)^(5/2)), x, 9, (b*(b*c - a*d)*(385*b^2*c^2 - 238*a*b*c*d + 5*a^2*d^2)*sqrt(c + d*x))/(64*a^5*c*(a + b*x)^(3/2)) + (11*c*(b*c - a*d)*sqrt(c + d*x))/(24*a^2*x^3*(a + b*x)^(3/2)) - ((99*b*c - 59*a*d)*(b*c - a*d)*sqrt(c + d*x))/(96*a^3*x^2*(a + b*x)^(3/2)) + ((b*c - a*d)*(231*b^2*c^2 - 156*a*b*c*d + 5*a^2*d^2)*sqrt(c + d*x))/(64*a^4*c*x*(a + b*x)^(3/2)) + (b*(1155*b^3*c^3 - 1715*a*b^2*c^2*d + 581*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(c + d*x))/(64*a^6*c*sqrt(a + b*x)) - (c*(c + d*x)^(3/2))/(4*a*x^4*(a + b*x)^(3/2)) - (5*(b*c - a*d)*(231*b^3*c^3 - 189*a*b^2*c^2*d + 21*a^2*b*c*d^2 + a^3*d^3)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(64*a^(13/2)*c^(3/2))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [x^2/((a + b*x)^(5/2)*(c + d*x)^(1/2)), x, 5, -((2*a^2*sqrt(c + d*x))/(3*b^2*(b*c - a*d)*(a + b*x)^(3/2))) + (4*a*(3*b*c - 2*a*d)*sqrt(c + d*x))/(3*b^2*(b*c - a*d)^2*sqrt(a + b*x)) + (2*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(b^(5/2)*sqrt(d))]

    @test_int [x^6/((a + b*x)^(5/2)*(c + d*x)^(5/2)), x, 8, (2*a*x^5)/(3*b*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2)) + (2*a*(13*b*c - 7*a*d)*x^4)/(3*b^2*(b*c - a*d)^2*sqrt(a + b*x)*(c + d*x)^(3/2)) - (2*c*(b^2*c^2 + 14*a*b*c*d - 7*a^2*d^2)*x^3*sqrt(a + b*x))/(3*b^2*d*(b*c - a*d)^3*(c + d*x)^(3/2)) - (2*c*(b*c + a*d)*(7*b^2*c^2 - 22*a*b*c*d + 7*a^2*d^2)*x^2*sqrt(a + b*x))/(3*b^2*d^2*(b*c - a*d)^4*sqrt(c + d*x)) - (sqrt(a + b*x)*sqrt(c + d*x)*((b*c + a*d)*(105*b^4*c^4 - 340*a*b^3*c^3*d + 406*a^2*b^2*c^2*d^2 - 340*a^3*b*c*d^3 + 105*a^4*d^4) - 2*b*d*(35*b^4*c^4 - 76*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 - 76*a^3*b*c*d^3 + 35*a^4*d^4)*x))/(12*b^4*d^4*(b*c - a*d)^4) + (5*(7*b^2*c^2 + 10*a*b*c*d + 7*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(4*b^(9/2)*d^(9/2))]
    @test_int [x^5/((a + b*x)^(5/2)*(c + d*x)^(5/2)), x, 7, (2*a*x^4)/(3*b*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2)) + (2*a*(11*b*c - 5*a*d)*x^3)/(3*b^2*(b*c - a*d)^2*sqrt(a + b*x)*(c + d*x)^(3/2)) - (2*c*(b^2*c^2 + 12*a*b*c*d - 5*a^2*d^2)*x^2*sqrt(a + b*x))/(3*b^2*d*(b*c - a*d)^3*(c + d*x)^(3/2)) + (sqrt(a + b*x)*(c*(15*b^4*c^4 - 40*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 - 40*a^3*b*c*d^3 + 15*a^4*d^4) + d*(b*c - a*d)*(5*b^3*c^3 - 9*a*b^2*c^2*d + 35*a^2*b*c*d^2 - 15*a^3*d^3)*x))/(3*b^3*d^3*(b*c - a*d)^4*sqrt(c + d*x)) - (5*(b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(b^(7/2)*d^(7/2))]
    @test_int [x^4/((a + b*x)^(5/2)*(c + d*x)^(5/2)), x, 6, (2*a*x^3)/(3*b*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2)) + (2*a*(3*b*c - a*d)*x^2)/(b^2*(b*c - a*d)^2*sqrt(a + b*x)*(c + d*x)^(3/2)) - (2*c*sqrt(a + b*x)*(c*(b*c + a*d)*(3*b^2*c^2 - 14*a*b*c*d + 3*a^2*d^2) + 2*d*(2*b^3*c^3 - a*b^2*c^2*d - 12*a^2*b*c*d^2 + 3*a^3*d^3)*x))/(3*b^2*d^2*(b*c - a*d)^4*(c + d*x)^(3/2)) + (2*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(b^(5/2)*d^(5/2))]
    @test_int [x^3/((a + b*x)^(5/2)*(c + d*x)^(5/2)), x, 4, -((2*x^3)/(3*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2))) - (4*a^2*c)/(b^2*(b*c - a*d)^2*sqrt(a + b*x)*(c + d*x)^(3/2)) - (4*c*(b^2*c^2 + 3*a^2*d^2)*sqrt(a + b*x))/(3*b^2*d*(b*c - a*d)^3*(c + d*x)^(3/2)) + (4*c*(b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*sqrt(a + b*x))/(3*b*d*(b*c - a*d)^4*sqrt(c + d*x))]
    @test_int [x^2/((a + b*x)^(5/2)*(c + d*x)^(5/2)), x, 4, -((2*a^2)/(3*b^2*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2))) + (4*a*c)/(b*(b*c - a*d)^2*sqrt(a + b*x)*(c + d*x)^(3/2)) + (2*(b^2*c^2 + 6*a*b*c*d + a^2*d^2)*sqrt(a + b*x))/(3*b^2*(b*c - a*d)^3*(c + d*x)^(3/2)) + (4*(b^2*c^2 + 6*a*b*c*d + a^2*d^2)*sqrt(a + b*x))/(3*b*(b*c - a*d)^4*sqrt(c + d*x))]
    @test_int [x^1/((a + b*x)^(5/2)*(c + d*x)^(5/2)), x, 4, -((2*c)/(3*d*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2))) + (2*(b*c + a*d))/(3*d*(b*c - a*d)^2*(a + b*x)^(3/2)*sqrt(c + d*x)) - (8*(b*c + a*d))/(3*(b*c - a*d)^3*sqrt(a + b*x)*sqrt(c + d*x)) - (16*d*(b*c + a*d)*sqrt(a + b*x))/(3*(b*c - a*d)^4*sqrt(c + d*x))]
    @test_int [x^0/((a + b*x)^(5/2)*(c + d*x)^(5/2)), x, 4, -(2/(3*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2))) + (4*d)/((b*c - a*d)^2*sqrt(a + b*x)*(c + d*x)^(3/2)) + (16*d^2*sqrt(a + b*x))/(3*(b*c - a*d)^3*(c + d*x)^(3/2)) + (32*b*d^2*sqrt(a + b*x))/(3*(b*c - a*d)^4*sqrt(c + d*x))]
    @test_int [1/(x^1*(a + b*x)^(5/2)*(c + d*x)^(5/2)), x, 7, (2*b)/(3*a*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2)) + (2*b*(b*c - 3*a*d))/(a^2*(b*c - a*d)^2*sqrt(a + b*x)*(c + d*x)^(3/2)) + (2*d*(3*b^2*c^2 - 10*a*b*c*d - a^2*d^2)*sqrt(a + b*x))/(3*a^2*c*(b*c - a*d)^3*(c + d*x)^(3/2)) + (2*d*(b*c + a*d)*(3*b^2*c^2 - 14*a*b*c*d + 3*a^2*d^2)*sqrt(a + b*x))/(3*a^2*c^2*(b*c - a*d)^4*sqrt(c + d*x)) - (2*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(a^(5/2)*c^(5/2))]
    @test_int [1/(x^2*(a + b*x)^(5/2)*(c + d*x)^(5/2)), x, 8, -((b*(5*b*c - 3*a*d))/(3*a^2*c*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2))) - 1/(a*c*x*(a + b*x)^(3/2)*(c + d*x)^(3/2)) - (b*(5*b^2*c^2 - 10*a*b*c*d + a^2*d^2))/(a^3*c*(b*c - a*d)^2*sqrt(a + b*x)*(c + d*x)^(3/2)) - (d*(15*b^3*c^3 - 35*a*b^2*c^2*d + 9*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(a + b*x))/(3*a^3*c^2*(b*c - a*d)^3*(c + d*x)^(3/2)) - (d*(15*b^4*c^4 - 40*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 - 40*a^3*b*c*d^3 + 15*a^4*d^4)*sqrt(a + b*x))/(3*a^3*c^3*(b*c - a*d)^4*sqrt(c + d*x)) + (5*(b*c + a*d)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(a^(7/2)*c^(7/2))]
    @test_int [1/(x^3*(a + b*x)^(5/2)*(c + d*x)^(5/2)), x, 9, (b*(35*b^2*c^2 - 6*a*b*c*d - 21*a^2*d^2))/(12*a^3*c^2*(b*c - a*d)*(a + b*x)^(3/2)*(c + d*x)^(3/2)) - 1/(2*a*c*x^2*(a + b*x)^(3/2)*(c + d*x)^(3/2)) + (7*(b*c + a*d))/(4*a^2*c^2*x*(a + b*x)^(3/2)*(c + d*x)^(3/2)) + (b*(35*b^3*c^3 - 55*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 7*a^3*d^3))/(4*a^4*c^2*(b*c - a*d)^2*sqrt(a + b*x)*(c + d*x)^(3/2)) + (d*(105*b^4*c^4 - 200*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 + 48*a^3*b*c*d^3 - 35*a^4*d^4)*sqrt(a + b*x))/(12*a^4*c^3*(b*c - a*d)^3*(c + d*x)^(3/2)) + (d*(b*c + a*d)*(105*b^4*c^4 - 340*a*b^3*c^3*d + 406*a^2*b^2*c^2*d^2 - 340*a^3*b*c*d^3 + 105*a^4*d^4)*sqrt(a + b*x))/(12*a^4*c^4*(b*c - a*d)^4*sqrt(c + d*x)) - (5*(7*b^2*c^2 + 10*a*b*c*d + 7*a^2*d^2)*atanh((sqrt(c)*sqrt(a + b*x))/(sqrt(a)*sqrt(c + d*x))))/(4*a^(9/2)*c^(9/2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x)^(n/2)*(a+b*x)^(p/2)=#

    #= Note*that*the*derivative*of*(a+b*x)^n/(-a-b*x)^n*is*zero. =#
    @test_int [x^2*sqrt(a + b*x)/sqrt(-a - b*x), x, 2, (x^3*sqrt(a + b*x))/(3*sqrt(-a - b*x))]
    @test_int [x*sqrt(a + b*x)/sqrt(-a - b*x), x, 2, (x^2*sqrt(a + b*x))/(2*sqrt(-a - b*x))]
    @test_int [sqrt(a + b*x)/sqrt(-a - b*x), x, 2, (x*sqrt(a + b*x))/sqrt(-a - b*x)]
    @test_int [sqrt(a + b*x)/(x*sqrt(-a - b*x)), x, 2, (sqrt(a + b*x)*log(x))/sqrt(-a - b*x)]
    @test_int [sqrt(a + b*x)/(x^2*sqrt(-a - b*x)), x, 2, -(sqrt(a + b*x)/(x*sqrt(-a - b*x)))]
    @test_int [sqrt(a + b*x)/(x^3*sqrt(-a - b*x)), x, 2, -(sqrt(a + b*x)/(2*x^2*sqrt(-a - b*x)))]
    @test_int [sqrt(a + b*x)/(x^m*sqrt(-a - b*x)), x, 2, (x^(1 - m)*sqrt(a + b*x))/((1 - m)*sqrt(-a - b*x))]

    @test_int [x^2*((a + b*x)^n/(-a - b*x)^n), x, 2, ((1/3)*x^3*(a + b*x)^n)/(-a - b*x)^n]
    @test_int [x*((a + b*x)^n/(-a - b*x)^n), x, 2, ((1/2)*x^2*(a + b*x)^n)/(-a - b*x)^n]
    @test_int [((a + b*x)^n/(-a - b*x)^n), x, 2, (x*(a + b*x)^n)/(-a - b*x)^n]
    @test_int [((a + b*x)^n/(x*(-a - b*x)^n)), x, 2, ((a + b*x)^n*log(x))/(-a - b*x)^n]
    @test_int [((a + b*x)^n/(x^2*(-a - b*x)^n)), x, 2, -((a + b*x)^n/((-a - b*x)^n*x))]
    @test_int [((a + b*x)^n/(x^3*(-a - b*x)^n)), x, 2, -((a + b*x)^n/((-a - b*x)^n*(2*x^2)))]
    @test_int [((a + b*x)^n/(x^m*(-a - b*x)^n)), x, 2, (x^(1 - m)*(a + b*x)^n)/((-a - b*x)^n*(1 - m))]

    @test_int [x^3*sqrt(1 + x)/(1 - x)^(5/2), x, 5, -((13*x^2*sqrt(1 + x))/(3*sqrt(1 - x))) + (2*x^3*sqrt(1 + x))/(3*(1 - x)^(3/2)) - (1/6)*sqrt(1 - x)*sqrt(1 + x)*(52 + 33*x) + (11*asin(x))/2]
    @test_int [x^2*sqrt(1 + x)/(1 - x)^(5/2), x, 6, -((4*sqrt(1 + x))/sqrt(1 - x)) - sqrt(1 - x)*sqrt(1 + x) + (1 + x)^(3/2)/(3*(1 - x)^(3/2)) + 3*asin(x), -3*sqrt(1 - x)*sqrt(1 + x) + (1 + x)^(3/2)/(3*(1 - x)^(3/2)) - (2*(1 + x)^(3/2))/sqrt(1 - x) + 3*asin(x)]
    @test_int [x*sqrt(1 + x)/(1 - x)^(5/2), x, 4, -((2*sqrt(1 + x))/sqrt(1 - x)) + (1 + x)^(3/2)/(3*(1 - x)^(3/2)) + asin(x)]
    @test_int [sqrt(1 + x)/(1 - x)^(5/2), x, 1, (1 + x)^(3/2)/(3*(1 - x)^(3/2))]
    @test_int [sqrt(1 + x)/(-1 + x)^(5/2), x, 1, -((1 + x)^(3/2)/(3*(-1 + x)^(3/2)))]
    @test_int [sqrt(1 + x)/(x*(1 - x)^(5/2)), x, 4, (2*sqrt(1 + x))/sqrt(1 - x) + (1 + x)^(3/2)/(3*(1 - x)^(3/2)) - atanh(sqrt(1 - x)*sqrt(1 + x))]
    @test_int [sqrt(1 + x)/(x^2*(1 - x)^(5/2)), x, 6, (14*sqrt(1 + x))/(3*sqrt(1 - x)) + (2*sqrt(1 + x))/(3*(1 - x)^(3/2)*x) - (5*sqrt(1 + x))/(3*sqrt(1 - x)*x) - 3*atanh(sqrt(1 - x)*sqrt(1 + x))]
    @test_int [sqrt(1 + x)/(x^3*(1 - x)^(5/2)), x, 7, (26*sqrt(1 + x))/(3*sqrt(1 - x)) + (2*sqrt(1 + x))/(3*(1 - x)^(3/2)*x^2) - (7*sqrt(1 + x))/(6*sqrt(1 - x)*x^2) - (19*sqrt(1 + x))/(6*sqrt(1 - x)*x) - (11/2)*atanh(sqrt(1 - x)*sqrt(1 + x))]

    @test_int [x^2/(sqrt(-1 + x)*sqrt(1 + x)), x, 2, (1/2)*sqrt(-1 + x)*x*sqrt(1 + x) + acosh(x)/2]
    @test_int [x/(sqrt(-1 + x)*sqrt(1 + x)), x, 1, sqrt(-1 + x)*sqrt(1 + x)]
    @test_int [1/(sqrt(-1 + x)*sqrt(1 + x)), x, 1, acosh(x)]
    @test_int [1/(x*sqrt(-1 + x)*sqrt(1 + x)), x, 2, atan(sqrt(-1 + x)*sqrt(1 + x))]
    @test_int [1/(x^2*sqrt(-1 + x)*sqrt(1 + x)), x, 1, (sqrt(-1 + x)*sqrt(1 + x))/x]

    @test_int [x^2*sqrt(-1 + x)*sqrt(1 + x), x, 3, (1/8)*sqrt(-1 + x)*x*sqrt(1 + x) + (1/4)*(-1 + x)^(3/2)*x*(1 + x)^(3/2) - acosh(x)/8]
    @test_int [x*sqrt(-1 + x)*sqrt(1 + x), x, 1, ((-1 + x)^(3/2)*(1 + x)^(3/2))/3]
    @test_int [sqrt(-1 + x)*sqrt(1 + x), x, 2, (1/2)*sqrt(-1 + x)*x*sqrt(1 + x) - acosh(x)/2]
    @test_int [sqrt(-1 + x)*sqrt(1 + x)/x, x, 3, sqrt(-1 + x)*sqrt(1 + x) - atan(sqrt(-1 + x)*sqrt(1 + x))]
    @test_int [sqrt(-1 + x)*sqrt(1 + x)/x^2, x, 2, -((sqrt(-1 + x)*sqrt(1 + x))/x) + acosh(x)]

    @test_int [1/(sqrt(1 + 2*x)*sqrt(3 + 2*x)), x, 2, asinh(sqrt(1 + 2*x)/sqrt(2))]
    @test_int [1/(x*sqrt(-2 + 3*x)*sqrt(3 + 5*x)), x, 2, sqrt(2/3)*atan((sqrt(3/2)*sqrt(-2 + 3*x))/sqrt(3 + 5*x))]

    @test_int [1/(x*(1 + x)^(3/2)*(-1 + x)^(3/2)), x, 3, -(1/(sqrt(-1 + x)*sqrt(1 + x))) - atan(sqrt(-1 + x)*sqrt(1 + x))]

    @test_int [x*sqrt(1 - x)*sqrt(1 + x), x, 1, (-(1/3))*(1 - x)^(3/2)*(1 + x)^(3/2)]

    @test_int [x^3*(2 + 3*x)^(3/2)*(1 + 4*x)^(1/2), x, 7, (213575*sqrt(2 + 3*x)*sqrt(1 + 4*x))/42467328 + (42715*(2 + 3*x)^(3/2)*sqrt(1 + 4*x))/15925248 - (8543*(2 + 3*x)^(5/2)*sqrt(1 + 4*x))/995328 + ((4103 - 7968*x)*(2 + 3*x)^(5/2)*(1 + 4*x)^(3/2))/829440 + (1/72)*x^2*(2 + 3*x)^(5/2)*(1 + 4*x)^(3/2) + (1067875*asinh(sqrt(3/5)*sqrt(1 + 4*x)))/(84934656*sqrt(3))]

    @test_int [1/(sqrt(-1 + a + b*x)*sqrt(1 + a + b*x)), x, 2, (2/b)*asinh(sqrt(-1 + a + b*x)/sqrt(2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^(m/2)*(c+d*x)^(n/2)*(a+b*x)^(p/2)=#

    @test_int [1/(sqrt(x)*sqrt(a + b*x)*sqrt(a - b*x)), x, 2, (2*sqrt(a)*sqrt(1 - (b*x)/a)*sqrt(1 + (b*x)/a)*Elliptic.F(asin((sqrt(b)*sqrt(x))/sqrt(a)), -1))/(sqrt(b)*sqrt(a - b*x)*sqrt(a + b*x))]
    @test_int [1/(sqrt(-x)*sqrt(a + b*x)*sqrt(a - b*x)), x, 2, -((2*sqrt(a)*sqrt(1 - (b*x)/a)*sqrt(1 + (b*x)/a)*Elliptic.F(asin((sqrt(b)*sqrt(-x))/sqrt(a)), -1))/(sqrt(b)*sqrt(a - b*x)*sqrt(a + b*x)))]
    @test_int [1/(sqrt(e*x)*sqrt(a + b*x)*sqrt(a - b*x)), x, 2, (2*sqrt(a)*sqrt(1 - (b*x)/a)*sqrt(1 + (b*x)/a)*Elliptic.F(asin((sqrt(b)*sqrt(e*x))/(sqrt(a)*sqrt(e))), -1))/(sqrt(b)*sqrt(e)*sqrt(a - b*x)*sqrt(a + b*x))]

    @test_int [1/(sqrt(x)*sqrt(2 + b*x)*sqrt(2 - b*x)), x, 1, (sqrt(2)*Elliptic.F(asin((sqrt(b)*sqrt(x))/sqrt(2)), -1))/sqrt(b)]
    @test_int [1/(sqrt(-x)*sqrt(2 + b*x)*sqrt(2 - b*x)), x, 1, -((sqrt(2)*Elliptic.F(asin((sqrt(b)*sqrt(-x))/sqrt(2)), -1))/sqrt(b))]
    @test_int [1/(sqrt(e*x)*sqrt(2 + b*x)*sqrt(2 - b*x)), x, 1, (sqrt(2)*Elliptic.F(asin((sqrt(b)*sqrt(e*x))/(sqrt(2)*sqrt(e))), -1))/(sqrt(b)*sqrt(e))]

    @test_int [1/(sqrt(x)*sqrt(2 + 3*x)*sqrt(2 - 3*x)), x, 1, sqrt(2/3)*Elliptic.F(asin(sqrt(3/2)*sqrt(x)), -1)]
    @test_int [1/(sqrt(-x)*sqrt(2 + 3*x)*sqrt(2 - 3*x)), x, 1, (-sqrt(2/3))*Elliptic.F(asin(sqrt(3/2)*sqrt(-x)), -1)]
    @test_int [1/(sqrt(e*x)*sqrt(2 + 3*x)*sqrt(2 - 3*x)), x, 1, (sqrt(2/3)*Elliptic.F(asin((sqrt(3/2)*sqrt(e*x))/sqrt(e)), -1))/sqrt(e)]

    @test_int [1/(sqrt(x)*sqrt(1 - x)*sqrt(1 + x)), x, 1, 2*Elliptic.F(asin(sqrt(x)), -1)]
    @test_int [1/(sqrt(1 + x)*sqrt(x - x^2)), x, 2, 2*Elliptic.F(asin(sqrt(x)), -1)]

    @test_int [1/(sqrt(b*x)*sqrt(1 - c*x)*sqrt(1 + c*x)), x, 1, (2*Elliptic.F(asin((sqrt(c)*sqrt(b*x))/sqrt(b)), -1))/(sqrt(b)*sqrt(c))]
    @test_int [1/(sqrt(b*x)*sqrt(1 - c*x)*sqrt(1 + d*x)), x, 1, (2*Elliptic.F(asin((sqrt(c)*sqrt(b*x))/sqrt(b)), -(d/c)))/(sqrt(b)*sqrt(c))]

    @test_int [sqrt(1 + x)/(sqrt(x)*sqrt(1 - x)), x, 1, 2*Elliptic.E(asin(sqrt(x)), -1)]
    @test_int [sqrt(1 + x)/sqrt(x - x^2), x, 2, 2*Elliptic.E(asin(sqrt(x)), -1)]

    @test_int [sqrt(1 + c*x)/(sqrt(b*x)*sqrt(1 - c*x)), x, 1, (2*Elliptic.E(asin((sqrt(c)*sqrt(b*x))/sqrt(b)), -1))/(sqrt(b)*sqrt(c))]
    @test_int [sqrt(1 + c*x)/(sqrt(b*x)*sqrt(1 - d*x)), x, 1, (2*Elliptic.E(asin((sqrt(d)*sqrt(b*x))/sqrt(b)), -(c/d)))/(sqrt(b)*sqrt(d))]

    #= Following*integrands*are*equal. =#
    @test_int [sqrt(1 - x)/(sqrt(x)*sqrt(1 + x)), x, 2, -((2*sqrt(-x)*Elliptic.E(asin(sqrt(-x)), -1))/sqrt(x))]
    @test_int [sqrt(-1 + 1/x)*sqrt(1/x)*sqrt(x)/sqrt(1 + x), x, 4, -((2*sqrt(-x)*Elliptic.E(asin(sqrt(-x)), -1))/sqrt(x)), -((2*sqrt(-1 + 1/x)*sqrt(1/x)*sqrt(-x)*sqrt(x)*Elliptic.E(asin(sqrt(-x)), -1))/sqrt(1 - x))]

    @test_int [sqrt(1 - c*x)/(sqrt(b*x)*sqrt(1 + c*x)), x, 1, -((2*Elliptic.E(asin((sqrt(c)*sqrt(b*x))/sqrt(-b)), -1))/(sqrt(-b)*sqrt(c)))]
    @test_int [sqrt(1 - c*x)/(sqrt(b*x)*sqrt(1 + d*x)), x, 1, -((2*Elliptic.E(asin((sqrt(d)*sqrt(b*x))/sqrt(-b)), -(c/d)))/(sqrt(-b)*sqrt(d)))]

    @test_int [1/(sqrt(2 - 3*x)*sqrt(x)*sqrt(d + e*x)), x, 2, (2*sqrt(1 + (e*x)/d)*Elliptic.F(asin(sqrt(3/2)*sqrt(x)), -((2*e)/(3*d))))/(sqrt(3)*sqrt(d + e*x))]

    @test_int [sqrt(d + e*x)/(sqrt(2 - 3*x)*sqrt(x)), x, 2, (2*sqrt(d + e*x)*Elliptic.E(asin(sqrt(3/2)*sqrt(x)), -((2*e)/(3*d))))/(sqrt(3)*sqrt(1 + (e*x)/d))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x)^(n/3)*(c+d*x)^(p/3)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x)^(n/3)*(c+d*x)^(p/3)=#

    @test_int [x^4/((1 - x)^(1/3)*(2 - x)^(1/3)), x, 8, (99/130)*(1 - x)^(2/3)*(2 - x)^(2/3)*x^2 + (3/13)*(1 - x)^(2/3)*(2 - x)^(2/3)*x^3 + (27/455)*(1 - x)^(2/3)*(2 - x)^(2/3)*(89 + 34*x) - (891*2^(2/3)*sqrt((3 - 2*x)^2)*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3))/(91*(3 - 2*x)*(1 - x)^(1/3)*(2 - x)^(1/3)*(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))) + (891*3^(1/4)*sqrt(2 - sqrt(3))*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3)*(1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))*sqrt((1 - 2^(2/3)*(2 - 3*x + x^2)^(1/3) + 2*2^(1/3)*(2 - 3*x + x^2)^(2/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)*Elliptic.E(asin((1 - sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))), -7 - 4*sqrt(3)))/(91*2^(1/3)*(3 - 2*x)*sqrt((3 - 2*x)^2)*(1 - x)^(1/3)*(2 - x)^(1/3)*sqrt((1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)) - (594*2^(1/6)*3^(3/4)*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3)*(1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))*sqrt((1 - 2^(2/3)*(2 - 3*x + x^2)^(1/3) + 2*2^(1/3)*(2 - 3*x + x^2)^(2/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)*Elliptic.F(asin((1 - sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))), -7 - 4*sqrt(3)))/(91*(3 - 2*x)*sqrt((3 - 2*x)^2)*(1 - x)^(1/3)*(2 - x)^(1/3)*sqrt((1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2))]
    @test_int [x^3/((1 - x)^(1/3)*(2 - x)^(1/3)), x, 7, (3/10)*(1 - x)^(2/3)*(2 - x)^(2/3)*x^2 + (9/70)*(1 - x)^(2/3)*(2 - x)^(2/3)*(23 + 8*x) - (81*sqrt((3 - 2*x)^2)*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3))/(7*2^(1/3)*(3 - 2*x)*(1 - x)^(1/3)*(2 - x)^(1/3)*(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))) + (81*3^(1/4)*sqrt(2 - sqrt(3))*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3)*(1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))*sqrt((1 - 2^(2/3)*(2 - 3*x + x^2)^(1/3) + 2*2^(1/3)*(2 - 3*x + x^2)^(2/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)*Elliptic.E(asin((1 - sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))), -7 - 4*sqrt(3)))/(14*2^(1/3)*(3 - 2*x)*sqrt((3 - 2*x)^2)*(1 - x)^(1/3)*(2 - x)^(1/3)*sqrt((1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)) - (27*2^(1/6)*3^(3/4)*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3)*(1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))*sqrt((1 - 2^(2/3)*(2 - 3*x + x^2)^(1/3) + 2*2^(1/3)*(2 - 3*x + x^2)^(2/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)*Elliptic.F(asin((1 - sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))), -7 - 4*sqrt(3)))/(7*(3 - 2*x)*sqrt((3 - 2*x)^2)*(1 - x)^(1/3)*(2 - x)^(1/3)*sqrt((1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2))]
    @test_int [x^2/((1 - x)^(1/3)*(2 - x)^(1/3)), x, 7, (45/28)*(1 - x)^(2/3)*(2 - x)^(2/3) + (3/7)*(1 - x)^(2/3)*(2 - x)^(2/3)*x - (99*sqrt((3 - 2*x)^2)*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3))/(14*2^(1/3)*(3 - 2*x)*(1 - x)^(1/3)*(2 - x)^(1/3)*(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))) + (99*3^(1/4)*sqrt(2 - sqrt(3))*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3)*(1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))*sqrt((1 - 2^(2/3)*(2 - 3*x + x^2)^(1/3) + 2*2^(1/3)*(2 - 3*x + x^2)^(2/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)*Elliptic.E(asin((1 - sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))), -7 - 4*sqrt(3)))/(28*2^(1/3)*(3 - 2*x)*sqrt((3 - 2*x)^2)*(1 - x)^(1/3)*(2 - x)^(1/3)*sqrt((1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)) - (33*3^(3/4)*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3)*(1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))*sqrt((1 - 2^(2/3)*(2 - 3*x + x^2)^(1/3) + 2*2^(1/3)*(2 - 3*x + x^2)^(2/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)*Elliptic.F(asin((1 - sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))), -7 - 4*sqrt(3)))/(7*2^(5/6)*(3 - 2*x)*sqrt((3 - 2*x)^2)*(1 - x)^(1/3)*(2 - x)^(1/3)*sqrt((1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2))]
    @test_int [x^1/((1 - x)^(1/3)*(2 - x)^(1/3)), x, 6, (3/4)*(1 - x)^(2/3)*(2 - x)^(2/3) - (9*sqrt((3 - 2*x)^2)*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3))/(2*2^(1/3)*(3 - 2*x)*(1 - x)^(1/3)*(2 - x)^(1/3)*(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))) + (9*3^(1/4)*sqrt(2 - sqrt(3))*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3)*(1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))*sqrt((1 - 2^(2/3)*(2 - 3*x + x^2)^(1/3) + 2*2^(1/3)*(2 - 3*x + x^2)^(2/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)*Elliptic.E(asin((1 - sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))), -7 - 4*sqrt(3)))/(4*2^(1/3)*(3 - 2*x)*sqrt((3 - 2*x)^2)*(1 - x)^(1/3)*(2 - x)^(1/3)*sqrt((1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)) - (3*3^(3/4)*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3)*(1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))*sqrt((1 - 2^(2/3)*(2 - 3*x + x^2)^(1/3) + 2*2^(1/3)*(2 - 3*x + x^2)^(2/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)*Elliptic.F(asin((1 - sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))), -7 - 4*sqrt(3)))/(2^(5/6)*(3 - 2*x)*sqrt((3 - 2*x)^2)*(1 - x)^(1/3)*(2 - x)^(1/3)*sqrt((1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2))]
    @test_int [x^0/((1 - x)^(1/3)*(2 - x)^(1/3)), x, 5, -((3*sqrt((3 - 2*x)^2)*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3))/(2^(1/3)*(3 - 2*x)*(1 - x)^(1/3)*(2 - x)^(1/3)*(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3)))) + (3*3^(1/4)*sqrt(2 - sqrt(3))*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3)*(1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))*sqrt((1 - 2^(2/3)*(2 - 3*x + x^2)^(1/3) + 2*2^(1/3)*(2 - 3*x + x^2)^(2/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)*Elliptic.E(asin((1 - sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))), -7 - 4*sqrt(3)))/(2*2^(1/3)*(3 - 2*x)*sqrt((3 - 2*x)^2)*(1 - x)^(1/3)*(2 - x)^(1/3)*sqrt((1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)) - (2^(1/6)*3^(3/4)*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3)*(1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))*sqrt((1 - 2^(2/3)*(2 - 3*x + x^2)^(1/3) + 2*2^(1/3)*(2 - 3*x + x^2)^(2/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)*Elliptic.F(asin((1 - sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))), -7 - 4*sqrt(3)))/((3 - 2*x)*sqrt((3 - 2*x)^2)*(1 - x)^(1/3)*(2 - x)^(1/3)*sqrt((1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2))]
    @test_int [1/(x^1*(1 - x)^(1/3)*(2 - x)^(1/3)), x, 1, -((sqrt(3)*atan(1/sqrt(3) + (2^(1/3)*(2 - x)^(2/3))/(sqrt(3)*(1 - x)^(1/3))))/(2*2^(1/3))) + (3*log(-(1 - x)^(1/3) + (2 - x)^(2/3)/2^(2/3)))/(4*2^(1/3)) - log(x)/(2*2^(1/3))]
    @test_int [1/(x^2*(1 - x)^(1/3)*(2 - x)^(1/3)), x, 8, -(((1 - x)^(2/3)*(2 - x)^(2/3))/(2*x)) - (sqrt((3 - 2*x)^2)*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3))/(2*2^(1/3)*(3 - 2*x)*(1 - x)^(1/3)*(2 - x)^(1/3)*(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))) - (sqrt(3)*atan(1/sqrt(3) + (2^(1/3)*(2 - x)^(2/3))/(sqrt(3)*(1 - x)^(1/3))))/(4*2^(1/3)) + (3^(1/4)*sqrt(2 - sqrt(3))*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3)*(1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))*sqrt((1 - 2^(2/3)*(2 - 3*x + x^2)^(1/3) + 2*2^(1/3)*(2 - 3*x + x^2)^(2/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)*Elliptic.E(asin((1 - sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))), -7 - 4*sqrt(3)))/(4*2^(1/3)*(3 - 2*x)*sqrt((3 - 2*x)^2)*(1 - x)^(1/3)*(2 - x)^(1/3)*sqrt((1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)) - (sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3)*(1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))*sqrt((1 - 2^(2/3)*(2 - 3*x + x^2)^(1/3) + 2*2^(1/3)*(2 - 3*x + x^2)^(2/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)*Elliptic.F(asin((1 - sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))), -7 - 4*sqrt(3)))/(2^(5/6)*3^(1/4)*(3 - 2*x)*sqrt((3 - 2*x)^2)*(1 - x)^(1/3)*(2 - x)^(1/3)*sqrt((1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)) + (3*log(-(1 - x)^(1/3) + (2 - x)^(2/3)/2^(2/3)))/(8*2^(1/3)) - log(x)/(4*2^(1/3))]
    @test_int [1/(x^3*(1 - x)^(1/3)*(2 - x)^(1/3)), x, 9, -(((1 - x)^(2/3)*(2 - x)^(2/3))/(4*x^2)) - ((1 - x)^(2/3)*(2 - x)^(2/3))/(2*x) - (sqrt((3 - 2*x)^2)*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3))/(2*2^(1/3)*(3 - 2*x)*(1 - x)^(1/3)*(2 - x)^(1/3)*(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))) - atan(1/sqrt(3) + (2^(1/3)*(2 - x)^(2/3))/(sqrt(3)*(1 - x)^(1/3)))/(2*2^(1/3)*sqrt(3)) + (3^(1/4)*sqrt(2 - sqrt(3))*sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3)*(1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))*sqrt((1 - 2^(2/3)*(2 - 3*x + x^2)^(1/3) + 2*2^(1/3)*(2 - 3*x + x^2)^(2/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)*Elliptic.E(asin((1 - sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))), -7 - 4*sqrt(3)))/(4*2^(1/3)*(3 - 2*x)*sqrt((3 - 2*x)^2)*(1 - x)^(1/3)*(2 - x)^(1/3)*sqrt((1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)) - (sqrt((-3 + 2*x)^2)*(2 - 3*x + x^2)^(1/3)*(1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))*sqrt((1 - 2^(2/3)*(2 - 3*x + x^2)^(1/3) + 2*2^(1/3)*(2 - 3*x + x^2)^(2/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)*Elliptic.F(asin((1 - sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))), -7 - 4*sqrt(3)))/(2^(5/6)*3^(1/4)*(3 - 2*x)*sqrt((3 - 2*x)^2)*(1 - x)^(1/3)*(2 - x)^(1/3)*sqrt((1 + 2^(2/3)*(2 - 3*x + x^2)^(1/3))/(1 + sqrt(3) + 2^(2/3)*(2 - 3*x + x^2)^(1/3))^2)) + log(-(1 - x)^(1/3) + (2 - x)^(2/3)/2^(2/3))/(4*2^(1/3)) - log(x)/(6*2^(1/3))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x)^(n/4)*(c+d*x)^(p/4)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x)^(n/4) / (c+d*x)^(1/4)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(a + b*x)^(1/4)/(c + d*x)^(1/4)*x^3, x, 8, -(((195*b^3*c^3 + 135*a*b^2*c^2*d + 105*a^2*b*c*d^2 + 77*a^3*d^3)*(a + b*x)^(1/4)*(c + d*x)^(3/4))/(512*b^3*d^4)) + (x^2*(a + b*x)^(5/4)*(c + d*x)^(3/4))/(4*b*d) + ((a + b*x)^(5/4)*(c + d*x)^(3/4)*(117*b^2*c^2 + 94*a*b*c*d + 77*a^2*d^2 - 8*b*d*(13*b*c + 11*a*d)*x))/(384*b^3*d^3) + ((b*c - a*d)*(195*b^3*c^3 + 135*a*b^2*c^2*d + 105*a^2*b*c*d^2 + 77*a^3*d^3)*atan((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/(1024*b^(15/4)*d^(17/4)) + ((b*c - a*d)*(195*b^3*c^3 + 135*a*b^2*c^2*d + 105*a^2*b*c*d^2 + 77*a^3*d^3)*atanh((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/(1024*b^(15/4)*d^(17/4))]
    @test_int [(a + b*x)^(1/4)/(c + d*x)^(1/4)*x^2, x, 8, ((15*b^2*c^2 + 10*a*b*c*d + 7*a^2*d^2)*(a + b*x)^(1/4)*(c + d*x)^(3/4))/(32*b^2*d^3) - ((9*b*c + 7*a*d)*(a + b*x)^(5/4)*(c + d*x)^(3/4))/(24*b^2*d^2) + (x*(a + b*x)^(5/4)*(c + d*x)^(3/4))/(3*b*d) - ((b*c - a*d)*(15*b^2*c^2 + 10*a*b*c*d + 7*a^2*d^2)*atan((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/(64*b^(11/4)*d^(13/4)) - ((b*c - a*d)*(15*b^2*c^2 + 10*a*b*c*d + 7*a^2*d^2)*atanh((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/(64*b^(11/4)*d^(13/4))]
    @test_int [(a + b*x)^(1/4)/(c + d*x)^(1/4)*x^1, x, 7, -(((5*b*c + 3*a*d)*(a + b*x)^(1/4)*(c + d*x)^(3/4))/(8*b*d^2)) + ((a + b*x)^(5/4)*(c + d*x)^(3/4))/(2*b*d) + ((b*c - a*d)*(5*b*c + 3*a*d)*atan((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/(16*b^(7/4)*d^(9/4)) + ((b*c - a*d)*(5*b*c + 3*a*d)*atanh((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/(16*b^(7/4)*d^(9/4))]
    @test_int [(a + b*x)^(1/4)/(c + d*x)^(1/4)*x^0, x, 6, ((a + b*x)^(1/4)*(c + d*x)^(3/4))/d - ((b*c - a*d)*atan((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/(2*b^(3/4)*d^(5/4)) - ((b*c - a*d)*atanh((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/(2*b^(3/4)*d^(5/4))]
    @test_int [(a + b*x)^(1/4)/(c + d*x)^(1/4)/x^1, x, 11, -((2*a^(1/4)*atan((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/c^(1/4)) + (2*b^(1/4)*atan((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/d^(1/4) - (2*a^(1/4)*atanh((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/c^(1/4) + (2*b^(1/4)*atanh((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/d^(1/4)]
    @test_int [(a + b*x)^(1/4)/(c + d*x)^(1/4)/x^2, x, 5, -(((a + b*x)^(1/4)*(c + d*x)^(3/4))/(c*x)) - ((b*c - a*d)*atan((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/(2*a^(3/4)*c^(5/4)) - ((b*c - a*d)*atanh((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/(2*a^(3/4)*c^(5/4))]
    @test_int [(a + b*x)^(1/4)/(c + d*x)^(1/4)/x^3, x, 6, ((3*b*c + 5*a*d)*(a + b*x)^(1/4)*(c + d*x)^(3/4))/(8*a*c^2*x) - ((a + b*x)^(5/4)*(c + d*x)^(3/4))/(2*a*c*x^2) + ((b*c - a*d)*(3*b*c + 5*a*d)*atan((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/(16*a^(7/4)*c^(9/4)) + ((b*c - a*d)*(3*b*c + 5*a*d)*atanh((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/(16*a^(7/4)*c^(9/4))]
    @test_int [(a + b*x)^(1/4)/(c + d*x)^(1/4)/x^4, x, 8, -(((a + b*x)^(1/4)*(c + d*x)^(3/4))/(3*c*x^3)) - ((b*c - 9*a*d)*(a + b*x)^(1/4)*(c + d*x)^(3/4))/(24*a*c^2*x^2) + ((7*b*c - 15*a*d)*(b*c + 3*a*d)*(a + b*x)^(1/4)*(c + d*x)^(3/4))/(96*a^2*c^3*x) - ((b*c - a*d)*(7*b^2*c^2 + 10*a*b*c*d + 15*a^2*d^2)*atan((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/(64*a^(11/4)*c^(13/4)) - ((b*c - a*d)*(7*b^2*c^2 + 10*a*b*c*d + 15*a^2*d^2)*atanh((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/(64*a^(11/4)*c^(13/4))]
    @test_int [(a + b*x)^(1/4)/(c + d*x)^(1/4)/x^5, x, 9, -(((a + b*x)^(1/4)*(c + d*x)^(3/4))/(4*c*x^4)) - ((b*c - 13*a*d)*(a + b*x)^(1/4)*(c + d*x)^(3/4))/(48*a*c^2*x^3) + ((11*b^2*c^2 + 10*a*b*c*d - 117*a^2*d^2)*(a + b*x)^(1/4)*(c + d*x)^(3/4))/(384*a^2*c^3*x^2) - ((77*b^3*c^3 + 61*a*b^2*c^2*d + 63*a^2*b*c*d^2 - 585*a^3*d^3)*(a + b*x)^(1/4)*(c + d*x)^(3/4))/(1536*a^3*c^4*x) + ((b*c - a*d)*(77*b^3*c^3 + 105*a*b^2*c^2*d + 135*a^2*b*c*d^2 + 195*a^3*d^3)*atan((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/(1024*a^(15/4)*c^(17/4)) + ((b*c - a*d)*(77*b^3*c^3 + 105*a*b^2*c^2*d + 135*a^2*b*c*d^2 + 195*a^3*d^3)*atanh((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/(1024*a^(15/4)*c^(17/4))]

    @test_int [(1 + x)^(1/4)/(1 - x)^(1/4)*x^2, x, 14, (-(3/8))*(1 - x)^(3/4)*(1 + x)^(1/4) - (1/12)*(1 - x)^(3/4)*(1 + x)^(5/4) - (1/3)*(1 - x)^(3/4)*x*(1 + x)^(5/4) + (3*atan(1 - (sqrt(2)*(1 - x)^(1/4))/(1 + x)^(1/4)))/(8*sqrt(2)) - (3*atan(1 + (sqrt(2)*(1 - x)^(1/4))/(1 + x)^(1/4)))/(8*sqrt(2)) - (3*log(1 + sqrt(1 - x)/sqrt(1 + x) - (sqrt(2)*(1 - x)^(1/4))/(1 + x)^(1/4)))/(16*sqrt(2)) + (3*log(1 + sqrt(1 - x)/sqrt(1 + x) + (sqrt(2)*(1 - x)^(1/4))/(1 + x)^(1/4)))/(16*sqrt(2))]
    @test_int [(1 + x)^(1/4)/(1 - x)^(1/4)*x^1, x, 13, (-(1/4))*(1 - x)^(3/4)*(1 + x)^(1/4) - (1/2)*(1 - x)^(3/4)*(1 + x)^(5/4) + atan(1 - (sqrt(2)*(1 - x)^(1/4))/(1 + x)^(1/4))/(4*sqrt(2)) - atan(1 + (sqrt(2)*(1 - x)^(1/4))/(1 + x)^(1/4))/(4*sqrt(2)) - log(1 + sqrt(1 - x)/sqrt(1 + x) - (sqrt(2)*(1 - x)^(1/4))/(1 + x)^(1/4))/(8*sqrt(2)) + log(1 + sqrt(1 - x)/sqrt(1 + x) + (sqrt(2)*(1 - x)^(1/4))/(1 + x)^(1/4))/(8*sqrt(2))]
    @test_int [(1 + x)^(1/4)/(1 - x)^(1/4)*x^0, x, 12, (-(1 - x)^(3/4))*(1 + x)^(1/4) + atan(1 - (sqrt(2)*(1 - x)^(1/4))/(1 + x)^(1/4))/sqrt(2) - atan(1 + (sqrt(2)*(1 - x)^(1/4))/(1 + x)^(1/4))/sqrt(2) - log(1 + sqrt(1 - x)/sqrt(1 + x) - (sqrt(2)*(1 - x)^(1/4))/(1 + x)^(1/4))/(2*sqrt(2)) + log(1 + sqrt(1 - x)/sqrt(1 + x) + (sqrt(2)*(1 - x)^(1/4))/(1 + x)^(1/4))/(2*sqrt(2))]
    @test_int [(1 + x)^(1/4)/(1 - x)^(1/4)/x^1, x, 16, -2*atan((1 + x)^(1/4)/(1 - x)^(1/4)) + sqrt(2)*atan(1 - (sqrt(2)*(1 - x)^(1/4))/(1 + x)^(1/4)) - sqrt(2)*atan(1 + (sqrt(2)*(1 - x)^(1/4))/(1 + x)^(1/4)) - 2*atanh((1 + x)^(1/4)/(1 - x)^(1/4)) - log(1 + sqrt(1 - x)/sqrt(1 + x) - (sqrt(2)*(1 - x)^(1/4))/(1 + x)^(1/4))/sqrt(2) + log(1 + sqrt(1 - x)/sqrt(1 + x) + (sqrt(2)*(1 - x)^(1/4))/(1 + x)^(1/4))/sqrt(2)]
    @test_int [(1 + x)^(1/4)/(1 - x)^(1/4)/x^2, x, 5, -(((1 - x)^(3/4)*(1 + x)^(1/4))/x) - atan((1 + x)^(1/4)/(1 - x)^(1/4)) - atanh((1 + x)^(1/4)/(1 - x)^(1/4))]
    @test_int [(1 + x)^(1/4)/(1 - x)^(1/4)/x^3, x, 6, -(((1 - x)^(3/4)*(1 + x)^(1/4))/(4*x)) - ((1 - x)^(3/4)*(1 + x)^(5/4))/(2*x^2) - (1/4)*atan((1 + x)^(1/4)/(1 - x)^(1/4)) - (1/4)*atanh((1 + x)^(1/4)/(1 - x)^(1/4))]
    @test_int [(1 + x)^(1/4)/(1 - x)^(1/4)/x^4, x, 8, -(((1 - x)^(3/4)*(1 + x)^(1/4))/(3*x^3)) - (5*(1 - x)^(3/4)*(1 + x)^(1/4))/(12*x^2) - (11*(1 - x)^(3/4)*(1 + x)^(1/4))/(24*x) - (3/8)*atan((1 + x)^(1/4)/(1 - x)^(1/4)) - (3/8)*atanh((1 + x)^(1/4)/(1 - x)^(1/4))]
    @test_int [(1 + x)^(1/4)/(1 - x)^(1/4)/x^5, x, 9, -(((1 - x)^(3/4)*(1 + x)^(1/4))/(4*x^4)) - (7*(1 - x)^(3/4)*(1 + x)^(1/4))/(24*x^3) - (29*(1 - x)^(3/4)*(1 + x)^(1/4))/(96*x^2) - (83*(1 - x)^(3/4)*(1 + x)^(1/4))/(192*x) - (11/64)*atan((1 + x)^(1/4)/(1 - x)^(1/4)) - (11/64)*atanh((1 + x)^(1/4)/(1 - x)^(1/4))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [x^3/((a + b*x)^(3/4)*(c + d*x)^(1/4)), x, 7, (x^2*(a + b*x)^(1/4)*(c + d*x)^(3/4))/(3*b*d) + ((a + b*x)^(1/4)*(c + d*x)^(3/4)*(45*b^2*c^2 + 54*a*b*c*d + 77*a^2*d^2 - 4*b*d*(9*b*c + 11*a*d)*x))/(96*b^3*d^3) - ((15*b^3*c^3 + 15*a*b^2*c^2*d + 21*a^2*b*c*d^2 + 77*a^3*d^3)*atan((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/(64*b^(15/4)*d^(13/4)) - ((15*b^3*c^3 + 15*a*b^2*c^2*d + 21*a^2*b*c*d^2 + 77*a^3*d^3)*atanh((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/(64*b^(15/4)*d^(13/4))]
    @test_int [x^2/((a + b*x)^(3/4)*(c + d*x)^(1/4)), x, 7, -(((5*b*c + 7*a*d)*(a + b*x)^(1/4)*(c + d*x)^(3/4))/(8*b^2*d^2)) + (x*(a + b*x)^(1/4)*(c + d*x)^(3/4))/(2*b*d) + ((5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*atan((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/(16*b^(11/4)*d^(9/4)) + ((5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*atanh((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/(16*b^(11/4)*d^(9/4))]
    @test_int [x^1/((a + b*x)^(3/4)*(c + d*x)^(1/4)), x, 6, ((a + b*x)^(1/4)*(c + d*x)^(3/4))/(b*d) - ((b*c + 3*a*d)*atan((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/(2*b^(7/4)*d^(5/4)) - ((b*c + 3*a*d)*atanh((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/(2*b^(7/4)*d^(5/4))]
    @test_int [x^0/((a + b*x)^(3/4)*(c + d*x)^(1/4)), x, 5, (2*atan((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/(b^(3/4)*d^(1/4)) + (2*atanh((d^(1/4)*(a + b*x)^(1/4))/(b^(1/4)*(c + d*x)^(1/4))))/(b^(3/4)*d^(1/4))]
    @test_int [1/(x^1*(a + b*x)^(3/4)*(c + d*x)^(1/4)), x, 4, -((2*atan((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/(a^(3/4)*c^(1/4))) - (2*atanh((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/(a^(3/4)*c^(1/4))]
    @test_int [1/(x^2*(a + b*x)^(3/4)*(c + d*x)^(1/4)), x, 5, -(((a + b*x)^(1/4)*(c + d*x)^(3/4))/(a*c*x)) + ((3*b*c + a*d)*atan((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/(2*a^(7/4)*c^(5/4)) + ((3*b*c + a*d)*atanh((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/(2*a^(7/4)*c^(5/4))]
    @test_int [1/(x^3*(a + b*x)^(3/4)*(c + d*x)^(1/4)), x, 7, -(((a + b*x)^(1/4)*(c + d*x)^(3/4))/(2*a*c*x^2)) + ((7*b*c + 5*a*d)*(a + b*x)^(1/4)*(c + d*x)^(3/4))/(8*a^2*c^2*x) - ((21*b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*atan((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/(16*a^(11/4)*c^(9/4)) - ((21*b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*atanh((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/(16*a^(11/4)*c^(9/4))]
    @test_int [1/(x^4*(a + b*x)^(3/4)*(c + d*x)^(1/4)), x, 8, -(((a + b*x)^(1/4)*(c + d*x)^(3/4))/(3*a*c*x^3)) + ((11*b*c + 9*a*d)*(a + b*x)^(1/4)*(c + d*x)^(3/4))/(24*a^2*c^2*x^2) - ((77*b^2*c^2 + 54*a*b*c*d + 45*a^2*d^2)*(a + b*x)^(1/4)*(c + d*x)^(3/4))/(96*a^3*c^3*x) + ((77*b^3*c^3 + 21*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 15*a^3*d^3)*atan((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/(64*a^(15/4)*c^(13/4)) + ((77*b^3*c^3 + 21*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 15*a^3*d^3)*atanh((c^(1/4)*(a + b*x)^(1/4))/(a^(1/4)*(c + d*x)^(1/4))))/(64*a^(15/4)*c^(13/4))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^(m/2)*(a+b*x)^(n/4)*(c+d*x)^(p/4)=#

    @test_int [(e*x)^(3/2)/((1 - x)^(1/4)*(1 + x)^(1/4)), x, 13, (-(1/2))*e*sqrt(e*x)*(1 - x^2)^(3/4) - (e^(3/2)*atan(1 - (sqrt(2)*sqrt(e*x))/(sqrt(e)*(1 - x^2)^(1/4))))/(4*sqrt(2)) + (e^(3/2)*atan(1 + (sqrt(2)*sqrt(e*x))/(sqrt(e)*(1 - x^2)^(1/4))))/(4*sqrt(2)) - (e^(3/2)*log(sqrt(e) + (sqrt(e)*x)/sqrt(1 - x^2) - (sqrt(2)*sqrt(e*x))/(1 - x^2)^(1/4)))/(8*sqrt(2)) + (e^(3/2)*log(sqrt(e) + (sqrt(e)*x)/sqrt(1 - x^2) + (sqrt(2)*sqrt(e*x))/(1 - x^2)^(1/4)))/(8*sqrt(2))]
    @test_int [1/((e*x)^(1/2)*(1 - x)^(1/4)*(1 + x)^(1/4)), x, 12, -(atan(1 - (sqrt(2)*sqrt(e*x))/(sqrt(e)*(1 - x^2)^(1/4)))/(sqrt(2)*sqrt(e))) + atan(1 + (sqrt(2)*sqrt(e*x))/(sqrt(e)*(1 - x^2)^(1/4)))/(sqrt(2)*sqrt(e)) - log(sqrt(e) + (sqrt(e)*x)/sqrt(1 - x^2) - (sqrt(2)*sqrt(e*x))/(1 - x^2)^(1/4))/(2*sqrt(2)*sqrt(e)) + log(sqrt(e) + (sqrt(e)*x)/sqrt(1 - x^2) + (sqrt(2)*sqrt(e*x))/(1 - x^2)^(1/4))/(2*sqrt(2)*sqrt(e))]
    @test_int [1/((e*x)^(5/2)*(1 - x)^(1/4)*(1 + x)^(1/4)), x, 1, -((2*(1 - x)^(3/4)*(1 + x)^(3/4))/(3*e*(e*x)^(3/2)))]
    @test_int [1/((e*x)^(9/2)*(1 - x)^(1/4)*(1 + x)^(1/4)), x, 3, -((2*(1 - x^2)^(3/4))/(3*e*(e*x)^(7/2))) + (8*(1 - x^2)^(7/4))/(21*e*(e*x)^(7/2))]
    @test_int [1/((e*x)^(13/2)*(1 - x)^(1/4)*(1 + x)^(1/4)), x, 4, -((2*(1 - x^2)^(3/4))/(3*e*(e*x)^(11/2))) + (16*(1 - x^2)^(7/4))/(21*e*(e*x)^(11/2)) - (64*(1 - x^2)^(11/4))/(231*e*(e*x)^(11/2))]

    @test_int [(e*x)^(5/2)/((1 - x)^(1/4)*(1 + x)^(1/4)), x, 6, -((e^3*(1 - x^2)^(3/4))/(2*sqrt(e*x))) - (1/3)*e*(e*x)^(3/2)*(1 - x^2)^(3/4) + (e^2*(1 - 1/x^2)^(1/4)*sqrt(e*x)*Elliptic.E(acsc(x)/2, 2))/(2*(1 - x^2)^(1/4))]
    @test_int [(e*x)^(1/2)/((1 - x)^(1/4)*(1 + x)^(1/4)), x, 5, -((e*(1 - x^2)^(3/4))/sqrt(e*x)) + ((1 - 1/x^2)^(1/4)*sqrt(e*x)*Elliptic.E(acsc(x)/2, 2))/(1 - x^2)^(1/4)]
    @test_int [1/((e*x)^(3/2)*(1 - x)^(1/4)*(1 + x)^(1/4)), x, 4, -((2*(1 - 1/x^2)^(1/4)*sqrt(e*x)*Elliptic.E(acsc(x)/2, 2))/(e^2*(1 - x^2)^(1/4)))]
    @test_int [1/((e*x)^(7/2)*(1 - x)^(1/4)*(1 + x)^(1/4)), x, 5, -((2*(1 - x^2)^(3/4))/(5*e*(e*x)^(5/2))) - (4*(1 - 1/x^2)^(1/4)*sqrt(e*x)*Elliptic.E(acsc(x)/2, 2))/(5*e^4*(1 - x^2)^(1/4))]
    @test_int [1/((e*x)^(11/2)*(1 - x)^(1/4)*(1 + x)^(1/4)), x, 6, -((2*(1 - x^2)^(3/4))/(9*e*(e*x)^(9/2))) - (4*(1 - x^2)^(3/4))/(15*e^3*(e*x)^(5/2)) - (8*(1 - 1/x^2)^(1/4)*sqrt(e*x)*Elliptic.E(acsc(x)/2, 2))/(15*e^6*(1 - x^2)^(1/4))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x)^n*(c+d*x)^p*with*n*symbolic=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x)^n*(c+d*x)^p*with*n*symbolic=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(a + b*x)^n*(c + d*x)*x^2, x, 2, (a^2*(b*c - a*d)*(a + b*x)^(1 + n))/(b^4*(1 + n)) - (a*(2*b*c - 3*a*d)*(a + b*x)^(2 + n))/(b^4*(2 + n)) + ((b*c - 3*a*d)*(a + b*x)^(3 + n))/(b^4*(3 + n)) + (d*(a + b*x)^(4 + n))/(b^4*(4 + n))]
    @test_int [(a + b*x)^n*(c + d*x)*x^1, x, 2, -((a*(b*c - a*d)*(a + b*x)^(1 + n))/(b^3*(1 + n))) + ((b*c - 2*a*d)*(a + b*x)^(2 + n))/(b^3*(2 + n)) + (d*(a + b*x)^(3 + n))/(b^3*(3 + n))]
    @test_int [(a + b*x)^n*(c + d*x)*x^0, x, 2, ((b*c - a*d)*(a + b*x)^(1 + n))/(b^2*(1 + n)) + (d*(a + b*x)^(2 + n))/(b^2*(2 + n))]
    @test_int [(a + b*x)^n*(c + d*x)/x^1, x, 2, (d*(a + b*x)^(1 + n))/(b*(1 + n)) - (c*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, 1 + (b*x)/a))/(a*(1 + n))]
    @test_int [(a + b*x)^n*(c + d*x)/x^2, x, 2, -((c*(a + b*x)^(1 + n))/(a*x)) - ((a*d + b*c*n)*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, 1 + (b*x)/a))/(a^2*(1 + n))]

    @test_int [(a + b*x)^n*(c + d*x)^2*x^2, x, 2, (a^2*(b*c - a*d)^2*(a + b*x)^(1 + n))/(b^5*(1 + n)) - (2*a*(b*c - 2*a*d)*(b*c - a*d)*(a + b*x)^(2 + n))/(b^5*(2 + n)) + ((b^2*c^2 - 6*a*b*c*d + 6*a^2*d^2)*(a + b*x)^(3 + n))/(b^5*(3 + n)) + (2*d*(b*c - 2*a*d)*(a + b*x)^(4 + n))/(b^5*(4 + n)) + (d^2*(a + b*x)^(5 + n))/(b^5*(5 + n))]
    @test_int [(a + b*x)^n*(c + d*x)^2*x^1, x, 2, -((a*(b*c - a*d)^2*(a + b*x)^(1 + n))/(b^4*(1 + n))) + ((b*c - 3*a*d)*(b*c - a*d)*(a + b*x)^(2 + n))/(b^4*(2 + n)) + (d*(2*b*c - 3*a*d)*(a + b*x)^(3 + n))/(b^4*(3 + n)) + (d^2*(a + b*x)^(4 + n))/(b^4*(4 + n))]
    @test_int [(a + b*x)^n*(c + d*x)^2*x^0, x, 2, ((b*c - a*d)^2*(a + b*x)^(1 + n))/(b^3*(1 + n)) + (2*d*(b*c - a*d)*(a + b*x)^(2 + n))/(b^3*(2 + n)) + (d^2*(a + b*x)^(3 + n))/(b^3*(3 + n))]
    @test_int [(a + b*x)^n*(c + d*x)^2/x^1, x, 3, (d*(2*b*c - a*d)*(a + b*x)^(1 + n))/(b^2*(1 + n)) + (d^2*(a + b*x)^(2 + n))/(b^2*(2 + n)) - (c^2*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, 1 + (b*x)/a))/(a*(1 + n))]
    @test_int [(a + b*x)^n*(c + d*x)^2/x^2, x, 3, (d^2*(a + b*x)^(1 + n))/(b*(1 + n)) - (c^2*(a + b*x)^(1 + n))/(a*x) - (c*(2*a*d + b*c*n)*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, 1 + (b*x)/a))/(a^2*(1 + n))]
    @test_int [(a + b*x)^n*(c + d*x)^2/x^3, x, 3, -((c^2*(a + b*x)^(1 + n))/(2*a*x^2)) - (c*(4*a*d - b*c*(1 - n))*(a + b*x)^(1 + n))/(2*a^2*x) - ((2*a^2*d^2 + 4*a*b*c*d*n - b^2*c^2*(1 - n)*n)*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, 1 + (b*x)/a))/(2*a^3*(1 + n))]
    @test_int [(a + b*x)^n*(c + d*x)^2/x^4, x, 3, -((c^2*(a + b*x)^(1 + n))/(3*a*x^3)) - (c*(6*a*d - b*c*(2 - n))*(a + b*x)^(1 + n))/(6*a^2*x^2) + (b*(6*a^2*d^2 - 6*a*b*c*d*(1 - n) + b^2*c^2*(2 - 3*n + n^2))*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(2, 1 + n, 2 + n, 1 + (b*x)/a))/(6*a^4*(1 + n))]

    @test_int [(a + b*x)^n*(c + d*x)^3*x^2, x, 2, (a^2*(b*c - a*d)^3*(a + b*x)^(1 + n))/(b^6*(1 + n)) - (a*(2*b*c - 5*a*d)*(b*c - a*d)^2*(a + b*x)^(2 + n))/(b^6*(2 + n)) + ((b*c - a*d)*(b^2*c^2 - 8*a*b*c*d + 10*a^2*d^2)*(a + b*x)^(3 + n))/(b^6*(3 + n)) + (d*(3*b^2*c^2 - 12*a*b*c*d + 10*a^2*d^2)*(a + b*x)^(4 + n))/(b^6*(4 + n)) + (d^2*(3*b*c - 5*a*d)*(a + b*x)^(5 + n))/(b^6*(5 + n)) + (d^3*(a + b*x)^(6 + n))/(b^6*(6 + n))]
    @test_int [(a + b*x)^n*(c + d*x)^3*x^1, x, 2, -((a*(b*c - a*d)^3*(a + b*x)^(1 + n))/(b^5*(1 + n))) + ((b*c - 4*a*d)*(b*c - a*d)^2*(a + b*x)^(2 + n))/(b^5*(2 + n)) + (3*d*(b*c - 2*a*d)*(b*c - a*d)*(a + b*x)^(3 + n))/(b^5*(3 + n)) + (d^2*(3*b*c - 4*a*d)*(a + b*x)^(4 + n))/(b^5*(4 + n)) + (d^3*(a + b*x)^(5 + n))/(b^5*(5 + n))]
    @test_int [(a + b*x)^n*(c + d*x)^3*x^0, x, 2, ((b*c - a*d)^3*(a + b*x)^(1 + n))/(b^4*(1 + n)) + (3*d*(b*c - a*d)^2*(a + b*x)^(2 + n))/(b^4*(2 + n)) + (3*d^2*(b*c - a*d)*(a + b*x)^(3 + n))/(b^4*(3 + n)) + (d^3*(a + b*x)^(4 + n))/(b^4*(4 + n))]
    @test_int [(a + b*x)^n*(c + d*x)^3/x^1, x, 3, (d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*(a + b*x)^(1 + n))/(b^3*(1 + n)) + (d^2*(3*b*c - 2*a*d)*(a + b*x)^(2 + n))/(b^3*(2 + n)) + (d^3*(a + b*x)^(3 + n))/(b^3*(3 + n)) - (c^3*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, 1 + (b*x)/a))/(a*(1 + n))]
    @test_int [(a + b*x)^n*(c + d*x)^3/x^2, x, 3, (d*(a + b*x)^(1 + n)*(c + d*x)^2)/(b*(2 + n)*x) - ((a + b*x)^(1 + n)*(b*c^2*(1 + n)*(a*d + b*c*(2 + n)) + a*d^2*(a*d - b*c*(4 + n))*x))/(a*b^2*(1 + n)*(2 + n)*x) - (c^2*(3*a*d + b*c*n)*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, 1 + (b*x)/a))/(a^2*(1 + n))]
    @test_int [(a + b*x)^n*(c + d*x)^3/x^3, x, 3, (d*(a + b*x)^(1 + n)*(c + d*x)^2)/(b*(1 + n)*x^2) - (c*(a + b*x)^(1 + n)*(a*c*(2*a*d + b*c*(1 + n)) + (4*a^2*d^2 + 6*a*b*c*d*(1 + n) - b^2*c^2*(1 - n^2))*x))/(2*a^2*b*(1 + n)*x^2) - (c*(6*a^2*d^2 + 6*a*b*c*d*n - b^2*c^2*(1 - n)*n)*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, 1 + (b*x)/a))/(2*a^3*(1 + n))]

    @test_int [x^(2*n+1)*(a + b*x)^n*(2*a + 3*b*x), x, 1, (x^(2*(1 + n))*(a + b*x)^(1 + n))/(1 + n)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(a + b*x)^n/(c + d*x)*x^2, x, 3, -(((b*c + a*d)*(a + b*x)^(1 + n))/(b^2*d^2*(1 + n))) + (a + b*x)^(2 + n)/(b^2*d*(2 + n)) + (c^2*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/(d^2*(b*c - a*d)*(1 + n))]
    @test_int [(a + b*x)^n/(c + d*x)*x^1, x, 2, (a + b*x)^(1 + n)/(b*d*(1 + n)) - (c*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/(d*(b*c - a*d)*(1 + n))]
    @test_int [(a + b*x)^n/(c + d*x)*x^0, x, 1, ((a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/((b*c - a*d)*(1 + n))]
    @test_int [(a + b*x)^n/(c + d*x)/x^1, x, 3, -((d*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/(c*(b*c - a*d)*(1 + n))) - ((a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, 1 + (b*x)/a))/(a*c*(1 + n))]
    @test_int [(a + b*x)^n/(c + d*x)/x^2, x, 4, -((a + b*x)^(1 + n)/(a*c*x)) + (d^2*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/(c^2*(b*c - a*d)*(1 + n)) + ((a*d - b*c*n)*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, 1 + (b*x)/a))/(a^2*c^2*(1 + n))]

    @test_int [(a + b*x)^n/(c + d*x)^2*x^3, x, 3, (x^2*(a + b*x)^(1 + n))/(b*d*(2 + n)*(c + d*x)) - ((a + b*x)^(1 + n)*(c*(b*c*(2 + n)*(a*d + b*c*(3 + n)) - a*d*(a*d + b*c*(5 + 3*n))) + d*(b*c - a*d)*(a*d + b*c*(3 + n))*x))/(b^2*d^3*(b*c - a*d)*(1 + n)*(2 + n)*(c + d*x)) - (c^2*(3*a*d - b*c*(3 + n))*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/(d^3*(b*c - a*d)^2*(1 + n))]
    @test_int [(a + b*x)^n/(c + d*x)^2*x^2, x, 3, (a + b*x)^(1 + n)/(b*d^2*(1 + n)) + (c^2*(a + b*x)^(1 + n))/(d^2*(b*c - a*d)*(c + d*x)) + (c*(2*a*d - b*c*(2 + n))*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/(d^2*(b*c - a*d)^2*(1 + n))]
    @test_int [(a + b*x)^n/(c + d*x)^2*x^1, x, 2, -((c*(a + b*x)^(1 + n))/(d*(b*c - a*d)*(c + d*x))) - ((a*d - b*c*(1 + n))*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/(d*(b*c - a*d)^2*(1 + n))]
    @test_int [(a + b*x)^n/(c + d*x)^2*x^0, x, 1, (b*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(2, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/((b*c - a*d)^2*(1 + n))]
    @test_int [(a + b*x)^n/(c + d*x)^2/x^1, x, 4, -((d*(a + b*x)^(1 + n))/(c*(b*c - a*d)*(c + d*x))) + (d*(a*d - b*c*(1 - n))*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/(c^2*(b*c - a*d)^2*(1 + n)) - ((a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, 1 + (b*x)/a))/(a*c^2*(1 + n))]
    @test_int [(a + b*x)^n/(c + d*x)^2/x^2, x, 5, -((d*(b*c - 2*a*d)*(a + b*x)^(1 + n))/(a*c^2*(b*c - a*d)*(c + d*x))) - (a + b*x)^(1 + n)/(a*c*x*(c + d*x)) - (d^2*(2*a*d - b*c*(2 - n))*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/(c^3*(b*c - a*d)^2*(1 + n)) + ((2*a*d - b*c*n)*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, 1 + (b*x)/a))/(a^2*c^3*(1 + n))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^(m/2)*(a+b*x)^n*(c+d*x)^p*with*n*symbolic=#

    @test_int [(b*x)^(5/2)*(c + d*x)^n*(e + f*x)^2, x, 4, -((2*f*(9*c*f - d*e*(13 + 2*n))*(b*x)^(7/2)*(c + d*x)^(1 + n))/(b*d^2*(9 + 2*n)*(11 + 2*n))) + (2*f*(b*x)^(7/2)*(c + d*x)^(1 + n)*(e + f*x))/(b*d*(11 + 2*n)) + (2*(63*c^2*f^2 - 14*c*d*e*f*(11 + 2*n) + d^2*e^2*(99 + 40*n + 4*n^2))*(b*x)^(7/2)*(c + d*x)^n*HypergeometricFunctions._₂F₁(7/2, -n, 9/2, -((d*x)/c)))/((1 + (d*x)/c)^n*(7*b*d^2*(9 + 2*n)*(11 + 2*n)))]
    @test_int [(b*x)^(5/2)*(c + d*x)^n*(e + f*x)^1, x, 3, (2*f*(b*x)^(7/2)*(c + d*x)^(1 + n))/(b*d*(9 + 2*n)) - (2*(7*c*f - d*e*(9 + 2*n))*(b*x)^(7/2)*(c + d*x)^n*HypergeometricFunctions._₂F₁(7/2, -n, 9/2, -((d*x)/c)))/((1 + (d*x)/c)^n*(7*b*d*(9 + 2*n)))]
    @test_int [(b*x)^(5/2)*(c + d*x)^n/(e + f*x)^1, x, 3, (2*(b*x)^(7/2)*(c + d*x)^n*AppellF1(7/2, -n, 1, 9/2, -((d*x)/c), -((f*x)/e)))/((1 + (d*x)/c)^n*(7*b*e))]
    @test_int [(b*x)^(5/2)*(c + d*x)^n/(e + f*x)^2, x, 3, (2*(b*x)^(7/2)*(c + d*x)^n*AppellF1(7/2, -n, 2, 9/2, -((d*x)/c), -((f*x)/e)))/((1 + (d*x)/c)^n*(7*b*e^2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x)^n*(c+d*x)^p*with*m*and*n*symbolic=#

    @test_int [(b*x)^m*(c + d*x)^n*(e + f*x)^2, x, 4, -((f*(c*f*(2 + m) - d*e*(4 + m + n))*(b*x)^(1 + m)*(c + d*x)^(1 + n))/(b*d^2*(2 + m + n)*(3 + m + n))) + (f*(b*x)^(1 + m)*(c + d*x)^(1 + n)*(e + f*x))/(b*d*(3 + m + n)) + ((c^2*f^2*(2 + 3*m + m^2) - 2*c*d*e*f*(1 + m)*(3 + m + n) + d^2*e^2*(6 + m^2 + 5*n + n^2 + m*(5 + 2*n)))*(b*x)^(1 + m)*(c + d*x)^n*HypergeometricFunctions._₂F₁(1 + m, -n, 2 + m, -((d*x)/c)))/((1 + (d*x)/c)^n*(b*d^2*(1 + m)*(2 + m + n)*(3 + m + n)))]
    @test_int [(b*x)^m*(c + d*x)^n*(e + f*x)^1, x, 3, (f*(b*x)^(1 + m)*(c + d*x)^(1 + n))/(b*d*(2 + m + n)) - ((c*f*(1 + m) - d*e*(2 + m + n))*(b*x)^(1 + m)*(c + d*x)^n*HypergeometricFunctions._₂F₁(1 + m, -n, 2 + m, -((d*x)/c)))/((1 + (d*x)/c)^n*(b*d*(1 + m)*(2 + m + n)))]
    @test_int [(b*x)^m*(c + d*x)^n/(e + f*x)^1, x, 2, ((b*x)^(1 + m)*(c + d*x)^n*AppellF1(1 + m, -n, 1, 2 + m, -((d*x)/c), -((f*x)/e)))/((1 + (d*x)/c)^n*(b*e*(1 + m)))]
    @test_int [(b*x)^m*(c + d*x)^n/(e + f*x)^2, x, 2, ((b*x)^(1 + m)*(c + d*x)^n*AppellF1(1 + m, -n, 2, 2 + m, -((d*x)/c), -((f*x)/e)))/((1 + (d*x)/c)^n*(b*e^2*(1 + m)))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x)^n*(c+d*x)^p*with*n*and*p*symbolic=#

    @test_int [(b*x)^m*(c + d*x)^n*(e + f*x)^p, x, 3, ((b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^p*AppellF1(1 + m, -n, -p, 2 + m, -((d*x)/c), -((f*x)/e)))/((1 + (d*x)/c)^n*(1 + (f*x)/e)^p*(b*(1 + m)))]

    @test_int [(e*x)^m*(a + b*x)^n*(a - b*x)^(n + 2), x, -11, -(((e*x)^(1 + m)*(a - b*x)^(1 + n)*(a + b*x)^(1 + n))/(e*(3 + m + 2*n))) + (2*a^2*(2 + m + n)*(e*x)^(1 + m)*(a - b*x)^n*(a + b*x)^n*HypergeometricFunctions._₂F₁((1 + m)/2, -n, (3 + m)/2, (b^2*x^2)/a^2))/((1 - (b^2*x^2)/a^2)^n*(e*(1 + m)*(3 + m + 2*n))) - (2*a*b*(e*x)^(2 + m)*(a - b*x)^n*(a + b*x)^n*HypergeometricFunctions._₂F₁((2 + m)/2, -n, (4 + m)/2, (b^2*x^2)/a^2))/((1 - (b^2*x^2)/a^2)^n*(e^2*(2 + m)))]

    @test_int [(a + b*x)^n*(c + d*x)^p*x^2, x, 4, -(((b*c*(2 + n) + a*d*(2 + p))*(a + b*x)^(1 + n)*(c + d*x)^(1 + p))/(b^2*d^2*(2 + n + p)*(3 + n + p))) + (x*(a + b*x)^(1 + n)*(c + d*x)^(1 + p))/(b*d*(3 + n + p)) - ((b^2*c^2*(2 + 3*n + n^2) + 2*a*b*c*d*(1 + n)*(1 + p) + a^2*d^2*(2 + 3*p + p^2))*(a + b*x)^(1 + n)*(c + d*x)^(1 + p)*HypergeometricFunctions._₂F₁(1, 2 + n + p, 2 + p, (b*(c + d*x))/(b*c - a*d)))/(b^2*d^2*(b*c - a*d)*(1 + p)*(2 + n + p)*(3 + n + p)), -(((b*c*(2 + n) + a*d*(2 + p))*(a + b*x)^(1 + n)*(c + d*x)^(1 + p))/(b^2*d^2*(2 + n + p)*(3 + n + p))) + (x*(a + b*x)^(1 + n)*(c + d*x)^(1 + p))/(b*d*(3 + n + p)) + ((b^2*c^2*(2 + 3*n + n^2) + 2*a*b*c*d*(1 + n)*(1 + p) + a^2*d^2*(2 + 3*p + p^2))*(a + b*x)^(1 + n)*(c + d*x)^p*HypergeometricFunctions._₂F₁(1 + n, -p, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/(((b*(c + d*x))/(b*c - a*d))^p*(b^3*d^2*(1 + n)*(2 + n + p)*(3 + n + p)))]
    @test_int [(a + b*x)^n*(c + d*x)^p*x^1, x, 3, ((a + b*x)^(1 + n)*(c + d*x)^(1 + p))/(b*d*(2 + n + p)) + ((b*c*(1 + n) + a*d*(1 + p))*(a + b*x)^(1 + n)*(c + d*x)^(1 + p)*HypergeometricFunctions._₂F₁(1, 2 + n + p, 2 + p, (b*(c + d*x))/(b*c - a*d)))/(b*d*(b*c - a*d)*(1 + p)*(2 + n + p)), ((a + b*x)^(1 + n)*(c + d*x)^(1 + p))/(b*d*(2 + n + p)) - ((b*c*(1 + n) + a*d*(1 + p))*(a + b*x)^(1 + n)*(c + d*x)^p*HypergeometricFunctions._₂F₁(1 + n, -p, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/(((b*(c + d*x))/(b*c - a*d))^p*(b^2*d*(1 + n)*(2 + n + p)))]
    @test_int [(a + b*x)^n*(c + d*x)^p*x^0, x, 2, -(((a + b*x)^(1 + n)*(c + d*x)^(1 + p)*HypergeometricFunctions._₂F₁(1, 2 + n + p, 2 + p, (b*(c + d*x))/(b*c - a*d)))/((b*c - a*d)*(1 + p))), ((a + b*x)^(1 + n)*(c + d*x)^p*HypergeometricFunctions._₂F₁(1 + n, -p, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/(((b*(c + d*x))/(b*c - a*d))^p*(b*(1 + n)))]
    @test_int [(a + b*x)^n*(c + d*x)^p/x^1, x, 2, -(((a + b*x)^(1 + n)*(c + d*x)^p*AppellF1(1 + n, -p, 1, 2 + n, -((d*(a + b*x))/(b*c - a*d)), (a + b*x)/a))/(((b*(c + d*x))/(b*c - a*d))^p*(a*(1 + n))))]
    @test_int [(a + b*x)^n*(c + d*x)^p/x^2, x, 2, (b*(a + b*x)^(1 + n)*(c + d*x)^p*AppellF1(1 + n, -p, 2, 2 + n, -((d*(a + b*x))/(b*c - a*d)), (a + b*x)/a))/(((b*(c + d*x))/(b*c - a*d))^p*(a^2*(1 + n)))]

    @test_int [(b*x)^(3/2)*(c + d*x)^n*(e + f*x)^p, x, 3, (2*(b*x)^(5/2)*(c + d*x)^n*(e + f*x)^p*AppellF1(5/2, -n, -p, 7/2, -((d*x)/c), -((f*x)/e)))/((1 + (d*x)/c)^n*(1 + (f*x)/e)^p*(5*b))]
    @test_int [(b*x)^(1/2)*(c + d*x)^n*(e + f*x)^p, x, 3, (2*(b*x)^(3/2)*(c + d*x)^n*(e + f*x)^p*AppellF1(3/2, -n, -p, 5/2, -((d*x)/c), -((f*x)/e)))/((1 + (d*x)/c)^n*(1 + (f*x)/e)^p*(3*b))]
    @test_int [(c + d*x)^n*(e + f*x)^p/(b*x)^(1/2), x, 3, (2*sqrt(b*x)*(c + d*x)^n*(e + f*x)^p*AppellF1(1/2, -n, -p, 3/2, -((d*x)/c), -((f*x)/e)))/((1 + (d*x)/c)^n*(1 + (f*x)/e)^p*b)]

    @test_int [(b*x)^m*(pi + d*x)^n*(ℯ + f*x)^p, x, 1, (ℯ^p*pi^n*(b*x)^(1 + m)*AppellF1(1 + m, -n, -p, 2 + m, -((d*x)/pi), -((f*x)/ℯ)))/(b*(1 + m))]
    @test_int [(b*x)^m*(pi + d*x)^n*(e + f*x)^p, x, 2, (pi^n*(b*x)^(1 + m)*(e + f*x)^p*AppellF1(1 + m, -n, -p, 2 + m, -((d*x)/pi), -((f*x)/e)))/((1 + (f*x)/e)^p*(b*(1 + m)))]

    @test_int [(b*x)^(5/2)*(pi + d*x)^n*(ℯ + f*x)^p, x, 1, (2*ℯ^p*pi^n*(b*x)^(7/2)*AppellF1(7/2, -n, -p, 9/2, -((d*x)/pi), -((f*x)/ℯ)))/(7*b)]
    @test_int [(b*x)^(5/2)*(pi + d*x)^n*(e + f*x)^p, x, 2, (2*pi^n*(b*x)^(7/2)*(e + f*x)^p*AppellF1(7/2, -n, -p, 9/2, -((d*x)/pi), -((f*x)/e)))/((1 + (f*x)/e)^p*(7*b))]

    @test_int [(a + b*x)^n/(c + d*x)^n*x^3, x, 4, (x^2*(a + b*x)^(1 + n)*(c + d*x)^(1 - n))/(4*b*d) + ((a + b*x)^(1 + n)*(c + d*x)^(1 - n)*(2*a*b*c*d*(3 - n^2) + a^2*d^2*(6 - 5*n + n^2) + b^2*c^2*(6 + 5*n + n^2) - 2*b*d*(a*d*(3 - n) + b*c*(3 + n))*x))/(24*b^3*d^3) - ((3*a*b^2*c^2*d*(2 + n - 2*n^2 - n^3) + a^3*d^3*(6 - 11*n + 6*n^2 - n^3) + 3*a^2*b*c*d^2*(2 - n - 2*n^2 + n^3) + b^3*c^3*(6 + 11*n + 6*n^2 + n^3))*(a + b*x)^(1 + n)*((b*(c + d*x))/(b*c - a*d))^n*HypergeometricFunctions._₂F₁(n, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^n*(24*b^4*d^3*(1 + n)))]
    @test_int [(a + b*x)^n/(c + d*x)^n*x^2, x, 4, -(((a*d*(2 - n) + b*c*(2 + n))*(a + b*x)^(1 + n)*(c + d*x)^(1 - n))/(6*b^2*d^2)) + (x*(a + b*x)^(1 + n)*(c + d*x)^(1 - n))/(3*b*d) + ((2*a*b*c*d*(1 - n^2) + a^2*d^2*(2 - 3*n + n^2) + b^2*c^2*(2 + 3*n + n^2))*(a + b*x)^(1 + n)*((b*(c + d*x))/(b*c - a*d))^n*HypergeometricFunctions._₂F₁(n, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^n*(6*b^3*d^2*(1 + n)))]
    @test_int [(a + b*x)^n/(c + d*x)^n*x^1, x, 3, ((a + b*x)^(1 + n)*(c + d*x)^(1 - n))/(2*b*d) - ((a*d*(1 - n) + b*c*(1 + n))*(a + b*x)^(1 + n)*((b*(c + d*x))/(b*c - a*d))^n*HypergeometricFunctions._₂F₁(n, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^n*(2*b^2*d*(1 + n)))]
    @test_int [(a + b*x)^n/(c + d*x)^n*x^0, x, 2, ((a + b*x)^(1 + n)*((b*(c + d*x))/(b*c - a*d))^n*HypergeometricFunctions._₂F₁(n, 1 + n, 2 + n, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^n*(b*(1 + n)))]
    @test_int [(a + b*x)^n/(c + d*x)^n/x^1, x, 5, -(((a + b*x)^n*HypergeometricFunctions._₂F₁(1, n, 1 + n, (c*(a + b*x))/(a*(c + d*x))))/((c + d*x)^n*n)) + ((a + b*x)^n*((b*(c + d*x))/(b*c - a*d))^n*HypergeometricFunctions._₂F₁(n, n, 1 + n, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^n*n)]
    @test_int [(a + b*x)^n/(c + d*x)^n/x^2, x, 1, ((b*c - a*d)*(a + b*x)^(1 + n)*(c + d*x)^(-1 - n)*HypergeometricFunctions._₂F₁(2, 1 + n, 2 + n, (c*(a + b*x))/(a*(c + d*x))))/(a^2*(1 + n))]
    @test_int [(a + b*x)^n/(c + d*x)^n/x^3, x, 2, -(((a + b*x)^(1 + n)*(c + d*x)^(1 - n))/(2*a*c*x^2)) - ((b*c - a*d)*(a*d*(1 + n) + b*(c - c*n))*(a + b*x)^(1 + n)*(c + d*x)^(-1 - n)*HypergeometricFunctions._₂F₁(2, 1 + n, 2 + n, (c*(a + b*x))/(a*(c + d*x))))/(2*a^3*c*(1 + n))]
    @test_int [(a + b*x)^n/(c + d*x)^n/x^4, x, 4, -(((a + b*x)^(1 + n)*(c + d*x)^(1 - n))/(3*a*c*x^3)) + ((b*c*(2 - n) + a*d*(2 + n))*(a + b*x)^(1 + n)*(c + d*x)^(1 - n))/(6*a^2*c^2*x^2) + ((b*c - a*d)*(2*a*b*c*d*(1 - n^2) + b^2*c^2*(2 - 3*n + n^2) + a^2*d^2*(2 + 3*n + n^2))*(a + b*x)^(1 + n)*(c + d*x)^(-1 - n)*HypergeometricFunctions._₂F₁(2, 1 + n, 2 + n, (c*(a + b*x))/(a*(c + d*x))))/(6*a^4*c^2*(1 + n))]

    @test_int [(1 - x)^n/(1 + x)^n*x^3, x, 3, (-(1/4))*(1 - x)^(1 + n)*x^2*(1 + x)^(1 - n) - (1/12)*(1 - x)^(1 + n)*(1 + x)^(1 - n)*(3 + 2*n^2 - 2*n*x) + (n*(2 + n^2)*(1 - x)^(1 + n)*HypergeometricFunctions._₂F₁(n, 1 + n, 2 + n, (1 - x)/2))/(2^n*(3*(1 + n)))]
    @test_int [(1 - x)^n/(1 + x)^n*x^2, x, 3, (1/3)*n*(1 - x)^(1 + n)*(1 + x)^(1 - n) - (1/3)*(1 - x)^(1 + n)*x*(1 + x)^(1 - n) - ((1 + 2*n^2)*(1 - x)^(1 + n)*HypergeometricFunctions._₂F₁(n, 1 + n, 2 + n, (1 - x)/2))/(2^n*(3*(1 + n)))]
    @test_int [(1 - x)^n/(1 + x)^n*x^1, x, 2, (-(1/2))*(1 - x)^(1 + n)*(1 + x)^(1 - n) + (n*(1 - x)^(1 + n)*HypergeometricFunctions._₂F₁(n, 1 + n, 2 + n, (1 - x)/2))/(2^n*(1 + n))]
    @test_int [(1 - x)^n/(1 + x)^n*x^0, x, 1, -(((1 - x)^(1 + n)*HypergeometricFunctions._₂F₁(n, 1 + n, 2 + n, (1 - x)/2))/(2^n*(1 + n)))]
    @test_int [(1 - x)^n/(1 + x)^n/x^1, x, 3, -(((1 - x)^n*HypergeometricFunctions._₂F₁(1, n, 1 + n, (1 - x)/(1 + x)))/((1 + x)^n*n)) + ((1 - x)^n*HypergeometricFunctions._₂F₁(n, n, 1 + n, (1 - x)/2))/(2^n*n)]
    @test_int [(1 - x)^n/(1 + x)^n/x^2, x, 1, -((2*(1 - x)^(1 + n)*(1 + x)^(-1 - n)*HypergeometricFunctions._₂F₁(2, 1 + n, 2 + n, (1 - x)/(1 + x)))/(1 + n))]
    @test_int [(1 - x)^n/(1 + x)^n/x^3, x, 2, -(((1 - x)^(1 + n)*(1 + x)^(1 - n))/(2*x^2)) + (2*n*(1 - x)^(1 + n)*(1 + x)^(-1 - n)*HypergeometricFunctions._₂F₁(2, 1 + n, 2 + n, (1 - x)/(1 + x)))/(1 + n)]
    @test_int [(1 - x)^n/(1 + x)^n/x^4, x, 4, -(((1 - x)^(1 + n)*(1 + x)^(1 - n))/(3*x^3)) + (n*(1 - x)^(1 + n)*(1 + x)^(1 - n))/(3*x^2) - (2*(1 + 2*n^2)*(1 - x)^(1 + n)*(1 + x)^(-1 - n)*HypergeometricFunctions._₂F₁(2, 1 + n, 2 + n, (1 - x)/(1 + x)))/(3*(1 + n))]

    #= Mathematica*8*cannot*verify*the*second*antiderivatives*of*the*following*pairs*correct, although*they*are. =#
    @test_int [x^m*(1 - a*x)^n*(1 + a*x)^n, x, 2, (x^(1 + m)*HypergeometricFunctions._₂F₁((1 + m)/2, -n, (3 + m)/2, a^2*x^2))/(1 + m)]
    @test_int [x^m*(1 - a*x)^n*(2 + 2*a*x)^n, x, 2, (2^n*x^(1 + m)*HypergeometricFunctions._₂F₁((1 + m)/2, -n, (3 + m)/2, a^2*x^2))/(1 + m)]

    @test_int [x^m*(2 - a*x)^n*(2 + a*x)^n, x, 2, (4^n*x^(1 + m)*HypergeometricFunctions._₂F₁((1 + m)/2, -n, (3 + m)/2, (a^2*x^2)/4))/(1 + m)]
    @test_int [x^m*(1 - a*x/2)^n*(2 + a*x)^n, x, 2, (2^n*x^(1 + m)*HypergeometricFunctions._₂F₁((1 + m)/2, -n, (3 + m)/2, (a^2*x^2)/4))/(1 + m)]

    #= Mathematica*8*cannot*verify*the*following*antiderivatives*correct, although*they*are. =#
    @test_int [x^m*(3 - 2*a*x)^(n + 2)*(6 + 4*a*x)^n, x, 8, (2^n*9^(1 + n)*x^(1 + m)*HypergeometricFunctions._₂F₁((1 + m)/2, -n, (3 + m)/2, (4*a^2*x^2)/9))/(1 + m) - (2^(2 + n)*3^(1 + 2*n)*a*x^(2 + m)*HypergeometricFunctions._₂F₁((2 + m)/2, -n, (4 + m)/2, (4*a^2*x^2)/9))/(2 + m) + (2^(2 + n)*9^n*a^2*x^(3 + m)*HypergeometricFunctions._₂F₁((3 + m)/2, -n, (5 + m)/2, (4*a^2*x^2)/9))/(3 + m)]
    @test_int [x^m*(3 - 2*a*x)^(n + 1)*(6 + 4*a*x)^n, x, 5, (2^n*3^(1 + 2*n)*x^(1 + m)*HypergeometricFunctions._₂F₁((1 + m)/2, -n, (3 + m)/2, (4*a^2*x^2)/9))/(1 + m) - (2^(1 + n)*9^n*a*x^(2 + m)*HypergeometricFunctions._₂F₁((2 + m)/2, -n, (4 + m)/2, (4*a^2*x^2)/9))/(2 + m)]
    @test_int [x^m*(3 - 2*a*x)^(n + 0)*(6 + 4*a*x)^n, x, 2, (18^n*x^(1 + m)*HypergeometricFunctions._₂F₁((1 + m)/2, -n, (3 + m)/2, (4*a^2*x^2)/9))/(1 + m)]
    @test_int [x^m*(3 - 2*a*x)^(n - 1)*(6 + 4*a*x)^n, x, 5, (2^n*3^(-1 + 2*n)*x^(1 + m)*HypergeometricFunctions._₂F₁((1 + m)/2, 1 - n, (3 + m)/2, (4*a^2*x^2)/9))/(1 + m) + (2^(1 + n)*9^(-1 + n)*a*x^(2 + m)*HypergeometricFunctions._₂F₁((2 + m)/2, 1 - n, (4 + m)/2, (4*a^2*x^2)/9))/(2 + m)]
    @test_int [x^m*(3 - 2*a*x)^(n - 2)*(6 + 4*a*x)^n, x, 8, (2^n*9^(-1 + n)*x^(1 + m)*HypergeometricFunctions._₂F₁((1 + m)/2, 2 - n, (3 + m)/2, (4*a^2*x^2)/9))/(1 + m) + (2^(2 + n)*3^(-3 + 2*n)*a*x^(2 + m)*HypergeometricFunctions._₂F₁((2 + m)/2, 2 - n, (4 + m)/2, (4*a^2*x^2)/9))/(2 + m) + (2^(2 + n)*9^(-2 + n)*a^2*x^(3 + m)*HypergeometricFunctions._₂F₁((3 + m)/2, 2 - n, (5 + m)/2, (4*a^2*x^2)/9))/(3 + m)]

    @test_int [x^m*(a + b*x)^(n + 1)*(c + d*x)^n, x, 3, (a*x^(1 + m)*(a + b*x)^n*(c + d*x)^n*AppellF1(1 + m, -1 - n, -n, 2 + m, -((b*x)/a), -((d*x)/c)))/((1 + (b*x)/a)^n*(1 + (d*x)/c)^n*(1 + m))]

    @test_int [(a - x)^m*(c + d*x)^n*(f*x)^p, x, 3, ((a - x)^m*(f*x)^(1 + p)*(c + d*x)^n*AppellF1(1 + p, -m, -n, 2 + p, x/a, -((d*x)/c)))/((1 - x/a)^m*(1 + (d*x)/c)^n*(f*(1 + p)))]

    @test_int [(1 - x)^(p - 1/2)*((1 + x)^(p + 1/2)/(c*x)^(2*(p + 1))), x, 1, -((4^(1 + p)*(1 - x)^(1/2 + p)*(x/(1 + x))^(2*(1 + p))*(1 + x)^(3/2 + p)*HypergeometricFunctions._₂F₁(1/2 + p, 2*(1 + p), 3/2 + p, (1 - x)/(1 + x)))/((c*x)^(2*(1 + p))*(1 + 2*p)))]

    @test_int [(1 + x/a)^(n/2)/((1 - x/a)^(n/2)*x^2), x, 1, -((4*(1 - x/a)^(1 - n/2)*(1 + x/a)^((1/2)*(-2 + n))*HypergeometricFunctions._₂F₁(2, 1 - n/2, 2 - n/2, (a - x)/(a + x)))/(a*(2 - n)))]

    @test_int [(1 - a*x)^m*(1 + a*x)^m/(b*x)^(2*m + 2), x, 2, -(((b*x)^(-1 - 2*m)*HypergeometricFunctions._₂F₁((1/2)*(-1 - 2*m), -m, (1/2)*(1 - 2*m), a^2*x^2))/(b*(1 + 2*m)))]

    @test_int [(1 + a*x)^n/(x*(1 - a*x)^n), x, 3, ((1 + a*x)^n*HypergeometricFunctions._₂F₁(1, -n, 1 - n, (1 - a*x)/(1 + a*x)))/((1 - a*x)^n*n) - (2^n*HypergeometricFunctions._₂F₁(-n, -n, 1 - n, (1/2)*(1 - a*x)))/((1 - a*x)^n*n)]

    @test_int [(1 - a*x)^(1 - n)*(1 + a*x)^(1 + n)/x^2, x, 3, -((2*a*(1 - a*x)^(1 - n)*(1 + a*x)^(-1 + n)*HypergeometricFunctions._₂F₁(2, 1 - n, 2 - n, (1 - a*x)/(1 + a*x)))/(1 - n)) + (2^n*a*(1 - a*x)^(1 - n)*HypergeometricFunctions._₂F₁(1 - n, -n, 2 - n, (1/2)*(1 - a*x)))/(1 - n)]

    @test_int [x^2/((1 - a*x)^7*(1 + a*x)^4), x, 1, -((1 - 3*a*x)/(24*a^3*(1 - a*x)^6*(1 + a*x)^3))]
    @test_int [x^2/((1 - a*x)^11*(1 + a*x)^7), x, 1, -((1 - 4*a*x)/(60*a^3*(1 - a*x)^10*(1 + a*x)^6))]
    @test_int [x^2/((1 - a*x)^16*(1 + a*x)^11), x, 1, -((1 - 5*a*x)/(120*a^3*(1 - a*x)^15*(1 + a*x)^10))]
    @test_int [x^2/((1 - a*x)^((n*(n + 1))/2 + 1)*(1 + a*x)^((n*(n - 1))/2 + 1)), x, 1, ((1 + a*x)^((1/2)*(1 - n)*n)*(1 - a*n*x))/((1 - a*x)^((1/2)*n*(1 + n))*(a^3*n*(1 - n^2)))]

    @test_int [(a + b*x)^(1 + n)/((a - b*x)^n*x^1), x, 6, ((a - b*x)^(1 - n)*(a + b*x)^n)/(2*n) - (a*(a + b*x)^n*HypergeometricFunctions._₂F₁(1, n, 1 + n, (a + b*x)/(a - b*x)))/((a - b*x)^n*n) + (2^(-1 - n)*(1 + 2*n)*((a - b*x)/a)^n*(a + b*x)^(1 + n)*HypergeometricFunctions._₂F₁(n, 1 + n, 2 + n, (a + b*x)/(2*a)))/((a - b*x)^n*(n*(1 + n)))]
    @test_int [(a + b*x)^(1 + n)/((a - b*x)^n*x^2), x, 5, -((a + b*x)^(1 + n)/((a - b*x)^n*x)) + (b*(1 + 2*n)*(a + b*x)^n*HypergeometricFunctions._₂F₁(1, -n, 1 - n, (a - b*x)/(a + b*x)))/((a - b*x)^n*n) - (2^n*b*(a + b*x)^n*HypergeometricFunctions._₂F₁(-n, -n, 1 - n, (a - b*x)/(2*a)))/((a - b*x)^n*((a + b*x)/a)^n*n)]
    @test_int [(a + b*x)^(1 + n)/((a - b*x)^n*x^3), x, 1, -((4*b^2*(a - b*x)^(1 - n)*(a + b*x)^(-1 + n)*HypergeometricFunctions._₂F₁(3, 1 - n, 2 - n, (a - b*x)/(a + b*x)))/(a*(1 - n)))]
    @test_int [(a + b*x)^(1 + n)/((a - b*x)^n*x^4), x, 2, -(((a - b*x)^(1 - n)*(a + b*x)^(2 + n))/(3*a^2*x^3)) - (4*b^3*(1 + 2*n)*(a - b*x)^(1 - n)*(a + b*x)^(-1 + n)*HypergeometricFunctions._₂F₁(3, 1 - n, 2 - n, (a - b*x)/(a + b*x)))/(3*a^2*(1 - n))]
    @test_int [(a + b*x)^(1 + n)/((a - b*x)^n*x^5), x, 4, -(((a - b*x)^(1 - n)*(a + b*x)^(2 + n))/(4*a^2*x^4)) - (b*(1 + 2*n)*(a - b*x)^(1 - n)*(a + b*x)^(2 + n))/(12*a^3*x^3) - (4*b^4*(1 + n + n^2)*(a - b*x)^(1 - n)*(a + b*x)^(-1 + n)*HypergeometricFunctions._₂F₁(3, 1 - n, 2 - n, (a - b*x)/(a + b*x)))/(3*a^3*(1 - n))]

    #= ::Title:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^n*(e+f*x)^p=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^n*(e+f*x)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(A+B*x)*(d+e*x)^p=#

    #= ::Subsubsection::Closed:: =#
    #=m>0=#

    @test_int [(a + b*x)*(A + B*x)*(d + e*x)^4, x, 2, ((b*d - a*e)*(B*d - A*e)*(d + e*x)^5)/(5*e^3) - ((2*b*B*d - A*b*e - a*B*e)*(d + e*x)^6)/(6*e^3) + (b*B*(d + e*x)^7)/(7*e^3)]
    @test_int [(a + b*x)*(A + B*x)*(d + e*x)^3, x, 2, ((b*d - a*e)*(B*d - A*e)*(d + e*x)^4)/(4*e^3) - ((2*b*B*d - A*b*e - a*B*e)*(d + e*x)^5)/(5*e^3) + (b*B*(d + e*x)^6)/(6*e^3)]
    @test_int [(a + b*x)*(A + B*x)*(d + e*x)^2, x, 2, ((b*d - a*e)*(B*d - A*e)*(d + e*x)^3)/(3*e^3) - ((2*b*B*d - A*b*e - a*B*e)*(d + e*x)^4)/(4*e^3) + (b*B*(d + e*x)^5)/(5*e^3)]

    @test_int [(a + b*x)*(A + B*x)*(d + e*x)^1, x, 2, a*A*d*x + (1/2)*(A*b*d + a*B*d + a*A*e)*x^2 + (1/3)*(b*B*d + A*b*e + a*B*e)*x^3 + (1/4)*b*B*e*x^4]
    @test_int [(a + b*x)*(A + B*x)*(d + e*x)^0, x, 2, a*A*x + ((A*b + a*B)*x^2)/2 + (b*B*x^3)/3]

    @test_int [((a + b*x)*(A + B*x))/(d + e*x), x, 2, -((b*(B*d - A*e)*x)/e^2) + (B*(a + b*x)^2)/(2*b*e) + ((b*d - a*e)*(B*d - A*e)*log(d + e*x))/e^3]
    @test_int [((a + b*x)*(A + B*x))/(d + e*x)^2, x, 2, (b*B*x)/e^2 - ((b*d - a*e)*(B*d - A*e))/(e^3*(d + e*x)) - ((2*b*B*d - A*b*e - a*B*e)*log(d + e*x))/e^3]
    @test_int [((a + b*x)*(A + B*x))/(d + e*x)^3, x, 2, -(((b*d - a*e)*(B*d - A*e))/(2*e^3*(d + e*x)^2)) + (2*b*B*d - A*b*e - a*B*e)/(e^3*(d + e*x)) + (b*B*log(d + e*x))/e^3]

    @test_int [((a + b*x)*(A + B*x))/(d + e*x)^4, x, 2, -(((b*d - a*e)*(B*d - A*e))/(3*e^3*(d + e*x)^3)) + (2*b*B*d - A*b*e - a*B*e)/(2*e^3*(d + e*x)^2) - (b*B)/(e^3*(d + e*x))]
    @test_int [((a + b*x)*(A + B*x))/(d + e*x)^5, x, 2, -(((b*d - a*e)*(B*d - A*e))/(4*e^3*(d + e*x)^4)) + (2*b*B*d - A*b*e - a*B*e)/(3*e^3*(d + e*x)^3) - (b*B)/(2*e^3*(d + e*x)^2)]
    @test_int [((a + b*x)*(A + B*x))/(d + e*x)^6, x, 2, -(((b*d - a*e)*(B*d - A*e))/(5*e^3*(d + e*x)^5)) + (2*b*B*d - A*b*e - a*B*e)/(4*e^3*(d + e*x)^4) - (b*B)/(3*e^3*(d + e*x)^3)]

    @test_int [(a + b*x)^2*(A + B*x)*(d + e*x)^4, x, 2, -(((b*d - a*e)^2*(B*d - A*e)*(d + e*x)^5)/(5*e^4)) + ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^6)/(6*e^4) - (b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^7)/(7*e^4) + (b^2*B*(d + e*x)^8)/(8*e^4)]
    @test_int [(a + b*x)^2*(A + B*x)*(d + e*x)^3, x, 2, -(((b*d - a*e)^2*(B*d - A*e)*(d + e*x)^4)/(4*e^4)) + ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^5)/(5*e^4) - (b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^6)/(6*e^4) + (b^2*B*(d + e*x)^7)/(7*e^4)]
    @test_int [(a + b*x)^2*(A + B*x)*(d + e*x)^2, x, 2, ((A*b - a*B)*(b*d - a*e)^2*(a + b*x)^3)/(3*b^4) + ((b*d - a*e)*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^4)/(4*b^4) + (e*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^5)/(5*b^4) + (B*e^2*(a + b*x)^6)/(6*b^4)]

    @test_int [(a + b*x)^2*(A + B*x)*(d + e*x)^1, x, 2, ((A*b - a*B)*(b*d - a*e)*(a + b*x)^3)/(3*b^3) + ((b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^4)/(4*b^3) + (B*e*(a + b*x)^5)/(5*b^3)]
    @test_int [(a + b*x)^2*(A + B*x)*(d + e*x)^0, x, 2, ((A*b - a*B)*(a + b*x)^3)/(3*b^2) + (B*(a + b*x)^4)/(4*b^2)]

    @test_int [((a + b*x)^2*(A + B*x))/(d + e*x), x, 2, (b*(b*d - a*e)*(B*d - A*e)*x)/e^3 - ((B*d - A*e)*(a + b*x)^2)/(2*e^2) + (B*(a + b*x)^3)/(3*b*e) - ((b*d - a*e)^2*(B*d - A*e)*log(d + e*x))/e^4]
    @test_int [((a + b*x)^2*(A + B*x))/(d + e*x)^2, x, 2, -((b*(2*b*B*d - A*b*e - 2*a*B*e)*x)/e^3) + (b^2*B*x^2)/(2*e^2) + ((b*d - a*e)^2*(B*d - A*e))/(e^4*(d + e*x)) + ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*log(d + e*x))/e^4]
    @test_int [((a + b*x)^2*(A + B*x))/(d + e*x)^3, x, 2, (b^2*B*x)/e^3 + ((b*d - a*e)^2*(B*d - A*e))/(2*e^4*(d + e*x)^2) - ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e))/(e^4*(d + e*x)) - (b*(3*b*B*d - A*b*e - 2*a*B*e)*log(d + e*x))/e^4]
    @test_int [((a + b*x)^2*(A + B*x))/(d + e*x)^4, x, 3, -(((B*d - A*e)*(a + b*x)^3)/(3*e*(b*d - a*e)*(d + e*x)^3)) - (B*(b*d - a*e)^2)/(2*e^4*(d + e*x)^2) + (2*b*B*(b*d - a*e))/(e^4*(d + e*x)) + (b^2*B*log(d + e*x))/e^4]

    @test_int [((a + b*x)^2*(A + B*x))/(d + e*x)^5, x, 2, -((B*d - A*e)*(a + b*x)^3)/(4*e*(b*d - a*e)*(d + e*x)^4) + ((3*b*B*d + A*b*e - 4*a*B*e)*(a + b*x)^3)/(12*e*(b*d - a*e)^2*(d + e*x)^3)]

    @test_int [((a + b*x)^2*(A + B*x))/(d + e*x)^6, x, 2, ((b*d - a*e)^2*(B*d - A*e))/(5*e^4*(d + e*x)^5) - ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e))/(4*e^4*(d + e*x)^4) + (b*(3*b*B*d - A*b*e - 2*a*B*e))/(3*e^4*(d + e*x)^3) - (b^2*B)/(2*e^4*(d + e*x)^2)]
    @test_int [((a + b*x)^2*(A + B*x))/(d + e*x)^7, x, 2, ((b*d - a*e)^2*(B*d - A*e))/(6*e^4*(d + e*x)^6) - ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e))/(5*e^4*(d + e*x)^5) + (b*(3*b*B*d - A*b*e - 2*a*B*e))/(4*e^4*(d + e*x)^4) - (b^2*B)/(3*e^4*(d + e*x)^3)]
    @test_int [((a + b*x)^2*(A + B*x))/(d + e*x)^8, x, 2, ((b*d - a*e)^2*(B*d - A*e))/(7*e^4*(d + e*x)^7) - ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e))/(6*e^4*(d + e*x)^6) + (b*(3*b*B*d - A*b*e - 2*a*B*e))/(5*e^4*(d + e*x)^5) - (b^2*B)/(4*e^4*(d + e*x)^4)]

    @test_int [(a + b*x)^3*(A + B*x)*(d + e*x)^5, x, 2, ((b*d - a*e)^3*(B*d - A*e)*(d + e*x)^6)/(6*e^5) - ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)^7)/(7*e^5) + (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^8)/(8*e^5) - (b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^9)/(9*e^5) + (b^3*B*(d + e*x)^10)/(10*e^5)]
    @test_int [(a + b*x)^3*(A + B*x)*(d + e*x)^4, x, 2, ((b*d - a*e)^3*(B*d - A*e)*(d + e*x)^5)/(5*e^5) - ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)^6)/(6*e^5) + (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^7)/(7*e^5) - (b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^8)/(8*e^5) + (b^3*B*(d + e*x)^9)/(9*e^5)]
    @test_int [(a + b*x)^3*(A + B*x)*(d + e*x)^3, x, 2, ((A*b - a*B)*(b*d - a*e)^3*(a + b*x)^4)/(4*b^5) + ((b*d - a*e)^2*(b*B*d + 3*A*b*e - 4*a*B*e)*(a + b*x)^5)/(5*b^5) + (e*(b*d - a*e)*(b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^6)/(2*b^5) + (e^2*(3*b*B*d + A*b*e - 4*a*B*e)*(a + b*x)^7)/(7*b^5) + (B*e^3*(a + b*x)^8)/(8*b^5)]

    @test_int [(a + b*x)^3*(A + B*x)*(d + e*x)^2, x, 2, ((A*b - a*B)*(b*d - a*e)^2*(a + b*x)^4)/(4*b^4) + ((b*d - a*e)*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^5)/(5*b^4) + (e*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^6)/(6*b^4) + (B*e^2*(a + b*x)^7)/(7*b^4)]
    @test_int [(a + b*x)^3*(A + B*x)*(d + e*x)^1, x, 2, ((A*b - a*B)*(b*d - a*e)*(a + b*x)^4)/(4*b^3) + ((b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^5)/(5*b^3) + (B*e*(a + b*x)^6)/(6*b^3)]
    @test_int [(a + b*x)^3*(A + B*x)*(d + e*x)^0, x, 2, ((A*b - a*B)*(a + b*x)^4)/(4*b^2) + (B*(a + b*x)^5)/(5*b^2)]

    @test_int [((a + b*x)^3*(A + B*x))/(d + e*x), x, 2, -((b*(b*d - a*e)^2*(B*d - A*e)*x)/e^4) + ((b*d - a*e)*(B*d - A*e)*(a + b*x)^2)/(2*e^3) - ((B*d - A*e)*(a + b*x)^3)/(3*e^2) + (B*(a + b*x)^4)/(4*b*e) + ((b*d - a*e)^3*(B*d - A*e)*log(d + e*x))/e^5]
    @test_int [((a + b*x)^3*(A + B*x))/(d + e*x)^2, x, 2, (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*x)/e^4 - ((b*d - a*e)^3*(B*d - A*e))/(e^5*(d + e*x)) - (b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^2)/(2*e^5) + (b^3*B*(d + e*x)^3)/(3*e^5) - ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*log(d + e*x))/e^5]
    @test_int [((a + b*x)^3*(A + B*x))/(d + e*x)^3, x, 2, -((b^2*(3*b*B*d - A*b*e - 3*a*B*e)*x)/e^4) + (b^3*B*x^2)/(2*e^3) - ((b*d - a*e)^3*(B*d - A*e))/(2*e^5*(d + e*x)^2) + ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e))/(e^5*(d + e*x)) + (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*log(d + e*x))/e^5]
    @test_int [((a + b*x)^3*(A + B*x))/(d + e*x)^4, x, 2, (b^3*B*x)/e^4 - ((b*d - a*e)^3*(B*d - A*e))/(3*e^5*(d + e*x)^3) + ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e))/(2*e^5*(d + e*x)^2) - (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e))/(e^5*(d + e*x)) - (b^2*(4*b*B*d - A*b*e - 3*a*B*e)*log(d + e*x))/e^5]
    @test_int [((a + b*x)^3*(A + B*x))/(d + e*x)^5, x, 3, -(((B*d - A*e)*(a + b*x)^4)/(4*e*(b*d - a*e)*(d + e*x)^4)) + (B*(b*d - a*e)^3)/(3*e^5*(d + e*x)^3) - (3*b*B*(b*d - a*e)^2)/(2*e^5*(d + e*x)^2) + (3*b^2*B*(b*d - a*e))/(e^5*(d + e*x)) + (b^3*B*log(d + e*x))/e^5]

    @test_int [((a + b*x)^3*(A + B*x))/(d + e*x)^6, x, 2, -(((B*d - A*e)*(a + b*x)^4)/(5*e*(b*d - a*e)*(d + e*x)^5)) + ((4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)^4)/(20*e*(b*d - a*e)^2*(d + e*x)^4)]
    @test_int [((a + b*x)^3*(A + B*x))/(d + e*x)^7, x, 3, -(((B*d - A*e)*(a + b*x)^4)/(6*e*(b*d - a*e)*(d + e*x)^6)) + ((2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^4)/(15*e*(b*d - a*e)^2*(d + e*x)^5) + (b*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^4)/(60*e*(b*d - a*e)^3*(d + e*x)^4)]

    @test_int [((a + b*x)^3*(A + B*x))/(d + e*x)^8, x, 2, -(((b*d - a*e)^3*(B*d - A*e))/(7*e^5*(d + e*x)^7)) + ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e))/(6*e^5*(d + e*x)^6) - (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e))/(5*e^5*(d + e*x)^5) + (b^2*(4*b*B*d - A*b*e - 3*a*B*e))/(4*e^5*(d + e*x)^4) - (b^3*B)/(3*e^5*(d + e*x)^3)]
    @test_int [((a + b*x)^3*(A + B*x))/(d + e*x)^9, x, 2, -(((b*d - a*e)^3*(B*d - A*e))/(8*e^5*(d + e*x)^8)) + ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e))/(7*e^5*(d + e*x)^7) - (b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e))/(2*e^5*(d + e*x)^6) + (b^2*(4*b*B*d - A*b*e - 3*a*B*e))/(5*e^5*(d + e*x)^5) - (b^3*B)/(4*e^5*(d + e*x)^4)]
    @test_int [((a + b*x)^3*(A + B*x))/(d + e*x)^10, x, 2, -(((b*d - a*e)^3*(B*d - A*e))/(9*e^5*(d + e*x)^9)) + ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e))/(8*e^5*(d + e*x)^8) - (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e))/(7*e^5*(d + e*x)^7) + (b^2*(4*b*B*d - A*b*e - 3*a*B*e))/(6*e^5*(d + e*x)^6) - (b^3*B)/(5*e^5*(d + e*x)^5)]

    @test_int [(a + b*x)^6*(A + B*x)*(d + e*x)^8, x, 2, -((b*d - a*e)^6*(B*d - A*e)*(d + e*x)^9)/(9*e^8) + ((b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x)^10)/(10*e^8) - (3*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^11)/(11*e^8) + (5*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^12)/(12*e^8) - (5*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^13)/(13*e^8) + (3*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^14)/(14*e^8) - (b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^15)/(15*e^8) + (b^6*B*(d + e*x)^16)/(16*e^8)]
    @test_int [(a + b*x)^6*(A + B*x)*(d + e*x)^7, x, 2, -((b*d - a*e)^6*(B*d - A*e)*(d + e*x)^8)/(8*e^8) + ((b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x)^9)/(9*e^8) - (3*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^10)/(10*e^8) + (5*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^11)/(11*e^8) - (5*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^12)/(12*e^8) + (3*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^13)/(13*e^8) - (b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^14)/(14*e^8) + (b^6*B*(d + e*x)^15)/(15*e^8)]
    @test_int [(a + b*x)^6*(A + B*x)*(d + e*x)^6, x, 2, ((A*b - a*B)*(b*d - a*e)^6*(a + b*x)^7)/(7*b^8) + ((b*d - a*e)^5*(b*B*d + 6*A*b*e - 7*a*B*e)*(a + b*x)^8)/(8*b^8) + (e*(b*d - a*e)^4*(2*b*B*d + 5*A*b*e - 7*a*B*e)*(a + b*x)^9)/(3*b^8) + (e^2*(b*d - a*e)^3*(3*b*B*d + 4*A*b*e - 7*a*B*e)*(a + b*x)^10)/(2*b^8) + (5*e^3*(b*d - a*e)^2*(4*b*B*d + 3*A*b*e - 7*a*B*e)*(a + b*x)^11)/(11*b^8) + (e^4*(b*d - a*e)*(5*b*B*d + 2*A*b*e - 7*a*B*e)*(a + b*x)^12)/(4*b^8) + (e^5*(6*b*B*d + A*b*e - 7*a*B*e)*(a + b*x)^13)/(13*b^8) + (B*e^6*(a + b*x)^14)/(14*b^8)]

    @test_int [(a + b*x)^6*(A + B*x)*(d + e*x)^5, x, 2, ((A*b - a*B)*(b*d - a*e)^5*(a + b*x)^7)/(7*b^7) + ((b*d - a*e)^4*(b*B*d + 5*A*b*e - 6*a*B*e)*(a + b*x)^8)/(8*b^7) + (5*e*(b*d - a*e)^3*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^9)/(9*b^7) + (e^2*(b*d - a*e)^2*(b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^10)/b^7 + (5*e^3*(b*d - a*e)*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^11)/(11*b^7) + (e^4*(5*b*B*d + A*b*e - 6*a*B*e)*(a + b*x)^12)/(12*b^7) + (B*e^5*(a + b*x)^13)/(13*b^7)]
    @test_int [(a + b*x)^6*(A + B*x)*(d + e*x)^4, x, 2, ((A*b - a*B)*(b*d - a*e)^4*(a + b*x)^7)/(7*b^6) + ((b*d - a*e)^3*(b*B*d + 4*A*b*e - 5*a*B*e)*(a + b*x)^8)/(8*b^6) + (2*e*(b*d - a*e)^2*(2*b*B*d + 3*A*b*e - 5*a*B*e)*(a + b*x)^9)/(9*b^6) + (e^2*(b*d - a*e)*(3*b*B*d + 2*A*b*e - 5*a*B*e)*(a + b*x)^10)/(5*b^6) + (e^3*(4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)^11)/(11*b^6) + (B*e^4*(a + b*x)^12)/(12*b^6)]
    @test_int [(a + b*x)^6*(A + B*x)*(d + e*x)^3, x, 2, ((A*b - a*B)*(b*d - a*e)^3*(a + b*x)^7)/(7*b^5) + ((b*d - a*e)^2*(b*B*d + 3*A*b*e - 4*a*B*e)*(a + b*x)^8)/(8*b^5) + (e*(b*d - a*e)*(b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^9)/(3*b^5) + (e^2*(3*b*B*d + A*b*e - 4*a*B*e)*(a + b*x)^10)/(10*b^5) + (B*e^3*(a + b*x)^11)/(11*b^5)]
    @test_int [(a + b*x)^6*(A + B*x)*(d + e*x)^2, x, 2, ((A*b - a*B)*(b*d - a*e)^2*(a + b*x)^7)/(7*b^4) + ((b*d - a*e)*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^8)/(8*b^4) + (e*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^9)/(9*b^4) + (B*e^2*(a + b*x)^10)/(10*b^4)]
    @test_int [(a + b*x)^6*(A + B*x)*(d + e*x), x, 2, ((A*b - a*B)*(b*d - a*e)*(a + b*x)^7)/(7*b^3) + ((b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^8)/(8*b^3) + (B*e*(a + b*x)^9)/(9*b^3)]
    @test_int [(a + b*x)^6*(A + B*x), x, 2, ((A*b - a*B)*(a + b*x)^7)/(7*b^2) + (B*(a + b*x)^8)/(8*b^2)]

    @test_int [((a + b*x)^6*(A + B*x))/(d + e*x), x, 2, (b*(b*d - a*e)^5*(B*d - A*e)*x)/e^7 - ((b*d - a*e)^4*(B*d - A*e)*(a + b*x)^2)/(2*e^6) + ((b*d - a*e)^3*(B*d - A*e)*(a + b*x)^3)/(3*e^5) - ((b*d - a*e)^2*(B*d - A*e)*(a + b*x)^4)/(4*e^4) + ((b*d - a*e)*(B*d - A*e)*(a + b*x)^5)/(5*e^3) - ((B*d - A*e)*(a + b*x)^6)/(6*e^2) + (B*(a + b*x)^7)/(7*b*e) - ((b*d - a*e)^6*(B*d - A*e)*log(d + e*x))/e^8]
    @test_int [((a + b*x)^6*(A + B*x))/(d + e*x)^2, x, 2, -((3*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*x)/e^7) + ((b*d - a*e)^6*(B*d - A*e))/(e^8*(d + e*x)) + (5*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^2)/(2*e^8) - (5*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^3)/(3*e^8) + (3*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^4)/(4*e^8) - (b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^5)/(5*e^8) + (b^6*B*(d + e*x)^6)/(6*e^8) + ((b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*log(d + e*x))/e^8]
    @test_int [((a + b*x)^6*(A + B*x))/(d + e*x)^3, x, 2, (5*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*x)/e^7 + ((b*d - a*e)^6*(B*d - A*e))/(2*e^8*(d + e*x)^2) - ((b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e))/(e^8*(d + e*x)) - (5*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^2)/(2*e^8) + (b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^3)/e^8 - (b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^4)/(4*e^8) + (b^6*B*(d + e*x)^5)/(5*e^8) - (3*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*log(d + e*x))/e^8]
    @test_int [((a + b*x)^6*(A + B*x))/(d + e*x)^4, x, 2, -((5*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*x)/e^7) + ((b*d - a*e)^6*(B*d - A*e))/(3*e^8*(d + e*x)^3) - ((b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e))/(2*e^8*(d + e*x)^2) + (3*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e))/(e^8*(d + e*x)) + (3*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^2)/(2*e^8) - (b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^3)/(3*e^8) + (b^6*B*(d + e*x)^4)/(4*e^8) + (5*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*log(d + e*x))/e^8]
    @test_int [((a + b*x)^6*(A + B*x))/(d + e*x)^5, x, 2, (3*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*x)/e^7 + ((b*d - a*e)^6*(B*d - A*e))/(4*e^8*(d + e*x)^4) - ((b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e))/(3*e^8*(d + e*x)^3) + (3*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e))/(2*e^8*(d + e*x)^2) - (5*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e))/(e^8*(d + e*x)) - (b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^2)/(2*e^8) + (b^6*B*(d + e*x)^3)/(3*e^8) - (5*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*log(d + e*x))/e^8]
    @test_int [((a + b*x)^6*(A + B*x))/(d + e*x)^6, x, 2, -((b^5*(6*b*B*d - A*b*e - 6*a*B*e)*x)/e^7) + (b^6*B*x^2)/(2*e^6) + ((b*d - a*e)^6*(B*d - A*e))/(5*e^8*(d + e*x)^5) - ((b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e))/(4*e^8*(d + e*x)^4) + (b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e))/(e^8*(d + e*x)^3) - (5*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e))/(2*e^8*(d + e*x)^2) + (5*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e))/(e^8*(d + e*x)) + (3*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*log(d + e*x))/e^8]
    @test_int [((a + b*x)^6*(A + B*x))/(d + e*x)^7, x, 2, (b^6*B*x)/e^7 + ((b*d - a*e)^6*(B*d - A*e))/(6*e^8*(d + e*x)^6) - ((b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e))/(5*e^8*(d + e*x)^5) + (3*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e))/(4*e^8*(d + e*x)^4) - (5*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e))/(3*e^8*(d + e*x)^3) + (5*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e))/(2*e^8*(d + e*x)^2) - (3*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e))/(e^8*(d + e*x)) - (b^5*(7*b*B*d - A*b*e - 6*a*B*e)*log(d + e*x))/e^8]
    @test_int [((a + b*x)^6*(A + B*x))/(d + e*x)^8, x, 3, -(((B*d - A*e)*(a + b*x)^7)/(7*e*(b*d - a*e)*(d + e*x)^7)) - (B*(b*d - a*e)^6)/(6*e^8*(d + e*x)^6) + (6*b*B*(b*d - a*e)^5)/(5*e^8*(d + e*x)^5) - (15*b^2*B*(b*d - a*e)^4)/(4*e^8*(d + e*x)^4) + (20*b^3*B*(b*d - a*e)^3)/(3*e^8*(d + e*x)^3) - (15*b^4*B*(b*d - a*e)^2)/(2*e^8*(d + e*x)^2) + (6*b^5*B*(b*d - a*e))/(e^8*(d + e*x)) + (b^6*B*log(d + e*x))/e^8]

    @test_int [((a + b*x)^6*(A + B*x))/(d + e*x)^9, x, 2, -((B*d - A*e)*(a + b*x)^7)/(8*e*(b*d - a*e)*(d + e*x)^8) + ((7*b*B*d + A*b*e - 8*a*B*e)*(a + b*x)^7)/(56*e*(b*d - a*e)^2*(d + e*x)^7)]
    @test_int [((a + b*x)^6*(A + B*x))/(d + e*x)^10, x, 3, -((B*d - A*e)*(a + b*x)^7)/(9*e*(b*d - a*e)*(d + e*x)^9) + ((7*b*B*d + 2*A*b*e - 9*a*B*e)*(a + b*x)^7)/(72*e*(b*d - a*e)^2*(d + e*x)^8) + (b*(7*b*B*d + 2*A*b*e - 9*a*B*e)*(a + b*x)^7)/(504*e*(b*d - a*e)^3*(d + e*x)^7)]
    @test_int [((a + b*x)^6*(A + B*x))/(d + e*x)^11, x, 4, -((B*d - A*e)*(a + b*x)^7)/(10*e*(b*d - a*e)*(d + e*x)^10) + ((7*b*B*d + 3*A*b*e - 10*a*B*e)*(a + b*x)^7)/(90*e*(b*d - a*e)^2*(d + e*x)^9) + (b*(7*b*B*d + 3*A*b*e - 10*a*B*e)*(a + b*x)^7)/(360*e*(b*d - a*e)^3*(d + e*x)^8) + (b^2*(7*b*B*d + 3*A*b*e - 10*a*B*e)*(a + b*x)^7)/(2520*e*(b*d - a*e)^4*(d + e*x)^7)]
    @test_int [((a + b*x)^6*(A + B*x))/(d + e*x)^12, x, 5, -((B*d - A*e)*(a + b*x)^7)/(11*e*(b*d - a*e)*(d + e*x)^11) + ((7*b*B*d + 4*A*b*e - 11*a*B*e)*(a + b*x)^7)/(110*e*(b*d - a*e)^2*(d + e*x)^10) + (b*(7*b*B*d + 4*A*b*e - 11*a*B*e)*(a + b*x)^7)/(330*e*(b*d - a*e)^3*(d + e*x)^9) + (b^2*(7*b*B*d + 4*A*b*e - 11*a*B*e)*(a + b*x)^7)/(1320*e*(b*d - a*e)^4*(d + e*x)^8) + (b^3*(7*b*B*d + 4*A*b*e - 11*a*B*e)*(a + b*x)^7)/(9240*e*(b*d - a*e)^5*(d + e*x)^7)]

    @test_int [((a + b*x)^6*(A + B*x))/(d + e*x)^13, x, 2, ((b*d - a*e)^6*(B*d - A*e))/(12*e^8*(d + e*x)^12) - ((b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e))/(11*e^8*(d + e*x)^11) + (3*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e))/(10*e^8*(d + e*x)^10) - (5*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e))/(9*e^8*(d + e*x)^9) + (5*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e))/(8*e^8*(d + e*x)^8) - (3*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e))/(7*e^8*(d + e*x)^7) + (b^5*(7*b*B*d - A*b*e - 6*a*B*e))/(6*e^8*(d + e*x)^6) - (b^6*B)/(5*e^8*(d + e*x)^5)]
    @test_int [((a + b*x)^6*(A + B*x))/(d + e*x)^14, x, 2, ((b*d - a*e)^6*(B*d - A*e))/(13*e^8*(d + e*x)^13) - ((b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e))/(12*e^8*(d + e*x)^12) + (3*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e))/(11*e^8*(d + e*x)^11) - (b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e))/(2*e^8*(d + e*x)^10) + (5*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e))/(9*e^8*(d + e*x)^9) - (3*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e))/(8*e^8*(d + e*x)^8) + (b^5*(7*b*B*d - A*b*e - 6*a*B*e))/(7*e^8*(d + e*x)^7) - (b^6*B)/(6*e^8*(d + e*x)^6)]
    @test_int [((a + b*x)^6*(A + B*x))/(d + e*x)^15, x, 2, ((b*d - a*e)^6*(B*d - A*e))/(14*e^8*(d + e*x)^14) - ((b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e))/(13*e^8*(d + e*x)^13) + (b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e))/(4*e^8*(d + e*x)^12) - (5*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e))/(11*e^8*(d + e*x)^11) + (b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e))/(2*e^8*(d + e*x)^10) - (b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e))/(3*e^8*(d + e*x)^9) + (b^5*(7*b*B*d - A*b*e - 6*a*B*e))/(8*e^8*(d + e*x)^8) - (b^6*B)/(7*e^8*(d + e*x)^7)]

    @test_int [(a + b*x)^10*(A + B*x)*(d + e*x)^13, x, 2, -(((b*d - a*e)^10*(B*d - A*e)*(d + e*x)^14)/(14*e^12)) + ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e)*(d + e*x)^15)/(15*e^12) - (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e)*(d + e*x)^16)/(16*e^12) + (15*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e)*(d + e*x)^17)/(17*e^12) - (5*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e)*(d + e*x)^18)/(3*e^12) + (42*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e)*(d + e*x)^19)/(19*e^12) - (21*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e)*(d + e*x)^20)/(10*e^12) + (10*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e)*(d + e*x)^21)/(7*e^12) - (15*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e)*(d + e*x)^22)/(22*e^12) + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*(d + e*x)^23)/(23*e^12) - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)*(d + e*x)^24)/(24*e^12) + (b^10*B*(d + e*x)^25)/(25*e^12)]
    @test_int [(a + b*x)^10*(A + B*x)*(d + e*x)^12, x, 2, -(((b*d - a*e)^10*(B*d - A*e)*(d + e*x)^13)/(13*e^12)) + ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e)*(d + e*x)^14)/(14*e^12) - (b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e)*(d + e*x)^15)/(3*e^12) + (15*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e)*(d + e*x)^16)/(16*e^12) - (30*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e)*(d + e*x)^17)/(17*e^12) + (7*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e)*(d + e*x)^18)/(3*e^12) - (42*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e)*(d + e*x)^19)/(19*e^12) + (3*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e)*(d + e*x)^20)/(2*e^12) - (5*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e)*(d + e*x)^21)/(7*e^12) + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*(d + e*x)^22)/(22*e^12) - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)*(d + e*x)^23)/(23*e^12) + (b^10*B*(d + e*x)^24)/(24*e^12)]
    @test_int [(a + b*x)^10*(A + B*x)*(d + e*x)^11, x, 2, -(((b*d - a*e)^10*(B*d - A*e)*(d + e*x)^12)/(12*e^12)) + ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e)*(d + e*x)^13)/(13*e^12) - (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e)*(d + e*x)^14)/(14*e^12) + (b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e)*(d + e*x)^15)/e^12 - (15*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e)*(d + e*x)^16)/(8*e^12) + (42*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e)*(d + e*x)^17)/(17*e^12) - (7*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e)*(d + e*x)^18)/(3*e^12) + (30*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e)*(d + e*x)^19)/(19*e^12) - (3*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e)*(d + e*x)^20)/(4*e^12) + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*(d + e*x)^21)/(21*e^12) - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)*(d + e*x)^22)/(22*e^12) + (b^10*B*(d + e*x)^23)/(23*e^12)]
    @test_int [(a + b*x)^10*(A + B*x)*(d + e*x)^10, x, 2, ((A*b - a*B)*(b*d - a*e)^10*(a + b*x)^11)/(11*b^12) + ((b*d - a*e)^9*(b*B*d + 10*A*b*e - 11*a*B*e)*(a + b*x)^12)/(12*b^12) + (5*e*(b*d - a*e)^8*(2*b*B*d + 9*A*b*e - 11*a*B*e)*(a + b*x)^13)/(13*b^12) + (15*e^2*(b*d - a*e)^7*(3*b*B*d + 8*A*b*e - 11*a*B*e)*(a + b*x)^14)/(14*b^12) + (2*e^3*(b*d - a*e)^6*(4*b*B*d + 7*A*b*e - 11*a*B*e)*(a + b*x)^15)/b^12 + (21*e^4*(b*d - a*e)^5*(5*b*B*d + 6*A*b*e - 11*a*B*e)*(a + b*x)^16)/(8*b^12) + (42*e^5*(b*d - a*e)^4*(6*b*B*d + 5*A*b*e - 11*a*B*e)*(a + b*x)^17)/(17*b^12) + (5*e^6*(b*d - a*e)^3*(7*b*B*d + 4*A*b*e - 11*a*B*e)*(a + b*x)^18)/(3*b^12) + (15*e^7*(b*d - a*e)^2*(8*b*B*d + 3*A*b*e - 11*a*B*e)*(a + b*x)^19)/(19*b^12) + (e^8*(b*d - a*e)*(9*b*B*d + 2*A*b*e - 11*a*B*e)*(a + b*x)^20)/(4*b^12) + (e^9*(10*b*B*d + A*b*e - 11*a*B*e)*(a + b*x)^21)/(21*b^12) + (B*e^10*(a + b*x)^22)/(22*b^12)]

    @test_int [(a + b*x)^10*(A + B*x)*(d + e*x)^9, x, 2, ((A*b - a*B)*(b*d - a*e)^9*(a + b*x)^11)/(11*b^11) + ((b*d - a*e)^8*(b*B*d + 9*A*b*e - 10*a*B*e)*(a + b*x)^12)/(12*b^11) + (9*e*(b*d - a*e)^7*(b*B*d + 4*A*b*e - 5*a*B*e)*(a + b*x)^13)/(13*b^11) + (6*e^2*(b*d - a*e)^6*(3*b*B*d + 7*A*b*e - 10*a*B*e)*(a + b*x)^14)/(7*b^11) + (14*e^3*(b*d - a*e)^5*(2*b*B*d + 3*A*b*e - 5*a*B*e)*(a + b*x)^15)/(5*b^11) + (63*e^4*(b*d - a*e)^4*(b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^16)/(8*b^11) + (42*e^5*(b*d - a*e)^3*(3*b*B*d + 2*A*b*e - 5*a*B*e)*(a + b*x)^17)/(17*b^11) + (2*e^6*(b*d - a*e)^2*(7*b*B*d + 3*A*b*e - 10*a*B*e)*(a + b*x)^18)/(3*b^11) + (9*e^7*(b*d - a*e)*(4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)^19)/(19*b^11) + (e^8*(9*b*B*d + A*b*e - 10*a*B*e)*(a + b*x)^20)/(20*b^11) + (B*e^9*(a + b*x)^21)/(21*b^11)]
    @test_int [(a + b*x)^10*(A + B*x)*(d + e*x)^8, x, 2, ((A*b - a*B)*(b*d - a*e)^8*(a + b*x)^11)/(11*b^10) + ((b*d - a*e)^7*(b*B*d + 8*A*b*e - 9*a*B*e)*(a + b*x)^12)/(12*b^10) + (4*e*(b*d - a*e)^6*(2*b*B*d + 7*A*b*e - 9*a*B*e)*(a + b*x)^13)/(13*b^10) + (2*e^2*(b*d - a*e)^5*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^14)/b^10 + (14*e^3*(b*d - a*e)^4*(4*b*B*d + 5*A*b*e - 9*a*B*e)*(a + b*x)^15)/(15*b^10) + (7*e^4*(b*d - a*e)^3*(5*b*B*d + 4*A*b*e - 9*a*B*e)*(a + b*x)^16)/(8*b^10) + (28*e^5*(b*d - a*e)^2*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^17)/(17*b^10) + (2*e^6*(b*d - a*e)*(7*b*B*d + 2*A*b*e - 9*a*B*e)*(a + b*x)^18)/(9*b^10) + (e^7*(8*b*B*d + A*b*e - 9*a*B*e)*(a + b*x)^19)/(19*b^10) + (B*e^8*(a + b*x)^20)/(20*b^10)]
    @test_int [(a + b*x)^10*(A + B*x)*(d + e*x)^7, x, 2, ((A*b - a*B)*(b*d - a*e)^7*(a + b*x)^11)/(11*b^9) + ((b*d - a*e)^6*(b*B*d + 7*A*b*e - 8*a*B*e)*(a + b*x)^12)/(12*b^9) + (7*e*(b*d - a*e)^5*(b*B*d + 3*A*b*e - 4*a*B*e)*(a + b*x)^13)/(13*b^9) + (e^2*(b*d - a*e)^4*(3*b*B*d + 5*A*b*e - 8*a*B*e)*(a + b*x)^14)/(2*b^9) + (7*e^3*(b*d - a*e)^3*(b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^15)/(3*b^9) + (7*e^4*(b*d - a*e)^2*(5*b*B*d + 3*A*b*e - 8*a*B*e)*(a + b*x)^16)/(16*b^9) + (7*e^5*(b*d - a*e)*(3*b*B*d + A*b*e - 4*a*B*e)*(a + b*x)^17)/(17*b^9) + (e^6*(7*b*B*d + A*b*e - 8*a*B*e)*(a + b*x)^18)/(18*b^9) + (B*e^7*(a + b*x)^19)/(19*b^9)]
    @test_int [(a + b*x)^10*(A + B*x)*(d + e*x)^6, x, 2, ((A*b - a*B)*(b*d - a*e)^6*(a + b*x)^11)/(11*b^8) + ((b*d - a*e)^5*(b*B*d + 6*A*b*e - 7*a*B*e)*(a + b*x)^12)/(12*b^8) + (3*e*(b*d - a*e)^4*(2*b*B*d + 5*A*b*e - 7*a*B*e)*(a + b*x)^13)/(13*b^8) + (5*e^2*(b*d - a*e)^3*(3*b*B*d + 4*A*b*e - 7*a*B*e)*(a + b*x)^14)/(14*b^8) + (e^3*(b*d - a*e)^2*(4*b*B*d + 3*A*b*e - 7*a*B*e)*(a + b*x)^15)/(3*b^8) + (3*e^4*(b*d - a*e)*(5*b*B*d + 2*A*b*e - 7*a*B*e)*(a + b*x)^16)/(16*b^8) + (e^5*(6*b*B*d + A*b*e - 7*a*B*e)*(a + b*x)^17)/(17*b^8) + (B*e^6*(a + b*x)^18)/(18*b^8)]
    @test_int [(a + b*x)^10*(A + B*x)*(d + e*x)^5, x, 2, ((A*b - a*B)*(b*d - a*e)^5*(a + b*x)^11)/(11*b^7) + ((b*d - a*e)^4*(b*B*d + 5*A*b*e - 6*a*B*e)*(a + b*x)^12)/(12*b^7) + (5*e*(b*d - a*e)^3*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^13)/(13*b^7) + (5*e^2*(b*d - a*e)^2*(b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^14)/(7*b^7) + (e^3*(b*d - a*e)*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^15)/(3*b^7) + (e^4*(5*b*B*d + A*b*e - 6*a*B*e)*(a + b*x)^16)/(16*b^7) + (B*e^5*(a + b*x)^17)/(17*b^7)]
    @test_int [(a + b*x)^10*(A + B*x)*(d + e*x)^4, x, 2, ((A*b - a*B)*(b*d - a*e)^4*(a + b*x)^11)/(11*b^6) + ((b*d - a*e)^3*(b*B*d + 4*A*b*e - 5*a*B*e)*(a + b*x)^12)/(12*b^6) + (2*e*(b*d - a*e)^2*(2*b*B*d + 3*A*b*e - 5*a*B*e)*(a + b*x)^13)/(13*b^6) + (e^2*(b*d - a*e)*(3*b*B*d + 2*A*b*e - 5*a*B*e)*(a + b*x)^14)/(7*b^6) + (e^3*(4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)^15)/(15*b^6) + (B*e^4*(a + b*x)^16)/(16*b^6)]
    @test_int [(a + b*x)^10*(A + B*x)*(d + e*x)^3, x, 2, ((A*b - a*B)*(b*d - a*e)^3*(a + b*x)^11)/(11*b^5) + ((b*d - a*e)^2*(b*B*d + 3*A*b*e - 4*a*B*e)*(a + b*x)^12)/(12*b^5) + (3*e*(b*d - a*e)*(b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^13)/(13*b^5) + (e^2*(3*b*B*d + A*b*e - 4*a*B*e)*(a + b*x)^14)/(14*b^5) + (B*e^3*(a + b*x)^15)/(15*b^5)]
    @test_int [(a + b*x)^10*(A + B*x)*(d + e*x)^2, x, 2, ((A*b - a*B)*(b*d - a*e)^2*(a + b*x)^11)/(11*b^4) + ((b*d - a*e)*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^12)/(12*b^4) + (e*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^13)/(13*b^4) + (B*e^2*(a + b*x)^14)/(14*b^4)]
    @test_int [(a + b*x)^10*(A + B*x)*(d + e*x), x, 2, ((A*b - a*B)*(b*d - a*e)*(a + b*x)^11)/(11*b^3) + ((b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^12)/(12*b^3) + (B*e*(a + b*x)^13)/(13*b^3)]
    @test_int [(a + b*x)^10*(A + B*x), x, 2, ((A*b - a*B)*(a + b*x)^11)/(11*b^2) + (B*(a + b*x)^12)/(12*b^2)]

    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x), x, 2, (b*(b*d - a*e)^9*(B*d - A*e)*x)/e^11 - ((b*d - a*e)^8*(B*d - A*e)*(a + b*x)^2)/(2*e^10) + ((b*d - a*e)^7*(B*d - A*e)*(a + b*x)^3)/(3*e^9) - ((b*d - a*e)^6*(B*d - A*e)*(a + b*x)^4)/(4*e^8) + ((b*d - a*e)^5*(B*d - A*e)*(a + b*x)^5)/(5*e^7) - ((b*d - a*e)^4*(B*d - A*e)*(a + b*x)^6)/(6*e^6) + ((b*d - a*e)^3*(B*d - A*e)*(a + b*x)^7)/(7*e^5) - ((b*d - a*e)^2*(B*d - A*e)*(a + b*x)^8)/(8*e^4) + ((b*d - a*e)*(B*d - A*e)*(a + b*x)^9)/(9*e^3) - ((B*d - A*e)*(a + b*x)^10)/(10*e^2) + (B*(a + b*x)^11)/(11*b*e) - ((b*d - a*e)^10*(B*d - A*e)*log(d + e*x))/e^12]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^2, x, 2, -((5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e)*x)/e^11) + ((b*d - a*e)^10*(B*d - A*e))/(e^12*(d + e*x)) + (15*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e)*(d + e*x)^2)/(2*e^12) - (10*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e)*(d + e*x)^3)/e^12 + (21*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e)*(d + e*x)^4)/(2*e^12) - (42*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e)*(d + e*x)^5)/(5*e^12) + (5*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e)*(d + e*x)^6)/e^12 - (15*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e)*(d + e*x)^7)/(7*e^12) + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*(d + e*x)^8)/(8*e^12) - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)*(d + e*x)^9)/(9*e^12) + (b^10*B*(d + e*x)^10)/(10*e^12) + ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e)*log(d + e*x))/e^12]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^3, x, 2, (15*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e)*x)/e^11 + ((b*d - a*e)^10*(B*d - A*e))/(2*e^12*(d + e*x)^2) - ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(e^12*(d + e*x)) - (15*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e)*(d + e*x)^2)/e^12 + (14*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e)*(d + e*x)^3)/e^12 - (21*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e)*(d + e*x)^4)/(2*e^12) + (6*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e)*(d + e*x)^5)/e^12 - (5*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e)*(d + e*x)^6)/(2*e^12) + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*(d + e*x)^7)/(7*e^12) - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)*(d + e*x)^8)/(8*e^12) + (b^10*B*(d + e*x)^9)/(9*e^12) - (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e)*log(d + e*x))/e^12]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^4, x, 2, -((30*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e)*x)/e^11) + ((b*d - a*e)^10*(B*d - A*e))/(3*e^12*(d + e*x)^3) - ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(2*e^12*(d + e*x)^2) + (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(e^12*(d + e*x)) + (21*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e)*(d + e*x)^2)/e^12 - (14*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e)*(d + e*x)^3)/e^12 + (15*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e)*(d + e*x)^4)/(2*e^12) - (3*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e)*(d + e*x)^5)/e^12 + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*(d + e*x)^6)/(6*e^12) - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)*(d + e*x)^7)/(7*e^12) + (b^10*B*(d + e*x)^8)/(8*e^12) + (15*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e)*log(d + e*x))/e^12]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^5, x, 2, (42*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e)*x)/e^11 + ((b*d - a*e)^10*(B*d - A*e))/(4*e^12*(d + e*x)^4) - ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(3*e^12*(d + e*x)^3) + (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(2*e^12*(d + e*x)^2) - (15*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(e^12*(d + e*x)) - (21*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e)*(d + e*x)^2)/e^12 + (10*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e)*(d + e*x)^3)/e^12 - (15*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e)*(d + e*x)^4)/(4*e^12) + (b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*(d + e*x)^5)/e^12 - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)*(d + e*x)^6)/(6*e^12) + (b^10*B*(d + e*x)^7)/(7*e^12) - (30*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e)*log(d + e*x))/e^12]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^6, x, 2, -((42*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e)*x)/e^11) + ((b*d - a*e)^10*(B*d - A*e))/(5*e^12*(d + e*x)^5) - ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(4*e^12*(d + e*x)^4) + (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(3*e^12*(d + e*x)^3) - (15*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(2*e^12*(d + e*x)^2) + (30*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(e^12*(d + e*x)) + (15*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e)*(d + e*x)^2)/e^12 - (5*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e)*(d + e*x)^3)/e^12 + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*(d + e*x)^4)/(4*e^12) - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)*(d + e*x)^5)/(5*e^12) + (b^10*B*(d + e*x)^6)/(6*e^12) + (42*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e)*log(d + e*x))/e^12]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^7, x, 2, (30*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e)*x)/e^11 + ((b*d - a*e)^10*(B*d - A*e))/(6*e^12*(d + e*x)^6) - ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(5*e^12*(d + e*x)^5) + (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(4*e^12*(d + e*x)^4) - (5*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(e^12*(d + e*x)^3) + (15*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(e^12*(d + e*x)^2) - (42*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e))/(e^12*(d + e*x)) - (15*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e)*(d + e*x)^2)/(2*e^12) + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*(d + e*x)^3)/(3*e^12) - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)*(d + e*x)^4)/(4*e^12) + (b^10*B*(d + e*x)^5)/(5*e^12) - (42*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e)*log(d + e*x))/e^12]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^8, x, 2, -((15*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e)*x)/e^11) + ((b*d - a*e)^10*(B*d - A*e))/(7*e^12*(d + e*x)^7) - ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(6*e^12*(d + e*x)^6) + (b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(e^12*(d + e*x)^5) - (15*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(4*e^12*(d + e*x)^4) + (10*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(e^12*(d + e*x)^3) - (21*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e))/(e^12*(d + e*x)^2) + (42*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e))/(e^12*(d + e*x)) + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*(d + e*x)^2)/(2*e^12) - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)*(d + e*x)^3)/(3*e^12) + (b^10*B*(d + e*x)^4)/(4*e^12) + (30*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e)*log(d + e*x))/e^12]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^9, x, 2, (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*x)/e^11 + ((b*d - a*e)^10*(B*d - A*e))/(8*e^12*(d + e*x)^8) - ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(7*e^12*(d + e*x)^7) + (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(6*e^12*(d + e*x)^6) - (3*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(e^12*(d + e*x)^5) + (15*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(2*e^12*(d + e*x)^4) - (14*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e))/(e^12*(d + e*x)^3) + (21*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e))/(e^12*(d + e*x)^2) - (30*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e))/(e^12*(d + e*x)) - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)*(d + e*x)^2)/(2*e^12) + (b^10*B*(d + e*x)^3)/(3*e^12) - (15*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e)*log(d + e*x))/e^12]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^10, x, 2, -((b^9*(10*b*B*d - A*b*e - 10*a*B*e)*x)/e^11) + (b^10*B*x^2)/(2*e^10) + ((b*d - a*e)^10*(B*d - A*e))/(9*e^12*(d + e*x)^9) - ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(8*e^12*(d + e*x)^8) + (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(7*e^12*(d + e*x)^7) - (5*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(2*e^12*(d + e*x)^6) + (6*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(e^12*(d + e*x)^5) - (21*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e))/(2*e^12*(d + e*x)^4) + (14*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e))/(e^12*(d + e*x)^3) - (15*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e))/(e^12*(d + e*x)^2) + (15*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e))/(e^12*(d + e*x)) + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*log(d + e*x))/e^12]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^11, x, 2, (b^10*B*x)/e^11 + ((b*d - a*e)^10*(B*d - A*e))/(10*e^12*(d + e*x)^10) - ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(9*e^12*(d + e*x)^9) + (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(8*e^12*(d + e*x)^8) - (15*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(7*e^12*(d + e*x)^7) + (5*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(e^12*(d + e*x)^6) - (42*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e))/(5*e^12*(d + e*x)^5) + (21*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e))/(2*e^12*(d + e*x)^4) - (10*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e))/(e^12*(d + e*x)^3) + (15*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e))/(2*e^12*(d + e*x)^2) - (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e))/(e^12*(d + e*x)) - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)*log(d + e*x))/e^12]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^12, x, 3, -(((B*d - A*e)*(a + b*x)^11)/(11*e*(b*d - a*e)*(d + e*x)^11)) - (B*(b*d - a*e)^10)/(10*e^12*(d + e*x)^10) + (10*b*B*(b*d - a*e)^9)/(9*e^12*(d + e*x)^9) - (45*b^2*B*(b*d - a*e)^8)/(8*e^12*(d + e*x)^8) + (120*b^3*B*(b*d - a*e)^7)/(7*e^12*(d + e*x)^7) - (35*b^4*B*(b*d - a*e)^6)/(e^12*(d + e*x)^6) + (252*b^5*B*(b*d - a*e)^5)/(5*e^12*(d + e*x)^5) - (105*b^6*B*(b*d - a*e)^4)/(2*e^12*(d + e*x)^4) + (40*b^7*B*(b*d - a*e)^3)/(e^12*(d + e*x)^3) - (45*b^8*B*(b*d - a*e)^2)/(2*e^12*(d + e*x)^2) + (10*b^9*B*(b*d - a*e))/(e^12*(d + e*x)) + (b^10*B*log(d + e*x))/e^12]

    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^13, x, 2, -((B*d - A*e)*(a + b*x)^11)/(12*e*(b*d - a*e)*(d + e*x)^12) + ((11*b*B*d + A*b*e - 12*a*B*e)*(a + b*x)^11)/(132*e*(b*d - a*e)^2*(d + e*x)^11)]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^14, x, 3, -((B*d - A*e)*(a + b*x)^11)/(13*e*(b*d - a*e)*(d + e*x)^13) + ((11*b*B*d + 2*A*b*e - 13*a*B*e)*(a + b*x)^11)/(156*e*(b*d - a*e)^2*(d + e*x)^12) + (b*(11*b*B*d + 2*A*b*e - 13*a*B*e)*(a + b*x)^11)/(1716*e*(b*d - a*e)^3*(d + e*x)^11)]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^15, x, 4, -((B*d - A*e)*(a + b*x)^11)/(14*e*(b*d - a*e)*(d + e*x)^14) + ((11*b*B*d + 3*A*b*e - 14*a*B*e)*(a + b*x)^11)/(182*e*(b*d - a*e)^2*(d + e*x)^13) + (b*(11*b*B*d + 3*A*b*e - 14*a*B*e)*(a + b*x)^11)/(1092*e*(b*d - a*e)^3*(d + e*x)^12) + (b^2*(11*b*B*d + 3*A*b*e - 14*a*B*e)*(a + b*x)^11)/(12012*e*(b*d - a*e)^4*(d + e*x)^11)]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^16, x, 5, -((B*d - A*e)*(a + b*x)^11)/(15*e*(b*d - a*e)*(d + e*x)^15) + ((11*b*B*d + 4*A*b*e - 15*a*B*e)*(a + b*x)^11)/(210*e*(b*d - a*e)^2*(d + e*x)^14) + (b*(11*b*B*d + 4*A*b*e - 15*a*B*e)*(a + b*x)^11)/(910*e*(b*d - a*e)^3*(d + e*x)^13) + (b^2*(11*b*B*d + 4*A*b*e - 15*a*B*e)*(a + b*x)^11)/(5460*e*(b*d - a*e)^4*(d + e*x)^12) + (b^3*(11*b*B*d + 4*A*b*e - 15*a*B*e)*(a + b*x)^11)/(60060*e*(b*d - a*e)^5*(d + e*x)^11)]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^17, x, 6, -((B*d - A*e)*(a + b*x)^11)/(16*e*(b*d - a*e)*(d + e*x)^16) + ((11*b*B*d + 5*A*b*e - 16*a*B*e)*(a + b*x)^11)/(240*e*(b*d - a*e)^2*(d + e*x)^15) + (b*(11*b*B*d + 5*A*b*e - 16*a*B*e)*(a + b*x)^11)/(840*e*(b*d - a*e)^3*(d + e*x)^14) + (b^2*(11*b*B*d + 5*A*b*e - 16*a*B*e)*(a + b*x)^11)/(3640*e*(b*d - a*e)^4*(d + e*x)^13) + (b^3*(11*b*B*d + 5*A*b*e - 16*a*B*e)*(a + b*x)^11)/(21840*e*(b*d - a*e)^5*(d + e*x)^12) + (b^4*(11*b*B*d + 5*A*b*e - 16*a*B*e)*(a + b*x)^11)/(240240*e*(b*d - a*e)^6*(d + e*x)^11)]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^18, x, 7, -((B*d - A*e)*(a + b*x)^11)/(17*e*(b*d - a*e)*(d + e*x)^17) + ((11*b*B*d + 6*A*b*e - 17*a*B*e)*(a + b*x)^11)/(272*e*(b*d - a*e)^2*(d + e*x)^16) + (b*(11*b*B*d + 6*A*b*e - 17*a*B*e)*(a + b*x)^11)/(816*e*(b*d - a*e)^3*(d + e*x)^15) + (b^2*(11*b*B*d + 6*A*b*e - 17*a*B*e)*(a + b*x)^11)/(2856*e*(b*d - a*e)^4*(d + e*x)^14) + (b^3*(11*b*B*d + 6*A*b*e - 17*a*B*e)*(a + b*x)^11)/(12376*e*(b*d - a*e)^5*(d + e*x)^13) + (b^4*(11*b*B*d + 6*A*b*e - 17*a*B*e)*(a + b*x)^11)/(74256*e*(b*d - a*e)^6*(d + e*x)^12) + (b^5*(11*b*B*d + 6*A*b*e - 17*a*B*e)*(a + b*x)^11)/(816816*e*(b*d - a*e)^7*(d + e*x)^11)]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^19, x, 8, -((B*d - A*e)*(a + b*x)^11)/(18*e*(b*d - a*e)*(d + e*x)^18) + ((11*b*B*d + 7*A*b*e - 18*a*B*e)*(a + b*x)^11)/(306*e*(b*d - a*e)^2*(d + e*x)^17) + (b*(11*b*B*d + 7*A*b*e - 18*a*B*e)*(a + b*x)^11)/(816*e*(b*d - a*e)^3*(d + e*x)^16) + (b^2*(11*b*B*d + 7*A*b*e - 18*a*B*e)*(a + b*x)^11)/(2448*e*(b*d - a*e)^4*(d + e*x)^15) + (b^3*(11*b*B*d + 7*A*b*e - 18*a*B*e)*(a + b*x)^11)/(8568*e*(b*d - a*e)^5*(d + e*x)^14) + (b^4*(11*b*B*d + 7*A*b*e - 18*a*B*e)*(a + b*x)^11)/(37128*e*(b*d - a*e)^6*(d + e*x)^13) + (b^5*(11*b*B*d + 7*A*b*e - 18*a*B*e)*(a + b*x)^11)/(222768*e*(b*d - a*e)^7*(d + e*x)^12) + (b^6*(11*b*B*d + 7*A*b*e - 18*a*B*e)*(a + b*x)^11)/(2450448*e*(b*d - a*e)^8*(d + e*x)^11)]

    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^20, x, 2, ((b*d - a*e)^10*(B*d - A*e))/(19*e^12*(d + e*x)^19) - ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(18*e^12*(d + e*x)^18) + (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(17*e^12*(d + e*x)^17) - (15*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(16*e^12*(d + e*x)^16) + (2*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(e^12*(d + e*x)^15) - (3*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e))/(e^12*(d + e*x)^14) + (42*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e))/(13*e^12*(d + e*x)^13) - (5*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e))/(2*e^12*(d + e*x)^12) + (15*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e))/(11*e^12*(d + e*x)^11) - (b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e))/(2*e^12*(d + e*x)^10) + (b^9*(11*b*B*d - A*b*e - 10*a*B*e))/(9*e^12*(d + e*x)^9) - (b^10*B)/(8*e^12*(d + e*x)^8)]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^21, x, 2, ((b*d - a*e)^10*(B*d - A*e))/(20*e^12*(d + e*x)^20) - ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(19*e^12*(d + e*x)^19) + (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(18*e^12*(d + e*x)^18) - (15*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(17*e^12*(d + e*x)^17) + (15*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(8*e^12*(d + e*x)^16) - (14*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e))/(5*e^12*(d + e*x)^15) + (3*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e))/(e^12*(d + e*x)^14) - (30*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e))/(13*e^12*(d + e*x)^13) + (5*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e))/(4*e^12*(d + e*x)^12) - (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e))/(11*e^12*(d + e*x)^11) + (b^9*(11*b*B*d - A*b*e - 10*a*B*e))/(10*e^12*(d + e*x)^10) - (b^10*B)/(9*e^12*(d + e*x)^9)]
    @test_int [((a + b*x)^10*(A + B*x))/(d + e*x)^22, x, 2, ((b*d - a*e)^10*(B*d - A*e))/(21*e^12*(d + e*x)^21) - ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(20*e^12*(d + e*x)^20) + (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(19*e^12*(d + e*x)^19) - (5*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(6*e^12*(d + e*x)^18) + (30*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(17*e^12*(d + e*x)^17) - (21*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e))/(8*e^12*(d + e*x)^16) + (14*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e))/(5*e^12*(d + e*x)^15) - (15*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e))/(7*e^12*(d + e*x)^14) + (15*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e))/(13*e^12*(d + e*x)^13) - (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e))/(12*e^12*(d + e*x)^12) + (b^9*(11*b*B*d - A*b*e - 10*a*B*e))/(11*e^12*(d + e*x)^11) - (b^10*B)/(10*e^12*(d + e*x)^10)]

    #= ::Subsubsection::Closed:: =#
    #=m<0=#

    @test_int [(A + B*x)*(d + e*x)^5/(a + b*x), x, 2, ((A*b - a*B)*e*(b*d - a*e)^4*x)/b^6 + ((A*b - a*B)*(b*d - a*e)^3*(d + e*x)^2)/(2*b^5) + ((A*b - a*B)*(b*d - a*e)^2*(d + e*x)^3)/(3*b^4) + ((A*b - a*B)*(b*d - a*e)*(d + e*x)^4)/(4*b^3) + ((A*b - a*B)*(d + e*x)^5)/(5*b^2) + (B*(d + e*x)^6)/(6*b*e) + ((A*b - a*B)*(b*d - a*e)^5*log(a + b*x))/b^7]
    @test_int [(A + B*x)*(d + e*x)^4/(a + b*x), x, 2, ((A*b - a*B)*e*(b*d - a*e)^3*x)/b^5 + ((A*b - a*B)*(b*d - a*e)^2*(d + e*x)^2)/(2*b^4) + ((A*b - a*B)*(b*d - a*e)*(d + e*x)^3)/(3*b^3) + ((A*b - a*B)*(d + e*x)^4)/(4*b^2) + (B*(d + e*x)^5)/(5*b*e) + ((A*b - a*B)*(b*d - a*e)^4*log(a + b*x))/b^6]
    @test_int [(A + B*x)*(d + e*x)^3/(a + b*x), x, 2, ((A*b - a*B)*e*(b*d - a*e)^2*x)/b^4 + ((A*b - a*B)*(b*d - a*e)*(d + e*x)^2)/(2*b^3) + ((A*b - a*B)*(d + e*x)^3)/(3*b^2) + (B*(d + e*x)^4)/(4*b*e) + ((A*b - a*B)*(b*d - a*e)^3*log(a + b*x))/b^5]
    @test_int [(A + B*x)*(d + e*x)^2/(a + b*x), x, 2, ((A*b - a*B)*e*(b*d - a*e)*x)/b^3 + ((A*b - a*B)*(d + e*x)^2)/(2*b^2) + (B*(d + e*x)^3)/(3*b*e) + ((A*b - a*B)*(b*d - a*e)^2*log(a + b*x))/b^4]
    @test_int [(A + B*x)*(d + e*x)^1/(a + b*x), x, 2, (B*(b*d - a*e)*x)/b^2 + (e*(A + B*x)^2)/(2*b*B) + ((A*b - a*B)*(b*d - a*e)*log(a + b*x))/b^3]
    @test_int [(A + B*x)*(d + e*x)^0/(a + b*x), x, 2, (B*x)/b + ((A*b - a*B)*log(a + b*x))/b^2]
    @test_int [(A + B*x)/((a + b*x)*(d + e*x)^1), x, 2, ((A*b - a*B)*log(a + b*x))/(b*(b*d - a*e)) + ((B*d - A*e)*log(d + e*x))/(e*(b*d - a*e))]
    @test_int [(A + B*x)/((a + b*x)*(d + e*x)^2), x, 2, -((B*d - A*e)/(e*(b*d - a*e)*(d + e*x))) + ((A*b - a*B)*log(a + b*x))/(b*d - a*e)^2 - ((A*b - a*B)*log(d + e*x))/(b*d - a*e)^2]
    @test_int [(A + B*x)/((a + b*x)*(d + e*x)^3), x, 2, -(B*d - A*e)/(2*e*(b*d - a*e)*(d + e*x)^2) + (A*b - a*B)/((b*d - a*e)^2*(d + e*x)) + (b*(A*b - a*B)*log(a + b*x))/(b*d - a*e)^3 - (b*(A*b - a*B)*log(d + e*x))/(b*d - a*e)^3]
    @test_int [(A + B*x)/((a + b*x)*(d + e*x)^4), x, 2, -(B*d - A*e)/(3*e*(b*d - a*e)*(d + e*x)^3) + (A*b - a*B)/(2*(b*d - a*e)^2*(d + e*x)^2) + (b*(A*b - a*B))/((b*d - a*e)^3*(d + e*x)) + (b^2*(A*b - a*B)*log(a + b*x))/(b*d - a*e)^4 - (b^2*(A*b - a*B)*log(d + e*x))/(b*d - a*e)^4]
    @test_int [(A + B*x)/((a + b*x)*(d + e*x)^5), x, 2, -(B*d - A*e)/(4*e*(b*d - a*e)*(d + e*x)^4) + (A*b - a*B)/(3*(b*d - a*e)^2*(d + e*x)^3) + (b*(A*b - a*B))/(2*(b*d - a*e)^3*(d + e*x)^2) + (b^2*(A*b - a*B))/((b*d - a*e)^4*(d + e*x)) + (b^3*(A*b - a*B)*log(a + b*x))/(b*d - a*e)^5 - (b^3*(A*b - a*B)*log(d + e*x))/(b*d - a*e)^5]

    @test_int [(A + B*x)*(d + e*x)^5/(a + b*x)^2, x, 2, (5*e*(b*d - a*e)^3*(b*B*d + 2*A*b*e - 3*a*B*e)*x)/b^6 - ((A*b - a*B)*(b*d - a*e)^5)/(b^7*(a + b*x)) + (5*e^2*(b*d - a*e)^2*(b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^2)/b^7 + (5*e^3*(b*d - a*e)*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^3)/(3*b^7) + (e^4*(5*b*B*d + A*b*e - 6*a*B*e)*(a + b*x)^4)/(4*b^7) + (B*e^5*(a + b*x)^5)/(5*b^7) + ((b*d - a*e)^4*(b*B*d + 5*A*b*e - 6*a*B*e)*log(a + b*x))/b^7]
    @test_int [(A + B*x)*(d + e*x)^4/(a + b*x)^2, x, 2, (2*e*(b*d - a*e)^2*(2*b*B*d + 3*A*b*e - 5*a*B*e)*x)/b^5 - ((A*b - a*B)*(b*d - a*e)^4)/(b^6*(a + b*x)) + (e^2*(b*d - a*e)*(3*b*B*d + 2*A*b*e - 5*a*B*e)*(a + b*x)^2)/b^6 + (e^3*(4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)^3)/(3*b^6) + (B*e^4*(a + b*x)^4)/(4*b^6) + ((b*d - a*e)^3*(b*B*d + 4*A*b*e - 5*a*B*e)*log(a + b*x))/b^6]
    @test_int [(A + B*x)*(d + e*x)^3/(a + b*x)^2, x, 2, (3*e*(b*d - a*e)*(b*B*d + A*b*e - 2*a*B*e)*x)/b^4 - ((A*b - a*B)*(b*d - a*e)^3)/(b^5*(a + b*x)) + (e^2*(3*b*B*d + A*b*e - 4*a*B*e)*(a + b*x)^2)/(2*b^5) + (B*e^3*(a + b*x)^3)/(3*b^5) + ((b*d - a*e)^2*(b*B*d + 3*A*b*e - 4*a*B*e)*log(a + b*x))/b^5]
    @test_int [(A + B*x)*(d + e*x)^2/(a + b*x)^2, x, 2, (e*(2*b*B*d + A*b*e - 2*a*B*e)*x)/b^3 + (B*e^2*x^2)/(2*b^2) - ((A*b - a*B)*(b*d - a*e)^2)/(b^4*(a + b*x)) + ((b*d - a*e)*(b*B*d + 2*A*b*e - 3*a*B*e)*log(a + b*x))/b^4]
    @test_int [(A + B*x)*(d + e*x)^1/(a + b*x)^2, x, 2, (B*e*x)/b^2 - ((A*b - a*B)*(b*d - a*e))/(b^3*(a + b*x)) + ((b*B*d + A*b*e - 2*a*B*e)*log(a + b*x))/b^3]
    @test_int [(A + B*x)*(d + e*x)^0/(a + b*x)^2, x, 2, -((A*b - a*B)/(b^2*(a + b*x))) + (B*log(a + b*x))/b^2]
    @test_int [(A + B*x)/((a + b*x)^2*(d + e*x)^1), x, 2, -((A*b - a*B)/(b*(b*d - a*e)*(a + b*x))) + ((B*d - A*e)*log(a + b*x))/(b*d - a*e)^2 - ((B*d - A*e)*log(d + e*x))/(b*d - a*e)^2]
    @test_int [(A + B*x)/((a + b*x)^2*(d + e*x)^2), x, 2, -((A*b - a*B)/((b*d - a*e)^2*(a + b*x))) + (B*d - A*e)/((b*d - a*e)^2*(d + e*x)) + ((b*B*d - 2*A*b*e + a*B*e)*log(a + b*x))/(b*d - a*e)^3 - ((b*B*d - 2*A*b*e + a*B*e)*log(d + e*x))/(b*d - a*e)^3]
    @test_int [(A + B*x)/((a + b*x)^2*(d + e*x)^3), x, 2, -((b*(A*b - a*B))/((b*d - a*e)^3*(a + b*x))) + (B*d - A*e)/(2*(b*d - a*e)^2*(d + e*x)^2) + (b*B*d - 2*A*b*e + a*B*e)/((b*d - a*e)^3*(d + e*x)) + (b*(b*B*d - 3*A*b*e + 2*a*B*e)*log(a + b*x))/(b*d - a*e)^4 - (b*(b*B*d - 3*A*b*e + 2*a*B*e)*log(d + e*x))/(b*d - a*e)^4]
    @test_int [(A + B*x)/((a + b*x)^2*(d + e*x)^4), x, 2, -((b^2*(A*b - a*B))/((b*d - a*e)^4*(a + b*x))) + (B*d - A*e)/(3*(b*d - a*e)^2*(d + e*x)^3) + (b*B*d - 2*A*b*e + a*B*e)/(2*(b*d - a*e)^3*(d + e*x)^2) + (b*(b*B*d - 3*A*b*e + 2*a*B*e))/((b*d - a*e)^4*(d + e*x)) + (b^2*(b*B*d - 4*A*b*e + 3*a*B*e)*log(a + b*x))/(b*d - a*e)^5 - (b^2*(b*B*d - 4*A*b*e + 3*a*B*e)*log(d + e*x))/(b*d - a*e)^5]
    @test_int [(A + B*x)/((a + b*x)^2*(d + e*x)^5), x, 2, -((b^3*(A*b - a*B))/((b*d - a*e)^5*(a + b*x))) + (B*d - A*e)/(4*(b*d - a*e)^2*(d + e*x)^4) + (b*B*d - 2*A*b*e + a*B*e)/(3*(b*d - a*e)^3*(d + e*x)^3) + (b*(b*B*d - 3*A*b*e + 2*a*B*e))/(2*(b*d - a*e)^4*(d + e*x)^2) + (b^2*(b*B*d - 4*A*b*e + 3*a*B*e))/((b*d - a*e)^5*(d + e*x)) + (b^3*(b*B*d - 5*A*b*e + 4*a*B*e)*log(a + b*x))/(b*d - a*e)^6 - (b^3*(b*B*d - 5*A*b*e + 4*a*B*e)*log(d + e*x))/(b*d - a*e)^6]

    @test_int [(A + B*x)*(d + e*x)^5/(a + b*x)^3, x, 2, (10*e^2*(b*d - a*e)^2*(b*B*d + A*b*e - 2*a*B*e)*x)/b^6 - ((A*b - a*B)*(b*d - a*e)^5)/(2*b^7*(a + b*x)^2) - ((b*d - a*e)^4*(b*B*d + 5*A*b*e - 6*a*B*e))/(b^7*(a + b*x)) + (5*e^3*(b*d - a*e)*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^2)/(2*b^7) + (e^4*(5*b*B*d + A*b*e - 6*a*B*e)*(a + b*x)^3)/(3*b^7) + (B*e^5*(a + b*x)^4)/(4*b^7) + (5*e*(b*d - a*e)^3*(b*B*d + 2*A*b*e - 3*a*B*e)*log(a + b*x))/b^7]
    @test_int [(A + B*x)*(d + e*x)^4/(a + b*x)^3, x, 2, (2*e^2*(b*d - a*e)*(3*b*B*d + 2*A*b*e - 5*a*B*e)*x)/b^5 - ((A*b - a*B)*(b*d - a*e)^4)/(2*b^6*(a + b*x)^2) - ((b*d - a*e)^3*(b*B*d + 4*A*b*e - 5*a*B*e))/(b^6*(a + b*x)) + (e^3*(4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)^2)/(2*b^6) + (B*e^4*(a + b*x)^3)/(3*b^6) + (2*e*(b*d - a*e)^2*(2*b*B*d + 3*A*b*e - 5*a*B*e)*log(a + b*x))/b^6]
    @test_int [(A + B*x)*(d + e*x)^3/(a + b*x)^3, x, 2, (e^2*(3*b*B*d + A*b*e - 3*a*B*e)*x)/b^4 + (B*e^3*x^2)/(2*b^3) - ((A*b - a*B)*(b*d - a*e)^3)/(2*b^5*(a + b*x)^2) - ((b*d - a*e)^2*(b*B*d + 3*A*b*e - 4*a*B*e))/(b^5*(a + b*x)) + (3*e*(b*d - a*e)*(b*B*d + A*b*e - 2*a*B*e)*log(a + b*x))/b^5]
    @test_int [(A + B*x)*(d + e*x)^2/(a + b*x)^3, x, 2, (B*e^2*x)/b^3 - ((A*b - a*B)*(b*d - a*e)^2)/(2*b^4*(a + b*x)^2) - ((b*d - a*e)*(b*B*d + 2*A*b*e - 3*a*B*e))/(b^4*(a + b*x)) + (e*(2*b*B*d + A*b*e - 3*a*B*e)*log(a + b*x))/b^4]
    @test_int [(A + B*x)*(d + e*x)^1/(a + b*x)^3, x, 2, -(((A*b - a*B)*(b*d - a*e))/(2*b^3*(a + b*x)^2)) - (b*B*d + A*b*e - 2*a*B*e)/(b^3*(a + b*x)) + (B*e*log(a + b*x))/b^3]
    @test_int [(A + B*x)*(d + e*x)^0/(a + b*x)^3, x, 1, -((A + B*x)^2/(2*(A*b - a*B)*(a + b*x)^2))]
    @test_int [(A + B*x)/((a + b*x)^3*(d + e*x)^1), x, 2, -(A*b - a*B)/(2*b*(b*d - a*e)*(a + b*x)^2) - (B*d - A*e)/((b*d - a*e)^2*(a + b*x)) - (e*(B*d - A*e)*log(a + b*x))/(b*d - a*e)^3 + (e*(B*d - A*e)*log(d + e*x))/(b*d - a*e)^3]
    @test_int [(A + B*x)/((a + b*x)^3*(d + e*x)^2), x, 2, -((A*b - a*B)/(2*(b*d - a*e)^2*(a + b*x)^2)) - (b*B*d - 2*A*b*e + a*B*e)/((b*d - a*e)^3*(a + b*x)) - (e*(B*d - A*e))/((b*d - a*e)^3*(d + e*x)) - (e*(2*b*B*d - 3*A*b*e + a*B*e)*log(a + b*x))/(b*d - a*e)^4 + (e*(2*b*B*d - 3*A*b*e + a*B*e)*log(d + e*x))/(b*d - a*e)^4]
    @test_int [(A + B*x)/((a + b*x)^3*(d + e*x)^3), x, 2, -((b*(A*b - a*B))/(2*(b*d - a*e)^3*(a + b*x)^2)) - (b*(b*B*d - 3*A*b*e + 2*a*B*e))/((b*d - a*e)^4*(a + b*x)) - (e*(B*d - A*e))/(2*(b*d - a*e)^3*(d + e*x)^2) - (e*(2*b*B*d - 3*A*b*e + a*B*e))/((b*d - a*e)^4*(d + e*x)) - (3*b*e*(b*B*d - 2*A*b*e + a*B*e)*log(a + b*x))/(b*d - a*e)^5 + (3*b*e*(b*B*d - 2*A*b*e + a*B*e)*log(d + e*x))/(b*d - a*e)^5]
    @test_int [(A + B*x)/((a + b*x)^3*(d + e*x)^4), x, 2, -((b^2*(A*b - a*B))/(2*(b*d - a*e)^4*(a + b*x)^2)) - (b^2*(b*B*d - 4*A*b*e + 3*a*B*e))/((b*d - a*e)^5*(a + b*x)) - (e*(B*d - A*e))/(3*(b*d - a*e)^3*(d + e*x)^3) - (e*(2*b*B*d - 3*A*b*e + a*B*e))/(2*(b*d - a*e)^4*(d + e*x)^2) - (3*b*e*(b*B*d - 2*A*b*e + a*B*e))/((b*d - a*e)^5*(d + e*x)) - (2*b^2*e*(2*b*B*d - 5*A*b*e + 3*a*B*e)*log(a + b*x))/(b*d - a*e)^6 + (2*b^2*e*(2*b*B*d - 5*A*b*e + 3*a*B*e)*log(d + e*x))/(b*d - a*e)^6]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^n*(e+f*x)^1=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x), x, 2, (-7*(2 + 3*x)^9)/243 + (37*(2 + 3*x)^10)/270 - (10*(2 + 3*x)^11)/297]
    @test_int [(1 - 2*x)*(2 + 3*x)^7*(3 + 5*x), x, 2, (-7*(2 + 3*x)^8)/216 + (37*(2 + 3*x)^9)/243 - (2 + 3*x)^10/27]
    @test_int [(1 - 2*x)*(2 + 3*x)^6*(3 + 5*x), x, 2, -(2 + 3*x)^7/27 + (37*(2 + 3*x)^8)/216 - (10*(2 + 3*x)^9)/243]
    @test_int [(1 - 2*x)*(2 + 3*x)^5*(3 + 5*x), x, 2, (-(7/162))*(2 + 3*x)^6 + (37/189)*(2 + 3*x)^7 - (5/108)*(2 + 3*x)^8]
    @test_int [(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x), x, 2, (-(7/135))*(2 + 3*x)^5 + (37/162)*(2 + 3*x)^6 - (10/189)*(2 + 3*x)^7]
    @test_int [(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x), x, 2, (-(7/108))*(2 + 3*x)^4 + (37/135)*(2 + 3*x)^5 - (5/81)*(2 + 3*x)^6]

    @test_int [(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x), x, 2, 12*x + 16*x^2 - (25*x^3)/3 - (129*x^4)/4 - 18*x^5]
    @test_int [(1 - 2*x)*(2 + 3*x)^1*(3 + 5*x), x, 2, 6*x + (7*x^2)/2 - (23*x^3)/3 - (15*x^4)/2]
    @test_int [(1 - 2*x)*(2 + 3*x)^0*(3 + 5*x), x, 2, 3*x - x^2/2 - (10*x^3)/3]
    @test_int [((1 - 2*x)*(3 + 5*x))/(2 + 3*x)^1, x, 2, (17*x)/9 - (5*x^2)/3 - (7/27)*log(2 + 3*x)]
    @test_int [((1 - 2*x)*(3 + 5*x))/(2 + 3*x)^2, x, 2, (-10*x)/9 + 7/(27*(2 + 3*x)) + (37*log(2 + 3*x))/27]
    @test_int [((1 - 2*x)*(3 + 5*x))/(2 + 3*x)^3, x, 2, 7/(54*(2 + 3*x)^2) - 37/(27*(2 + 3*x)) - (10*log(2 + 3*x))/27]
    @test_int [((1 - 2*x)*(3 + 5*x))/(2 + 3*x)^4, x, 2, 7/(81*(2 + 3*x)^3) - 37/(54*(2 + 3*x)^2) + 10/(27*(2 + 3*x))]
    @test_int [((1 - 2*x)*(3 + 5*x))/(2 + 3*x)^5, x, 2, 7/(108*(2 + 3*x)^4) - 37/(81*(2 + 3*x)^3) + 5/(27*(2 + 3*x)^2)]
    @test_int [((1 - 2*x)*(3 + 5*x))/(2 + 3*x)^6, x, 2, 7/(135*(2 + 3*x)^5) - 37/(108*(2 + 3*x)^4) + 10/(81*(2 + 3*x)^3)]

    @test_int [(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x)^2, x, 2, (7*(2 + 3*x)^9)/729 - (4*(2 + 3*x)^10)/45 + (65*(2 + 3*x)^11)/297 - (25*(2 + 3*x)^12)/486]
    @test_int [(1 - 2*x)*(2 + 3*x)^7*(3 + 5*x)^2, x, 2, (7*(2 + 3*x)^8)/648 - (8*(2 + 3*x)^9)/81 + (13*(2 + 3*x)^10)/54 - (50*(2 + 3*x)^11)/891]
    @test_int [(1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)^2, x, 2, (1/81)*(2 + 3*x)^7 - (1/9)*(2 + 3*x)^8 + (65/243)*(2 + 3*x)^9 - (5/81)*(2 + 3*x)^10]
    @test_int [(1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)^2, x, 2, (7/486)*(2 + 3*x)^6 - (8/63)*(2 + 3*x)^7 + (65/216)*(2 + 3*x)^8 - (50/729)*(2 + 3*x)^9]
    @test_int [(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^2, x, 2, (7/405)*(2 + 3*x)^5 - (4/27)*(2 + 3*x)^6 + (65/189)*(2 + 3*x)^7 - (25/324)*(2 + 3*x)^8]
    @test_int [(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^2, x, 2, 72*x + 210*x^2 + (638*x^3)/3 - (769*x^4)/4 - (3366*x^5)/5 - (1215*x^6)/2 - (1350*x^7)/7]
    @test_int [(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^2, x, 2, 36*x + 78*x^2 + (85*x^3)/3 - 128*x^4 - 183*x^5 - 75*x^6]
    @test_int [(1 - 2*x)*(2 + 3*x)^1*(3 + 5*x)^2, x, 2, 18*x + (51*x^2)/2 - (34*x^3)/3 - (205*x^4)/4 - 30*x^5]
    @test_int [(1 - 2*x)*(2 + 3*x)^0*(3 + 5*x)^2, x, 2, 9*x + 6*x^2 - (35*x^3)/3 - (25*x^4)/2]
    @test_int [((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x), x, 2, (118*x)/27 - (5*x^2)/18 - (50*x^3)/9 + (7/81)*log(2 + 3*x)]
    @test_int [((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^2, x, 2, (95*x)/27 - (25*x^2)/9 - 7/(81*(2 + 3*x)) - (8*log(2 + 3*x))/9]
    @test_int [((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^3, x, 2, (-50*x)/27 - 7/(162*(2 + 3*x)^2) + 8/(9*(2 + 3*x)) + (65*log(2 + 3*x))/27]
    @test_int [((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^4, x, 2, -(7/(243*(2 + 3*x)^3)) + 4/(9*(2 + 3*x)^2) - 65/(27*(2 + 3*x)) - (50/81)*log(2 + 3*x)]
    @test_int [((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^5, x, 2, (7*(3 + 5*x)^3)/(12*(2 + 3*x)^4) + (3*(3 + 5*x)^3)/(4*(2 + 3*x)^3)]
    @test_int [((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^6, x, 2, -7/(405*(2 + 3*x)^5) + 2/(9*(2 + 3*x)^4) - 65/(81*(2 + 3*x)^3) + 25/(81*(2 + 3*x)^2)]
    @test_int [((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^7, x, 2, -7/(486*(2 + 3*x)^6) + 8/(45*(2 + 3*x)^5) - 65/(108*(2 + 3*x)^4) + 50/(243*(2 + 3*x)^3)]
    @test_int [((1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^8, x, 2, -1/(81*(2 + 3*x)^7) + 4/(27*(2 + 3*x)^6) - 13/(27*(2 + 3*x)^5) + 25/(162*(2 + 3*x)^4)]

    @test_int [(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x)^3, x, 2, (-7*(2 + 3*x)^9)/2187 + (107*(2 + 3*x)^10)/2430 - (185*(2 + 3*x)^11)/891 + (1025*(2 + 3*x)^12)/2916 - (250*(2 + 3*x)^13)/3159]
    @test_int [(1 - 2*x)*(2 + 3*x)^7*(3 + 5*x)^3, x, 2, -((7*(2 + 3*x)^8)/1944) + (107*(2 + 3*x)^9)/2187 - (37/162)*(2 + 3*x)^10 + (1025*(2 + 3*x)^11)/2673 - (125*(2 + 3*x)^12)/1458]
    @test_int [(1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)^3, x, 2, (-(1/243))*(2 + 3*x)^7 + (107*(2 + 3*x)^8)/1944 - (185/729)*(2 + 3*x)^9 + (205/486)*(2 + 3*x)^10 - (250*(2 + 3*x)^11)/2673]
    @test_int [(1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)^3, x, 2, -((7*(2 + 3*x)^6)/1458) + (107*(2 + 3*x)^7)/1701 - (185/648)*(2 + 3*x)^8 + (1025*(2 + 3*x)^9)/2187 - (25/243)*(2 + 3*x)^10]
    @test_int [(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^3, x, 2, -((7*(2 + 3*x)^5)/1215) + (107*(2 + 3*x)^6)/1458 - (185/567)*(2 + 3*x)^7 + (1025*(2 + 3*x)^8)/1944 - (250*(2 + 3*x)^9)/2187]
    @test_int [(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^3, x, 2, 216*x + 810*x^2 + 1338*x^3 + (883*x^4)/4 - (13943*x^5)/5 - (9255*x^6)/2 - (22275*x^7)/7 - (3375*x^8)/4]
    @test_int [(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^3, x, 2, 108*x + 324*x^2 + 345*x^3 - (1111*x^4)/4 - 1061*x^5 - (1975*x^6)/2 - (2250*x^7)/7]
    @test_int [(1 - 2*x)*(2 + 3*x)^1*(3 + 5*x)^3, x, 2, (11/500)*(3 + 5*x)^4 + (31/625)*(3 + 5*x)^5 - (1/125)*(3 + 5*x)^6]
    @test_int [(1 - 2*x)*(2 + 3*x)^0*(3 + 5*x)^3, x, 2, (11/100)*(3 + 5*x)^4 - (2/125)*(3 + 5*x)^5]
    @test_int [((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x), x, 2, (1097*x)/81 + (545*x^2)/54 - (475*x^3)/27 - (125*x^4)/6 - (7/243)*log(2 + 3*x)]
    @test_int [((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^2, x, 2, (55*x)/9 + (25*x^2)/54 - (250*x^3)/27 + 7/(243*(2 + 3*x)) + (107*log(2 + 3*x))/243]
    @test_int [((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^3, x, 2, (175*x)/27 - (125*x^2)/27 + 7/(486*(2 + 3*x)^2) - 107/(243*(2 + 3*x)) - (185*log(2 + 3*x))/81]
    @test_int [((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^4, x, 2, (-250*x)/81 + 7/(729*(2 + 3*x)^3) - 107/(486*(2 + 3*x)^2) + 185/(81*(2 + 3*x)) + (1025*log(2 + 3*x))/243]
    @test_int [((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^5, x, 2, 7/(972*(2 + 3*x)^4) - 107/(729*(2 + 3*x)^3) + 185/(162*(2 + 3*x)^2) - 1025/(243*(2 + 3*x)) - (250/243)*log(2 + 3*x)]
    @test_int [((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^6, x, 2, (7*(3 + 5*x)^4)/(15*(2 + 3*x)^5) + (5*(3 + 5*x)^4)/(12*(2 + 3*x)^4)]
    @test_int [((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^7, x, 3, (7*(3 + 5*x)^4)/(18*(2 + 3*x)^6) + (29*(3 + 5*x)^4)/(45*(2 + 3*x)^5) + (29*(3 + 5*x)^4)/(36*(2 + 3*x)^4)]
    @test_int [((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^8, x, 2, 1/(243*(2 + 3*x)^7) - 107/(1458*(2 + 3*x)^6) + 37/(81*(2 + 3*x)^5) - 1025/(972*(2 + 3*x)^4) + 250/(729*(2 + 3*x)^3)]

    @test_int [(5 - 2*x)^6*(2 + 3*x)^3*(-16 + 33*x), x, 1, (-(1/2))*(5 - 2*x)^7*(2 + 3*x)^4]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [((1 - 2*x)*(2 + 3*x)^6)/(3 + 5*x), x, 2, (1666663*x)/78125 + (1777779*x^2)/31250 + (152469*x^3)/3125 - (152469*x^4)/2500 - (106677*x^5)/625 - (7047*x^6)/50 - (1458*x^7)/35 + (11*log(3 + 5*x))/390625]
    @test_int [((1 - 2*x)*(2 + 3*x)^5)/(3 + 5*x), x, 2, (166663*x)/15625 + (127779*x^2)/6250 + (2469*x^3)/625 - (17469*x^4)/500 - (5427*x^5)/125 - (81*x^6)/5 + (11*log(3 + 5*x))/78125]
    @test_int [((1 - 2*x)*(2 + 3*x)^4)/(3 + 5*x), x, 2, (16663*x)/3125 + (7779*x^2)/1250 - (531*x^3)/125 - (1269*x^4)/100 - (162*x^5)/25 + (11*log(3 + 5*x))/15625]
    @test_int [((1 - 2*x)*(2 + 3*x)^3)/(3 + 5*x), x, 2, (1663*x)/625 + (279*x^2)/250 - (81*x^3)/25 - (27*x^4)/10 + (11*log(3 + 5*x))/3125]
    @test_int [((1 - 2*x)*(2 + 3*x)^2)/(3 + 5*x), x, 2, (163*x)/125 - (21*x^2)/50 - (6*x^3)/5 + (11/625)*log(3 + 5*x)]
    @test_int [((1 - 2*x)*(2 + 3*x)^1)/(3 + 5*x), x, 2, (13*x)/25 - (3*x^2)/5 + (11/125)*log(3 + 5*x)]
    @test_int [(1 - 2*x)/(3 + 5*x), x, 2, (-2*x)/5 + (11*log(3 + 5*x))/25]
    @test_int [(1 - 2*x)/((2 + 3*x)*(3 + 5*x)), x, 2, (-7*log(2 + 3*x))/3 + (11*log(3 + 5*x))/5]
    @test_int [(1 - 2*x)/((2 + 3*x)^2*(3 + 5*x)), x, 2, 7/(3*(2 + 3*x)) - 11*log(2 + 3*x) + 11*log(3 + 5*x)]
    @test_int [(1 - 2*x)/((2 + 3*x)^3*(3 + 5*x)), x, 2, 7/(6*(2 + 3*x)^2) + 11/(2 + 3*x) - 55*log(2 + 3*x) + 55*log(3 + 5*x)]
    @test_int [(1 - 2*x)/((2 + 3*x)^4*(3 + 5*x)), x, 2, 7/(9*(2 + 3*x)^3) + 11/(2*(2 + 3*x)^2) + 55/(2 + 3*x) - 275*log(2 + 3*x) + 275*log(3 + 5*x)]
    @test_int [(1 - 2*x)/((2 + 3*x)^5*(3 + 5*x)), x, 2, 7/(12*(2 + 3*x)^4) + 11/(3*(2 + 3*x)^3) + 55/(2*(2 + 3*x)^2) + 275/(2 + 3*x) - 1375*log(2 + 3*x) + 1375*log(3 + 5*x)]
    @test_int [(1 - 2*x)/((2 + 3*x)^6*(3 + 5*x)), x, 2, 7/(15*(2 + 3*x)^5) + 11/(4*(2 + 3*x)^4) + 55/(3*(2 + 3*x)^3) + 275/(2*(2 + 3*x)^2) + 1375/(2 + 3*x) - 6875*log(2 + 3*x) + 6875*log(3 + 5*x)]
    @test_int [(1 - 2*x)/((2 + 3*x)^7*(3 + 5*x)), x, 2, 7/(18*(2 + 3*x)^6) + 11/(5*(2 + 3*x)^5) + 55/(4*(2 + 3*x)^4) + 275/(3*(2 + 3*x)^3) + 1375/(2*(2 + 3*x)^2) + 6875/(2 + 3*x) - 34375*log(2 + 3*x) + 34375*log(3 + 5*x)]

    @test_int [((1 - 2*x)*(2 + 3*x)^7)/(3 + 5*x)^2, x, 2, (5555478*x)/390625 + (5740767*x^2)/156250 + (92592*x^3)/3125 - (513783*x^4)/12500 - (336798*x^5)/3125 - (21627*x^6)/250 - (4374*x^7)/175 - 11/(1953125*(3 + 5*x)) + (229*log(3 + 5*x))/1953125]
    @test_int [((1 - 2*x)*(2 + 3*x)^6)/(3 + 5*x)^2, x, 2, (555489*x)/78125 + (40743*x^2)/3125 + (5553*x^3)/3125 - (14094*x^4)/625 - (16767*x^5)/625 - (243*x^6)/25 - 11/(390625*(3 + 5*x)) + (196*log(3 + 5*x))/390625]
    @test_int [((1 - 2*x)*(2 + 3*x)^5)/(3 + 5*x)^2, x, 2, (444*x)/125 + (24093*x^2)/6250 - (1854*x^3)/625 - (3969*x^4)/500 - (486*x^5)/125 - 11/(78125*(3 + 5*x)) + (163*log(3 + 5*x))/78125]
    @test_int [((1 - 2*x)*(2 + 3*x)^4)/(3 + 5*x)^2, x, 2, (5511*x)/3125 + (378*x^2)/625 - (261*x^3)/125 - (81*x^4)/50 - 11/(15625*(3 + 5*x)) + (26*log(3 + 5*x))/3125]
    @test_int [((1 - 2*x)*(2 + 3*x)^3)/(3 + 5*x)^2, x, 2, (522*x)/625 - (81*x^2)/250 - (18*x^3)/25 - 11/(3125*(3 + 5*x)) + (97*log(3 + 5*x))/3125]
    @test_int [((1 - 2*x)*(2 + 3*x)^2)/(3 + 5*x)^2, x, 2, (33*x)/125 - (9*x^2)/25 - 11/(625*(3 + 5*x)) + (64*log(3 + 5*x))/625]
    @test_int [((1 - 2*x)*(2 + 3*x))/(3 + 5*x)^2, x, 2, (-6*x)/25 - 11/(125*(3 + 5*x)) + (31*log(3 + 5*x))/125]
    @test_int [(1 - 2*x)/(3 + 5*x)^2, x, 2, -11/(25*(3 + 5*x)) - (2*log(3 + 5*x))/25]
    @test_int [(1 - 2*x)/((2 + 3*x)*(3 + 5*x)^2), x, 2, -11/(5*(3 + 5*x)) + 7*log(2 + 3*x) - 7*log(3 + 5*x)]
    @test_int [(1 - 2*x)/((2 + 3*x)^2*(3 + 5*x)^2), x, 2, -7/(2 + 3*x) - 11/(3 + 5*x) + 68*log(2 + 3*x) - 68*log(3 + 5*x)]
    @test_int [(1 - 2*x)/((2 + 3*x)^3*(3 + 5*x)^2), x, 2, -7/(2*(2 + 3*x)^2) - 68/(2 + 3*x) - 55/(3 + 5*x) + 505*log(2 + 3*x) - 505*log(3 + 5*x)]
    @test_int [(1 - 2*x)/((2 + 3*x)^4*(3 + 5*x)^2), x, 2, -7/(3*(2 + 3*x)^3) - 34/(2 + 3*x)^2 - 505/(2 + 3*x) - 275/(3 + 5*x) + 3350*log(2 + 3*x) - 3350*log(3 + 5*x)]
    @test_int [(1 - 2*x)/((2 + 3*x)^5*(3 + 5*x)^2), x, 2, -7/(4*(2 + 3*x)^4) - 68/(3*(2 + 3*x)^3) - 505/(2*(2 + 3*x)^2) - 3350/(2 + 3*x) - 1375/(3 + 5*x) + 20875*log(2 + 3*x) - 20875*log(3 + 5*x)]
    @test_int [(1 - 2*x)/((2 + 3*x)^6*(3 + 5*x)^2), x, 2, -7/(5*(2 + 3*x)^5) - 17/(2 + 3*x)^4 - 505/(3*(2 + 3*x)^3) - 1675/(2 + 3*x)^2 - 20875/(2 + 3*x) - 6875/(3 + 5*x) + 125000*log(2 + 3*x) - 125000*log(3 + 5*x)]
    @test_int [(1 - 2*x)/((2 + 3*x)^7*(3 + 5*x)^2), x, 2, -7/(6*(2 + 3*x)^6) - 68/(5*(2 + 3*x)^5) - 505/(4*(2 + 3*x)^4) - 3350/(3*(2 + 3*x)^3) - 20875/(2*(2 + 3*x)^2) - 125000/(2 + 3*x) - 34375/(3 + 5*x) + 728125*log(2 + 3*x) - 728125*log(3 + 5*x)]

    @test_int [((1 - 2*x)*(2 + 3*x)^7)/(3 + 5*x)^3, x, 2, (1851147*x)/390625 + (129654*x^2)/15625 + (2052*x^3)/3125 - (181521*x^4)/12500 - (51759*x^5)/3125 - (729*x^6)/125 - 11/(3906250*(3 + 5*x)^2) - 229/(1953125*(3 + 5*x)) + (2037*log(3 + 5*x))/1953125]
    @test_int [((1 - 2*x)*(2 + 3*x)^6)/(3 + 5*x)^3, x, 2, (36936*x)/15625 + (297*x^2)/125 - (6399*x^3)/3125 - (12393*x^4)/2500 - (1458*x^5)/625 - 11/(781250*(3 + 5*x)^2) - 196/(390625*(3 + 5*x)) + (1449*log(3 + 5*x))/390625]
    @test_int [((1 - 2*x)*(2 + 3*x)^5)/(3 + 5*x)^3, x, 2, (3636*x)/3125 + (1971*x^2)/6250 - (837*x^3)/625 - (243*x^4)/250 - 11/(156250*(3 + 5*x)^2) - 163/(78125*(3 + 5*x)) + (192*log(3 + 5*x))/15625]
    @test_int [((1 - 2*x)*(2 + 3*x)^4)/(3 + 5*x)^3, x, 2, (1647*x)/3125 - (297*x^2)/1250 - (54*x^3)/125 - 11/(31250*(3 + 5*x)^2) - 26/(3125*(3 + 5*x)) + (114*log(3 + 5*x))/3125]
    @test_int [((1 - 2*x)*(2 + 3*x)^3)/(3 + 5*x)^3, x, 2, (81*x)/625 - (27*x^2)/125 - 11/(6250*(3 + 5*x)^2) - 97/(3125*(3 + 5*x)) + (279*log(3 + 5*x))/3125]
    @test_int [((1 - 2*x)*(2 + 3*x)^2)/(3 + 5*x)^3, x, 2, (-18*x)/125 - 11/(1250*(3 + 5*x)^2) - 64/(625*(3 + 5*x)) + (87*log(3 + 5*x))/625]
    @test_int [((1 - 2*x)*(2 + 3*x))/(3 + 5*x)^3, x, 2, -11/(250*(3 + 5*x)^2) - 31/(125*(3 + 5*x)) - (6*log(3 + 5*x))/125]
    @test_int [(1 - 2*x)/(3 + 5*x)^3, x, 1, -(1 - 2*x)^2/(22*(3 + 5*x)^2)]
    @test_int [(1 - 2*x)/((2 + 3*x)*(3 + 5*x)^3), x, 2, -11/(10*(3 + 5*x)^2) + 7/(3 + 5*x) - 21*log(2 + 3*x) + 21*log(3 + 5*x)]
    @test_int [(1 - 2*x)/((2 + 3*x)^2*(3 + 5*x)^3), x, 2, 21/(2 + 3*x) - 11/(2*(3 + 5*x)^2) + 68/(3 + 5*x) - 309*log(2 + 3*x) + 309*log(3 + 5*x)]
    @test_int [(1 - 2*x)/((2 + 3*x)^3*(3 + 5*x)^3), x, 2, 21/(2*(2 + 3*x)^2) + 309/(2 + 3*x) - 55/(2*(3 + 5*x)^2) + 505/(3 + 5*x) - 3060*log(2 + 3*x) + 3060*log(3 + 5*x)]
    @test_int [(1 - 2*x)/((2 + 3*x)^4*(3 + 5*x)^3), x, 2, 7/(2 + 3*x)^3 + 309/(2*(2 + 3*x)^2) + 3060/(2 + 3*x) - 275/(2*(3 + 5*x)^2) + 3350/(3 + 5*x) - 25350*log(2 + 3*x) + 25350*log(3 + 5*x)]
    @test_int [(1 - 2*x)/((2 + 3*x)^5*(3 + 5*x)^3), x, 2, 21/(4*(2 + 3*x)^4) + 103/(2 + 3*x)^3 + 1530/(2 + 3*x)^2 + 25350/(2 + 3*x) - 1375/(2*(3 + 5*x)^2) + 20875/(3 + 5*x) - 189375*log(2 + 3*x) + 189375*log(3 + 5*x)]
    @test_int [(1 - 2*x)/((2 + 3*x)^6*(3 + 5*x)^3), x, 2, 21/(5*(2 + 3*x)^5) + 309/(4*(2 + 3*x)^4) + 1020/(2 + 3*x)^3 + 12675/(2 + 3*x)^2 + 189375/(2 + 3*x) - 6875/(2*(3 + 5*x)^2) + 125000/(3 + 5*x) - 1321875*log(2 + 3*x) + 1321875*log(3 + 5*x)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^n*(e+f*x)^2=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x), x, 2, (-49*(2 + 3*x)^9)/729 + (91*(2 + 3*x)^10)/270 - (16*(2 + 3*x)^11)/99 + (5*(2 + 3*x)^12)/243]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x), x, 2, (-49*(2 + 3*x)^8)/648 + (91*(2 + 3*x)^9)/243 - (8*(2 + 3*x)^10)/45 + (20*(2 + 3*x)^11)/891]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x), x, 2, (-(7/81))*(2 + 3*x)^7 + (91/216)*(2 + 3*x)^8 - (16/81)*(2 + 3*x)^9 + (2/81)*(2 + 3*x)^10]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x), x, 2, (-(49/486))*(2 + 3*x)^6 + (13/27)*(2 + 3*x)^7 - (2/9)*(2 + 3*x)^8 + (20/729)*(2 + 3*x)^9]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x), x, 2, (-(49/405))*(2 + 3*x)^5 + (91/162)*(2 + 3*x)^6 - (16/63)*(2 + 3*x)^7 + (5/162)*(2 + 3*x)^8]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x), x, 2, 24*x + 26*x^2 - (154*x^3)/3 - (425*x^4)/4 + (99*x^5)/5 + 144*x^6 + (540*x^7)/7]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x), x, 2, 12*x + 4*x^2 - (89*x^3)/3 - (79*x^4)/4 + (168*x^5)/5 + 30*x^6]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^1*(3 + 5*x), x, 2, 6*x - (5*x^2)/2 - (37*x^3)/3 + 4*x^4 + 12*x^5]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^0*(3 + 5*x), x, 2, 3*x - (7*x^2)/2 - (8*x^3)/3 + 5*x^4]
    @test_int [((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x), x, 2, (65*x)/27 - (32*x^2)/9 + (20*x^3)/9 - (49/81)*log(2 + 3*x)]
    @test_int [((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^2, x, 2, (-104*x)/27 + (10*x^2)/9 + 49/(81*(2 + 3*x)) + (91*log(2 + 3*x))/27]
    @test_int [((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^3, x, 2, (20*x)/27 + 49/(162*(2 + 3*x)^2) - 91/(27*(2 + 3*x)) - (16*log(2 + 3*x))/9]
    @test_int [((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^4, x, 2, 49/(243*(2 + 3*x)^3) - 91/(54*(2 + 3*x)^2) + 16/(9*(2 + 3*x)) + (20/81)*log(2 + 3*x)]
    @test_int [((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^5, x, 2, (1 - 2*x)^3/(84*(2 + 3*x)^4) - (23*(1 - 2*x)^3)/(294*(2 + 3*x)^3)]
    @test_int [((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^6, x, 2, 49/(405*(2 + 3*x)^5) - 91/(108*(2 + 3*x)^4) + 16/(27*(2 + 3*x)^3) - 10/(81*(2 + 3*x)^2)]
    @test_int [((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^7, x, 2, 49/(486*(2 + 3*x)^6) - 91/(135*(2 + 3*x)^5) + 4/(9*(2 + 3*x)^4) - 20/(243*(2 + 3*x)^3)]
    @test_int [((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^8, x, 2, 7/(81*(2 + 3*x)^7) - 91/(162*(2 + 3*x)^6) + 16/(45*(2 + 3*x)^5) - 5/(81*(2 + 3*x)^4)]

    @test_int [(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x)^2, x, 2, (49*(2 + 3*x)^9)/2187 - (259*(2 + 3*x)^10)/1215 + (503*(2 + 3*x)^11)/891 - (185*(2 + 3*x)^12)/729 + (100*(2 + 3*x)^13)/3159]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x)^2, x, 2, (49*(2 + 3*x)^8)/1944 - (518*(2 + 3*x)^9)/2187 + (503/810)*(2 + 3*x)^10 - (740*(2 + 3*x)^11)/2673 + (25/729)*(2 + 3*x)^12]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x)^2, x, 2, (7/243)*(2 + 3*x)^7 - (259/972)*(2 + 3*x)^8 + (503/729)*(2 + 3*x)^9 - (74/243)*(2 + 3*x)^10 + (100*(2 + 3*x)^11)/2673]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x)^2, x, 2, (49*(2 + 3*x)^6)/1458 - (74/243)*(2 + 3*x)^7 + (503/648)*(2 + 3*x)^8 - (740*(2 + 3*x)^9)/2187 + (10/243)*(2 + 3*x)^10]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^2, x, 2, (49*(2 + 3*x)^5)/1215 - (259/729)*(2 + 3*x)^6 + (503/567)*(2 + 3*x)^7 - (185/486)*(2 + 3*x)^8 + (100*(2 + 3*x)^9)/2187]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x)^2, x, 2, 72*x + 138*x^2 - (202*x^3)/3 - (2045*x^4)/4 - (1828*x^5)/5 + (1029*x^6)/2 + (5940*x^7)/7 + (675*x^8)/2]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x)^2, x, 2, 36*x + 42*x^2 - (227*x^3)/3 - (341*x^4)/2 + (109*x^5)/5 + 230*x^6 + (900*x^7)/7]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^1*(3 + 5*x)^2, x, 2, 18*x + (15*x^2)/2 - (136*x^3)/3 - (137*x^4)/4 + 52*x^5 + 50*x^6]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^0*(3 + 5*x)^2, x, 2, 9*x - 3*x^2 - (59*x^3)/3 + 5*x^4 + 20*x^5]
    @test_int [((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x), x, 2, (340*x)/81 - (251*x^2)/54 - (140*x^3)/27 + (25*x^4)/3 + (49*log(2 + 3*x))/243]
    @test_int [((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^2, x, 2, (143*x)/27 - (170*x^2)/27 + (100*x^3)/27 - 49/(243*(2 + 3*x)) - (518*log(2 + 3*x))/243]
    @test_int [((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^3, x, 2, (-20*x)/3 + (50*x^2)/27 - 49/(486*(2 + 3*x)^2) + 518/(243*(2 + 3*x)) + (503*log(2 + 3*x))/81]
    @test_int [((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^4, x, 2, (100*x)/81 - 49/(729*(2 + 3*x)^3) + 259/(243*(2 + 3*x)^2) - 503/(81*(2 + 3*x)) - (740*log(2 + 3*x))/243]
    @test_int [((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^5, x, 2, -49/(972*(2 + 3*x)^4) + 518/(729*(2 + 3*x)^3) - 503/(162*(2 + 3*x)^2) + 740/(243*(2 + 3*x)) + (100*log(2 + 3*x))/243]
    @test_int [((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^6, x, 2, -49/(1215*(2 + 3*x)^5) + 259/(486*(2 + 3*x)^4) - 503/(243*(2 + 3*x)^3) + 370/(243*(2 + 3*x)^2) - 100/(243*(2 + 3*x))]
    @test_int [((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^7, x, 2, -49/(1458*(2 + 3*x)^6) + 518/(1215*(2 + 3*x)^5) - 503/(324*(2 + 3*x)^4) + 740/(729*(2 + 3*x)^3) - 50/(243*(2 + 3*x)^2)]
    @test_int [((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^8, x, 2, -7/(243*(2 + 3*x)^7) + 259/(729*(2 + 3*x)^6) - 503/(405*(2 + 3*x)^5) + 185/(243*(2 + 3*x)^4) - 100/(729*(2 + 3*x)^3)]

    @test_int [(1 - 2*x)^2*(2 + 3*x)^10*(3 + 5*x)^3, x, 2, -((49*(2 + 3*x)^11)/8019) + (763*(2 + 3*x)^12)/8748 - (4099*(2 + 3*x)^13)/9477 + (8285*(2 + 3*x)^14)/10206 - (760*(2 + 3*x)^15)/2187 + (125*(2 + 3*x)^16)/2916]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^9*(3 + 5*x)^3, x, 2, -((49*(2 + 3*x)^10)/7290) + (763*(2 + 3*x)^11)/8019 - (4099*(2 + 3*x)^12)/8748 + (8285*(2 + 3*x)^13)/9477 - (1900*(2 + 3*x)^14)/5103 + (100*(2 + 3*x)^15)/2187]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x)^3, x, 2, -((49*(2 + 3*x)^9)/6561) + (763*(2 + 3*x)^10)/7290 - (4099*(2 + 3*x)^11)/8019 + (8285*(2 + 3*x)^12)/8748 - (3800*(2 + 3*x)^13)/9477 + (250*(2 + 3*x)^14)/5103]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x)^3, x, 2, -((49*(2 + 3*x)^8)/5832) + (763*(2 + 3*x)^9)/6561 - (4099*(2 + 3*x)^10)/7290 + (8285*(2 + 3*x)^11)/8019 - (950*(2 + 3*x)^12)/2187 + (500*(2 + 3*x)^13)/9477]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x)^3, x, 2, (-(7/729))*(2 + 3*x)^7 + (763*(2 + 3*x)^8)/5832 - (4099*(2 + 3*x)^9)/6561 + (1657*(2 + 3*x)^10)/1458 - (3800*(2 + 3*x)^11)/8019 + (125*(2 + 3*x)^12)/2187]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x)^3, x, 2, -((49*(2 + 3*x)^6)/4374) + (109/729)*(2 + 3*x)^7 - (4099*(2 + 3*x)^8)/5832 + (8285*(2 + 3*x)^9)/6561 - (380/729)*(2 + 3*x)^10 + (500*(2 + 3*x)^11)/8019]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^3, x, 2, -((49*(2 + 3*x)^5)/3645) + (763*(2 + 3*x)^6)/4374 - (4099*(2 + 3*x)^7)/5103 + (8285*(2 + 3*x)^8)/5832 - (3800*(2 + 3*x)^9)/6561 + (50/729)*(2 + 3*x)^10]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x)^3, x, 2, 216*x + 594*x^2 + 258*x^3 - (7145*x^4)/4 - (15709*x^5)/5 + (121*x^6)/6 + (33255*x^7)/7 + 4725*x^8 + 1500*x^9]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x)^3, x, 2, 108*x + 216*x^2 - 87*x^3 - (3181*x^4)/4 - (3083*x^5)/5 + (4685*x^6)/6 + (9600*x^7)/7 + (1125*x^8)/2]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^1*(3 + 5*x)^3, x, 2, 54*x + (135*x^2)/2 - 111*x^3 - (1091*x^4)/4 + 19*x^5 + (1100*x^6)/3 + (1500*x^7)/7]
    @test_int [(1 - 2*x)^2*(2 + 3*x)^0*(3 + 5*x)^3, x, 2, (121/500)*(3 + 5*x)^4 - (44/625)*(3 + 5*x)^5 + (2/375)*(3 + 5*x)^6]
    @test_int [((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^1, x, 2, (3305*x)/243 - (559*x^2)/162 - (2515*x^3)/81 + (50*x^4)/9 + (100*x^5)/3 - (49*log(2 + 3*x))/729]
    @test_int [((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^2, x, 2, (1271*x)/243 - (305*x^2)/54 - (800*x^3)/81 + (125*x^4)/9 + 49/(729*(2 + 3*x)) + (763*log(2 + 3*x))/729]
    @test_int [((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^3, x, 2, (895*x)/81 - (100*x^2)/9 + (500*x^3)/81 + 49/(1458*(2 + 3*x)^2) - 763/(729*(2 + 3*x)) - (4099*log(2 + 3*x))/729]
    @test_int [((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^4, x, 2, (-2800*x)/243 + (250*x^2)/81 + 49/(2187*(2 + 3*x)^3) - 763/(1458*(2 + 3*x)^2) + 4099/(729*(2 + 3*x)) + (8285*log(2 + 3*x))/729]
    @test_int [((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^5, x, 2, (500*x)/243 + 49/(2916*(2 + 3*x)^4) - 763/(2187*(2 + 3*x)^3) + 4099/(1458*(2 + 3*x)^2) - 8285/(729*(2 + 3*x)) - (3800*log(2 + 3*x))/729]
    @test_int [((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^6, x, 2, 49/(3645*(2 + 3*x)^5) - 763/(2916*(2 + 3*x)^4) + 4099/(2187*(2 + 3*x)^3) - 8285/(1458*(2 + 3*x)^2) + 3800/(729*(2 + 3*x)) + (500*log(2 + 3*x))/729]
    @test_int [((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^7, x, 2, 49/(4374*(2 + 3*x)^6) - 763/(3645*(2 + 3*x)^5) + 4099/(2916*(2 + 3*x)^4) - 8285/(2187*(2 + 3*x)^3) + 1900/(729*(2 + 3*x)^2) - 500/(729*(2 + 3*x))]
    @test_int [((1 - 2*x)^2*(3 + 5*x)^3)/(2 + 3*x)^8, x, 2, 7/(729*(2 + 3*x)^7) - 763/(4374*(2 + 3*x)^6) + 4099/(3645*(2 + 3*x)^5) - 8285/(2916*(2 + 3*x)^4) + 3800/(2187*(2 + 3*x)^3) - 250/(729*(2 + 3*x)^2)]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [((1 - 2*x)^2*(2 + 3*x)^7)/(3 + 5*x), x, 2, (83333293*x)/1953125 + (80555569*x^2)/781250 + (1327159*x^3)/78125 - (20577159*x^4)/62500 - (7315947*x^5)/15625 + (130383*x^6)/1250 + (672867*x^7)/875 + (16767*x^8)/25 + (972*x^9)/5 + (121*log(3 + 5*x))/9765625]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^6)/(3 + 5*x), x, 2, (8333293*x)/390625 + (5555569*x^2)/156250 - (422841*x^3)/15625 - (1677159*x^4)/12500 - (228447*x^5)/3125 + (35883*x^6)/250 + (34992*x^7)/175 + (729*x^8)/10 + (121*log(3 + 5*x))/1953125]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^5)/(3 + 5*x), x, 2, (833293*x)/78125 + (305569*x^2)/31250 - (72841*x^3)/3125 - (102159*x^4)/2500 + (7803*x^5)/625 + (1404*x^6)/25 + (972*x^7)/35 + (121*log(3 + 5*x))/390625]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^4)/(3 + 5*x), x, 2, (83293*x)/15625 + (5569*x^2)/6250 - (7841*x^3)/625 - (3159*x^4)/500 + (1728*x^5)/125 + (54*x^6)/5 + (121*log(3 + 5*x))/78125]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^3)/(3 + 5*x), x, 2, (8293*x)/3125 - (1931*x^2)/1250 - (591*x^3)/125 + (54*x^4)/25 + (108*x^5)/25 + (121*log(3 + 5*x))/15625]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^2)/(3 + 5*x), x, 2, (793*x)/625 - (431*x^2)/250 - (16*x^3)/25 + (9*x^4)/5 + (121*log(3 + 5*x))/3125]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^1)/(3 + 5*x), x, 2, (43*x)/125 - (28*x^2)/25 + (4*x^3)/5 + (121/625)*log(3 + 5*x)]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^0)/(3 + 5*x), x, 2, -((32*x)/25) + (2*x^2)/5 + (121/125)*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^1*(3 + 5*x)), x, 2, (4*x)/15 - (49*log(2 + 3*x))/9 + (121*log(3 + 5*x))/25]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^2*(3 + 5*x)), x, 2, 49/(9*(2 + 3*x)) - (217*log(2 + 3*x))/9 + (121*log(3 + 5*x))/5]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^3*(3 + 5*x)), x, 2, 49/(18*(2 + 3*x)^2) + 217/(9*(2 + 3*x)) - 121*log(2 + 3*x) + 121*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^4*(3 + 5*x)), x, 2, 49/(27*(2 + 3*x)^3) + 217/(18*(2 + 3*x)^2) + 121/(2 + 3*x) - 605*log(2 + 3*x) + 605*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^5*(3 + 5*x)), x, 2, 49/(36*(2 + 3*x)^4) + 217/(27*(2 + 3*x)^3) + 121/(2*(2 + 3*x)^2) + 605/(2 + 3*x) - 3025*log(2 + 3*x) + 3025*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^6*(3 + 5*x)), x, 2, 49/(45*(2 + 3*x)^5) + 217/(36*(2 + 3*x)^4) + 121/(3*(2 + 3*x)^3) + 605/(2*(2 + 3*x)^2) + 3025/(2 + 3*x) - 15125*log(2 + 3*x) + 15125*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^7*(3 + 5*x)), x, 2, 49/(54*(2 + 3*x)^6) + 217/(45*(2 + 3*x)^5) + 121/(4*(2 + 3*x)^4) + 605/(3*(2 + 3*x)^3) + 3025/(2*(2 + 3*x)^2) + 15125/(2 + 3*x) - 75625*log(2 + 3*x) + 75625*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^8*(3 + 5*x)), x, 2, 7/(9*(2 + 3*x)^7) + 217/(54*(2 + 3*x)^6) + 121/(5*(2 + 3*x)^5) + 605/(4*(2 + 3*x)^4) + 3025/(3*(2 + 3*x)^3) + 15125/(2*(2 + 3*x)^2) + 75625/(2 + 3*x) - 378125*log(2 + 3*x) + 378125*log(3 + 5*x)]

    @test_int [((1 - 2*x)^2*(2 + 3*x)^7)/(3 + 5*x)^2, x, 2, (27776932*x)/1953125 + (17592879*x^2)/781250 - (1512378*x^3)/78125 - (213867*x^4)/2500 - (656424*x^5)/15625 + (116397*x^6)/1250 + (107892*x^7)/875 + (2187*x^8)/50 - 121/(9765625*(3 + 5*x)) + (2497*log(3 + 5*x))/9765625]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^6)/(3 + 5*x)^2, x, 2, (2777053*x)/390625 + (463086*x^2)/78125 - (48771*x^3)/3125 - (157599*x^4)/6250 + (28917*x^5)/3125 + (4374*x^6)/125 + (2916*x^7)/175 - 121/(1953125*(3 + 5*x)) + (2134*log(3 + 5*x))/1953125]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^5)/(3 + 5*x)^2, x, 2, (277174*x)/78125 + (1893*x^2)/6250 - (25332*x^3)/3125 - (8721*x^4)/2500 + (5508*x^5)/625 + (162*x^6)/25 - 121/(390625*(3 + 5*x)) + (1771*log(3 + 5*x))/390625]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^4)/(3 + 5*x)^2, x, 2, (5459*x)/3125 - (3621*x^2)/3125 - (1809*x^3)/625 + (189*x^4)/125 + (324*x^5)/125 - 121/(78125*(3 + 5*x)) + (1408*log(3 + 5*x))/78125]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^3)/(3 + 5*x)^2, x, 2, (2416*x)/3125 - (1449*x^2)/1250 - (36*x^3)/125 + (27*x^4)/25 - 121/(15625*(3 + 5*x)) + (209*log(3 + 5*x))/3125]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^2)/(3 + 5*x)^2, x, 2, (37*x)/625 - (78*x^2)/125 + (12*x^3)/25 - 121/(3125*(3 + 5*x)) + (682*log(3 + 5*x))/3125]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^1)/(3 + 5*x)^2, x, 2, (-92*x)/125 + (6*x^2)/25 - 121/(625*(3 + 5*x)) + (319*log(3 + 5*x))/625]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^0)/(3 + 5*x)^2, x, 2, (4*x)/25 - 121/(125*(3 + 5*x)) - (44*log(3 + 5*x))/125]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^1*(3 + 5*x)^2), x, 2, -121/(25*(3 + 5*x)) + (49*log(2 + 3*x))/3 - (407*log(3 + 5*x))/25]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^2*(3 + 5*x)^2), x, 2, -49/(3*(2 + 3*x)) - 121/(5*(3 + 5*x)) + 154*log(2 + 3*x) - 154*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^3*(3 + 5*x)^2), x, 2, -49/(6*(2 + 3*x)^2) - 154/(2 + 3*x) - 121/(3 + 5*x) + 1133*log(2 + 3*x) - 1133*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^4*(3 + 5*x)^2), x, 2, -49/(9*(2 + 3*x)^3) - 77/(2 + 3*x)^2 - 1133/(2 + 3*x) - 605/(3 + 5*x) + 7480*log(2 + 3*x) - 7480*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^5*(3 + 5*x)^2), x, 2, -49/(12*(2 + 3*x)^4) - 154/(3*(2 + 3*x)^3) - 1133/(2*(2 + 3*x)^2) - 7480/(2 + 3*x) - 3025/(3 + 5*x) + 46475*log(2 + 3*x) - 46475*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^6*(3 + 5*x)^2), x, 2, -49/(15*(2 + 3*x)^5) - 77/(2*(2 + 3*x)^4) - 1133/(3*(2 + 3*x)^3) - 3740/(2 + 3*x)^2 - 46475/(2 + 3*x) - 15125/(3 + 5*x) + 277750*log(2 + 3*x) - 277750*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^7*(3 + 5*x)^2), x, 2, -49/(18*(2 + 3*x)^6) - 154/(5*(2 + 3*x)^5) - 1133/(4*(2 + 3*x)^4) - 7480/(3*(2 + 3*x)^3) - 46475/(2*(2 + 3*x)^2) - 277750/(2 + 3*x) - 75625/(3 + 5*x) + 1615625*log(2 + 3*x) - 1615625*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^8*(3 + 5*x)^2), x, 2, -7/(3*(2 + 3*x)^7) - 77/(3*(2 + 3*x)^6) - 1133/(5*(2 + 3*x)^5) - 1870/(2 + 3*x)^4 - 46475/(3*(2 + 3*x)^3) - 138875/(2 + 3*x)^2 - 1615625/(2 + 3*x) - 378125/(3 + 5*x) + 9212500*log(2 + 3*x) - 9212500*log(3 + 5*x)]

    @test_int [((1 - 2*x)^2*(2 + 3*x)^8)/(3 + 5*x)^3, x, 2, (92582457*x)/9765625 + (55559043*x^2)/3906250 - (5350194*x^3)/390625 - (1700919*x^4)/31250 - (74601*x^5)/3125 + (376407*x^6)/6250 + (332424*x^7)/4375 + (6561*x^8)/250 - 121/(97656250*(3 + 5*x)^2) - 572/(9765625*(3 + 5*x)) + (5888*log(3 + 5*x))/9765625]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^7)/(3 + 5*x)^3, x, 2, (9251661*x)/1953125 + (1390203*x^2)/390625 - (162612*x^3)/15625 - (193833*x^4)/12500 + (104247*x^5)/15625 + (13608*x^6)/625 + (8748*x^7)/875 - 121/(19531250*(3 + 5*x)^2) - 2497/(9765625*(3 + 5*x)) + (21949*log(3 + 5*x))/9765625]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^6)/(3 + 5*x)^3, x, 2, (920502*x)/390625 + (189*x^2)/15625 - (16299*x^3)/3125 - (23571*x^4)/12500 + (17496*x^5)/3125 + (486*x^6)/125 - 121/(3906250*(3 + 5*x)^2) - 2134/(1953125*(3 + 5*x)) + (15547*log(3 + 5*x))/1953125]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^5)/(3 + 5*x)^3, x, 2, (17796*x)/15625 - (5301*x^2)/6250 - (5499*x^3)/3125 + (648*x^4)/625 + (972*x^5)/625 - 121/(781250*(3 + 5*x)^2) - 1771/(390625*(3 + 5*x)) + (10234*log(3 + 5*x))/390625]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^4)/(3 + 5*x)^3, x, 2, (1419*x)/3125 - (4779*x^2)/6250 - (72*x^3)/625 + (81*x^4)/125 - 121/(156250*(3 + 5*x)^2) - 1408/(78125*(3 + 5*x)) + (1202*log(3 + 5*x))/15625]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^3)/(3 + 5*x)^3, x, 2, (-153*x)/3125 - (216*x^2)/625 + (36*x^3)/125 - 121/(31250*(3 + 5*x)^2) - 209/(3125*(3 + 5*x)) + (23*log(3 + 5*x))/125]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^2)/(3 + 5*x)^3, x, 2, (-264*x)/625 + (18*x^2)/125 - 121/(6250*(3 + 5*x)^2) - 682/(3125*(3 + 5*x)) + (829*log(3 + 5*x))/3125]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^1)/(3 + 5*x)^3, x, 2, (12*x)/125 - 121/(1250*(3 + 5*x)^2) - 319/(625*(3 + 5*x)) - (128*log(3 + 5*x))/625]
    @test_int [((1 - 2*x)^2*(2 + 3*x)^0)/(3 + 5*x)^3, x, 2, -121/(250*(3 + 5*x)^2) + 44/(125*(3 + 5*x)) + (4*log(3 + 5*x))/125]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^1*(3 + 5*x)^3), x, 2, -121/(50*(3 + 5*x)^2) + 407/(25*(3 + 5*x)) - 49*log(2 + 3*x) + 49*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^2*(3 + 5*x)^3), x, 2, 49/(2 + 3*x) - 121/(10*(3 + 5*x)^2) + 154/(3 + 5*x) - 707*log(2 + 3*x) + 707*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^3*(3 + 5*x)^3), x, 2, 49/(2*(2 + 3*x)^2) + 707/(2 + 3*x) - 121/(2*(3 + 5*x)^2) + 1133/(3 + 5*x) - 6934*log(2 + 3*x) + 6934*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^4*(3 + 5*x)^3), x, 2, 49/(3*(2 + 3*x)^3) + 707/(2*(2 + 3*x)^2) + 6934/(2 + 3*x) - 605/(2*(3 + 5*x)^2) + 7480/(3 + 5*x) - 57110*log(2 + 3*x) + 57110*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^5*(3 + 5*x)^3), x, 2, 49/(4*(2 + 3*x)^4) + 707/(3*(2 + 3*x)^3) + 3467/(2 + 3*x)^2 + 57110/(2 + 3*x) - 3025/(2*(3 + 5*x)^2) + 46475/(3 + 5*x) - 424975*log(2 + 3*x) + 424975*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^6*(3 + 5*x)^3), x, 2, 49/(5*(2 + 3*x)^5) + 707/(4*(2 + 3*x)^4) + 6934/(3*(2 + 3*x)^3) + 28555/(2 + 3*x)^2 + 424975/(2 + 3*x) - 15125/(2*(3 + 5*x)^2) + 277750/(3 + 5*x) - 2958125*log(2 + 3*x) + 2958125*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^7*(3 + 5*x)^3), x, 2, 49/(6*(2 + 3*x)^6) + 707/(5*(2 + 3*x)^5) + 3467/(2*(2 + 3*x)^4) + 57110/(3*(2 + 3*x)^3) + 424975/(2*(2 + 3*x)^2) + 2958125/(2 + 3*x) - 75625/(2*(3 + 5*x)^2) + 1615625/(3 + 5*x) - 19637500*log(2 + 3*x) + 19637500*log(3 + 5*x)]
    @test_int [(1 - 2*x)^2/((2 + 3*x)^8*(3 + 5*x)^3), x, 2, 7/(2 + 3*x)^7 + 707/(6*(2 + 3*x)^6) + 6934/(5*(2 + 3*x)^5) + 28555/(2*(2 + 3*x)^4) + 424975/(3*(2 + 3*x)^3) + 2958125/(2*(2 + 3*x)^2) + 19637500/(2 + 3*x) - 378125/(2*(3 + 5*x)^2) + 9212500/(3 + 5*x) - 125825000*log(2 + 3*x) + 125825000*log(3 + 5*x)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^n*(e+f*x)^3=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(1 - 2*x)^3*(2 + 3*x)^8*(3 + 5*x), x, 2, (-343*(2 + 3*x)^9)/2187 + (2009*(2 + 3*x)^10)/2430 - (518*(2 + 3*x)^11)/891 + (107*(2 + 3*x)^12)/729 - (40*(2 + 3*x)^13)/3159]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^7*(3 + 5*x), x, 2, -((343*(2 + 3*x)^8)/1944) + (2009*(2 + 3*x)^9)/2187 - (259/405)*(2 + 3*x)^10 + (428*(2 + 3*x)^11)/2673 - (10/729)*(2 + 3*x)^12]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x), x, 2, (-(49/243))*(2 + 3*x)^7 + (2009*(2 + 3*x)^8)/1944 - (518/729)*(2 + 3*x)^9 + (214*(2 + 3*x)^10)/1215 - (40*(2 + 3*x)^11)/2673]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^5*(3 + 5*x), x, 2, -((343*(2 + 3*x)^6)/1458) + (287/243)*(2 + 3*x)^7 - (259/324)*(2 + 3*x)^8 + (428*(2 + 3*x)^9)/2187 - (4/243)*(2 + 3*x)^10]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x), x, 2, -((343*(2 + 3*x)^5)/1215) + (2009*(2 + 3*x)^6)/1458 - (74/81)*(2 + 3*x)^7 + (107/486)*(2 + 3*x)^8 - (40*(2 + 3*x)^9)/2187]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x), x, 2, 24*x + 2*x^2 - 86*x^3 - (117*x^4)/4 + (949*x^5)/5 + 111*x^6 - (1188*x^7)/7 - 135*x^8]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x), x, 2, 12*x - 8*x^2 - 35*x^3 + (99*x^4)/4 + (326*x^5)/5 - 26*x^6 - (360*x^7)/7]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^1*(3 + 5*x), x, 2, (-(77/32))*(1 - 2*x)^4 + (17/10)*(1 - 2*x)^5 - (5/16)*(1 - 2*x)^6]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^0*(3 + 5*x), x, 2, (-(11/16))*(1 - 2*x)^4 + (1/4)*(1 - 2*x)^5]
    @test_int [((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^1, x, 2, (293*x)/81 - (161*x^2)/27 + (188*x^3)/27 - (10*x^4)/3 - (343/243)*log(2 + 3*x)]
    @test_int [((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^2, x, 2, (-286*x)/27 + (134*x^2)/27 - (40*x^3)/27 + 343/(243*(2 + 3*x)) + (2009*log(2 + 3*x))/243]
    @test_int [((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^3, x, 2, (116*x)/27 - (20*x^2)/27 + 343/(486*(2 + 3*x)^2) - 2009/(243*(2 + 3*x)) - (518*log(2 + 3*x))/81]
    @test_int [((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^4, x, 2, (-40*x)/81 + 343/(729*(2 + 3*x)^3) - 2009/(486*(2 + 3*x)^2) + 518/(81*(2 + 3*x)) + (428*log(2 + 3*x))/243]
    @test_int [((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^5, x, 2, 343/(972*(2 + 3*x)^4) - 2009/(729*(2 + 3*x)^3) + 259/(81*(2 + 3*x)^2) - 428/(243*(2 + 3*x)) - (40/243)*log(2 + 3*x)]
    @test_int [((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^6, x, 2, (1 - 2*x)^4/(105*(2 + 3*x)^5) - (173*(1 - 2*x)^4)/(2940*(2 + 3*x)^4)]
    @test_int [((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^7, x, 3, (1 - 2*x)^4/(126*(2 + 3*x)^6) - (103*(1 - 2*x)^4)/(2205*(2 + 3*x)^5) - (103*(1 - 2*x)^4)/(30870*(2 + 3*x)^4)]
    @test_int [((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^8, x, 2, 49/(243*(2 + 3*x)^7) - 2009/(1458*(2 + 3*x)^6) + 518/(405*(2 + 3*x)^5) - 107/(243*(2 + 3*x)^4) + 40/(729*(2 + 3*x)^3)]

    @test_int [(1 - 2*x)^3*(2 + 3*x)^8*(3 + 5*x)^2, x, 2, (343*(2 + 3*x)^9)/6561 - (1862*(2 + 3*x)^10)/3645 + (11599*(2 + 3*x)^11)/8019 - (4099*(2 + 3*x)^12)/4374 + (2180*(2 + 3*x)^13)/9477 - (100*(2 + 3*x)^14)/5103]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^7*(3 + 5*x)^2, x, 2, (343*(2 + 3*x)^8)/5832 - (3724*(2 + 3*x)^9)/6561 + (11599*(2 + 3*x)^10)/7290 - (8198*(2 + 3*x)^11)/8019 + (545*(2 + 3*x)^12)/2187 - (200*(2 + 3*x)^13)/9477]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^2, x, 2, (49/729)*(2 + 3*x)^7 - (931*(2 + 3*x)^8)/1458 + (11599*(2 + 3*x)^9)/6561 - (4099*(2 + 3*x)^10)/3645 + (2180*(2 + 3*x)^11)/8019 - (50*(2 + 3*x)^12)/2187]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^5*(3 + 5*x)^2, x, 2, (343*(2 + 3*x)^6)/4374 - (532/729)*(2 + 3*x)^7 + (11599*(2 + 3*x)^8)/5832 - (8198*(2 + 3*x)^9)/6561 + (218/729)*(2 + 3*x)^10 - (200*(2 + 3*x)^11)/8019]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^2, x, 2, (343*(2 + 3*x)^5)/3645 - (1862*(2 + 3*x)^6)/2187 + (1657/729)*(2 + 3*x)^7 - (4099*(2 + 3*x)^8)/2916 + (2180*(2 + 3*x)^9)/6561 - (20/729)*(2 + 3*x)^10]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^2, x, 2, 72*x + 66*x^2 - (754*x^3)/3 - (1641*x^4)/4 + (2262*x^5)/5 + (6743*x^6)/6 - (234*x^7)/7 - (2295*x^8)/2 - 600*x^9]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)^2, x, 2, 36*x + 6*x^2 - (395*x^3)/3 - 57*x^4 + (1473*x^5)/5 + (581*x^6)/3 - (1860*x^7)/7 - 225*x^8]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^1*(3 + 5*x)^2, x, 2, 18*x - (21*x^2)/2 - (166*x^3)/3 + (135*x^4)/4 + (534*x^5)/5 - (110*x^6)/3 - (600*x^7)/7]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^0*(3 + 5*x)^2, x, 2, (-(121/32))*(1 - 2*x)^4 + (11/4)*(1 - 2*x)^5 - (25/48)*(1 - 2*x)^6]
    @test_int [((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x), x, 2, (922*x)/243 - (1433*x^2)/162 + (82*x^3)/81 + (145*x^4)/9 - (40*x^5)/3 + (343*log(2 + 3*x))/729]
    @test_int [((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^2, x, 2, (2323*x)/243 - (313*x^2)/27 + (980*x^3)/81 - (50*x^4)/9 - 343/(729*(2 + 3*x)) - (3724*log(2 + 3*x))/729]
    @test_int [((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^3, x, 2, (-1546*x)/81 + (230*x^2)/27 - (200*x^3)/81 - 343/(1458*(2 + 3*x)^2) + 3724/(729*(2 + 3*x)) + (11599*log(2 + 3*x))/729]
    @test_int [((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^4, x, 2, (1780*x)/243 - (100*x^2)/81 - 343/(2187*(2 + 3*x)^3) + 1862/(729*(2 + 3*x)^2) - 11599/(729*(2 + 3*x)) - (8198*log(2 + 3*x))/729]
    @test_int [((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^5, x, 2, (-200*x)/243 - 343/(2916*(2 + 3*x)^4) + 3724/(2187*(2 + 3*x)^3) - 11599/(1458*(2 + 3*x)^2) + 8198/(729*(2 + 3*x)) + (2180*log(2 + 3*x))/729]
    @test_int [((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^6, x, 2, -343/(3645*(2 + 3*x)^5) + 931/(729*(2 + 3*x)^4) - 11599/(2187*(2 + 3*x)^3) + 4099/(729*(2 + 3*x)^2) - 2180/(729*(2 + 3*x)) - (200*log(2 + 3*x))/729]
    @test_int [((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^7, x, 2, -343/(4374*(2 + 3*x)^6) + 3724/(3645*(2 + 3*x)^5) - 11599/(2916*(2 + 3*x)^4) + 8198/(2187*(2 + 3*x)^3) - 1090/(729*(2 + 3*x)^2) + 200/(729*(2 + 3*x))]
    @test_int [((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^8, x, 2, -49/(729*(2 + 3*x)^7) + 1862/(2187*(2 + 3*x)^6) - 11599/(3645*(2 + 3*x)^5) + 4099/(1458*(2 + 3*x)^4) - 2180/(2187*(2 + 3*x)^3) + 100/(729*(2 + 3*x)^2)]

    @test_int [(1 - 2*x)^3*(2 + 3*x)^7*(3 + 5*x)^3, x, 2, -((343*(2 + 3*x)^8)/17496) + (1813*(2 + 3*x)^9)/6561 - (10073*(2 + 3*x)^10)/7290 + (66193*(2 + 3*x)^11)/24057 - (7195*(2 + 3*x)^12)/4374 + (3700*(2 + 3*x)^13)/9477 - (500*(2 + 3*x)^14)/15309]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x)^3, x, 2, -((49*(2 + 3*x)^7)/2187) + (1813*(2 + 3*x)^8)/5832 - (10073*(2 + 3*x)^9)/6561 + (66193*(2 + 3*x)^10)/21870 - (14390*(2 + 3*x)^11)/8019 + (925*(2 + 3*x)^12)/2187 - (1000*(2 + 3*x)^13)/28431]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^5*(3 + 5*x)^3, x, 2, -((343*(2 + 3*x)^6)/13122) + (259/729)*(2 + 3*x)^7 - (10073*(2 + 3*x)^8)/5832 + (66193*(2 + 3*x)^9)/19683 - (1439/729)*(2 + 3*x)^10 + (3700*(2 + 3*x)^11)/8019 - (250*(2 + 3*x)^12)/6561]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^3, x, 2, 432*x + 1080*x^2 - 312*x^3 - 5548*x^4 - (28917*x^5)/5 + (19607*x^6)/2 + 22949*x^7 + (41619*x^8)/8 - 23370*x^9 - 24030*x^10 - (81000*x^11)/11]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^3, x, 2, 216*x + 378*x^2 - 534*x^3 - (8693*x^4)/4 - (1419*x^5)/5 + (10513*x^6)/2 + (33013*x^7)/7 - (14355*x^8)/4 - 6900*x^9 - 2700*x^10]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)^3, x, 2, 108*x + 108*x^2 - 375*x^3 - (2659*x^4)/4 + (3279*x^5)/5 + (3617*x^6)/2 + (230*x^7)/7 - (3675*x^8)/2 - 1000*x^9]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^1*(3 + 5*x)^3, x, 2, 54*x + (27*x^2)/2 - 201*x^3 - (425*x^4)/4 + (2277*x^5)/5 + 335*x^6 - (2900*x^7)/7 - 375*x^8]
    @test_int [(1 - 2*x)^3*(2 + 3*x)^0*(3 + 5*x)^3, x, 2, 27*x - (27*x^2)/2 - 87*x^3 + (179*x^4)/4 + 174*x^5 - 50*x^6 - (1000*x^7)/7]
    @test_int [((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^1, x, 2, (10013*x)/729 - (8287*x^2)/486 - (6427*x^3)/243 + (2815*x^4)/54 + (220*x^5)/9 - (500*x^6)/9 - (343*log(2 + 3*x))/2187]
    @test_int [((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^2, x, 2, (2287*x)/729 - (5287*x^2)/486 - (190*x^3)/81 + (775*x^4)/27 - (200*x^5)/9 + 343/(2187*(2 + 3*x)) + (1813*log(2 + 3*x))/729]
    @test_int [((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^3, x, 2, (16253*x)/729 - (1795*x^2)/81 + (1700*x^3)/81 - (250*x^4)/27 + 343/(4374*(2 + 3*x)^2) - 1813/(729*(2 + 3*x)) - (10073*log(2 + 3*x))/729]
    @test_int [((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^4, x, 2, (-24970*x)/729 + (3550*x^2)/243 - (1000*x^3)/243 + 343/(6561*(2 + 3*x)^3) - 1813/(1458*(2 + 3*x)^2) + 10073/(729*(2 + 3*x)) + (66193*log(2 + 3*x))/2187]
    @test_int [((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^5, x, 2, (9100*x)/729 - (500*x^2)/243 + 343/(8748*(2 + 3*x)^4) - 1813/(2187*(2 + 3*x)^3) + 10073/(1458*(2 + 3*x)^2) - 66193/(2187*(2 + 3*x)) - (14390*log(2 + 3*x))/729]
    @test_int [((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^6, x, 2, (-1000*x)/729 + 343/(10935*(2 + 3*x)^5) - 1813/(2916*(2 + 3*x)^4) + 10073/(2187*(2 + 3*x)^3) - 66193/(4374*(2 + 3*x)^2) + 14390/(729*(2 + 3*x)) + (3700*log(2 + 3*x))/729]
    @test_int [((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^7, x, 2, 343/(13122*(2 + 3*x)^6) - 1813/(3645*(2 + 3*x)^5) + 10073/(2916*(2 + 3*x)^4) - 66193/(6561*(2 + 3*x)^3) + 7195/(729*(2 + 3*x)^2) - 3700/(729*(2 + 3*x)) - (1000*log(2 + 3*x))/2187]
    @test_int [((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^8, x, 2, 49/(2187*(2 + 3*x)^7) - 1813/(4374*(2 + 3*x)^6) + 10073/(3645*(2 + 3*x)^5) - 66193/(8748*(2 + 3*x)^4) + 14390/(2187*(2 + 3*x)^3) - 1850/(729*(2 + 3*x)^2) + 1000/(2187*(2 + 3*x))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [((1 - 2*x)^3*(2 + 3*x)^6)/(3 + 5*x), x, 2, (41666223*x)/1953125 + (11111259*x^2)/781250 - (17453753*x^3)/234375 - (5848749*x^4)/62500 + (2212083*x^5)/15625 + (331713*x^6)/1250 - (40338*x^7)/875 - (13851*x^8)/50 - (648*x^9)/5 + (1331*log(3 + 5*x))/9765625]
    @test_int [((1 - 2*x)^3*(2 + 3*x)^5)/(3 + 5*x), x, 2, (4166223*x)/390625 - (138741*x^2)/156250 - (1703753*x^3)/46875 - (73749*x^4)/12500 + (243333*x^5)/3125 + (4419*x^6)/125 - (11988*x^7)/175 - (243*x^8)/5 + (1331*log(3 + 5*x))/1953125]
    @test_int [((1 - 2*x)^3*(2 + 3*x)^4)/(3 + 5*x), x, 2, (416223*x)/78125 - (138741*x^2)/31250 - (128753*x^3)/9375 + (31251*x^4)/2500 + (14958*x^5)/625 - (306*x^6)/25 - (648*x^7)/35 + (1331*log(3 + 5*x))/390625]
    @test_int [((1 - 2*x)^3*(2 + 3*x)^3)/(3 + 5*x), x, 2, (41223*x)/15625 - (26241*x^2)/6250 - (5003*x^3)/1875 + (2313*x^4)/250 + (108*x^5)/125 - (36*x^6)/5 + (1331*log(3 + 5*x))/78125]
    @test_int [((1 - 2*x)^3*(2 + 3*x)^2)/(3 + 5*x), x, 2, (3723*x)/3125 - (3741*x^2)/1250 + (622*x^3)/375 + (69*x^4)/25 - (72*x^5)/25 + (1331*log(3 + 5*x))/15625]
    @test_int [((1 - 2*x)^3*(2 + 3*x)^1)/(3 + 5*x), x, 2, -((27*x)/625) - (183*x^2)/125 + (172*x^3)/75 - (6*x^4)/5 + (1331*log(3 + 5*x))/3125]
    @test_int [(1 - 2*x)^3/(3 + 5*x), x, 2, -((402*x)/125) + (42*x^2)/25 - (8*x^3)/15 + (1331/625)*log(3 + 5*x)]
    @test_int [(1 - 2*x)^3/((2 + 3*x)*(3 + 5*x)), x, 2, (332*x)/225 - (4*x^2)/15 - (343*log(2 + 3*x))/27 + (1331*log(3 + 5*x))/125]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^2*(3 + 5*x)), x, 2, (-8*x)/45 + 343/(27*(2 + 3*x)) - (1421*log(2 + 3*x))/27 + (1331*log(3 + 5*x))/25]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^3*(3 + 5*x)), x, 2, 343/(54*(2 + 3*x)^2) + 1421/(27*(2 + 3*x)) - (7189*log(2 + 3*x))/27 + (1331*log(3 + 5*x))/5]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^4*(3 + 5*x)), x, 2, 343/(81*(2 + 3*x)^3) + 1421/(54*(2 + 3*x)^2) + 7189/(27*(2 + 3*x)) - 1331*log(2 + 3*x) + 1331*log(3 + 5*x)]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^5*(3 + 5*x)), x, 2, 343/(108*(2 + 3*x)^4) + 1421/(81*(2 + 3*x)^3) + 7189/(54*(2 + 3*x)^2) + 1331/(2 + 3*x) - 6655*log(2 + 3*x) + 6655*log(3 + 5*x)]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^6*(3 + 5*x)), x, 2, 343/(135*(2 + 3*x)^5) + 1421/(108*(2 + 3*x)^4) + 7189/(81*(2 + 3*x)^3) + 1331/(2*(2 + 3*x)^2) + 6655/(2 + 3*x) - 33275*log(2 + 3*x) + 33275*log(3 + 5*x)]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^7*(3 + 5*x)), x, 2, 343/(162*(2 + 3*x)^6) + 1421/(135*(2 + 3*x)^5) + 7189/(108*(2 + 3*x)^4) + 1331/(3*(2 + 3*x)^3) + 6655/(2*(2 + 3*x)^2) + 33275/(2 + 3*x) - 166375*log(2 + 3*x) + 166375*log(3 + 5*x)]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^8*(3 + 5*x)), x, 2, 49/(27*(2 + 3*x)^7) + 1421/(162*(2 + 3*x)^6) + 7189/(135*(2 + 3*x)^5) + 1331/(4*(2 + 3*x)^4) + 6655/(3*(2 + 3*x)^3) + 33275/(2*(2 + 3*x)^2) + 166375/(2 + 3*x) - 831875*log(2 + 3*x) + 831875*log(3 + 5*x)]

    @test_int [((1 - 2*x)^3*(2 + 3*x)^6)/(3 + 5*x)^2, x, 2, (13880997*x)/1953125 - (461623*x^2)/390625 - (1836723*x^3)/78125 - (5643*x^4)/3125 + (774981*x^5)/15625 + (12231*x^6)/625 - (37908*x^7)/875 - (729*x^8)/25 - 1331/(9765625*(3 + 5*x)) + (23232*log(3 + 5*x))/9765625]
    @test_int [((1 - 2*x)^3*(2 + 3*x)^5)/(3 + 5*x)^2, x, 2, (1382328*x)/390625 - (507023*x^2)/156250 - (26594*x^3)/3125 + (108387*x^4)/12500 + (44982*x^5)/3125 - (1026*x^6)/125 - (1944*x^7)/175 - 1331/(1953125*(3 + 5*x)) + (19239*log(3 + 5*x))/1953125]
    @test_int [((1 - 2*x)^3*(2 + 3*x)^4)/(3 + 5*x)^2, x, 2, (133659*x)/78125 - (1816*x^2)/625 - (4217*x^3)/3125 + (7317*x^4)/1250 + (108*x^5)/625 - (108*x^6)/25 - 1331/(390625*(3 + 5*x)) + (15246*log(3 + 5*x))/390625]
    @test_int [((1 - 2*x)^3*(2 + 3*x)^3)/(3 + 5*x)^2, x, 2, (1998*x)/3125 - (12077*x^2)/6250 + (786*x^3)/625 + (189*x^4)/125 - (216*x^5)/125 - 1331/(78125*(3 + 5*x)) + (11253*log(3 + 5*x))/78125]
    @test_int [((1 - 2*x)^3*(2 + 3*x)^2)/(3 + 5*x)^2, x, 2, (-1179*x)/3125 - (427*x^2)/625 + (164*x^3)/125 - (18*x^4)/25 - 1331/(15625*(3 + 5*x)) + (1452*log(3 + 5*x))/3125]
    @test_int [((1 - 2*x)^3*(2 + 3*x))/(3 + 5*x)^2, x, 2, (-1098*x)/625 + (122*x^2)/125 - (8*x^3)/25 - 1331/(3125*(3 + 5*x)) + (3267*log(3 + 5*x))/3125]
    @test_int [(1 - 2*x)^3/(3 + 5*x)^2, x, 2, (108*x)/125 - (4*x^2)/25 - 1331/(625*(3 + 5*x)) - (726*log(3 + 5*x))/625]
    @test_int [(1 - 2*x)^3/((2 + 3*x)*(3 + 5*x)^2), x, 2, (-8*x)/75 - 1331/(125*(3 + 5*x)) + (343*log(2 + 3*x))/9 - (4719*log(3 + 5*x))/125]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^2*(3 + 5*x)^2), x, 2, -343/(9*(2 + 3*x)) - 1331/(25*(3 + 5*x)) + (3136*log(2 + 3*x))/9 - (8712*log(3 + 5*x))/25]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^3*(3 + 5*x)^2), x, 2, -343/(18*(2 + 3*x)^2) - 3136/(9*(2 + 3*x)) - 1331/(5*(3 + 5*x)) + 2541*log(2 + 3*x) - 2541*log(3 + 5*x)]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^4*(3 + 5*x)^2), x, 2, -343/(27*(2 + 3*x)^3) - 1568/(9*(2 + 3*x)^2) - 2541/(2 + 3*x) - 1331/(3 + 5*x) + 16698*log(2 + 3*x) - 16698*log(3 + 5*x)]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^5*(3 + 5*x)^2), x, 2, -343/(36*(2 + 3*x)^4) - 3136/(27*(2 + 3*x)^3) - 2541/(2*(2 + 3*x)^2) - 16698/(2 + 3*x) - 6655/(3 + 5*x) + 103455*log(2 + 3*x) - 103455*log(3 + 5*x)]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^6*(3 + 5*x)^2), x, 2, -343/(45*(2 + 3*x)^5) - 784/(9*(2 + 3*x)^4) - 847/(2 + 3*x)^3 - 8349/(2 + 3*x)^2 - 103455/(2 + 3*x) - 33275/(3 + 5*x) + 617100*log(2 + 3*x) - 617100*log(3 + 5*x)]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^7*(3 + 5*x)^2), x, 2, -343/(54*(2 + 3*x)^6) - 3136/(45*(2 + 3*x)^5) - 2541/(4*(2 + 3*x)^4) - 5566/(2 + 3*x)^3 - 103455/(2*(2 + 3*x)^2) - 617100/(2 + 3*x) - 166375/(3 + 5*x) + 3584625*log(2 + 3*x) - 3584625*log(3 + 5*x)]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^8*(3 + 5*x)^2), x, 2, -49/(9*(2 + 3*x)^7) - 1568/(27*(2 + 3*x)^6) - 2541/(5*(2 + 3*x)^5) - 8349/(2*(2 + 3*x)^4) - 34485/(2 + 3*x)^3 - 308550/(2 + 3*x)^2 - 3584625/(2 + 3*x) - 831875/(3 + 5*x) + 20418750*log(2 + 3*x) - 20418750*log(3 + 5*x)]

    @test_int [((1 - 2*x)^3*(2 + 3*x)^7)/(3 + 5*x)^3, x, 2, (46214407*x)/9765625 - (2300646*x^2)/1953125 - (5918904*x^3)/390625 + (6507*x^4)/62500 + (491913*x^5)/15625 + (33291*x^6)/3125 - (119556*x^7)/4375 - (2187*x^8)/125 - 1331/(97656250*(3 + 5*x)^2) - 1089/(1953125*(3 + 5*x)) + (47289*log(3 + 5*x))/9765625]
    @test_int [((1 - 2*x)^3*(2 + 3*x)^6)/(3 + 5*x)^3, x, 2, (4571416*x)/1953125 - (915777*x^2)/390625 - (81747*x^3)/15625 + (74223*x^4)/12500 + (134622*x^5)/15625 - (3402*x^6)/625 - (5832*x^7)/875 - 1331/(19531250*(3 + 5*x)^2) - 23232/(9765625*(3 + 5*x)) + (166749*log(3 + 5*x))/9765625]
    @test_int [((1 - 2*x)^3*(2 + 3*x)^5)/(3 + 5*x)^3, x, 2, (424432*x)/390625 - (62097*x^2)/31250 - (393*x^3)/625 + (22977*x^4)/6250 - (324*x^5)/3125 - (324*x^6)/125 - 1331/(3906250*(3 + 5*x)^2) - 19239/(1953125*(3 + 5*x)) + (109032*log(3 + 5*x))/1953125]
    @test_int [((1 - 2*x)^3*(2 + 3*x)^4)/(3 + 5*x)^3, x, 2, (4691*x)/15625 - (7617*x^2)/6250 + (2826*x^3)/3125 + (513*x^4)/625 - (648*x^5)/625 - 1331/(781250*(3 + 5*x)^2) - 15246/(390625*(3 + 5*x)) + (63294*log(3 + 5*x))/390625]
    @test_int [((1 - 2*x)^3*(2 + 3*x)^3)/(3 + 5*x)^3, x, 2, (-1303*x)/3125 - (927*x^2)/3125 + (468*x^3)/625 - (54*x^4)/125 - 1331/(156250*(3 + 5*x)^2) - 11253/(78125*(3 + 5*x)) + (5907*log(3 + 5*x))/15625]
    @test_int [((1 - 2*x)^3*(2 + 3*x)^2)/(3 + 5*x)^3, x, 2, (-2978*x)/3125 + (354*x^2)/625 - (24*x^3)/125 - 1331/(31250*(3 + 5*x)^2) - 1452/(3125*(3 + 5*x)) + (1551*log(3 + 5*x))/3125]
    @test_int [((1 - 2*x)^3*(2 + 3*x))/(3 + 5*x)^3, x, 2, (316*x)/625 - (12*x^2)/125 - 1331/(6250*(3 + 5*x)^2) - 3267/(3125*(3 + 5*x)) - (2046*log(3 + 5*x))/3125]
    @test_int [(1 - 2*x)^3/(3 + 5*x)^3, x, 2, (-8*x)/125 - 1331/(1250*(3 + 5*x)^2) + 726/(625*(3 + 5*x)) + (132*log(3 + 5*x))/625]
    @test_int [(1 - 2*x)^3/((2 + 3*x)*(3 + 5*x)^3), x, 2, -1331/(250*(3 + 5*x)^2) + 4719/(125*(3 + 5*x)) - (343*log(2 + 3*x))/3 + (14289*log(3 + 5*x))/125]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^2*(3 + 5*x)^3), x, 2, 343/(3*(2 + 3*x)) - 1331/(50*(3 + 5*x)^2) + 8712/(25*(3 + 5*x)) - 1617*log(2 + 3*x) + 1617*log(3 + 5*x)]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^3*(3 + 5*x)^3), x, 2, 343/(6*(2 + 3*x)^2) + 1617/(2 + 3*x) - 1331/(10*(3 + 5*x)^2) + 2541/(3 + 5*x) - 15708*log(2 + 3*x) + 15708*log(3 + 5*x)]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^4*(3 + 5*x)^3), x, 2, 343/(9*(2 + 3*x)^3) + 1617/(2*(2 + 3*x)^2) + 15708/(2 + 3*x) - 1331/(2*(3 + 5*x)^2) + 16698/(3 + 5*x) - 128634*log(2 + 3*x) + 128634*log(3 + 5*x)]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^5*(3 + 5*x)^3), x, 2, 343/(12*(2 + 3*x)^4) + 539/(2 + 3*x)^3 + 7854/(2 + 3*x)^2 + 128634/(2 + 3*x) - 6655/(2*(3 + 5*x)^2) + 103455/(3 + 5*x) - 953535*log(2 + 3*x) + 953535*log(3 + 5*x)]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^6*(3 + 5*x)^3), x, 2, 343/(15*(2 + 3*x)^5) + 1617/(4*(2 + 3*x)^4) + 5236/(2 + 3*x)^3 + 64317/(2 + 3*x)^2 + 953535/(2 + 3*x) - 33275/(2*(3 + 5*x)^2) + 617100/(3 + 5*x) - 6618975*log(2 + 3*x) + 6618975*log(3 + 5*x)]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^7*(3 + 5*x)^3), x, 2, 343/(18*(2 + 3*x)^6) + 1617/(5*(2 + 3*x)^5) + 3927/(2 + 3*x)^4 + 42878/(2 + 3*x)^3 + 953535/(2*(2 + 3*x)^2) + 6618975/(2 + 3*x) - 166375/(2*(3 + 5*x)^2) + 3584625/(3 + 5*x) - 43848750*log(2 + 3*x) + 43848750*log(3 + 5*x)]
    @test_int [(1 - 2*x)^3/((2 + 3*x)^8*(3 + 5*x)^3), x, 2, 49/(3*(2 + 3*x)^7) + 539/(2*(2 + 3*x)^6) + 15708/(5*(2 + 3*x)^5) + 64317/(2*(2 + 3*x)^4) + 317845/(2 + 3*x)^3 + 6618975/(2*(2 + 3*x)^2) + 43848750/(2 + 3*x) - 831875/(2*(3 + 5*x)^2) + 20418750/(3 + 5*x) - 280500000*log(2 + 3*x) + 280500000*log(3 + 5*x)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^n / (e+f*x)^1=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [((2 + 3*x)^8*(3 + 5*x))/(1 - 2*x), x, 2, -((63019595*x)/512) - (60332619*x^2)/512 - (17391129*x^3)/128 - (37722699*x^4)/256 - (21272139*x^5)/160 - (2929689*x^6)/32 - (353565*x^7)/8 - (422091*x^8)/32 - (3645*x^9)/2 - (63412811*log(1 - 2*x))/1024]
    @test_int [((2 + 3*x)^7*(3 + 5*x))/(1 - 2*x), x, 2, -((8960669*x)/256) - (8362653*x^2)/256 - (2257119*x^3)/64 - (4352157*x^4)/128 - (2053917*x^5)/80 - (218943*x^6)/16 - (126117*x^7)/28 - (10935*x^8)/16 - (9058973/512)*log(1 - 2*x)]
    @test_int [((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x), x, 2, -((1269563*x)/128) - (1138491*x^2)/128 - (279657*x^3)/32 - (458811*x^4)/64 - (169371*x^5)/40 - (12393*x^6)/8 - (3645*x^7)/14 - (1294139/256)*log(1 - 2*x)]
    @test_int [((2 + 3*x)^5*(3 + 5*x))/(1 - 2*x), x, 2, -((178733*x)/64) - (150573*x^2)/64 - (32271*x^3)/16 - (42093*x^4)/32 - (10773*x^5)/20 - (405*x^6)/4 - (184877/128)*log(1 - 2*x)]
    @test_int [((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x), x, 2, -((24875*x)/32) - (18987*x^2)/32 - (3321*x^3)/8 - (3051*x^4)/16 - (81*x^5)/2 - (26411/64)*log(1 - 2*x)]
    @test_int [((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x), x, 2, -((3389*x)/16) - (2205*x^2)/16 - (279*x^3)/4 - (135*x^4)/8 - (3773/32)*log(1 - 2*x)]
    @test_int [((2 + 3*x)^2*(3 + 5*x))/(1 - 2*x), x, 2, -((443*x)/8) - (219*x^2)/8 - (15*x^3)/2 - (539/16)*log(1 - 2*x)]
    @test_int [((2 + 3*x)^1*(3 + 5*x))/(1 - 2*x), x, 2, -((53*x)/4) - (15*x^2)/4 - (77/8)*log(1 - 2*x)]
    @test_int [(3 + 5*x)/(1 - 2*x), x, 2, (-5*x)/2 - (11*log(1 - 2*x))/4]
    @test_int [(3 + 5*x)/((1 - 2*x)*(2 + 3*x)), x, 2, (-11*log(1 - 2*x))/14 - log(2 + 3*x)/21]
    @test_int [(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^2), x, 2, 1/(21*(2 + 3*x)) - (11*log(1 - 2*x))/49 + (11*log(2 + 3*x))/49]
    @test_int [(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^3), x, 2, 1/(42*(2 + 3*x)^2) - 11/(49*(2 + 3*x)) - (22*log(1 - 2*x))/343 + (22*log(2 + 3*x))/343]
    @test_int [(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^4), x, 2, 1/(63*(2 + 3*x)^3) - 11/(98*(2 + 3*x)^2) - 22/(343*(2 + 3*x)) - (44*log(1 - 2*x))/2401 + (44*log(2 + 3*x))/2401]
    @test_int [(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^5), x, 2, 1/(84*(2 + 3*x)^4) - 11/(147*(2 + 3*x)^3) - 11/(343*(2 + 3*x)^2) - 44/(2401*(2 + 3*x)) - (88*log(1 - 2*x))/16807 + (88*log(2 + 3*x))/16807]
    @test_int [(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^6), x, 2, 1/(105*(2 + 3*x)^5) - 11/(196*(2 + 3*x)^4) - 22/(1029*(2 + 3*x)^3) - 22/(2401*(2 + 3*x)^2) - 88/(16807*(2 + 3*x)) - (176*log(1 - 2*x))/117649 + (176*log(2 + 3*x))/117649]
    @test_int [(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^7), x, 2, 1/(126*(2 + 3*x)^6) - 11/(245*(2 + 3*x)^5) - 11/(686*(2 + 3*x)^4) - 44/(7203*(2 + 3*x)^3) - 44/(16807*(2 + 3*x)^2) - 176/(117649*(2 + 3*x)) - (352*log(1 - 2*x))/823543 + (352*log(2 + 3*x))/823543]
    @test_int [(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^8), x, 2, 1/(147*(2 + 3*x)^7) - 11/(294*(2 + 3*x)^6) - 22/(1715*(2 + 3*x)^5) - 11/(2401*(2 + 3*x)^4) - 88/(50421*(2 + 3*x)^3) - 88/(117649*(2 + 3*x)^2) - 352/(823543*(2 + 3*x)) - (704*log(1 - 2*x))/5764801 + (704*log(2 + 3*x))/5764801]

    @test_int [((2 + 3*x)^8*(3 + 5*x)^2)/(1 - 2*x), x, 2, (-695181625*x)/1024 - (677093689*x^2)/1024 - (204901139*x^3)/256 - (487203129*x^4)/512 - (316246329*x^5)/320 - (53031699*x^6)/64 - (8399295*x^7)/16 - (14907321*x^8)/64 - (256365*x^9)/4 - (32805*x^10)/4 - (697540921*log(1 - 2*x))/2048]
    @test_int [((2 + 3*x)^7*(3 + 5*x)^2)/(1 - 2*x), x, 2, (-99058879*x)/512 - (94979263*x^2)/512 - (27480469*x^3)/128 - (59969727*x^4)/256 - (34084287*x^5)/160 - (4736853*x^6)/32 - (4040847*x^7)/56 - (696195*x^8)/32 - (6075*x^9)/2 - (99648703*log(1 - 2*x))/1024]
    @test_int [((2 + 3*x)^6*(3 + 5*x)^2)/(1 - 2*x), x, 2, (-14088073*x)/256 - (13178761*x^2)/256 - (3575427*x^3)/64 - (6947721*x^4)/128 - (3310281*x^5)/80 - (356643*x^6)/16 - (207765*x^7)/28 - (18225*x^8)/16 - (14235529*log(1 - 2*x))/512]
    @test_int [((2 + 3*x)^5*(3 + 5*x)^2)/(1 - 2*x), x, 2, (-1996783*x)/128 - (1797103*x^2)/128 - (444581*x^3)/32 - (736623*x^4)/64 - (275103*x^5)/40 - (20385*x^6)/8 - (6075*x^7)/14 - (2033647*log(1 - 2*x))/256]
    @test_int [((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x), x, 2, (-281305*x)/64 - (238297*x^2)/64 - (51571*x^3)/16 - (68121*x^4)/32 - (3537*x^5)/4 - (675*x^6)/4 - (290521*log(1 - 2*x))/128]
    @test_int [((2 + 3*x)^3*(3 + 5*x)^2)/(1 - 2*x), x, 2, (-39199*x)/32 - (30175*x^2)/32 - (5349*x^3)/8 - (4995*x^4)/16 - (135*x^5)/2 - (41503*log(1 - 2*x))/64]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x), x, 2, (-5353*x)/16 - (3529*x^2)/16 - (455*x^3)/4 - (225*x^4)/8 - (5929*log(1 - 2*x))/32]
    @test_int [((2 + 3*x)^1*(3 + 5*x)^2)/(1 - 2*x), x, 2, -((703*x)/8) - (355*x^2)/8 - (25*x^3)/2 - (847/16)*log(1 - 2*x)]
    @test_int [(3 + 5*x)^2/(1 - 2*x), x, 2, -((85*x)/4) - (25*x^2)/4 - (121/8)*log(1 - 2*x)]
    @test_int [(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)), x, 2, (-25*x)/6 - (121*log(1 - 2*x))/28 + log(2 + 3*x)/63]
    @test_int [(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^2), x, 2, -1/(63*(2 + 3*x)) - (121*log(1 - 2*x))/98 - (68*log(2 + 3*x))/441]
    @test_int [(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^3), x, 2, -1/(126*(2 + 3*x)^2) + 68/(441*(2 + 3*x)) - (121*log(1 - 2*x))/343 + (121*log(2 + 3*x))/343]
    @test_int [(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^4), x, 2, -1/(189*(2 + 3*x)^3) + 34/(441*(2 + 3*x)^2) - 121/(343*(2 + 3*x)) - (242*log(1 - 2*x))/2401 + (242*log(2 + 3*x))/2401]
    @test_int [(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^5), x, 2, -1/(252*(2 + 3*x)^4) + 68/(1323*(2 + 3*x)^3) - 121/(686*(2 + 3*x)^2) - 242/(2401*(2 + 3*x)) - (484*log(1 - 2*x))/16807 + (484*log(2 + 3*x))/16807]
    @test_int [(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^6), x, 2, -1/(315*(2 + 3*x)^5) + 17/(441*(2 + 3*x)^4) - 121/(1029*(2 + 3*x)^3) - 121/(2401*(2 + 3*x)^2) - 484/(16807*(2 + 3*x)) - (968*log(1 - 2*x))/117649 + (968*log(2 + 3*x))/117649]
    @test_int [(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^7), x, 2, -1/(378*(2 + 3*x)^6) + 68/(2205*(2 + 3*x)^5) - 121/(1372*(2 + 3*x)^4) - 242/(7203*(2 + 3*x)^3) - 242/(16807*(2 + 3*x)^2) - 968/(117649*(2 + 3*x)) - (1936*log(1 - 2*x))/823543 + (1936*log(2 + 3*x))/823543]
    @test_int [(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^8), x, 2, -1/(441*(2 + 3*x)^7) + 34/(1323*(2 + 3*x)^6) - 121/(1715*(2 + 3*x)^5) - 121/(4802*(2 + 3*x)^4) - 484/(50421*(2 + 3*x)^3) - 484/(117649*(2 + 3*x)^2) - 1936/(823543*(2 + 3*x)) - (3872*log(1 - 2*x))/5764801 + (3872*log(2 + 3*x))/5764801]

    @test_int [((2 + 3*x)^7*(3 + 5*x)^3)/(1 - 2*x), x, 2, (-1092596789*x)/1024 - (1065169973*x^2)/1024 - (969544757*x^3)/768 - (772025397*x^4)/512 - (504354357*x^5)/320 - (85228263*x^6)/64 - (95297877*x^7)/112 - (24381405*x^8)/64 - (423225*x^9)/4 - (54675*x^10)/4 - (1096135733*log(1 - 2*x))/2048]
    @test_int [((2 + 3*x)^6*(3 + 5*x)^3)/(1 - 2*x), x, 2, (-155706083*x)/512 - (149512931*x^2)/512 - (130251491*x^3)/384 - (95317731*x^4)/256 - (54600291*x^5)/160 - (7656993*x^6)/32 - (6596235*x^7)/56 - (1148175*x^8)/32 - (10125*x^9)/2 - (156590819*log(1 - 2*x))/1024]
    @test_int [((2 + 3*x)^5*(3 + 5*x)^3)/(1 - 2*x), x, 2, (-22148933*x)/256 - (20766533*x^2)/256 - (16987973*x^3)/192 - (11088453*x^4)/128 - (5333733*x^5)/80 - (580815*x^6)/16 - (342225*x^7)/28 - (30375*x^8)/16 - (22370117*log(1 - 2*x))/512]
    @test_int [((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x), x, 2, (-3140435*x)/128 - (2836307*x^2)/128 - (2119763*x^3)/96 - (1182291*x^4)/64 - (89343*x^5)/8 - (33525*x^6)/8 - (10125*x^7)/14 - (3195731*log(1 - 2*x))/256]
    @test_int [((2 + 3*x)^3*(3 + 5*x)^3)/(1 - 2*x), x, 2, (-442709*x)/64 - (377045*x^2)/64 - (247157*x^3)/48 - (110205*x^4)/32 - (5805*x^5)/4 - (1125*x^6)/4 - (456533*log(1 - 2*x))/128]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^3)/(1 - 2*x), x, 2, (-61763*x)/32 - (47939*x^2)/32 - (25835*x^3)/24 - (8175*x^4)/16 - (225*x^5)/2 - (65219*log(1 - 2*x))/64]
    @test_int [((2 + 3*x)^1*(3 + 5*x)^3)/(1 - 2*x), x, 2, -((8453*x)/16) - (5645*x^2)/16 - (2225*x^3)/12 - (375*x^4)/8 - (9317/32)*log(1 - 2*x)]
    @test_int [(3 + 5*x)^3/(1 - 2*x), x, 2, -((1115*x)/8) - (575*x^2)/8 - (125*x^3)/6 - (1331/16)*log(1 - 2*x)]
    @test_int [(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)), x, 2, (-1225*x)/36 - (125*x^2)/12 - (1331*log(1 - 2*x))/56 - log(2 + 3*x)/189]
    @test_int [(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^2), x, 2, (-125*x)/18 + 1/(189*(2 + 3*x)) - (1331*log(1 - 2*x))/196 + (103*log(2 + 3*x))/1323]
    @test_int [(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^3), x, 2, 1/(378*(2 + 3*x)^2) - 103/(1323*(2 + 3*x)) - (1331*log(1 - 2*x))/686 - (3469*log(2 + 3*x))/9261]
    @test_int [(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^4), x, 2, 1/(567*(2 + 3*x)^3) - 103/(2646*(2 + 3*x)^2) + 3469/(9261*(2 + 3*x)) - (1331*log(1 - 2*x))/2401 + (1331*log(2 + 3*x))/2401]
    @test_int [(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^5), x, 2, 1/(756*(2 + 3*x)^4) - 103/(3969*(2 + 3*x)^3) + 3469/(18522*(2 + 3*x)^2) - 1331/(2401*(2 + 3*x)) - (2662*log(1 - 2*x))/16807 + (2662*log(2 + 3*x))/16807]
    @test_int [(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^6), x, 2, 1/(945*(2 + 3*x)^5) - 103/(5292*(2 + 3*x)^4) + 3469/(27783*(2 + 3*x)^3) - 1331/(4802*(2 + 3*x)^2) - 2662/(16807*(2 + 3*x)) - (5324*log(1 - 2*x))/117649 + (5324*log(2 + 3*x))/117649]
    @test_int [(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^7), x, 2, 1/(1134*(2 + 3*x)^6) - 103/(6615*(2 + 3*x)^5) + 3469/(37044*(2 + 3*x)^4) - 1331/(7203*(2 + 3*x)^3) - 1331/(16807*(2 + 3*x)^2) - 5324/(117649*(2 + 3*x)) - (10648*log(1 - 2*x))/823543 + (10648*log(2 + 3*x))/823543]
    @test_int [(3 + 5*x)^3/((1 - 2*x)*(2 + 3*x)^8), x, 2, 1/(1323*(2 + 3*x)^7) - 103/(7938*(2 + 3*x)^6) + 3469/(46305*(2 + 3*x)^5) - 1331/(9604*(2 + 3*x)^4) - 2662/(50421*(2 + 3*x)^3) - 2662/(117649*(2 + 3*x)^2) - 10648/(823543*(2 + 3*x)) - (21296*log(1 - 2*x))/5764801 + (21296*log(2 + 3*x))/5764801]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(a + b*x)^3/((c + d*x)*(e + f*x)), x, 2, -((b^2*(b*d*e + b*c*f - 3*a*d*f)*x)/(d^2*f^2)) + (b^3*x^2)/(2*d*f) - ((b*c - a*d)^3*log(c + d*x))/(d^3*(d*e - c*f)) + ((b*e - a*f)^3*log(e + f*x))/(f^3*(d*e - c*f))]

    @test_int [(2 + 3*x)^8/((1 - 2*x)*(3 + 5*x)), x, 2, (-40089855591*x)/10000000 - (7136193339*x^2)/2000000 - (345533877*x^3)/100000 - (111146499*x^4)/40000 - (8018271*x^5)/5000 - (114453*x^6)/200 - (6561*x^7)/70 - (5764801*log(1 - 2*x))/2816 + log(3 + 5*x)/4296875]
    @test_int [(2 + 3*x)^7/((1 - 2*x)*(3 + 5*x)), x, 2, (-1127138733*x)/1000000 - (187738857*x^2)/200000 - (7889751*x^3)/10000 - (2006937*x^4)/4000 - (99873*x^5)/500 - (729*x^6)/20 - (823543*log(1 - 2*x))/1408 + log(3 + 5*x)/859375]
    @test_int [(2 + 3*x)^6/((1 - 2*x)*(3 + 5*x)), x, 2, (-31289679*x)/100000 - (4693491*x^2)/20000 - (159813*x^3)/1000 - (28431*x^4)/400 - (729*x^5)/50 - (117649*log(1 - 2*x))/704 + log(3 + 5*x)/171875]
    @test_int [(2 + 3*x)^5/((1 - 2*x)*(3 + 5*x)), x, 2, (-848277*x)/10000 - (107433*x^2)/2000 - (2619*x^3)/100 - (243*x^4)/40 - (16807*log(1 - 2*x))/352 + log(3 + 5*x)/34375]
    @test_int [(2 + 3*x)^4/((1 - 2*x)*(3 + 5*x)), x, 2, (-21951*x)/1000 - (2079*x^2)/200 - (27*x^3)/10 - (2401*log(1 - 2*x))/176 + log(3 + 5*x)/6875]
    @test_int [(2 + 3*x)^3/((1 - 2*x)*(3 + 5*x)), x, 2, (-513*x)/100 - (27*x^2)/20 - (343*log(1 - 2*x))/88 + log(3 + 5*x)/1375]
    @test_int [(2 + 3*x)^2/((1 - 2*x)*(3 + 5*x)), x, 2, (-9*x)/10 - (49*log(1 - 2*x))/44 + log(3 + 5*x)/275]
    @test_int [(2 + 3*x)/((1 - 2*x)*(3 + 5*x)), x, 2, (-7*log(1 - 2*x))/22 + log(3 + 5*x)/55]
    @test_int [1/((1 - 2*x)*(3 + 5*x)), x, 3, (-(1/11))*log(1 - 2*x) + (1/11)*log(3 + 5*x)]
    @test_int [1/((1 - 2*x)*(2 + 3*x)*(3 + 5*x)), x, 2, (-2*log(1 - 2*x))/77 - (3*log(2 + 3*x))/7 + (5*log(3 + 5*x))/11]
    @test_int [1/((1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)), x, 2, 3/(7*(2 + 3*x)) - (4*log(1 - 2*x))/539 - (111*log(2 + 3*x))/49 + (25*log(3 + 5*x))/11]
    @test_int [1/((1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)), x, 2, 3/(14*(2 + 3*x)^2) + 111/(49*(2 + 3*x)) - (8*log(1 - 2*x))/3773 - (3897*log(2 + 3*x))/343 + (125*log(3 + 5*x))/11]
    @test_int [1/((1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)), x, 2, 1/(7*(2 + 3*x)^3) + 111/(98*(2 + 3*x)^2) + 3897/(343*(2 + 3*x)) - (16*log(1 - 2*x))/26411 - (136419*log(2 + 3*x))/2401 + (625*log(3 + 5*x))/11]
    @test_int [1/((1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)), x, 2, 3/(28*(2 + 3*x)^4) + 37/(49*(2 + 3*x)^3) + 3897/(686*(2 + 3*x)^2) + 136419/(2401*(2 + 3*x)) - (32*log(1 - 2*x))/184877 - (4774713*log(2 + 3*x))/16807 + (3125*log(3 + 5*x))/11]
    @test_int [1/((1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)), x, 2, 3/(35*(2 + 3*x)^5) + 111/(196*(2 + 3*x)^4) + 1299/(343*(2 + 3*x)^3) + 136419/(4802*(2 + 3*x)^2) + 4774713/(16807*(2 + 3*x)) - (64*log(1 - 2*x))/1294139 - (167115051*log(2 + 3*x))/117649 + (15625*log(3 + 5*x))/11]
    @test_int [1/((1 - 2*x)*(2 + 3*x)^7*(3 + 5*x)), x, 2, 1/(14*(2 + 3*x)^6) + 111/(245*(2 + 3*x)^5) + 3897/(1372*(2 + 3*x)^4) + 45473/(2401*(2 + 3*x)^3) + 4774713/(33614*(2 + 3*x)^2) + 167115051/(117649*(2 + 3*x)) - (128*log(1 - 2*x))/9058973 - (5849026977*log(2 + 3*x))/823543 + (78125*log(3 + 5*x))/11]

    @test_int [(2 + 3*x)^8/((1 - 2*x)*(3 + 5*x)^2), x, 2, (-3579885909*x)/5000000 - (118543581*x^2)/200000 - (24660207*x^3)/50000 - (6194313*x^4)/20000 - (303993*x^5)/2500 - (2187*x^6)/100 - 1/(4296875*(3 + 5*x)) - (5764801*log(1 - 2*x))/15488 + (266*log(3 + 5*x))/47265625]
    @test_int [(2 + 3*x)^7/((1 - 2*x)*(3 + 5*x)^2), x, 2, (-19846971*x)/100000 - (14750667*x^2)/100000 - (495477*x^3)/5000 - (86751*x^4)/2000 - (2187*x^5)/250 - 1/(859375*(3 + 5*x)) - (823543*log(1 - 2*x))/7744 + (233*log(3 + 5*x))/9453125]
    @test_int [(2 + 3*x)^6/((1 - 2*x)*(3 + 5*x)^2), x, 2, (-2682909*x)/50000 - (335097*x^2)/10000 - (8019*x^3)/500 - (729*x^4)/200 - 1/(171875*(3 + 5*x)) - (117649*log(1 - 2*x))/3872 + (8*log(3 + 5*x))/75625]
    @test_int [(2 + 3*x)^5/((1 - 2*x)*(3 + 5*x)^2), x, 2, (-69039*x)/5000 - (6399*x^2)/1000 - (81*x^3)/50 - 1/(34375*(3 + 5*x)) - (16807*log(1 - 2*x))/1936 + (167*log(3 + 5*x))/378125]
    @test_int [(2 + 3*x)^4/((1 - 2*x)*(3 + 5*x)^2), x, 2, (-1593*x)/500 - (81*x^2)/100 - 1/(6875*(3 + 5*x)) - (2401*log(1 - 2*x))/968 + (134*log(3 + 5*x))/75625]
    @test_int [(2 + 3*x)^3/((1 - 2*x)*(3 + 5*x)^2), x, 2, (-27*x)/50 - 1/(1375*(3 + 5*x)) - (343*log(1 - 2*x))/484 + (101*log(3 + 5*x))/15125]
    @test_int [(2 + 3*x)^2/((1 - 2*x)*(3 + 5*x)^2), x, 2, -1/(275*(3 + 5*x)) - (49*log(1 - 2*x))/242 + (68*log(3 + 5*x))/3025]
    @test_int [(2 + 3*x)/((1 - 2*x)*(3 + 5*x)^2), x, 2, -1/(55*(3 + 5*x)) - (7*log(1 - 2*x))/121 + (7*log(3 + 5*x))/121]
    @test_int [1/((1 - 2*x)*(3 + 5*x)^2), x, 2, -1/(11*(3 + 5*x)) - (2*log(1 - 2*x))/121 + (2*log(3 + 5*x))/121]
    @test_int [1/((1 - 2*x)*(2 + 3*x)*(3 + 5*x)^2), x, 2, -5/(11*(3 + 5*x)) - (4*log(1 - 2*x))/847 + (9*log(2 + 3*x))/7 - (155*log(3 + 5*x))/121]
    @test_int [1/((1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^2), x, 2, -9/(7*(2 + 3*x)) - 25/(11*(3 + 5*x)) - (8*log(1 - 2*x))/5929 + (648*log(2 + 3*x))/49 - (1600*log(3 + 5*x))/121]
    @test_int [1/((1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^2), x, 2, -9/(14*(2 + 3*x)^2) - 648/(49*(2 + 3*x)) - 125/(11*(3 + 5*x)) - (16*log(1 - 2*x))/41503 + (34371*log(2 + 3*x))/343 - (12125*log(3 + 5*x))/121]
    @test_int [1/((1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^2), x, 2, -3/(7*(2 + 3*x)^3) - 324/(49*(2 + 3*x)^2) - 34371/(343*(2 + 3*x)) - 625/(11*(3 + 5*x)) - (32*log(1 - 2*x))/290521 + (1612242*log(2 + 3*x))/2401 - (81250*log(3 + 5*x))/121]
    @test_int [1/((1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)^2), x, 2, -9/(28*(2 + 3*x)^4) - 216/(49*(2 + 3*x)^3) - 34371/(686*(2 + 3*x)^2) - 1612242/(2401*(2 + 3*x)) - 3125/(11*(3 + 5*x)) - (64*log(1 - 2*x))/2033647 + (70752609*log(2 + 3*x))/16807 - (509375*log(3 + 5*x))/121]
    @test_int [1/((1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)^2), x, 2, -9/(35*(2 + 3*x)^5) - 162/(49*(2 + 3*x)^4) - 11457/(343*(2 + 3*x)^3) - 806121/(2401*(2 + 3*x)^2) - 70752609/(16807*(2 + 3*x)) - 15625/(11*(3 + 5*x)) - (128*log(1 - 2*x))/14235529 + (2977686468*log(2 + 3*x))/117649 - (3062500*log(3 + 5*x))/121]

    @test_int [(2 + 3*x)^8/((1 - 2*x)*(3 + 5*x)^3), x, 2, (-62934003*x)/500000 - (9268263*x^2)/100000 - (1535517*x^3)/25000 - (264627*x^4)/10000 - (6561*x^5)/1250 - 1/(8593750*(3 + 5*x)^2) - 266/(47265625*(3 + 5*x)) - (5764801*log(1 - 2*x))/85184 + (31024*log(3 + 5*x))/519921875]
    @test_int [(2 + 3*x)^7/((1 - 2*x)*(3 + 5*x)^3), x, 2, (-339309*x)/10000 - (1044657*x^2)/50000 - (24543*x^3)/2500 - (2187*x^4)/1000 - 1/(1718750*(3 + 5*x)^2) - 233/(9453125*(3 + 5*x)) - (823543*log(1 - 2*x))/42592 + (4667*log(3 + 5*x))/20796875]
    @test_int [(2 + 3*x)^6/((1 - 2*x)*(3 + 5*x)^3), x, 2, (-216999*x)/25000 - (19683*x^2)/5000 - (243*x^3)/250 - 1/(343750*(3 + 5*x)^2) - 8/(75625*(3 + 5*x)) - (117649*log(1 - 2*x))/21296 + (3347*log(3 + 5*x))/4159375]
    @test_int [(2 + 3*x)^5/((1 - 2*x)*(3 + 5*x)^3), x, 2, (-4941*x)/2500 - (243*x^2)/500 - 1/(68750*(3 + 5*x)^2) - 167/(378125*(3 + 5*x)) - (16807*log(1 - 2*x))/10648 + (11224*log(3 + 5*x))/4159375]
    @test_int [(2 + 3*x)^4/((1 - 2*x)*(3 + 5*x)^3), x, 2, (-81*x)/250 - 1/(13750*(3 + 5*x)^2) - 134/(75625*(3 + 5*x)) - (2401*log(1 - 2*x))/5324 + (6802*log(3 + 5*x))/831875]
    @test_int [(2 + 3*x)^3/((1 - 2*x)*(3 + 5*x)^3), x, 2, -1/(2750*(3 + 5*x)^2) - 101/(15125*(3 + 5*x)) - (343*log(1 - 2*x))/2662 + (3469*log(3 + 5*x))/166375]
    @test_int [(2 + 3*x)^2/((1 - 2*x)*(3 + 5*x)^3), x, 2, -1/(550*(3 + 5*x)^2) - 68/(3025*(3 + 5*x)) - (49*log(1 - 2*x))/1331 + (49*log(3 + 5*x))/1331]
    @test_int [(2 + 3*x)/((1 - 2*x)*(3 + 5*x)^3), x, 2, -1/(110*(3 + 5*x)^2) - 7/(121*(3 + 5*x)) - (14*log(1 - 2*x))/1331 + (14*log(3 + 5*x))/1331]
    @test_int [1/((1 - 2*x)*(3 + 5*x)^3), x, 2, -1/(22*(3 + 5*x)^2) - 2/(121*(3 + 5*x)) - (4*log(1 - 2*x))/1331 + (4*log(3 + 5*x))/1331]
    @test_int [1/((1 - 2*x)*(2 + 3*x)*(3 + 5*x)^3), x, 2, -5/(22*(3 + 5*x)^2) + 155/(121*(3 + 5*x)) - (8*log(1 - 2*x))/9317 - (27*log(2 + 3*x))/7 + (5135*log(3 + 5*x))/1331]
    @test_int [1/((1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^3), x, 2, 27/(7*(2 + 3*x)) - 25/(22*(3 + 5*x)^2) + 1600/(121*(3 + 5*x)) - (16*log(1 - 2*x))/65219 - (2889*log(2 + 3*x))/49 + (78475*log(3 + 5*x))/1331]
    @test_int [1/((1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^3), x, 2, 27/(14*(2 + 3*x)^2) + 2889/(49*(2 + 3*x)) - 125/(22*(3 + 5*x)^2) + 12125/(121*(3 + 5*x)) - (32*log(1 - 2*x))/456533 - (204228*log(2 + 3*x))/343 + (792500*log(3 + 5*x))/1331]
    @test_int [1/((1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^3), x, 2, 9/(7*(2 + 3*x)^3) + 2889/(98*(2 + 3*x)^2) + 204228/(343*(2 + 3*x)) - 625/(22*(3 + 5*x)^2) + 81250/(121*(3 + 5*x)) - (64*log(1 - 2*x))/3195731 - (11984706*log(2 + 3*x))/2401 + (6643750*log(3 + 5*x))/1331]
    @test_int [1/((1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)^3), x, 2, 27/(28*(2 + 3*x)^4) + 963/(49*(2 + 3*x)^3) + 102114/(343*(2 + 3*x)^2) + 11984706/(2401*(2 + 3*x)) - 3125/(22*(3 + 5*x)^2) + 509375/(121*(3 + 5*x)) - (128*log(1 - 2*x))/22370117 - (631722537*log(2 + 3*x))/16807 + (50028125*log(3 + 5*x))/1331]

    @test_int [(c + d*x)^4/((a - b*x)*(a + b*x)), x, 2, -((d^2*(6*b^2*c^2 + a^2*d^2)*x)/b^4) - (2*c*d^3*x^2)/b^2 - (d^4*x^3)/(3*b^2) - ((b*c + a*d)^4*log(a - b*x))/(2*a*b^5) + ((b*c - a*d)^4*log(a + b*x))/(2*a*b^5)]
    @test_int [(c + d*x)^3/((a - b*x)*(a + b*x)), x, 2, -((3*c*d^2*x)/b^2) - (d^3*x^2)/(2*b^2) - ((b*c + a*d)^3*log(a - b*x))/(2*a*b^4) + ((b*c - a*d)^3*log(a + b*x))/(2*a*b^4)]
    @test_int [(c + d*x)^2/((a - b*x)*(a + b*x)), x, 2, -((d^2*x)/b^2) - ((b*c + a*d)^2*log(a - b*x))/(2*a*b^3) + ((b*c - a*d)^2*log(a + b*x))/(2*a*b^3)]
    @test_int [(c + d*x)^1/((a - b*x)*(a + b*x)), x, 2, -(((b*c + a*d)*log(a - b*x))/(2*a*b^2)) + ((b*c - a*d)*log(a + b*x))/(2*a*b^2)]
    @test_int [(c + d*x)^0/((a - b*x)*(a + b*x)), x, 2, atanh((b*x)/a)/(a*b)]
    @test_int [1/((a + b*x)*(a - b*x)*(c + d*x)^1), x, 2, -(log(a - b*x)/(2*a*(b*c + a*d))) + log(a + b*x)/(2*a*(b*c - a*d)) - (d*log(c + d*x))/(b^2*c^2 - a^2*d^2)]
    @test_int [1/((a + b*x)*(a - b*x)*(c + d*x)^2), x, 2, d/((b^2*c^2 - a^2*d^2)*(c + d*x)) - (b*log(a - b*x))/(2*a*(b*c + a*d)^2) + (b*log(a + b*x))/(2*a*(b*c - a*d)^2) - (2*b^2*c*d*log(c + d*x))/(b^2*c^2 - a^2*d^2)^2]
    @test_int [1/((a + b*x)*(a - b*x)*(c + d*x)^3), x, 2, d/(2*(b^2*c^2 - a^2*d^2)*(c + d*x)^2) + (2*b^2*c*d)/((b^2*c^2 - a^2*d^2)^2*(c + d*x)) - (b^2*log(a - b*x))/(2*a*(b*c + a*d)^3) + (b^2*log(a + b*x))/(2*a*(b*c - a*d)^3) - (b^2*d*(3*b^2*c^2 + a^2*d^2)*log(c + d*x))/(b^2*c^2 - a^2*d^2)^3]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^n / (e+f*x)^2=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [((2 + 3*x)^8*(3 + 5*x))/(1 - 2*x)^2, x, 2, 63412811/(1024*(1 - 2*x)) + (91609881*x)/256 + (122887143*x^2)/512 + (5892813*x^3)/32 + (32991057*x^4)/256 + (5859459*x^5)/80 + (976617*x^6)/32 + (56862*x^7)/7 + (32805*x^8)/32 + (246239357*log(1 - 2*x))/1024]
    @test_int [((2 + 3*x)^7*(3 + 5*x))/(1 - 2*x)^2, x, 2, 9058973/(512*(1 - 2*x)) + (22333965*x)/256 + (873207*x^2)/16 + (2399985*x^3)/64 + (1423899*x^4)/64 + (793881*x^5)/80 + (11421*x^6)/4 + (10935*x^7)/28 + (15647317*log(1 - 2*x))/256]
    @test_int [((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x)^2, x, 2, 1294139/(256*(1 - 2*x)) + (661617*x)/32 + (1507977*x^2)/128 + (111501*x^3)/16 + (210195*x^4)/64 + (5103*x^5)/5 + (1215*x^6)/8 + (3916031*log(1 - 2*x))/256]
    @test_int [((2 + 3*x)^5*(3 + 5*x))/(1 - 2*x)^2, x, 2, 184877/(128*(1 - 2*x)) + (301467*x)/64 + (75447*x^2)/32 + (18027*x^3)/16 + (2997*x^4)/8 + (243*x^5)/4 + (60025*log(1 - 2*x))/16]
    @test_int [((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x)^2, x, 2, 26411/(64*(1 - 2*x)) + (16203*x)/16 + (13419*x^2)/32 + 144*x^3 + (405*x^4)/16 + (57281*log(1 - 2*x))/64]
    @test_int [((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x)^2, x, 2, 3773/(32*(1 - 2*x)) + (3177*x)/16 + (243*x^2)/4 + (45*x^3)/4 + (3283*log(1 - 2*x))/16]
    @test_int [((2 + 3*x)^2*(3 + 5*x))/(1 - 2*x)^2, x, 2, 539/(16*(1 - 2*x)) + 33*x + (45*x^2)/8 + (707*log(1 - 2*x))/16]
    @test_int [((2 + 3*x)*(3 + 5*x))/(1 - 2*x)^2, x, 2, 77/(8*(1 - 2*x)) + (15*x)/4 + (17*log(1 - 2*x))/2]
    @test_int [(3 + 5*x)/(1 - 2*x)^2, x, 2, 11/(4*(1 - 2*x)) + (5*log(1 - 2*x))/4]
    @test_int [(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)), x, 2, 11/(14*(1 - 2*x)) + log(1 - 2*x)/49 - log(2 + 3*x)/49]
    @test_int [(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^2), x, 2, 11/(49*(1 - 2*x)) + 1/(49*(2 + 3*x)) - (31*log(1 - 2*x))/343 + (31*log(2 + 3*x))/343]
    @test_int [(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^3), x, 2, 22/(343*(1 - 2*x)) + 1/(98*(2 + 3*x)^2) - 31/(343*(2 + 3*x)) - (128*log(1 - 2*x))/2401 + (128*log(2 + 3*x))/2401]
    @test_int [(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^4), x, 2, 44/(2401*(1 - 2*x)) + 1/(147*(2 + 3*x)^3) - 31/(686*(2 + 3*x)^2) - 128/(2401*(2 + 3*x)) - (388*log(1 - 2*x))/16807 + (388*log(2 + 3*x))/16807]
    @test_int [(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^5), x, 2, 88/(16807*(1 - 2*x)) + 1/(196*(2 + 3*x)^4) - 31/(1029*(2 + 3*x)^3) - 64/(2401*(2 + 3*x)^2) - 388/(16807*(2 + 3*x)) - (1040*log(1 - 2*x))/117649 + (1040*log(2 + 3*x))/117649]
    @test_int [(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^6), x, 2, 176/(117649*(1 - 2*x)) + 1/(245*(2 + 3*x)^5) - 31/(1372*(2 + 3*x)^4) - 128/(7203*(2 + 3*x)^3) - 194/(16807*(2 + 3*x)^2) - 1040/(117649*(2 + 3*x)) - (2608*log(1 - 2*x))/823543 + (2608*log(2 + 3*x))/823543]
    @test_int [(3 + 5*x)/((1 - 2*x)^2*(2 + 3*x)^7), x, 2, 352/(823543*(1 - 2*x)) + 1/(294*(2 + 3*x)^6) - 31/(1715*(2 + 3*x)^5) - 32/(2401*(2 + 3*x)^4) - 388/(50421*(2 + 3*x)^3) - 520/(117649*(2 + 3*x)^2) - 2608/(823543*(2 + 3*x)) - (128*log(1 - 2*x))/117649 + (128*log(2 + 3*x))/117649]

    @test_int [((2 + 3*x)^8*(3 + 5*x)^2)/(1 - 2*x)^2, x, 2, 697540921/(2048*(1 - 2*x)) + (2330515357*x)/1024 + (413355417*x^2)/256 + (346239417*x^3)/256 + (275757561*x^4)/256 + (235268793*x^5)/320 + 396738*x^6 + (17378631*x^7)/112 + (1235655*x^8)/32 + (18225*x^9)/4 + (1512848491*log(1 - 2*x))/1024]
    @test_int [((2 + 3*x)^7*(3 + 5*x)^2)/(1 - 2*x)^2, x, 2, 99648703/(1024*(1 - 2*x)) + (9077405*x)/16 + (195497697*x^2)/512 + (18842715*x^3)/64 + (53086563*x^4)/256 + (4750569*x^5)/40 + (1597239*x^6)/32 + (375435*x^7)/28 + (54675*x^8)/32 + (389535839*log(1 - 2*x))/1024]
    @test_int [((2 + 3*x)^6*(3 + 5*x)^2)/(1 - 2*x)^2, x, 2, 14235529/(512*(1 - 2*x)) + (35458963*x)/256 + (11140101*x^2)/128 + (3851307*x^3)/64 + (575775*x^4)/16 + (1295919*x^5)/80 + (37665*x^6)/8 + (18225*x^7)/28 + (12386759*log(1 - 2*x))/128]
    @test_int [((2 + 3*x)^5*(3 + 5*x)^2)/(1 - 2*x)^2, x, 2, 2033647/(256*(1 - 2*x)) + (2104901*x)/64 + (2412699*x^2)/128 + (89913*x^3)/8 + (342333*x^4)/64 + (6723*x^5)/4 + (2025*x^6)/8 + (6206585*log(1 - 2*x))/256]
    @test_int [((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^2, x, 2, 290521/(128*(1 - 2*x)) + (480841*x)/64 + (15159*x^2)/4 + (29277*x^3)/16 + (9855*x^4)/16 + (405*x^5)/4 + (381073*log(1 - 2*x))/64]
    @test_int [((2 + 3*x)^3*(3 + 5*x)^2)/(1 - 2*x)^2, x, 2, 41503/(64*(1 - 2*x)) + (12973*x)/8 + (21717*x^2)/32 + (945*x^3)/4 + (675*x^4)/16 + (91091*log(1 - 2*x))/64]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x)^2, x, 2, 5929/(32*(1 - 2*x)) + (5119*x)/16 + (795*x^2)/8 + (75*x^3)/4 + (1309*log(1 - 2*x))/4]
    @test_int [((2 + 3*x)*(3 + 5*x)^2)/(1 - 2*x)^2, x, 2, 847/(16*(1 - 2*x)) + (215*x)/4 + (75*x^2)/8 + (1133*log(1 - 2*x))/16]
    @test_int [(3 + 5*x)^2/(1 - 2*x)^2, x, 2, 121/(8*(1 - 2*x)) + (25*x)/4 + (55*log(1 - 2*x))/4]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)), x, 2, 121/(28*(1 - 2*x)) + (407*log(1 - 2*x))/196 + log(2 + 3*x)/147]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^2), x, 2, 121/(98*(1 - 2*x)) - 1/(147*(2 + 3*x)) + (22*log(1 - 2*x))/343 - (22*log(2 + 3*x))/343]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^3), x, 2, 121/(343*(1 - 2*x)) - 1/(294*(2 + 3*x)^2) + 22/(343*(2 + 3*x)) - (319*log(1 - 2*x))/2401 + (319*log(2 + 3*x))/2401]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^4), x, 2, 242/(2401*(1 - 2*x)) - 1/(441*(2 + 3*x)^3) + 11/(343*(2 + 3*x)^2) - 319/(2401*(2 + 3*x)) - (1364*log(1 - 2*x))/16807 + (1364*log(2 + 3*x))/16807]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^5), x, 2, 484/(16807*(1 - 2*x)) - 1/(588*(2 + 3*x)^4) + 22/(1029*(2 + 3*x)^3) - 319/(4802*(2 + 3*x)^2) - 1364/(16807*(2 + 3*x)) - (4180*log(1 - 2*x))/117649 + (4180*log(2 + 3*x))/117649]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^6), x, 2, 968/(117649*(1 - 2*x)) - 1/(735*(2 + 3*x)^5) + 11/(686*(2 + 3*x)^4) - 319/(7203*(2 + 3*x)^3) - 682/(16807*(2 + 3*x)^2) - 4180/(117649*(2 + 3*x)) - (11264*log(1 - 2*x))/823543 + (11264*log(2 + 3*x))/823543]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^7), x, 2, 1936/(823543*(1 - 2*x)) - 1/(882*(2 + 3*x)^6) + 22/(1715*(2 + 3*x)^5) - 319/(9604*(2 + 3*x)^4) - 1364/(50421*(2 + 3*x)^3) - 2090/(117649*(2 + 3*x)^2) - 11264/(823543*(2 + 3*x)) - (4048*log(1 - 2*x))/823543 + (4048*log(2 + 3*x))/823543]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^8), x, 2, 3872/(5764801*(1 - 2*x)) - 1/(1029*(2 + 3*x)^7) + 11/(1029*(2 + 3*x)^6) - 319/(12005*(2 + 3*x)^5) - 341/(16807*(2 + 3*x)^4) - 4180/(352947*(2 + 3*x)^3) - 5632/(823543*(2 + 3*x)^2) - 4048/(823543*(2 + 3*x)) - (68288*log(1 - 2*x))/40353607 + (68288*log(2 + 3*x))/40353607]

    @test_int [((2 + 3*x)^8*(3 + 5*x)^3)/(1 - 2*x)^2, x, 2, 7672950131/(4096*(1 - 2*x)) + (7277894263*x)/512 + (21573106793*x^2)/2048 + (2416569641*x^3)/256 + (8502681987*x^4)/1024 + (260574273*x^5)/40 + (544462047*x^6)/128 + (242570133*x^7)/112 + (101721015*x^8)/128 + (370575*x^9)/2 + (164025*x^10)/8 + (36770371407*log(1 - 2*x))/4096]
    @test_int [((2 + 3*x)^7*(3 + 5*x)^3)/(1 - 2*x)^2, x, 2, 1096135733/(2048*(1 - 2*x)) + (3690540955*x)/1024 + (1312685491*x^2)/512 + (551942075*x^3)/256 + (220950207*x^4)/128 + (379446471*x^5)/320 + (20626947*x^6)/32 + (28463805*x^7)/112 + (127575*x^8)/2 + (30375*x^9)/4 + (298946109*log(1 - 2*x))/128]
    @test_int [((2 + 3*x)^6*(3 + 5*x)^3)/(1 - 2*x)^2, x, 2, 156590819/(1024*(1 - 2*x)) + (230244479*x)/256 + (310976027*x^2)/512 + (7530189*x^3)/16 + (85406805*x^4)/256 + (15403257*x^5)/80 + (2611845*x^6)/32 + (309825*x^7)/14 + (91125*x^8)/32 + (616195041*log(1 - 2*x))/1024]
    @test_int [((2 + 3*x)^5*(3 + 5*x)^3)/(1 - 2*x)^2, x, 2, 22370117/(512*(1 - 2*x)) + (56291737*x)/256 + (8881301*x^2)/64 + (6179077*x^3)/64 + (3724389*x^4)/64 + (423009*x^5)/16 + (15525*x^6)/2 + (30375*x^7)/28 + (39220335*log(1 - 2*x))/256]
    @test_int [((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x)^2, x, 2, 3195731/(256*(1 - 2*x)) + (209243*x)/4 + (3859469*x^2)/128 + (289951*x^3)/16 + (557415*x^4)/64 + (5535*x^5)/2 + (3375*x^6)/8 + (9836211*log(1 - 2*x))/256]
    @test_int [((2 + 3*x)^3*(3 + 5*x)^3)/(1 - 2*x)^2, x, 2, 456533/(128*(1 - 2*x)) + (766807*x)/64 + (194881*x^2)/32 + (47535*x^3)/16 + (2025*x^4)/2 + (675*x^5)/4 + (302379*log(1 - 2*x))/32]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^3)/(1 - 2*x)^2, x, 2, 65219/(64*(1 - 2*x)) + (41537*x)/16 + (35135*x^2)/32 + (775*x^3)/2 + (1125*x^4)/16 + (144837*log(1 - 2*x))/64]
    @test_int [((2 + 3*x)*(3 + 5*x)^3)/(1 - 2*x)^2, x, 2, 9317/(32*(1 - 2*x)) + (8245*x)/16 + (325*x^2)/2 + (125*x^3)/4 + (8349*log(1 - 2*x))/16]
    @test_int [(3 + 5*x)^3/(1 - 2*x)^2, x, 2, 1331/(16*(1 - 2*x)) + (175*x)/2 + (125*x^2)/8 + (1815*log(1 - 2*x))/16]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)), x, 2, 1331/(56*(1 - 2*x)) + (125*x)/12 + (1089*log(1 - 2*x))/49 - log(2 + 3*x)/441]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^2), x, 2, 1331/(196*(1 - 2*x)) + 1/(441*(2 + 3*x)) + (4719*log(1 - 2*x))/1372 + (101*log(2 + 3*x))/3087]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^3), x, 2, 1331/(686*(1 - 2*x)) + 1/(882*(2 + 3*x)^2) - 101/(3087*(2 + 3*x)) + (363*log(1 - 2*x))/2401 - (363*log(2 + 3*x))/2401]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^4), x, 2, 1331/(2401*(1 - 2*x)) + 1/(1323*(2 + 3*x)^3) - 101/(6174*(2 + 3*x)^2) + 363/(2401*(2 + 3*x)) - (3267*log(1 - 2*x))/16807 + (3267*log(2 + 3*x))/16807]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^5), x, 2, 2662/(16807*(1 - 2*x)) + 1/(1764*(2 + 3*x)^4) - 101/(9261*(2 + 3*x)^3) + 363/(4802*(2 + 3*x)^2) - 3267/(16807*(2 + 3*x)) - (14520*log(1 - 2*x))/117649 + (14520*log(2 + 3*x))/117649]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^6), x, 2, 5324/(117649*(1 - 2*x)) + 1/(2205*(2 + 3*x)^5) - 101/(12348*(2 + 3*x)^4) + 121/(2401*(2 + 3*x)^3) - 3267/(33614*(2 + 3*x)^2) - 14520/(117649*(2 + 3*x)) - (45012*log(1 - 2*x))/823543 + (45012*log(2 + 3*x))/823543]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^7), x, 2, 10648/(823543*(1 - 2*x)) + 1/(2646*(2 + 3*x)^6) - 101/(15435*(2 + 3*x)^5) + 363/(9604*(2 + 3*x)^4) - 1089/(16807*(2 + 3*x)^3) - 7260/(117649*(2 + 3*x)^2) - 45012/(823543*(2 + 3*x)) - (17424*log(1 - 2*x))/823543 + (17424*log(2 + 3*x))/823543]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^2*(2 + 3*x)^8), x, 2, 21296/(5764801*(1 - 2*x)) + 1/(3087*(2 + 3*x)^7) - 101/(18522*(2 + 3*x)^6) + 363/(12005*(2 + 3*x)^5) - 3267/(67228*(2 + 3*x)^4) - 4840/(117649*(2 + 3*x)^3) - 22506/(823543*(2 + 3*x)^2) - 17424/(823543*(2 + 3*x)) - (307824*log(1 - 2*x))/40353607 + (307824*log(2 + 3*x))/40353607]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(2 + 3*x)^8/((1 - 2*x)^2*(3 + 5*x)), x, 2, 5764801/(2816*(1 - 2*x)) + (2041906293*x)/250000 + (1839811401*x^2)/400000 + (26773659*x^3)/10000 + (9899091*x^4)/8000 + (94041*x^5)/250 + (2187*x^6)/40 + (188591347*log(1 - 2*x))/30976 + log(3 + 5*x)/9453125]
    @test_int [(2 + 3*x)^7/((1 - 2*x)^2*(3 + 5*x)), x, 2, 823543/(1408*(1 - 2*x)) + (370109547*x)/200000 + (18237069*x^2)/20000 + (853659*x^3)/2000 + (13851*x^4)/100 + (2187*x^5)/100 + (5764801*log(1 - 2*x))/3872 + log(3 + 5*x)/1890625]
    @test_int [(2 + 3*x)^6/((1 - 2*x)^2*(3 + 5*x)), x, 2, 117649/(704*(1 - 2*x)) + (3946293*x)/10000 + (639819*x^2)/4000 + (2673*x^3)/50 + (729*x^4)/80 + (2739541*log(1 - 2*x))/7744 + log(3 + 5*x)/378125]
    @test_int [(2 + 3*x)^5/((1 - 2*x)^2*(3 + 5*x)), x, 2, 16807/(352*(1 - 2*x)) + (152793*x)/2000 + (567*x^2)/25 + (81*x^3)/20 + (156065*log(1 - 2*x))/1936 + log(3 + 5*x)/75625]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^2*(3 + 5*x)), x, 2, 2401/(176*(1 - 2*x)) + (621*x)/50 + (81*x^2)/40 + (33271*log(1 - 2*x))/1936 + log(3 + 5*x)/15125]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^2*(3 + 5*x)), x, 2, 343/(88*(1 - 2*x)) + (27*x)/20 + (392*log(1 - 2*x))/121 + log(3 + 5*x)/3025]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^2*(3 + 5*x)), x, 2, 49/(44*(1 - 2*x)) + (217*log(1 - 2*x))/484 + log(3 + 5*x)/605]
    @test_int [(2 + 3*x)/((1 - 2*x)^2*(3 + 5*x)), x, 2, 7/(22*(1 - 2*x)) - log(1 - 2*x)/121 + log(3 + 5*x)/121]
    @test_int [1/((1 - 2*x)^2*(3 + 5*x)), x, 2, 1/(11*(1 - 2*x)) - (5*log(1 - 2*x))/121 + (5*log(3 + 5*x))/121]
    @test_int [1/((1 - 2*x)^2*(2 + 3*x)*(3 + 5*x)), x, 2, 2/(77*(1 - 2*x)) - (136*log(1 - 2*x))/5929 - (9*log(2 + 3*x))/49 + (25*log(3 + 5*x))/121]
    @test_int [1/((1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x)), x, 2, 4/(539*(1 - 2*x)) + 9/(49*(2 + 3*x)) - (404*log(1 - 2*x))/41503 - (351*log(2 + 3*x))/343 + (125*log(3 + 5*x))/121]
    @test_int [1/((1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x)), x, 2, 8/(3773*(1 - 2*x)) + 9/(98*(2 + 3*x)^2) + 351/(343*(2 + 3*x)) - (1072*log(1 - 2*x))/290521 - (12393*log(2 + 3*x))/2401 + (625*log(3 + 5*x))/121]
    @test_int [1/((1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)), x, 2, 16/(26411*(1 - 2*x)) + 3/(49*(2 + 3*x)^3) + 351/(686*(2 + 3*x)^2) + 12393/(2401*(2 + 3*x)) - (2672*log(1 - 2*x))/2033647 - (434043*log(2 + 3*x))/16807 + (3125*log(3 + 5*x))/121]
    @test_int [1/((1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x)), x, 2, 32/(184877*(1 - 2*x)) + 9/(196*(2 + 3*x)^4) + 117/(343*(2 + 3*x)^3) + 12393/(4802*(2 + 3*x)^2) + 434043/(16807*(2 + 3*x)) - (6400*log(1 - 2*x))/14235529 - (15192225*log(2 + 3*x))/117649 + (15625*log(3 + 5*x))/121]
    @test_int [1/((1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x)), x, 2, 64/(1294139*(1 - 2*x)) + 9/(245*(2 + 3*x)^5) + 351/(1372*(2 + 3*x)^4) + 4131/(2401*(2 + 3*x)^3) + 434043/(33614*(2 + 3*x)^2) + 15192225/(117649*(2 + 3*x)) - (14912*log(1 - 2*x))/99648703 - (531729603*log(2 + 3*x))/823543 + (78125*log(3 + 5*x))/121]

    @test_int [(2 + 3*x)^8/((1 - 2*x)^2*(3 + 5*x)^2), x, 2, 5764801/(15488*(1 - 2*x)) + (231915717*x)/200000 + (14171517*x^2)/25000 + (2626101*x^3)/10000 + (168399*x^4)/2000 + (6561*x^5)/500 - 1/(9453125*(3 + 5*x)) + (79883671*log(1 - 2*x))/85184 + (268*log(3 + 5*x))/103984375]
    @test_int [(2 + 3*x)^7/((1 - 2*x)^2*(3 + 5*x)^2), x, 2, 823543/(7744*(1 - 2*x)) + (6156243*x)/25000 + (1974861*x^2)/20000 + (16281*x^3)/500 + (2187*x^4)/400 - 1/(1890625*(3 + 5*x)) + (18941489*log(1 - 2*x))/85184 + (47*log(3 + 5*x))/4159375]
    @test_int [(2 + 3*x)^6/((1 - 2*x)^2*(3 + 5*x)^2), x, 2, 117649/(3872*(1 - 2*x)) + (473607*x)/10000 + (13851*x^2)/1000 + (243*x^3)/100 - 1/(378125*(3 + 5*x)) + (67228*log(1 - 2*x))/1331 + (202*log(3 + 5*x))/4159375]
    @test_int [(2 + 3*x)^5/((1 - 2*x)^2*(3 + 5*x)^2), x, 2, 16807/(1936*(1 - 2*x)) + (3807*x)/500 + (243*x^2)/200 - 1/(75625*(3 + 5*x)) + (228095*log(1 - 2*x))/21296 + (169*log(3 + 5*x))/831875]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^2*(3 + 5*x)^2), x, 2, 2401/(968*(1 - 2*x)) + (81*x)/100 - 1/(15125*(3 + 5*x)) + (10633*log(1 - 2*x))/5324 + (136*log(3 + 5*x))/166375]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^2*(3 + 5*x)^2), x, 2, 343/(484*(1 - 2*x)) - 1/(3025*(3 + 5*x)) + (1421*log(1 - 2*x))/5324 + (103*log(3 + 5*x))/33275]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^2*(3 + 5*x)^2), x, 2, 49/(242*(1 - 2*x)) - 1/(605*(3 + 5*x)) - (14*log(1 - 2*x))/1331 + (14*log(3 + 5*x))/1331]
    @test_int [(2 + 3*x)/((1 - 2*x)^2*(3 + 5*x)^2), x, 2, 7/(121*(1 - 2*x)) - 1/(121*(3 + 5*x)) - (37*log(1 - 2*x))/1331 + (37*log(3 + 5*x))/1331]
    @test_int [1/((1 - 2*x)^2*(3 + 5*x)^2), x, 2, 2/(121*(1 - 2*x)) - 5/(121*(3 + 5*x)) - (20*log(1 - 2*x))/1331 + (20*log(3 + 5*x))/1331]
    @test_int [1/((1 - 2*x)^2*(2 + 3*x)*(3 + 5*x)^2), x, 2, 4/(847*(1 - 2*x)) - 25/(121*(3 + 5*x)) - (412*log(1 - 2*x))/65219 + (27*log(2 + 3*x))/49 - (725*log(3 + 5*x))/1331]
    @test_int [1/((1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x)^2), x, 2, 8/(5929*(1 - 2*x)) - 27/(49*(2 + 3*x)) - 125/(121*(3 + 5*x)) - (1088*log(1 - 2*x))/456533 + (1998*log(2 + 3*x))/343 - (7750*log(3 + 5*x))/1331]
    @test_int [1/((1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x)^2), x, 2, 16/(41503*(1 - 2*x)) - 27/(98*(2 + 3*x)^2) - 1998/(343*(2 + 3*x)) - 625/(121*(3 + 5*x)) - (2704*log(1 - 2*x))/3195731 + (107109*log(2 + 3*x))/2401 - (59375*log(3 + 5*x))/1331]
    @test_int [1/((1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^2), x, 2, 32/(290521*(1 - 2*x)) - 9/(49*(2 + 3*x)^3) - 999/(343*(2 + 3*x)^2) - 107109/(2401*(2 + 3*x)) - 3125/(121*(3 + 5*x)) - (6464*log(1 - 2*x))/22370117 + (5050944*log(2 + 3*x))/16807 - (400000*log(3 + 5*x))/1331]
    @test_int [1/((1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x)^2), x, 2, 64/(2033647*(1 - 2*x)) - 27/(196*(2 + 3*x)^4) - 666/(343*(2 + 3*x)^3) - 107109/(4802*(2 + 3*x)^2) - 5050944/(16807*(2 + 3*x)) - 15625/(121*(3 + 5*x)) - (15040*log(1 - 2*x))/156590819 + (222359715*log(2 + 3*x))/117649 - (2515625*log(3 + 5*x))/1331]

    @test_int [(2 + 3*x)^8/((1 - 2*x)^2*(3 + 5*x)^3), x, 2, 5764801/(85184*(1 - 2*x)) + (7680987*x)/50000 + (6093711*x^2)/100000 + (12393*x^3)/625 + (6561*x^4)/2000 - 1/(18906250*(3 + 5*x)^2) - 268/(103984375*(3 + 5*x)) + (130943337*log(1 - 2*x))/937024 + (6312*log(3 + 5*x))/228765625]
    @test_int [(2 + 3*x)^7/((1 - 2*x)^2*(3 + 5*x)^3), x, 2, 823543/(42592*(1 - 2*x)) + (1467477*x)/50000 + (21141*x^2)/2500 + (729*x^3)/500 - 1/(3781250*(3 + 5*x)^2) - 47/(4159375*(3 + 5*x)) + (7411887*log(1 - 2*x))/234256 + (4761*log(3 + 5*x))/45753125]
    @test_int [(2 + 3*x)^6/((1 - 2*x)^2*(3 + 5*x)^3), x, 2, 117649/(21296*(1 - 2*x)) + (2916*x)/625 + (729*x^2)/1000 - 1/(756250*(3 + 5*x)^2) - 202/(4159375*(3 + 5*x)) + (1563051*log(1 - 2*x))/234256 + (17139*log(3 + 5*x))/45753125]
    @test_int [(2 + 3*x)^5/((1 - 2*x)^2*(3 + 5*x)^3), x, 2, 16807/(10648*(1 - 2*x)) + (243*x)/500 - 1/(151250*(3 + 5*x)^2) - 169/(831875*(3 + 5*x)) + (36015*log(1 - 2*x))/29282 + (11562*log(3 + 5*x))/9150625]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^2*(3 + 5*x)^3), x, 2, 2401/(5324*(1 - 2*x)) - 1/(30250*(3 + 5*x)^2) - 136/(166375*(3 + 5*x)) + (9261*log(1 - 2*x))/58564 + (7074*log(3 + 5*x))/1830125]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^2*(3 + 5*x)^3), x, 2, 343/(2662*(1 - 2*x)) - 1/(6050*(3 + 5*x)^2) - 103/(33275*(3 + 5*x)) - (147*log(1 - 2*x))/14641 + (147*log(3 + 5*x))/14641]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^2*(3 + 5*x)^3), x, 2, 49/(1331*(1 - 2*x)) - 1/(1210*(3 + 5*x)^2) - 14/(1331*(3 + 5*x)) - (273*log(1 - 2*x))/14641 + (273*log(3 + 5*x))/14641]
    @test_int [(2 + 3*x)/((1 - 2*x)^2*(3 + 5*x)^3), x, 2, 14/(1331*(1 - 2*x)) - 1/(242*(3 + 5*x)^2) - 37/(1331*(3 + 5*x)) - (144*log(1 - 2*x))/14641 + (144*log(3 + 5*x))/14641]
    @test_int [1/((1 - 2*x)^2*(3 + 5*x)^3), x, 2, 4/(1331*(1 - 2*x)) - 5/(242*(3 + 5*x)^2) - 20/(1331*(3 + 5*x)) - (60*log(1 - 2*x))/14641 + (60*log(3 + 5*x))/14641]
    @test_int [1/((1 - 2*x)^2*(2 + 3*x)*(3 + 5*x)^3), x, 2, 8/(9317*(1 - 2*x)) - 25/(242*(3 + 5*x)^2) + 725/(1331*(3 + 5*x)) - (1104*log(1 - 2*x))/717409 - (81*log(2 + 3*x))/49 + (24225*log(3 + 5*x))/14641]
    @test_int [1/((1 - 2*x)^2*(2 + 3*x)^2*(3 + 5*x)^3), x, 2, 16/(65219*(1 - 2*x)) + 81/(49*(2 + 3*x)) - 125/(242*(3 + 5*x)^2) + 7750/(1331*(3 + 5*x)) - (2736*log(1 - 2*x))/5021863 - (8829*log(2 + 3*x))/343 + (376875*log(3 + 5*x))/14641]
    @test_int [1/((1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x)^3), x, 2, 32/(456533*(1 - 2*x)) + 81/(98*(2 + 3*x)^2) + 8829/(343*(2 + 3*x)) - 625/(242*(3 + 5*x)^2) + 59375/(1331*(3 + 5*x)) - (6528*log(1 - 2*x))/35153041 - (630342*log(2 + 3*x))/2401 + (3843750*log(3 + 5*x))/14641]
    @test_int [1/((1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^3), x, 2, 64/(3195731*(1 - 2*x)) + 27/(49*(2 + 3*x)^3) + 8829/(686*(2 + 3*x)^2) + 630342/(2401*(2 + 3*x)) - 3125/(242*(3 + 5*x)^2) + 400000/(1331*(3 + 5*x)) - (15168*log(1 - 2*x))/246071287 - (37214802*log(2 + 3*x))/16807 + (32418750*log(3 + 5*x))/14641]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^n / (e+f*x)^3=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [((2 + 3*x)^8*(3 + 5*x))/(1 - 2*x)^3, x, 2, 63412811/(2048*(1 - 2*x)^2) - 246239357/(1024*(1 - 2*x)) - (120864213*x)/256 - (118841283*x^2)/512 - (16042509*x^3)/128 - (7568235*x^4)/128 - (213597*x^5)/10 - (162567*x^6)/32 - (32805*x^7)/56 - (106237047*log(1 - 2*x))/256]
    @test_int [((2 + 3*x)^7*(3 + 5*x))/(1 - 2*x)^3, x, 2, 9058973/(1024*(1 - 2*x)^2) - 15647317/(256*(1 - 2*x)) - (24960933*x)/256 - (10989621*x^2)/256 - (631611*x^3)/32 - (235467*x^4)/32 - (147987*x^5)/80 - (3645*x^6)/16 - (23647449*log(1 - 2*x))/256]
    @test_int [((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x)^3, x, 2, 1294139/(512*(1 - 2*x)^2) - 3916031/(256*(1 - 2*x)) - (2431647*x)/128 - (461835*x^2)/64 - (10611*x^3)/4 - (44469*x^4)/64 - (729*x^5)/8 - (5078115*log(1 - 2*x))/256]
    @test_int [((2 + 3*x)^5*(3 + 5*x))/(1 - 2*x)^3, x, 2, 184877/(256*(1 - 2*x)^2) - 60025/(16*(1 - 2*x)) - (109089*x)/32 - (16821*x^2)/16 - (4401*x^3)/16 - (1215*x^4)/32 - (519645*log(1 - 2*x))/128]
    @test_int [((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x)^3, x, 2, 26411/(128*(1 - 2*x)^2) - 57281/(64*(1 - 2*x)) - 540*x - (3861*x^2)/32 - (135*x^3)/8 - (24843*log(1 - 2*x))/32]
    @test_int [((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x)^3, x, 2, 3773/(64*(1 - 2*x)^2) - 3283/(16*(1 - 2*x)) - (1107*x)/16 - (135*x^2)/16 - (1071*log(1 - 2*x))/8]
    @test_int [((2 + 3*x)^2*(3 + 5*x))/(1 - 2*x)^3, x, 2, 539/(32*(1 - 2*x)^2) - 707/(16*(1 - 2*x)) - (45*x)/8 - (309*log(1 - 2*x))/16]
    @test_int [((2 + 3*x)*(3 + 5*x))/(1 - 2*x)^3, x, 2, 77/(16*(1 - 2*x)^2) - 17/(2*(1 - 2*x)) - (15*log(1 - 2*x))/8]
    @test_int [(3 + 5*x)/(1 - 2*x)^3, x, 1, (3 + 5*x)^2/(22*(1 - 2*x)^2)]
    @test_int [(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)), x, 2, 11/(28*(1 - 2*x)^2) - 1/(49*(1 - 2*x)) + (3*log(1 - 2*x))/343 - (3*log(2 + 3*x))/343]
    @test_int [(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)^2), x, 2, 11/(98*(1 - 2*x)^2) + 31/(343*(1 - 2*x)) + 3/(343*(2 + 3*x)) - (87*log(1 - 2*x))/2401 + (87*log(2 + 3*x))/2401]
    @test_int [(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)^3), x, 2, 11/(343*(1 - 2*x)^2) + 128/(2401*(1 - 2*x)) + 3/(686*(2 + 3*x)^2) - 87/(2401*(2 + 3*x)) - (558*log(1 - 2*x))/16807 + (558*log(2 + 3*x))/16807]
    @test_int [(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)^4), x, 2, 22/(2401*(1 - 2*x)^2) + 388/(16807*(1 - 2*x)) + 1/(343*(2 + 3*x)^3) - 87/(4802*(2 + 3*x)^2) - 558/(16807*(2 + 3*x)) - (2280*log(1 - 2*x))/117649 + (2280*log(2 + 3*x))/117649]
    @test_int [(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)^5), x, 2, 44/(16807*(1 - 2*x)^2) + 1040/(117649*(1 - 2*x)) + 3/(1372*(2 + 3*x)^4) - 29/(2401*(2 + 3*x)^3) - 279/(16807*(2 + 3*x)^2) - 2280/(117649*(2 + 3*x)) - (7680*log(1 - 2*x))/823543 + (7680*log(2 + 3*x))/823543]
    @test_int [(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)^6), x, 2, 88/(117649*(1 - 2*x)^2) + 2608/(823543*(1 - 2*x)) + 3/(1715*(2 + 3*x)^5) - 87/(9604*(2 + 3*x)^4) - 186/(16807*(2 + 3*x)^3) - 1140/(117649*(2 + 3*x)^2) - 7680/(823543*(2 + 3*x)) - (3312*log(1 - 2*x))/823543 + (3312*log(2 + 3*x))/823543]

    @test_int [((2 + 3*x)^7*(3 + 5*x)^2)/(1 - 2*x)^3, x, 2, 99648703/(2048*(1 - 2*x)^2) - 389535839/(1024*(1 - 2*x)) - (48280011*x)/64 - (190742391*x^2)/512 - (25895367*x^3)/128 - (12299769*x^4)/128 - (2798631*x^5)/80 - (268515*x^6)/32 - (54675*x^7)/56 - (84589631*log(1 - 2*x))/128]
    @test_int [((2 + 3*x)^6*(3 + 5*x)^2)/(1 - 2*x)^3, x, 2, 14235529/(1024*(1 - 2*x)^2) - 12386759/(128*(1 - 2*x)) - (39980457*x)/256 - (17700255*x^2)/256 - (1024389*x^3)/32 - (770067*x^4)/64 - (48843*x^5)/16 - (6075*x^6)/16 - (18859855*log(1 - 2*x))/128]
    @test_int [((2 + 3*x)^5*(3 + 5*x)^2)/(1 - 2*x)^3, x, 2, 2033647/(512*(1 - 2*x)^2) - 6206585/(256*(1 - 2*x)) - (3907293*x)/128 - (747297*x^2)/64 - (69273*x^3)/16 - (73305*x^4)/64 - (1215*x^5)/8 - (8117095*log(1 - 2*x))/256]
    @test_int [((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^3, x, 2, 290521/(256*(1 - 2*x)^2) - 381073/(64*(1 - 2*x)) - (176055*x)/32 - (54783*x^2)/32 - (7245*x^3)/16 - (2025*x^4)/32 - (832951*log(1 - 2*x))/128]
    @test_int [((2 + 3*x)^3*(3 + 5*x)^2)/(1 - 2*x)^3, x, 2, 41503/(128*(1 - 2*x)^2) - 91091/(64*(1 - 2*x)) - (14031*x)/16 - (6345*x^2)/32 - (225*x^3)/8 - (39977*log(1 - 2*x))/32]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x)^3, x, 2, 5929/(64*(1 - 2*x)^2) - 1309/(4*(1 - 2*x)) - (1815*x)/16 - (225*x^2)/16 - (3467*log(1 - 2*x))/16]
    @test_int [((2 + 3*x)*(3 + 5*x)^2)/(1 - 2*x)^3, x, 2, 847/(32*(1 - 2*x)^2) - 1133/(16*(1 - 2*x)) - (75*x)/8 - (505*log(1 - 2*x))/16]
    @test_int [(3 + 5*x)^2/(1 - 2*x)^3, x, 2, 121/(16*(1 - 2*x)^2) - 55/(4*(1 - 2*x)) - (25*log(1 - 2*x))/8]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)), x, 2, 121/(56*(1 - 2*x)^2) - 407/(196*(1 - 2*x)) - log(1 - 2*x)/343 + log(2 + 3*x)/343]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^2), x, 2, 121/(196*(1 - 2*x)^2) - 22/(343*(1 - 2*x)) - 1/(343*(2 + 3*x)) + (64*log(1 - 2*x))/2401 - (64*log(2 + 3*x))/2401]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^3), x, 2, 121/(686*(1 - 2*x)^2) + 319/(2401*(1 - 2*x)) - 1/(686*(2 + 3*x)^2) + 64/(2401*(2 + 3*x)) - (829*log(1 - 2*x))/16807 + (829*log(2 + 3*x))/16807]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^4), x, 2, 121/(2401*(1 - 2*x)^2) + 1364/(16807*(1 - 2*x)) - 1/(1029*(2 + 3*x)^3) + 32/(2401*(2 + 3*x)^2) - 829/(16807*(2 + 3*x)) - (5750*log(1 - 2*x))/117649 + (5750*log(2 + 3*x))/117649]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^5), x, 2, 242/(16807*(1 - 2*x)^2) + 4180/(117649*(1 - 2*x)) - 1/(1372*(2 + 3*x)^4) + 64/(7203*(2 + 3*x)^3) - 829/(33614*(2 + 3*x)^2) - 5750/(117649*(2 + 3*x)) - (24040*log(1 - 2*x))/823543 + (24040*log(2 + 3*x))/823543]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^6), x, 2, 484/(117649*(1 - 2*x)^2) + 11264/(823543*(1 - 2*x)) - 1/(1715*(2 + 3*x)^5) + 16/(2401*(2 + 3*x)^4) - 829/(50421*(2 + 3*x)^3) - 2875/(117649*(2 + 3*x)^2) - 24040/(823543*(2 + 3*x)) - (11696*log(1 - 2*x))/823543 + (11696*log(2 + 3*x))/823543]

    @test_int [((2 + 3*x)^6*(3 + 5*x)^3)/(1 - 2*x)^3, x, 2, 156590819/(2048*(1 - 2*x)^2) - 616195041/(1024*(1 - 2*x)) - (308539921*x)/256 - (306103815*x^2)/512 - (41793093*x^3)/128 - (19986237*x^4)/128 - (229149*x^5)/4 - (443475*x^6)/32 - (91125*x^7)/56 - (33674025*log(1 - 2*x))/32]
    @test_int [((2 + 3*x)^5*(3 + 5*x)^3)/(1 - 2*x)^3, x, 2, 22370117/(1024*(1 - 2*x)^2) - 39220335/(256*(1 - 2*x)) - (64029233*x)/256 - (28504029*x^2)/256 - (1661133*x^3)/32 - (629505*x^4)/32 - (80595*x^5)/16 - (10125*x^6)/16 - (60160485*log(1 - 2*x))/256]
    @test_int [((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x)^3, x, 2, 3195731/(512*(1 - 2*x)^2) - 9836211/(256*(1 - 2*x)) - (6277415*x)/128 - (1208973*x^2)/64 - 7065*x^3 - (120825*x^4)/64 - (2025*x^5)/8 - (12973191*log(1 - 2*x))/256]
    @test_int [((2 + 3*x)^3*(3 + 5*x)^3)/(1 - 2*x)^3, x, 2, 456533/(256*(1 - 2*x)^2) - 302379/(32*(1 - 2*x)) - (284071*x)/32 - (44595*x^2)/16 - (11925*x^3)/16 - (3375*x^4)/32 - (1334949*log(1 - 2*x))/128]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^3)/(1 - 2*x)^3, x, 2, 65219/(128*(1 - 2*x)^2) - 144837/(64*(1 - 2*x)) - (5695*x)/4 - (10425*x^2)/32 - (375*x^3)/8 - (64317*log(1 - 2*x))/32]
    @test_int [((2 + 3*x)*(3 + 5*x)^3)/(1 - 2*x)^3, x, 2, 9317/(64*(1 - 2*x)^2) - 8349/(16*(1 - 2*x)) - (2975*x)/16 - (375*x^2)/16 - (2805*log(1 - 2*x))/8]
    @test_int [(3 + 5*x)^3/(1 - 2*x)^3, x, 2, 1331/(32*(1 - 2*x)^2) - 1815/(16*(1 - 2*x)) - (125*x)/8 - (825*log(1 - 2*x))/16]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^3*(2 + 3*x)), x, 2, 1331/(112*(1 - 2*x)^2) - 1089/(49*(1 - 2*x)) - (14289*log(1 - 2*x))/2744 - log(2 + 3*x)/1029]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^3*(2 + 3*x)^2), x, 2, 1331/(392*(1 - 2*x)^2) - 4719/(1372*(1 - 2*x)) + 1/(1029*(2 + 3*x)) - (33*log(1 - 2*x))/2401 + (33*log(2 + 3*x))/2401]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^3*(2 + 3*x)^3), x, 2, 1331/(1372*(1 - 2*x)^2) - 363/(2401*(1 - 2*x)) + 1/(2058*(2 + 3*x)^2) - 33/(2401*(2 + 3*x)) + (1023*log(1 - 2*x))/16807 - (1023*log(2 + 3*x))/16807]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^3*(2 + 3*x)^4), x, 2, 1331/(4802*(1 - 2*x)^2) + 3267/(16807*(1 - 2*x)) + 1/(3087*(2 + 3*x)^3) - 33/(4802*(2 + 3*x)^2) + 1023/(16807*(2 + 3*x)) - (7755*log(1 - 2*x))/117649 + (7755*log(2 + 3*x))/117649]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^3*(2 + 3*x)^5), x, 2, 1331/(16807*(1 - 2*x)^2) + 14520/(117649*(1 - 2*x)) + 1/(4116*(2 + 3*x)^4) - 11/(2401*(2 + 3*x)^3) + 1023/(33614*(2 + 3*x)^2) - 7755/(117649*(2 + 3*x)) - (59070*log(1 - 2*x))/823543 + (59070*log(2 + 3*x))/823543]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(2 + 3*x)^8/((1 - 2*x)^3*(3 + 5*x)), x, 2, 5764801/(5632*(1 - 2*x)^2) - 188591347/(30976*(1 - 2*x)) - (2941619571*x)/400000 - (110180817*x^2)/40000 - (124416*x^3)/125 - (408969*x^4)/1600 - (6561*x^5)/200 - (2644396573*log(1 - 2*x))/340736 + log(3 + 5*x)/20796875]
    @test_int [(2 + 3*x)^7/((1 - 2*x)^3*(3 + 5*x)), x, 2, 823543/(2816*(1 - 2*x)^2) - 5764801/(3872*(1 - 2*x)) - (26161299*x)/20000 - (792423*x^2)/2000 - (40581*x^3)/400 - (2187*x^4)/160 - (269063263*log(1 - 2*x))/170368 + log(3 + 5*x)/4159375]
    @test_int [(2 + 3*x)^6/((1 - 2*x)^3*(3 + 5*x)), x, 2, 117649/(1408*(1 - 2*x)^2) - 2739541/(7744*(1 - 2*x)) - (102303*x)/500 - (35721*x^2)/800 - (243*x^3)/40 - (12761315*log(1 - 2*x))/42592 + log(3 + 5*x)/831875]
    @test_int [(2 + 3*x)^5/((1 - 2*x)^3*(3 + 5*x)), x, 2, 16807/(704*(1 - 2*x)^2) - 156065/(1936*(1 - 2*x)) - (10287*x)/400 - (243*x^2)/80 - (543655*log(1 - 2*x))/10648 + log(3 + 5*x)/166375]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^3*(3 + 5*x)), x, 2, 2401/(352*(1 - 2*x)^2) - 33271/(1936*(1 - 2*x)) - (81*x)/40 - (153811*log(1 - 2*x))/21296 + log(3 + 5*x)/33275]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^3*(3 + 5*x)), x, 2, 343/(176*(1 - 2*x)^2) - 392/(121*(1 - 2*x)) - (7189*log(1 - 2*x))/10648 + log(3 + 5*x)/6655]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^3*(3 + 5*x)), x, 2, 49/(88*(1 - 2*x)^2) - 217/(484*(1 - 2*x)) - log(1 - 2*x)/1331 + log(3 + 5*x)/1331]
    @test_int [(2 + 3*x)/((1 - 2*x)^3*(3 + 5*x)), x, 2, 7/(44*(1 - 2*x)^2) + 1/(121*(1 - 2*x)) - (5*log(1 - 2*x))/1331 + (5*log(3 + 5*x))/1331]
    @test_int [1/((1 - 2*x)^3*(3 + 5*x)), x, 2, 1/(22*(1 - 2*x)^2) + 5/(121*(1 - 2*x)) - (25*log(1 - 2*x))/1331 + (25*log(3 + 5*x))/1331]
    @test_int [1/((1 - 2*x)^3*(2 + 3*x)*(3 + 5*x)), x, 2, 1/(77*(1 - 2*x)^2) + 136/(5929*(1 - 2*x)) - (6938*log(1 - 2*x))/456533 - (27*log(2 + 3*x))/343 + (125*log(3 + 5*x))/1331]
    @test_int [1/((1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)), x, 2, 2/(539*(1 - 2*x)^2) + 404/(41503*(1 - 2*x)) + 27/(343*(2 + 3*x)) - (27208*log(1 - 2*x))/3195731 - (1107*log(2 + 3*x))/2401 + (625*log(3 + 5*x))/1331]
    @test_int [1/((1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)), x, 2, 4/(3773*(1 - 2*x)^2) + 1072/(290521*(1 - 2*x)) + 27/(686*(2 + 3*x)^2) + 1107/(2401*(2 + 3*x)) - (89792*log(1 - 2*x))/22370117 - (39393*log(2 + 3*x))/16807 + (3125*log(3 + 5*x))/1331]
    @test_int [1/((1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)), x, 2, 8/(26411*(1 - 2*x)^2) + 2672/(2033647*(1 - 2*x)) + 9/(343*(2 + 3*x)^3) + 1107/(4802*(2 + 3*x)^2) + 39393/(16807*(2 + 3*x)) - (267760*log(1 - 2*x))/156590819 - (1380915*log(2 + 3*x))/117649 + (15625*log(3 + 5*x))/1331]

    @test_int [(2 + 3*x)^8/((1 - 2*x)^3*(3 + 5*x)^2), x, 2, 5764801/(30976*(1 - 2*x)^2) - 79883671/(85184*(1 - 2*x)) - (81001863*x)/100000 - (4863159*x^2)/20000 - (123201*x^3)/2000 - (6561*x^4)/800 - 1/(20796875*(3 + 5*x)) - (1845559863*log(1 - 2*x))/1874048 + (54*log(3 + 5*x))/45753125]
    @test_int [(2 + 3*x)^7/((1 - 2*x)^3*(3 + 5*x)^2), x, 2, 823543/(15488*(1 - 2*x)^2) - 18941489/(85184*(1 - 2*x)) - (1258983*x)/10000 - (108621*x^2)/4000 - (729*x^3)/200 - 1/(4159375*(3 + 5*x)) - (87177909*log(1 - 2*x))/468512 + (237*log(3 + 5*x))/45753125]
    @test_int [(2 + 3*x)^6/((1 - 2*x)^3*(3 + 5*x)^2), x, 2, 117649/(7744*(1 - 2*x)^2) - 67228/(1331*(1 - 2*x)) - (31347*x)/2000 - (729*x^2)/400 - 1/(831875*(3 + 5*x)) - (7383075*log(1 - 2*x))/234256 + (204*log(3 + 5*x))/9150625]
    @test_int [(2 + 3*x)^5/((1 - 2*x)^3*(3 + 5*x)^2), x, 2, 16807/(3872*(1 - 2*x)^2) - 228095/(21296*(1 - 2*x)) - (243*x)/200 - 1/(166375*(3 + 5*x)) - (1034145*log(1 - 2*x))/234256 + (171*log(3 + 5*x))/1830125]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^3*(3 + 5*x)^2), x, 2, 2401/(1936*(1 - 2*x)^2) - 10633/(5324*(1 - 2*x)) - 1/(33275*(3 + 5*x)) - (47481*log(1 - 2*x))/117128 + (138*log(3 + 5*x))/366025]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^3*(3 + 5*x)^2), x, 2, 343/(968*(1 - 2*x)^2) - 1421/(5324*(1 - 2*x)) - 1/(6655*(3 + 5*x)) - (21*log(1 - 2*x))/14641 + (21*log(3 + 5*x))/14641]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^3*(3 + 5*x)^2), x, 2, 49/(484*(1 - 2*x)^2) + 14/(1331*(1 - 2*x)) - 1/(1331*(3 + 5*x)) - (72*log(1 - 2*x))/14641 + (72*log(3 + 5*x))/14641]
    @test_int [(2 + 3*x)/((1 - 2*x)^3*(3 + 5*x)^2), x, 2, 7/(242*(1 - 2*x)^2) + 37/(1331*(1 - 2*x)) - 5/(1331*(3 + 5*x)) - (195*log(1 - 2*x))/14641 + (195*log(3 + 5*x))/14641]
    @test_int [1/((1 - 2*x)^3*(3 + 5*x)^2), x, 2, 1/(121*(1 - 2*x)^2) + 20/(1331*(1 - 2*x)) - 25/(1331*(3 + 5*x)) - (150*log(1 - 2*x))/14641 + (150*log(3 + 5*x))/14641]
    @test_int [1/((1 - 2*x)^3*(2 + 3*x)*(3 + 5*x)^2), x, 2, 2/(847*(1 - 2*x)^2) + 412/(65219*(1 - 2*x)) - 125/(1331*(3 + 5*x)) - (28296*log(1 - 2*x))/5021863 + (81*log(2 + 3*x))/343 - (3375*log(3 + 5*x))/14641]
    @test_int [1/((1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)^2), x, 2, 4/(5929*(1 - 2*x)^2) + 1088/(456533*(1 - 2*x)) - 81/(343*(2 + 3*x)) - 625/(1331*(3 + 5*x)) - (92496*log(1 - 2*x))/35153041 + (6156*log(2 + 3*x))/2401 - (37500*log(3 + 5*x))/14641]
    @test_int [1/((1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^2), x, 2, 8/(41503*(1 - 2*x)^2) + 2704/(3195731*(1 - 2*x)) - 81/(686*(2 + 3*x)^2) - 6156/(2401*(2 + 3*x)) - 3125/(1331*(3 + 5*x)) - (274224*log(1 - 2*x))/246071287 + (333639*log(2 + 3*x))/16807 - (290625*log(3 + 5*x))/14641]
    @test_int [1/((1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^2), x, 2, 16/(290521*(1 - 2*x)^2) + 6464/(22370117*(1 - 2*x)) - 27/(343*(2 + 3*x)^3) - 3078/(2401*(2 + 3*x)^2) - 333639/(16807*(2 + 3*x)) - 15625/(1331*(3 + 5*x)) - (761760*log(1 - 2*x))/1722499009 + (15820110*log(2 + 3*x))/117649 - (1968750*log(3 + 5*x))/14641]

    @test_int [(2 + 3*x)^9/((1 - 2*x)^3*(3 + 5*x)^3), x, 2, 40353607/(340736*(1 - 2*x)^2) - 17294403/(29282*(1 - 2*x)) - (50150097*x)/100000 - (7459857*x^2)/50000 - (373977*x^3)/10000 - (19683*x^4)/4000 - 1/(207968750*(3 + 5*x)^2) - 303/(1143828125*(3 + 5*x)) - (12657032367*log(1 - 2*x))/20614528 + (8202*log(3 + 5*x))/2516421875]
    @test_int [(2 + 3*x)^8/((1 - 2*x)^3*(3 + 5*x)^3), x, 2, 5764801/(170368*(1 - 2*x)^2) - 130943337/(937024*(1 - 2*x)) - (242028*x)/3125 - (330237*x^2)/20000 - (2187*x^3)/1000 - 1/(41593750*(3 + 5*x)^2) - 54/(45753125*(3 + 5*x)) - (595421589*log(1 - 2*x))/5153632 + (1284*log(3 + 5*x))/100656875]
    @test_int [(2 + 3*x)^7/((1 - 2*x)^3*(3 + 5*x)^3), x, 2, 823543/(85184*(1 - 2*x)^2) - 7411887/(234256*(1 - 2*x)) - (95499*x)/10000 - (2187*x^2)/2000 - 1/(8318750*(3 + 5*x)^2) - 237/(45753125*(3 + 5*x)) - (25059237*log(1 - 2*x))/1288408 + (24279*log(3 + 5*x))/503284375]
    @test_int [(2 + 3*x)^6/((1 - 2*x)^3*(3 + 5*x)^3), x, 2, 117649/(42592*(1 - 2*x)^2) - 1563051/(234256*(1 - 2*x)) - (729*x)/1000 - 1/(1663750*(3 + 5*x)^2) - 204/(9150625*(3 + 5*x)) - (6950895*log(1 - 2*x))/2576816 + (17547*log(3 + 5*x))/100656875]
    @test_int [(2 + 3*x)^5/((1 - 2*x)^3*(3 + 5*x)^3), x, 2, 16807/(21296*(1 - 2*x)^2) - 36015/(29282*(1 - 2*x)) - 1/(332750*(3 + 5*x)^2) - 171/(1830125*(3 + 5*x)) - (313845*log(1 - 2*x))/1288408 + (11904*log(3 + 5*x))/20131375]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^3*(3 + 5*x)^3), x, 2, 2401/(10648*(1 - 2*x)^2) - 9261/(58564*(1 - 2*x)) - 1/(66550*(3 + 5*x)^2) - 138/(366025*(3 + 5*x)) - (294*log(1 - 2*x))/161051 + (294*log(3 + 5*x))/161051]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^3*(3 + 5*x)^3), x, 2, 343/(5324*(1 - 2*x)^2) + 147/(14641*(1 - 2*x)) - 1/(13310*(3 + 5*x)^2) - 21/(14641*(3 + 5*x)) - (777*log(1 - 2*x))/161051 + (777*log(3 + 5*x))/161051]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^3*(3 + 5*x)^3), x, 2, 49/(2662*(1 - 2*x)^2) + 273/(14641*(1 - 2*x)) - 1/(2662*(3 + 5*x)^2) - 72/(14641*(3 + 5*x)) - (1509*log(1 - 2*x))/161051 + (1509*log(3 + 5*x))/161051]
    @test_int [(2 + 3*x)/((1 - 2*x)^3*(3 + 5*x)^3), x, 2, 7/(1331*(1 - 2*x)^2) + 144/(14641*(1 - 2*x)) - 5/(2662*(3 + 5*x)^2) - 195/(14641*(3 + 5*x)) - (1110*log(1 - 2*x))/161051 + (1110*log(3 + 5*x))/161051]
    @test_int [1/((1 - 2*x)^3*(3 + 5*x)^3), x, 2, 2/(1331*(1 - 2*x)^2) + 60/(14641*(1 - 2*x)) - 25/(2662*(3 + 5*x)^2) - 150/(14641*(3 + 5*x)) - (600*log(1 - 2*x))/161051 + (600*log(3 + 5*x))/161051]
    @test_int [1/((1 - 2*x)^3*(2 + 3*x)*(3 + 5*x)^3), x, 2, 4/(9317*(1 - 2*x)^2) + 1104/(717409*(1 - 2*x)) - 125/(2662*(3 + 5*x)^2) + 3375/(14641*(3 + 5*x)) - (95232*log(1 - 2*x))/55240493 - (243*log(2 + 3*x))/343 + (114375*log(3 + 5*x))/161051]
    @test_int [1/((1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)^3), x, 2, 8/(65219*(1 - 2*x)^2) + 2736/(5021863*(1 - 2*x)) + 243/(343*(2 + 3*x)) - 625/(2662*(3 + 5*x)^2) + 37500/(14641*(3 + 5*x)) - (280752*log(1 - 2*x))/386683451 - (26973*log(2 + 3*x))/2401 + (1809375*log(3 + 5*x))/161051]
    @test_int [1/((1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^3), x, 2, 16/(456533*(1 - 2*x)^2) + 6528/(35153041*(1 - 2*x)) + 243/(686*(2 + 3*x)^2) + 26973/(2401*(2 + 3*x)) - 3125/(2662*(3 + 5*x)^2) + 290625/(14641*(3 + 5*x)) - (776928*log(1 - 2*x))/2706784157 - (1944972*log(2 + 3*x))/16807 + (18637500*log(3 + 5*x))/161051]
    @test_int [1/((1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^3), x, 2, 32/(3195731*(1 - 2*x)^2) + 15168/(246071287*(1 - 2*x)) + 81/(343*(2 + 3*x)^3) + 26973/(4802*(2 + 3*x)^2) + 1944972/(16807*(2 + 3*x)) - 15625/(2662*(3 + 5*x)^2) + 1968750/(14641*(3 + 5*x)) - (2054400*log(1 - 2*x))/18947489099 - (115534350*log(2 + 3*x))/117649 + (158156250*log(3 + 5*x))/161051]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^n*(e+f*x)^p=#

    @test_int [((a + b*x)*(c + d*x)*(e + f*x))^3, x, 2, ((b*c - a*d)^3*(b*e - a*f)^3*(a + b*x)^4)/(4*b^7) + (3*(b*c - a*d)^2*(b*e - a*f)^2*(b*d*e + b*c*f - 2*a*d*f)*(a + b*x)^5)/(5*b^7) + ((b*c - a*d)*(b*e - a*f)*(5*a^2*d^2*f^2 - 5*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + 3*c*d*e*f + c^2*f^2))*(a + b*x)^6)/(2*b^7) + ((b*d*e + b*c*f - 2*a*d*f)*(10*a^2*d^2*f^2 - 10*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + 8*c*d*e*f + c^2*f^2))*(a + b*x)^7)/(7*b^7) + (3*d*f*(5*a^2*d^2*f^2 - 5*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + 3*c*d*e*f + c^2*f^2))*(a + b*x)^8)/(8*b^7) + (d^2*f^2*(b*d*e + b*c*f - 2*a*d*f)*(a + b*x)^9)/(3*b^7) + (d^3*f^3*(a + b*x)^10)/(10*b^7)]
    @test_int [((a + b*x)*(c + d*x)*(e + f*x))^2, x, 2, ((b*c - a*d)^2*(b*e - a*f)^2*(a + b*x)^3)/(3*b^5) + ((b*c - a*d)*(b*e - a*f)*(b*d*e + b*c*f - 2*a*d*f)*(a + b*x)^4)/(2*b^5) + ((6*a^2*d^2*f^2 - 6*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + 4*c*d*e*f + c^2*f^2))*(a + b*x)^5)/(5*b^5) + (d*f*(b*d*e + b*c*f - 2*a*d*f)*(a + b*x)^6)/(3*b^5) + (d^2*f^2*(a + b*x)^7)/(7*b^5)]
    @test_int [((a + b*x)*(c + d*x)*(e + f*x))^1, x, 2, a*c*e*x + (1/2)*(b*c*e + a*d*e + a*c*f)*x^2 + (1/3)*(b*d*e + b*c*f + a*d*f)*x^3 + (1/4)*b*d*f*x^4]
    @test_int [1/((a + b*x)*(c + d*x)*(e + f*x))^1, x, 2, (b*log(a + b*x))/((b*c - a*d)*(b*e - a*f)) - (d*log(c + d*x))/((b*c - a*d)*(d*e - c*f)) + (f*log(e + f*x))/((b*e - a*f)*(d*e - c*f))]
    @test_int [1/((a + b*x)*(c + d*x)*(e + f*x))^2, x, 2, -(b^3/((b*c - a*d)^2*(b*e - a*f)^2*(a + b*x))) - d^3/((b*c - a*d)^2*(d*e - c*f)^2*(c + d*x)) - f^3/((b*e - a*f)^2*(d*e - c*f)^2*(e + f*x)) - (2*b^3*(b*d*e + b*c*f - 2*a*d*f)*log(a + b*x))/((b*c - a*d)^3*(b*e - a*f)^3) + (2*d^3*(b*d*e - 2*b*c*f + a*d*f)*log(c + d*x))/((b*c - a*d)^3*(d*e - c*f)^3) + (2*f^3*(2*b*d*e - b*c*f - a*d*f)*log(e + f*x))/((b*e - a*f)^3*(d*e - c*f)^3)]
    @test_int [1/((a + b*x)*(c + d*x)*(e + f*x))^3, x, 2, -(b^5/(2*(b*c - a*d)^3*(b*e - a*f)^3*(a + b*x)^2)) + (3*b^5*(b*d*e + b*c*f - 2*a*d*f))/((b*c - a*d)^4*(b*e - a*f)^4*(a + b*x)) + d^5/(2*(b*c - a*d)^3*(d*e - c*f)^3*(c + d*x)^2) + (3*d^5*(b*d*e - 2*b*c*f + a*d*f))/((b*c - a*d)^4*(d*e - c*f)^4*(c + d*x)) - f^5/(2*(b*e - a*f)^3*(d*e - c*f)^3*(e + f*x)^2) - (3*f^5*(2*b*d*e - b*c*f - a*d*f))/((b*e - a*f)^4*(d*e - c*f)^4*(e + f*x)) + (3*b^5*(7*a^2*d^2*f^2 - 7*a*b*d*f*(d*e + c*f) + b^2*(2*d^2*e^2 + 3*c*d*e*f + 2*c^2*f^2))*log(a + b*x))/((b*c - a*d)^5*(b*e - a*f)^5) - (3*d^5*(2*a^2*d^2*f^2 + a*b*d*f*(3*d*e - 7*c*f) + b^2*(2*d^2*e^2 - 7*c*d*e*f + 7*c^2*f^2))*log(c + d*x))/((b*c - a*d)^5*(d*e - c*f)^5) + (3*f^5*(2*a^2*d^2*f^2 - a*b*d*f*(7*d*e - 3*c*f) + b^2*(7*d^2*e^2 - 7*c*d*e*f + 2*c^2*f^2))*log(e + f*x))/((b*e - a*f)^5*(d*e - c*f)^5)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^n*(e+f*x)^(p/2)=#

    @test_int [(c + d*x)^(3/2)/((a + b*x)^2*(e + f*x)), x, 6, -(((b*c - a*d)*sqrt(c + d*x))/(b*(b*e - a*f)*(a + b*x))) + (2*(d*e - c*f)^(3/2)*atan((sqrt(f)*sqrt(c + d*x))/sqrt(d*e - c*f)))/(sqrt(f)*(b*e - a*f)^2) - (sqrt(b*c - a*d)*(3*b*d*e - 2*b*c*f - a*d*f)*atanh((sqrt(b)*sqrt(c + d*x))/sqrt(b*c - a*d)))/(b^(3/2)*(b*e - a*f)^2)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(A+B*x)*(d+e*x)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=m>0=#

    @test_int [(a + b*x)*(A + B*x)*(d + e*x)^(7/2), x, 2, (2*(b*d - a*e)*(B*d - A*e)*(d + e*x)^(9/2))/(9*e^3) - (2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(11/2))/(11*e^3) + (2*b*B*(d + e*x)^(13/2))/(13*e^3)]
    @test_int [(a + b*x)*(A + B*x)*(d + e*x)^(5/2), x, 2, (2*(b*d - a*e)*(B*d - A*e)*(d + e*x)^(7/2))/(7*e^3) - (2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(9/2))/(9*e^3) + (2*b*B*(d + e*x)^(11/2))/(11*e^3)]
    @test_int [(a + b*x)*(A + B*x)*(d + e*x)^(3/2), x, 2, (2*(b*d - a*e)*(B*d - A*e)*(d + e*x)^(5/2))/(5*e^3) - (2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(7/2))/(7*e^3) + (2*b*B*(d + e*x)^(9/2))/(9*e^3)]
    @test_int [(a + b*x)*(A + B*x)*sqrt(d + e*x), x, 2, (2*(b*d - a*e)*(B*d - A*e)*(d + e*x)^(3/2))/(3*e^3) - (2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(5/2))/(5*e^3) + (2*b*B*(d + e*x)^(7/2))/(7*e^3)]
    @test_int [((a + b*x)*(A + B*x))/sqrt(d + e*x), x, 2, (2*(b*d - a*e)*(B*d - A*e)*sqrt(d + e*x))/e^3 - (2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(3/2))/(3*e^3) + (2*b*B*(d + e*x)^(5/2))/(5*e^3)]
    @test_int [((a + b*x)*(A + B*x))/(d + e*x)^(3/2), x, 2, (-2*(b*d - a*e)*(B*d - A*e))/(e^3*sqrt(d + e*x)) - (2*(2*b*B*d - A*b*e - a*B*e)*sqrt(d + e*x))/e^3 + (2*b*B*(d + e*x)^(3/2))/(3*e^3)]
    @test_int [((a + b*x)*(A + B*x))/(d + e*x)^(5/2), x, 2, (-2*(b*d - a*e)*(B*d - A*e))/(3*e^3*(d + e*x)^(3/2)) + (2*(2*b*B*d - A*b*e - a*B*e))/(e^3*sqrt(d + e*x)) + (2*b*B*sqrt(d + e*x))/e^3]
    @test_int [((a + b*x)*(A + B*x))/(d + e*x)^(7/2), x, 2, (-2*(b*d - a*e)*(B*d - A*e))/(5*e^3*(d + e*x)^(5/2)) + (2*(2*b*B*d - A*b*e - a*B*e))/(3*e^3*(d + e*x)^(3/2)) - (2*b*B)/(e^3*sqrt(d + e*x))]

    @test_int [(a + b*x)^2*(A + B*x)*(d + e*x)^(7/2), x, 2, (-2*(b*d - a*e)^2*(B*d - A*e)*(d + e*x)^(9/2))/(9*e^4) + (2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(11/2))/(11*e^4) - (2*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(13/2))/(13*e^4) + (2*b^2*B*(d + e*x)^(15/2))/(15*e^4)]
    @test_int [(a + b*x)^2*(A + B*x)*(d + e*x)^(5/2), x, 2, (-2*(b*d - a*e)^2*(B*d - A*e)*(d + e*x)^(7/2))/(7*e^4) + (2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(9/2))/(9*e^4) - (2*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(11/2))/(11*e^4) + (2*b^2*B*(d + e*x)^(13/2))/(13*e^4)]
    @test_int [(a + b*x)^2*(A + B*x)*(d + e*x)^(3/2), x, 2, (-2*(b*d - a*e)^2*(B*d - A*e)*(d + e*x)^(5/2))/(5*e^4) + (2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(7/2))/(7*e^4) - (2*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(9/2))/(9*e^4) + (2*b^2*B*(d + e*x)^(11/2))/(11*e^4)]
    @test_int [(a + b*x)^2*(A + B*x)*sqrt(d + e*x), x, 2, (-2*(b*d - a*e)^2*(B*d - A*e)*(d + e*x)^(3/2))/(3*e^4) + (2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(5/2))/(5*e^4) - (2*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(7/2))/(7*e^4) + (2*b^2*B*(d + e*x)^(9/2))/(9*e^4)]
    @test_int [((a + b*x)^2*(A + B*x))/sqrt(d + e*x), x, 2, (-2*(b*d - a*e)^2*(B*d - A*e)*sqrt(d + e*x))/e^4 + (2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(3/2))/(3*e^4) - (2*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(5/2))/(5*e^4) + (2*b^2*B*(d + e*x)^(7/2))/(7*e^4)]
    @test_int [((a + b*x)^2*(A + B*x))/(d + e*x)^(3/2), x, 2, (2*(b*d - a*e)^2*(B*d - A*e))/(e^4*sqrt(d + e*x)) + (2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*sqrt(d + e*x))/e^4 - (2*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(3/2))/(3*e^4) + (2*b^2*B*(d + e*x)^(5/2))/(5*e^4)]
    @test_int [((a + b*x)^2*(A + B*x))/(d + e*x)^(5/2), x, 2, (2*(b*d - a*e)^2*(B*d - A*e))/(3*e^4*(d + e*x)^(3/2)) - (2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e))/(e^4*sqrt(d + e*x)) - (2*b*(3*b*B*d - A*b*e - 2*a*B*e)*sqrt(d + e*x))/e^4 + (2*b^2*B*(d + e*x)^(3/2))/(3*e^4)]
    @test_int [((a + b*x)^2*(A + B*x))/(d + e*x)^(7/2), x, 2, (2*(b*d - a*e)^2*(B*d - A*e))/(5*e^4*(d + e*x)^(5/2)) - (2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e))/(3*e^4*(d + e*x)^(3/2)) + (2*b*(3*b*B*d - A*b*e - 2*a*B*e))/(e^4*sqrt(d + e*x)) + (2*b^2*B*sqrt(d + e*x))/e^4]

    @test_int [(a + b*x)^3*(A + B*x)*(d + e*x)^(7/2), x, 2, (2*(b*d - a*e)^3*(B*d - A*e)*(d + e*x)^(9/2))/(9*e^5) - (2*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)^(11/2))/(11*e^5) + (6*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(13/2))/(13*e^5) - (2*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^(15/2))/(15*e^5) + (2*b^3*B*(d + e*x)^(17/2))/(17*e^5)]
    @test_int [(a + b*x)^3*(A + B*x)*(d + e*x)^(5/2), x, 2, (2*(b*d - a*e)^3*(B*d - A*e)*(d + e*x)^(7/2))/(7*e^5) - (2*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)^(9/2))/(9*e^5) + (6*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(11/2))/(11*e^5) - (2*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^(13/2))/(13*e^5) + (2*b^3*B*(d + e*x)^(15/2))/(15*e^5)]
    @test_int [(a + b*x)^3*(A + B*x)*(d + e*x)^(3/2), x, 2, (2*(b*d - a*e)^3*(B*d - A*e)*(d + e*x)^(5/2))/(5*e^5) - (2*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)^(7/2))/(7*e^5) + (2*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(9/2))/(3*e^5) - (2*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^(11/2))/(11*e^5) + (2*b^3*B*(d + e*x)^(13/2))/(13*e^5)]
    @test_int [(a + b*x)^3*(A + B*x)*sqrt(d + e*x), x, 2, (2*(b*d - a*e)^3*(B*d - A*e)*(d + e*x)^(3/2))/(3*e^5) - (2*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)^(5/2))/(5*e^5) + (6*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(7/2))/(7*e^5) - (2*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^(9/2))/(9*e^5) + (2*b^3*B*(d + e*x)^(11/2))/(11*e^5)]
    @test_int [((a + b*x)^3*(A + B*x))/sqrt(d + e*x), x, 2, (2*(b*d - a*e)^3*(B*d - A*e)*sqrt(d + e*x))/e^5 - (2*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)^(3/2))/(3*e^5) + (6*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(5/2))/(5*e^5) - (2*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^(7/2))/(7*e^5) + (2*b^3*B*(d + e*x)^(9/2))/(9*e^5)]
    @test_int [((a + b*x)^3*(A + B*x))/(d + e*x)^(3/2), x, 2, (-2*(b*d - a*e)^3*(B*d - A*e))/(e^5*sqrt(d + e*x)) - (2*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*sqrt(d + e*x))/e^5 + (2*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(3/2))/e^5 - (2*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^(5/2))/(5*e^5) + (2*b^3*B*(d + e*x)^(7/2))/(7*e^5)]
    @test_int [((a + b*x)^3*(A + B*x))/(d + e*x)^(5/2), x, 2, (-2*(b*d - a*e)^3*(B*d - A*e))/(3*e^5*(d + e*x)^(3/2)) + (2*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e))/(e^5*sqrt(d + e*x)) + (6*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*sqrt(d + e*x))/e^5 - (2*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^(3/2))/(3*e^5) + (2*b^3*B*(d + e*x)^(5/2))/(5*e^5)]
    @test_int [((a + b*x)^3*(A + B*x))/(d + e*x)^(7/2), x, 2, (-2*(b*d - a*e)^3*(B*d - A*e))/(5*e^5*(d + e*x)^(5/2)) + (2*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e))/(3*e^5*(d + e*x)^(3/2)) - (6*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e))/(e^5*sqrt(d + e*x)) - (2*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*sqrt(d + e*x))/e^5 + (2*b^3*B*(d + e*x)^(3/2))/(3*e^5)]

    #= ::Subsubsection::Closed:: =#
    #=m<0=#

    @test_int [((A + B*x)*(d + e*x)^(7/2))/(a + b*x), x, 7, (2*(A*b - a*B)*(b*d - a*e)^3*sqrt(d + e*x))/b^5 + (2*(A*b - a*B)*(b*d - a*e)^2*(d + e*x)^(3/2))/(3*b^4) + (2*(A*b - a*B)*(b*d - a*e)*(d + e*x)^(5/2))/(5*b^3) + (2*(A*b - a*B)*(d + e*x)^(7/2))/(7*b^2) + (2*B*(d + e*x)^(9/2))/(9*b*e) - (2*(A*b - a*B)*(b*d - a*e)^(7/2)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/b^(11/2)]
    @test_int [((A + B*x)*(d + e*x)^(5/2))/(a + b*x), x, 6, (2*(A*b - a*B)*(b*d - a*e)^2*sqrt(d + e*x))/b^4 + (2*(A*b - a*B)*(b*d - a*e)*(d + e*x)^(3/2))/(3*b^3) + (2*(A*b - a*B)*(d + e*x)^(5/2))/(5*b^2) + (2*B*(d + e*x)^(7/2))/(7*b*e) - (2*(A*b - a*B)*(b*d - a*e)^(5/2)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/b^(9/2)]
    @test_int [((A + B*x)*(d + e*x)^(3/2))/(a + b*x), x, 5, (2*(A*b - a*B)*(b*d - a*e)*sqrt(d + e*x))/b^3 + (2*(A*b - a*B)*(d + e*x)^(3/2))/(3*b^2) + (2*B*(d + e*x)^(5/2))/(5*b*e) - (2*(A*b - a*B)*(b*d - a*e)^(3/2)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/b^(7/2)]
    @test_int [((A + B*x)*sqrt(d + e*x))/(a + b*x), x, 4, (2*(A*b - a*B)*sqrt(d + e*x))/b^2 + (2*B*(d + e*x)^(3/2))/(3*b*e) - (2*(A*b - a*B)*sqrt(b*d - a*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/b^(5/2)]
    @test_int [(A + B*x)/((a + b*x)*sqrt(d + e*x)), x, 3, (2*B*sqrt(d + e*x))/(b*e) - (2*(A*b - a*B)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(b^(3/2)*sqrt(b*d - a*e))]
    @test_int [(A + B*x)/((a + b*x)*(d + e*x)^(3/2)), x, 3, (-2*(B*d - A*e))/(e*(b*d - a*e)*sqrt(d + e*x)) - (2*(A*b - a*B)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(sqrt(b)*(b*d - a*e)^(3/2))]
    @test_int [(A + B*x)/((a + b*x)*(d + e*x)^(5/2)), x, 4, (-2*(B*d - A*e))/(3*e*(b*d - a*e)*(d + e*x)^(3/2)) + (2*(A*b - a*B))/((b*d - a*e)^2*sqrt(d + e*x)) - (2*sqrt(b)*(A*b - a*B)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(b*d - a*e)^(5/2)]
    @test_int [(A + B*x)/((a + b*x)*(d + e*x)^(7/2)), x, 5, (-2*(B*d - A*e))/(5*e*(b*d - a*e)*(d + e*x)^(5/2)) + (2*(A*b - a*B))/(3*(b*d - a*e)^2*(d + e*x)^(3/2)) + (2*b*(A*b - a*B))/((b*d - a*e)^3*sqrt(d + e*x)) - (2*b^(3/2)*(A*b - a*B)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(b*d - a*e)^(7/2)]

    @test_int [((A + B*x)*(d + e*x)^(7/2))/(a + b*x)^2, x, 7, ((b*d - a*e)^2*(2*b*B*d + 7*A*b*e - 9*a*B*e)*sqrt(d + e*x))/b^5 + ((b*d - a*e)*(2*b*B*d + 7*A*b*e - 9*a*B*e)*(d + e*x)^(3/2))/(3*b^4) + ((2*b*B*d + 7*A*b*e - 9*a*B*e)*(d + e*x)^(5/2))/(5*b^3) + ((2*b*B*d + 7*A*b*e - 9*a*B*e)*(d + e*x)^(7/2))/(7*b^2*(b*d - a*e)) - ((A*b - a*B)*(d + e*x)^(9/2))/(b*(b*d - a*e)*(a + b*x)) - ((b*d - a*e)^(5/2)*(2*b*B*d + 7*A*b*e - 9*a*B*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/b^(11/2)]
    @test_int [((A + B*x)*(d + e*x)^(5/2))/(a + b*x)^2, x, 6, ((b*d - a*e)*(2*b*B*d + 5*A*b*e - 7*a*B*e)*sqrt(d + e*x))/b^4 + ((2*b*B*d + 5*A*b*e - 7*a*B*e)*(d + e*x)^(3/2))/(3*b^3) + ((2*b*B*d + 5*A*b*e - 7*a*B*e)*(d + e*x)^(5/2))/(5*b^2*(b*d - a*e)) - ((A*b - a*B)*(d + e*x)^(7/2))/(b*(b*d - a*e)*(a + b*x)) - ((b*d - a*e)^(3/2)*(2*b*B*d + 5*A*b*e - 7*a*B*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/b^(9/2)]
    @test_int [((A + B*x)*(d + e*x)^(3/2))/(a + b*x)^2, x, 5, ((2*b*B*d + 3*A*b*e - 5*a*B*e)*sqrt(d + e*x))/b^3 + ((2*b*B*d + 3*A*b*e - 5*a*B*e)*(d + e*x)^(3/2))/(3*b^2*(b*d - a*e)) - ((A*b - a*B)*(d + e*x)^(5/2))/(b*(b*d - a*e)*(a + b*x)) - (sqrt(b*d - a*e)*(2*b*B*d + 3*A*b*e - 5*a*B*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/b^(7/2)]
    @test_int [((A + B*x)*sqrt(d + e*x))/(a + b*x)^2, x, 4, ((2*b*B*d + A*b*e - 3*a*B*e)*sqrt(d + e*x))/(b^2*(b*d - a*e)) - ((A*b - a*B)*(d + e*x)^(3/2))/(b*(b*d - a*e)*(a + b*x)) - ((2*b*B*d + A*b*e - 3*a*B*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(b^(5/2)*sqrt(b*d - a*e))]
    @test_int [(A + B*x)/((a + b*x)^2*sqrt(d + e*x)), x, 3, -(((A*b - a*B)*sqrt(d + e*x))/(b*(b*d - a*e)*(a + b*x))) - ((2*b*B*d - A*b*e - a*B*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(b^(3/2)*(b*d - a*e)^(3/2))]
    @test_int [(A + B*x)/((a + b*x)^2*(d + e*x)^(3/2)), x, 4, (2*b*B*d - 3*A*b*e + a*B*e)/(b*(b*d - a*e)^2*sqrt(d + e*x)) - (A*b - a*B)/(b*(b*d - a*e)*(a + b*x)*sqrt(d + e*x)) - ((2*b*B*d - 3*A*b*e + a*B*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(sqrt(b)*(b*d - a*e)^(5/2))]
    @test_int [(A + B*x)/((a + b*x)^2*(d + e*x)^(5/2)), x, 5, (2*b*B*d - 5*A*b*e + 3*a*B*e)/(3*b*(b*d - a*e)^2*(d + e*x)^(3/2)) - (A*b - a*B)/(b*(b*d - a*e)*(a + b*x)*(d + e*x)^(3/2)) + (2*b*B*d - 5*A*b*e + 3*a*B*e)/((b*d - a*e)^3*sqrt(d + e*x)) - (sqrt(b)*(2*b*B*d - 5*A*b*e + 3*a*B*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(b*d - a*e)^(7/2)]
    @test_int [(A + B*x)/((a + b*x)^2*(d + e*x)^(7/2)), x, 6, (2*b*B*d - 7*A*b*e + 5*a*B*e)/(5*b*(b*d - a*e)^2*(d + e*x)^(5/2)) - (A*b - a*B)/(b*(b*d - a*e)*(a + b*x)*(d + e*x)^(5/2)) + (2*b*B*d - 7*A*b*e + 5*a*B*e)/(3*(b*d - a*e)^3*(d + e*x)^(3/2)) + (b*(2*b*B*d - 7*A*b*e + 5*a*B*e))/((b*d - a*e)^4*sqrt(d + e*x)) - (b^(3/2)*(2*b*B*d - 7*A*b*e + 5*a*B*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(b*d - a*e)^(9/2)]

    @test_int [((A + B*x)*(d + e*x)^(7/2))/(a + b*x)^3, x, 7, (7*e*(b*d - a*e)*(4*b*B*d + 5*A*b*e - 9*a*B*e)*sqrt(d + e*x))/(4*b^5) + (7*e*(4*b*B*d + 5*A*b*e - 9*a*B*e)*(d + e*x)^(3/2))/(12*b^4) + (7*e*(4*b*B*d + 5*A*b*e - 9*a*B*e)*(d + e*x)^(5/2))/(20*b^3*(b*d - a*e)) - ((4*b*B*d + 5*A*b*e - 9*a*B*e)*(d + e*x)^(7/2))/(4*b^2*(b*d - a*e)*(a + b*x)) - ((A*b - a*B)*(d + e*x)^(9/2))/(2*b*(b*d - a*e)*(a + b*x)^2) - (7*e*(b*d - a*e)^(3/2)*(4*b*B*d + 5*A*b*e - 9*a*B*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(4*b^(11/2))]
    @test_int [((A + B*x)*(d + e*x)^(5/2))/(a + b*x)^3, x, 6, (5*e*(4*b*B*d + 3*A*b*e - 7*a*B*e)*sqrt(d + e*x))/(4*b^4) + (5*e*(4*b*B*d + 3*A*b*e - 7*a*B*e)*(d + e*x)^(3/2))/(12*b^3*(b*d - a*e)) - ((4*b*B*d + 3*A*b*e - 7*a*B*e)*(d + e*x)^(5/2))/(4*b^2*(b*d - a*e)*(a + b*x)) - ((A*b - a*B)*(d + e*x)^(7/2))/(2*b*(b*d - a*e)*(a + b*x)^2) - (5*e*sqrt(b*d - a*e)*(4*b*B*d + 3*A*b*e - 7*a*B*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(4*b^(9/2))]
    @test_int [((A + B*x)*(d + e*x)^(3/2))/(a + b*x)^3, x, 5, (3*e*(4*b*B*d + A*b*e - 5*a*B*e)*sqrt(d + e*x))/(4*b^3*(b*d - a*e)) - ((4*b*B*d + A*b*e - 5*a*B*e)*(d + e*x)^(3/2))/(4*b^2*(b*d - a*e)*(a + b*x)) - ((A*b - a*B)*(d + e*x)^(5/2))/(2*b*(b*d - a*e)*(a + b*x)^2) - (3*e*(4*b*B*d + A*b*e - 5*a*B*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(4*b^(7/2)*sqrt(b*d - a*e))]
    @test_int [((A + B*x)*sqrt(d + e*x))/(a + b*x)^3, x, 4, -((4*b*B*d - A*b*e - 3*a*B*e)*sqrt(d + e*x))/(4*b^2*(b*d - a*e)*(a + b*x)) - ((A*b - a*B)*(d + e*x)^(3/2))/(2*b*(b*d - a*e)*(a + b*x)^2) - (e*(4*b*B*d - A*b*e - 3*a*B*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(4*b^(5/2)*(b*d - a*e)^(3/2))]
    @test_int [(A + B*x)/((a + b*x)^3*sqrt(d + e*x)), x, 4, -((A*b - a*B)*sqrt(d + e*x))/(2*b*(b*d - a*e)*(a + b*x)^2) - ((4*b*B*d - 3*A*b*e - a*B*e)*sqrt(d + e*x))/(4*b*(b*d - a*e)^2*(a + b*x)) + (e*(4*b*B*d - 3*A*b*e - a*B*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(4*b^(3/2)*(b*d - a*e)^(5/2))]
    @test_int [(A + B*x)/((a + b*x)^3*(d + e*x)^(3/2)), x, 5, (-3*e*(4*b*B*d - 5*A*b*e + a*B*e))/(4*b*(b*d - a*e)^3*sqrt(d + e*x)) - (A*b - a*B)/(2*b*(b*d - a*e)*(a + b*x)^2*sqrt(d + e*x)) - (4*b*B*d - 5*A*b*e + a*B*e)/(4*b*(b*d - a*e)^2*(a + b*x)*sqrt(d + e*x)) + (3*e*(4*b*B*d - 5*A*b*e + a*B*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(4*sqrt(b)*(b*d - a*e)^(7/2))]
    @test_int [(A + B*x)/((a + b*x)^3*(d + e*x)^(5/2)), x, 6, (-5*e*(4*b*B*d - 7*A*b*e + 3*a*B*e))/(12*b*(b*d - a*e)^3*(d + e*x)^(3/2)) - (A*b - a*B)/(2*b*(b*d - a*e)*(a + b*x)^2*(d + e*x)^(3/2)) - (4*b*B*d - 7*A*b*e + 3*a*B*e)/(4*b*(b*d - a*e)^2*(a + b*x)*(d + e*x)^(3/2)) - (5*e*(4*b*B*d - 7*A*b*e + 3*a*B*e))/(4*(b*d - a*e)^4*sqrt(d + e*x)) + (5*sqrt(b)*e*(4*b*B*d - 7*A*b*e + 3*a*B*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(4*(b*d - a*e)^(9/2))]
    @test_int [(A + B*x)/((a + b*x)^3*(d + e*x)^(7/2)), x, 7, (-7*e*(4*b*B*d - 9*A*b*e + 5*a*B*e))/(20*b*(b*d - a*e)^3*(d + e*x)^(5/2)) - (A*b - a*B)/(2*b*(b*d - a*e)*(a + b*x)^2*(d + e*x)^(5/2)) - (4*b*B*d - 9*A*b*e + 5*a*B*e)/(4*b*(b*d - a*e)^2*(a + b*x)*(d + e*x)^(5/2)) - (7*e*(4*b*B*d - 9*A*b*e + 5*a*B*e))/(12*(b*d - a*e)^4*(d + e*x)^(3/2)) - (7*b*e*(4*b*B*d - 9*A*b*e + 5*a*B*e))/(4*(b*d - a*e)^5*sqrt(d + e*x)) + (7*b^(3/2)*e*(4*b*B*d - 9*A*b*e + 5*a*B*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(4*(b*d - a*e)^(11/2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m / (c+d*x)*(e+f*x)^(p/2)=#

    @test_int [(a + b*x)^1/(c + d*x)*(e + f*x)^(5/2), x, 6, -((2*(b*c - a*d)*(d*e - c*f)^2*sqrt(e + f*x))/d^4) - (2*(b*c - a*d)*(d*e - c*f)*(e + f*x)^(3/2))/(3*d^3) - (2*(b*c - a*d)*(e + f*x)^(5/2))/(5*d^2) + (2*b*(e + f*x)^(7/2))/(7*d*f) + (2*(b*c - a*d)*(d*e - c*f)^(5/2)*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/d^(9/2)]
    @test_int [(a + b*x)^1/(c + d*x)*(e + f*x)^(3/2), x, 5, -((2*(b*c - a*d)*(d*e - c*f)*sqrt(e + f*x))/d^3) - (2*(b*c - a*d)*(e + f*x)^(3/2))/(3*d^2) + (2*b*(e + f*x)^(5/2))/(5*d*f) + (2*(b*c - a*d)*(d*e - c*f)^(3/2)*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/d^(7/2)]
    @test_int [(a + b*x)^1/(c + d*x)*(e + f*x)^(1/2), x, 4, -((2*(b*c - a*d)*sqrt(e + f*x))/d^2) + (2*b*(e + f*x)^(3/2))/(3*d*f) + (2*(b*c - a*d)*sqrt(d*e - c*f)*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/d^(5/2)]
    @test_int [(a + b*x)^1/(c + d*x)/(e + f*x)^(1/2), x, 3, (2*b*sqrt(e + f*x))/(d*f) + (2*(b*c - a*d)*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/(d^(3/2)*sqrt(d*e - c*f))]
    @test_int [(a + b*x)^1/(c + d*x)/(e + f*x)^(3/2), x, 3, -((2*(b*e - a*f))/(f*(d*e - c*f)*sqrt(e + f*x))) + (2*(b*c - a*d)*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/(sqrt(d)*(d*e - c*f)^(3/2))]
    @test_int [(a + b*x)^1/(c + d*x)/(e + f*x)^(5/2), x, 4, -((2*(b*e - a*f))/(3*f*(d*e - c*f)*(e + f*x)^(3/2))) - (2*(b*c - a*d))/((d*e - c*f)^2*sqrt(e + f*x)) + (2*sqrt(d)*(b*c - a*d)*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/(d*e - c*f)^(5/2)]
    @test_int [(a + b*x)^1/(c + d*x)/(e + f*x)^(7/2), x, 5, -((2*(b*e - a*f))/(5*f*(d*e - c*f)*(e + f*x)^(5/2))) - (2*(b*c - a*d))/(3*(d*e - c*f)^2*(e + f*x)^(3/2)) - (2*d*(b*c - a*d))/((d*e - c*f)^3*sqrt(e + f*x)) + (2*d^(3/2)*(b*c - a*d)*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/(d*e - c*f)^(7/2)]
    @test_int [(a + b*x)^1/(c + d*x)/(e + f*x)^(9/2), x, 6, -((2*(b*e - a*f))/(7*f*(d*e - c*f)*(e + f*x)^(7/2))) - (2*(b*c - a*d))/(5*(d*e - c*f)^2*(e + f*x)^(5/2)) - (2*d*(b*c - a*d))/(3*(d*e - c*f)^3*(e + f*x)^(3/2)) - (2*d^2*(b*c - a*d))/((d*e - c*f)^4*sqrt(e + f*x)) + (2*d^(5/2)*(b*c - a*d)*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/(d*e - c*f)^(9/2)]

    @test_int [(a + b*x)^2/(c + d*x)*(e + f*x)^(5/2), x, 7, (2*(b*c - a*d)^2*(d*e - c*f)^2*sqrt(e + f*x))/d^5 + (2*(b*c - a*d)^2*(d*e - c*f)*(e + f*x)^(3/2))/(3*d^4) + (2*(b*c - a*d)^2*(e + f*x)^(5/2))/(5*d^3) - (2*b*(b*d*e + b*c*f - 2*a*d*f)*(e + f*x)^(7/2))/(7*d^2*f^2) + (2*b^2*(e + f*x)^(9/2))/(9*d*f^2) - (2*(b*c - a*d)^2*(d*e - c*f)^(5/2)*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/d^(11/2)]
    @test_int [(a + b*x)^2/(c + d*x)*(e + f*x)^(3/2), x, 6, (2*(b*c - a*d)^2*(d*e - c*f)*sqrt(e + f*x))/d^4 + (2*(b*c - a*d)^2*(e + f*x)^(3/2))/(3*d^3) - (2*b*(b*d*e + b*c*f - 2*a*d*f)*(e + f*x)^(5/2))/(5*d^2*f^2) + (2*b^2*(e + f*x)^(7/2))/(7*d*f^2) - (2*(b*c - a*d)^2*(d*e - c*f)^(3/2)*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/d^(9/2)]
    @test_int [(a + b*x)^2/(c + d*x)*(e + f*x)^(1/2), x, 5, (2*(b*c - a*d)^2*sqrt(e + f*x))/d^3 - (2*b*(b*d*e + b*c*f - 2*a*d*f)*(e + f*x)^(3/2))/(3*d^2*f^2) + (2*b^2*(e + f*x)^(5/2))/(5*d*f^2) - (2*(b*c - a*d)^2*sqrt(d*e - c*f)*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/d^(7/2)]
    @test_int [(a + b*x)^2/(c + d*x)/(e + f*x)^(1/2), x, 4, -((2*b*(b*d*e + b*c*f - 2*a*d*f)*sqrt(e + f*x))/(d^2*f^2)) + (2*b^2*(e + f*x)^(3/2))/(3*d*f^2) - (2*(b*c - a*d)^2*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/(d^(5/2)*sqrt(d*e - c*f))]
    @test_int [(a + b*x)^2/(c + d*x)/(e + f*x)^(3/2), x, 4, (2*(b*e - a*f)^2)/(f^2*(d*e - c*f)*sqrt(e + f*x)) + (2*b^2*sqrt(e + f*x))/(d*f^2) - (2*(b*c - a*d)^2*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/(d^(3/2)*(d*e - c*f)^(3/2))]
    @test_int [(a + b*x)^2/(c + d*x)/(e + f*x)^(5/2), x, 4, (2*(b*e - a*f)^2)/(3*f^2*(d*e - c*f)*(e + f*x)^(3/2)) - (2*(b*e - a*f)*(b*d*e - 2*b*c*f + a*d*f))/(f^2*(d*e - c*f)^2*sqrt(e + f*x)) - (2*(b*c - a*d)^2*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/(sqrt(d)*(d*e - c*f)^(5/2))]
    @test_int [(a + b*x)^2/(c + d*x)/(e + f*x)^(7/2), x, 4, (2*(b*e - a*f)^2)/(5*f^2*(d*e - c*f)*(e + f*x)^(5/2)) - (2*(b*e - a*f)*(b*d*e - 2*b*c*f + a*d*f))/(3*f^2*(d*e - c*f)^2*(e + f*x)^(3/2)) + (2*(b*c - a*d)^2)/((d*e - c*f)^3*sqrt(e + f*x)) - (2*sqrt(d)*(b*c - a*d)^2*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/(d*e - c*f)^(7/2)]
    @test_int [(a + b*x)^2/(c + d*x)/(e + f*x)^(9/2), x, 4, (2*(b*e - a*f)^2)/(7*f^2*(d*e - c*f)*(e + f*x)^(7/2)) - (2*(b*e - a*f)*(b*d*e - 2*b*c*f + a*d*f))/(5*f^2*(d*e - c*f)^2*(e + f*x)^(5/2)) + (2*(b*c - a*d)^2)/(3*(d*e - c*f)^3*(e + f*x)^(3/2)) + (2*d*(b*c - a*d)^2)/((d*e - c*f)^4*sqrt(e + f*x)) - (2*d^(3/2)*(b*c - a*d)^2*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/(d*e - c*f)^(9/2)]

    @test_int [(a + b*x)^3/(c + d*x)*(e + f*x)^(5/2), x, 7, -((2*(b*c - a*d)^3*(d*e - c*f)^2*sqrt(e + f*x))/d^6) - (2*(b*c - a*d)^3*(d*e - c*f)*(e + f*x)^(3/2))/(3*d^5) - (2*(b*c - a*d)^3*(e + f*x)^(5/2))/(5*d^4) + (2*b*(3*a^2*d^2*f^2 - 3*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + c*d*e*f + c^2*f^2))*(e + f*x)^(7/2))/(7*d^3*f^3) - (2*b^2*(2*b*d*e + b*c*f - 3*a*d*f)*(e + f*x)^(9/2))/(9*d^2*f^3) + (2*b^3*(e + f*x)^(11/2))/(11*d*f^3) + (2*(b*c - a*d)^3*(d*e - c*f)^(5/2)*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/d^(13/2)]
    @test_int [(a + b*x)^3/(c + d*x)*(e + f*x)^(3/2), x, 6, -((2*(b*c - a*d)^3*(d*e - c*f)*sqrt(e + f*x))/d^5) - (2*(b*c - a*d)^3*(e + f*x)^(3/2))/(3*d^4) + (2*b*(3*a^2*d^2*f^2 - 3*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + c*d*e*f + c^2*f^2))*(e + f*x)^(5/2))/(5*d^3*f^3) - (2*b^2*(2*b*d*e + b*c*f - 3*a*d*f)*(e + f*x)^(7/2))/(7*d^2*f^3) + (2*b^3*(e + f*x)^(9/2))/(9*d*f^3) + (2*(b*c - a*d)^3*(d*e - c*f)^(3/2)*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/d^(11/2)]
    @test_int [(a + b*x)^3/(c + d*x)*(e + f*x)^(1/2), x, 5, -((2*(b*c - a*d)^3*sqrt(e + f*x))/d^4) + (2*b*(3*a^2*d^2*f^2 - 3*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + c*d*e*f + c^2*f^2))*(e + f*x)^(3/2))/(3*d^3*f^3) - (2*b^2*(2*b*d*e + b*c*f - 3*a*d*f)*(e + f*x)^(5/2))/(5*d^2*f^3) + (2*b^3*(e + f*x)^(7/2))/(7*d*f^3) + (2*(b*c - a*d)^3*sqrt(d*e - c*f)*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/d^(9/2)]
    @test_int [(a + b*x)^3/(c + d*x)/(e + f*x)^(1/2), x, 4, (2*b*(3*a^2*d^2*f^2 - 3*a*b*d*f*(d*e + c*f) + b^2*(d^2*e^2 + c*d*e*f + c^2*f^2))*sqrt(e + f*x))/(d^3*f^3) - (2*b^2*(2*b*d*e + b*c*f - 3*a*d*f)*(e + f*x)^(3/2))/(3*d^2*f^3) + (2*b^3*(e + f*x)^(5/2))/(5*d*f^3) + (2*(b*c - a*d)^3*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/(d^(7/2)*sqrt(d*e - c*f))]
    @test_int [(a + b*x)^3/(c + d*x)/(e + f*x)^(3/2), x, 6, -((2*(b*e - a*f)^3)/(f^3*(d*e - c*f)*sqrt(e + f*x))) - (2*b^2*(2*b*d*e + b*c*f - 3*a*d*f)*sqrt(e + f*x))/(d^2*f^3) + (2*b^3*(e + f*x)^(3/2))/(3*d*f^3) + (2*(b*c - a*d)^3*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/(d^(5/2)*(d*e - c*f)^(3/2)), -((2*(b*e - a*f)^3)/(f^3*(d*e - c*f)*sqrt(e + f*x))) - (2*b^3*e*sqrt(e + f*x))/(d*f^3) - (2*b^2*(b*d*e + b*c*f - 3*a*d*f)*sqrt(e + f*x))/(d^2*f^3) + (2*b^3*(e + f*x)^(3/2))/(3*d*f^3) + (2*(b*c - a*d)^3*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/(d^(5/2)*(d*e - c*f)^(3/2))]
    @test_int [(a + b*x)^3/(c + d*x)/(e + f*x)^(5/2), x, 4, -((2*(b*e - a*f)^3)/(3*f^3*(d*e - c*f)*(e + f*x)^(3/2))) + (2*(b*e - a*f)^2*(2*b*d*e - 3*b*c*f + a*d*f))/(f^3*(d*e - c*f)^2*sqrt(e + f*x)) + (2*b^3*sqrt(e + f*x))/(d*f^3) + (2*(b*c - a*d)^3*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/(d^(3/2)*(d*e - c*f)^(5/2))]
    @test_int [(a + b*x)^3/(c + d*x)/(e + f*x)^(7/2), x, 4, -((2*(b*e - a*f)^3)/(5*f^3*(d*e - c*f)*(e + f*x)^(5/2))) + (2*(b*e - a*f)^2*(2*b*d*e - 3*b*c*f + a*d*f))/(3*f^3*(d*e - c*f)^2*(e + f*x)^(3/2)) - (2*(b*e - a*f)*(a^2*d^2*f^2 + a*b*d*f*(d*e - 3*c*f) + b^2*(d^2*e^2 - 3*c*d*e*f + 3*c^2*f^2)))/(f^3*(d*e - c*f)^3*sqrt(e + f*x)) + (2*(b*c - a*d)^3*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/(sqrt(d)*(d*e - c*f)^(7/2))]
    @test_int [(a + b*x)^3/(c + d*x)/(e + f*x)^(9/2), x, 4, -((2*(b*e - a*f)^3)/(7*f^3*(d*e - c*f)*(e + f*x)^(7/2))) + (2*(b*e - a*f)^2*(2*b*d*e - 3*b*c*f + a*d*f))/(5*f^3*(d*e - c*f)^2*(e + f*x)^(5/2)) - (2*(b*e - a*f)*(a^2*d^2*f^2 + a*b*d*f*(d*e - 3*c*f) + b^2*(d^2*e^2 - 3*c*d*e*f + 3*c^2*f^2)))/(3*f^3*(d*e - c*f)^3*(e + f*x)^(3/2)) - (2*(b*c - a*d)^3)/((d*e - c*f)^4*sqrt(e + f*x)) + (2*sqrt(d)*(b*c - a*d)^3*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/(d*e - c*f)^(9/2)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(2+3*x)^m*(3+5*x)^n*(1-2*x)^(1/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^6*(3 + 5*x), x, 2, (-1294139*(1 - 2*x)^(3/2))/384 + (3916031*(1 - 2*x)^(5/2))/640 - (725445*(1 - 2*x)^(7/2))/128 + (406455*(1 - 2*x)^(9/2))/128 - (1580985*(1 - 2*x)^(11/2))/1408 + (409941*(1 - 2*x)^(13/2))/1664 - (19683*(1 - 2*x)^(15/2))/640 + (3645*(1 - 2*x)^(17/2))/2176]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^5*(3 + 5*x), x, 2, (-184877*(1 - 2*x)^(3/2))/192 + (12005*(1 - 2*x)^(5/2))/8 - (74235*(1 - 2*x)^(7/2))/64 + (4165*(1 - 2*x)^(9/2))/8 - (97335*(1 - 2*x)^(11/2))/704 + (81*(1 - 2*x)^(13/2))/4 - (81*(1 - 2*x)^(15/2))/64]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x), x, 2, (-26411*(1 - 2*x)^(3/2))/96 + (57281*(1 - 2*x)^(5/2))/160 - (3549*(1 - 2*x)^(7/2))/16 + (1197*(1 - 2*x)^(9/2))/16 - (4671*(1 - 2*x)^(11/2))/352 + (405*(1 - 2*x)^(13/2))/416]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x), x, 2, (-3773*(1 - 2*x)^(3/2))/48 + (3283*(1 - 2*x)^(5/2))/40 - (153*(1 - 2*x)^(7/2))/4 + (69*(1 - 2*x)^(9/2))/8 - (135*(1 - 2*x)^(11/2))/176]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x), x, 2, (-539*(1 - 2*x)^(3/2))/24 + (707*(1 - 2*x)^(5/2))/40 - (309*(1 - 2*x)^(7/2))/56 + (5*(1 - 2*x)^(9/2))/8]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x), x, 2, (-77*(1 - 2*x)^(3/2))/12 + (17*(1 - 2*x)^(5/2))/5 - (15*(1 - 2*x)^(7/2))/28]
    @test_int [sqrt(1 - 2*x)*(3 + 5*x), x, 2, (-11*(1 - 2*x)^(3/2))/6 + (1 - 2*x)^(5/2)/2]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x))/(2 + 3*x), x, 4, (-2*sqrt(1 - 2*x))/9 - (5*(1 - 2*x)^(3/2))/9 + (2*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/9]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x))/(2 + 3*x)^2, x, 4, (8*sqrt(1 - 2*x))/7 + (1 - 2*x)^(3/2)/(21*(2 + 3*x)) - (8*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/sqrt(21)]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x))/(2 + 3*x)^3, x, 4, (1 - 2*x)^(3/2)/(42*(2 + 3*x)^2) - (23*sqrt(1 - 2*x))/(42*(2 + 3*x)) + (23*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(21*sqrt(21))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x))/(2 + 3*x)^4, x, 5, (1 - 2*x)^(3/2)/(63*(2 + 3*x)^3) - (17*sqrt(1 - 2*x))/(63*(2 + 3*x)^2) + (17*sqrt(1 - 2*x))/(441*(2 + 3*x)) + (34*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(441*sqrt(21))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x))/(2 + 3*x)^5, x, 6, (1 - 2*x)^(3/2)/(84*(2 + 3*x)^4) - (5*sqrt(1 - 2*x))/(28*(2 + 3*x)^3) + (5*sqrt(1 - 2*x))/(392*(2 + 3*x)^2) + (15*sqrt(1 - 2*x))/(2744*(2 + 3*x)) + (5*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/1372]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x))/(2 + 3*x)^6, x, 7, (1 - 2*x)^(3/2)/(105*(2 + 3*x)^5) - (2*sqrt(1 - 2*x))/(15*(2 + 3*x)^4) + (2*sqrt(1 - 2*x))/(315*(2 + 3*x)^3) + sqrt(1 - 2*x)/(441*(2 + 3*x)^2) + sqrt(1 - 2*x)/(1029*(2 + 3*x)) + (2*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(1029*sqrt(21))]

    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^2, x, 2, (-(290521/192))*(1 - 2*x)^(3/2) + (381073/160)*(1 - 2*x)^(5/2) - (118993/64)*(1 - 2*x)^(7/2) + (40453/48)*(1 - 2*x)^(9/2) - (159111/704)*(1 - 2*x)^(11/2) + (13905/416)*(1 - 2*x)^(13/2) - (135/64)*(1 - 2*x)^(15/2)]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^2, x, 2, (-(41503/96))*(1 - 2*x)^(3/2) + (91091/160)*(1 - 2*x)^(5/2) - (5711/16)*(1 - 2*x)^(7/2) + (1949/16)*(1 - 2*x)^(9/2) - (7695/352)*(1 - 2*x)^(11/2) + (675/416)*(1 - 2*x)^(13/2)]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^2, x, 2, (-(5929/48))*(1 - 2*x)^(3/2) + (1309/10)*(1 - 2*x)^(5/2) - (3467/56)*(1 - 2*x)^(7/2) + (85/6)*(1 - 2*x)^(9/2) - (225/176)*(1 - 2*x)^(11/2)]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^2, x, 2, (-847*(1 - 2*x)^(3/2))/24 + (1133*(1 - 2*x)^(5/2))/40 - (505*(1 - 2*x)^(7/2))/56 + (25*(1 - 2*x)^(9/2))/24]
    @test_int [sqrt(1 - 2*x)*(3 + 5*x)^2, x, 2, (-121*(1 - 2*x)^(3/2))/12 + (11*(1 - 2*x)^(5/2))/2 - (25*(1 - 2*x)^(7/2))/28]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x), x, 5, (2/27)*sqrt(1 - 2*x) - (155/54)*(1 - 2*x)^(3/2) + (5/6)*(1 - 2*x)^(5/2) - (2/27)*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^2, x, 5, (-(142/189))*sqrt(1 - 2*x) - (25/27)*(1 - 2*x)^(3/2) - (1 - 2*x)^(3/2)/(63*(2 + 3*x)) + (142*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(27*sqrt(21))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^3, x, 5, (863/441)*sqrt(1 - 2*x) - (1 - 2*x)^(3/2)/(126*(2 + 3*x)^2) + (139*(1 - 2*x)^(3/2))/(882*(2 + 3*x)) - (863*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(63*sqrt(21))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^4, x, 5, -((1 - 2*x)^(3/2)/(189*(2 + 3*x)^3)) + (23*(1 - 2*x)^(3/2))/(294*(2 + 3*x)^2) - (2381*sqrt(1 - 2*x))/(2646*(2 + 3*x)) + (2381*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(1323*sqrt(21))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^5, x, 6, -((1 - 2*x)^(3/2)/(252*(2 + 3*x)^4)) + (275*(1 - 2*x)^(3/2))/(5292*(2 + 3*x)^3) - (4625*sqrt(1 - 2*x))/(10584*(2 + 3*x)^2) + (4625*sqrt(1 - 2*x))/(74088*(2 + 3*x)) + (4625*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(37044*sqrt(21))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^6, x, 7, -((1 - 2*x)^(3/2)/(315*(2 + 3*x)^5)) + (7*(1 - 2*x)^(3/2))/(180*(2 + 3*x)^4) - (31*sqrt(1 - 2*x))/(108*(2 + 3*x)^3) + (31*sqrt(1 - 2*x))/(1512*(2 + 3*x)^2) + (31*sqrt(1 - 2*x))/(3528*(2 + 3*x)) + (31*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(1764*sqrt(21))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^2)/(2 + 3*x)^7, x, 8, -((1 - 2*x)^(3/2)/(378*(2 + 3*x)^6)) + (137*(1 - 2*x)^(3/2))/(4410*(2 + 3*x)^5) - (1613*sqrt(1 - 2*x))/(7560*(2 + 3*x)^4) + (1613*sqrt(1 - 2*x))/(158760*(2 + 3*x)^3) + (1613*sqrt(1 - 2*x))/(444528*(2 + 3*x)^2) + (1613*sqrt(1 - 2*x))/(1037232*(2 + 3*x)) + (1613*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(518616*sqrt(21))]

    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^3, x, 2, (-(3195731/384))*(1 - 2*x)^(3/2) + (9836211/640)*(1 - 2*x)^(5/2) - (1853313/128)*(1 - 2*x)^(7/2) + (9504551*(1 - 2*x)^(9/2))/1152 - (4177401*(1 - 2*x)^(11/2))/1408 + (1101465*(1 - 2*x)^(13/2))/1664 - (10755/128)*(1 - 2*x)^(15/2) + (10125*(1 - 2*x)^(17/2))/2176]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^3, x, 2, (-(456533/192))*(1 - 2*x)^(3/2) + (302379/80)*(1 - 2*x)^(5/2) - (190707/64)*(1 - 2*x)^(7/2) + (98209/72)*(1 - 2*x)^(9/2) - (260055/704)*(1 - 2*x)^(11/2) + (11475/208)*(1 - 2*x)^(13/2) - (225/64)*(1 - 2*x)^(15/2)]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^3, x, 2, (-(65219/96))*(1 - 2*x)^(3/2) + (144837/160)*(1 - 2*x)^(5/2) - (64317/112)*(1 - 2*x)^(7/2) + (28555/144)*(1 - 2*x)^(9/2) - (12675/352)*(1 - 2*x)^(11/2) + (1125/416)*(1 - 2*x)^(13/2)]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^3, x, 2, (-9317*(1 - 2*x)^(3/2))/48 + (8349*(1 - 2*x)^(5/2))/40 - (2805*(1 - 2*x)^(7/2))/28 + (1675*(1 - 2*x)^(9/2))/72 - (375*(1 - 2*x)^(11/2))/176]
    @test_int [sqrt(1 - 2*x)*(3 + 5*x)^3, x, 2, (-1331*(1 - 2*x)^(3/2))/24 + (363*(1 - 2*x)^(5/2))/8 - (825*(1 - 2*x)^(7/2))/56 + (125*(1 - 2*x)^(9/2))/72]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x), x, 5, (-(2/81))*sqrt(1 - 2*x) - (5135/324)*(1 - 2*x)^(3/2) + (80/9)*(1 - 2*x)^(5/2) - (125/84)*(1 - 2*x)^(7/2) + (2/81)*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^2, x, 5, (7/9)*sqrt(1 - 2*x)*(3 + 5*x)^2 - (sqrt(1 - 2*x)*(3 + 5*x)^3)/(3*(2 + 3*x)) - (2/81)*sqrt(1 - 2*x)*(211 + 170*x) - (212*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(81*sqrt(21))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^3, x, 5, -((53*sqrt(1 - 2*x)*(3 + 5*x)^2)/(63*(2 + 3*x))) - (sqrt(1 - 2*x)*(3 + 5*x)^3)/(6*(2 + 3*x)^2) + (5*sqrt(1 - 2*x)*(323 + 2815*x))/1134 + (7559*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(567*sqrt(21))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^4, x, 5, -((53*sqrt(1 - 2*x)*(3 + 5*x)^2)/(189*(2 + 3*x)^2)) - (sqrt(1 - 2*x)*(3 + 5*x)^3)/(9*(2 + 3*x)^3) + (2*sqrt(1 - 2*x)*(18016 + 26075*x))/(3969*(2 + 3*x)) - (92996*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(3969*sqrt(21))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^5, x, 5, -((53*sqrt(1 - 2*x)*(3 + 5*x)^2)/(378*(2 + 3*x)^3)) - (sqrt(1 - 2*x)*(3 + 5*x)^3)/(12*(2 + 3*x)^4) - (5*sqrt(1 - 2*x)*(70429 + 110981*x))/(222264*(2 + 3*x)^2) + (328715*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(111132*sqrt(21))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^6, x, 6, (11237*sqrt(1 - 2*x))/(111132*(2 + 3*x)) - (53*sqrt(1 - 2*x)*(3 + 5*x)^2)/(630*(2 + 3*x)^4) - (sqrt(1 - 2*x)*(3 + 5*x)^3)/(15*(2 + 3*x)^5) - (sqrt(1 - 2*x)*(37224 + 59665*x))/(79380*(2 + 3*x)^3) + (11237*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(55566*sqrt(21))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^7, x, 7, (43957*sqrt(1 - 2*x))/(1333584*(2 + 3*x)^2) + (43957*sqrt(1 - 2*x))/(3111696*(2 + 3*x)) - (53*sqrt(1 - 2*x)*(3 + 5*x)^2)/(945*(2 + 3*x)^5) - (sqrt(1 - 2*x)*(3 + 5*x)^3)/(18*(2 + 3*x)^6) - (sqrt(1 - 2*x)*(98995 + 160029*x))/(476280*(2 + 3*x)^4) + (43957*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(1555848*sqrt(21))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^8, x, 8, (47434*sqrt(1 - 2*x))/(2917215*(2 + 3*x)^3) + (23717*sqrt(1 - 2*x))/(4084101*(2 + 3*x)^2) + (23717*sqrt(1 - 2*x))/(9529569*(2 + 3*x)) - (53*sqrt(1 - 2*x)*(3 + 5*x)^2)/(1323*(2 + 3*x)^6) - (sqrt(1 - 2*x)*(3 + 5*x)^3)/(21*(2 + 3*x)^7) - (2*sqrt(1 - 2*x)*(54227 + 88099*x))/(972405*(2 + 3*x)^5) + (47434*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(9529569*sqrt(21))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^4)/(3 + 5*x), x, 5, (2*sqrt(1 - 2*x))/3125 - (45473*(1 - 2*x)^(3/2))/5000 + (34371*(1 - 2*x)^(5/2))/5000 - (2889*(1 - 2*x)^(7/2))/1400 + (9/40)*(1 - 2*x)^(9/2) - (2*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/3125]
    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^3)/(3 + 5*x), x, 5, (2/625)*sqrt(1 - 2*x) - (1299/500)*(1 - 2*x)^(3/2) + (162/125)*(1 - 2*x)^(5/2) - (27/140)*(1 - 2*x)^(7/2) - (2/625)*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^2)/(3 + 5*x), x, 5, (2/125)*sqrt(1 - 2*x) - (37/50)*(1 - 2*x)^(3/2) + (9/50)*(1 - 2*x)^(5/2) - (2/125)*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(sqrt(1 - 2*x)*(2 + 3*x))/(3 + 5*x), x, 4, (2*sqrt(1 - 2*x))/25 - (1 - 2*x)^(3/2)/5 - (2*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/25]
    @test_int [sqrt(1 - 2*x)/(3 + 5*x), x, 3, (2*sqrt(1 - 2*x))/5 - (2*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/5]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)*(3 + 5*x)), x, 5, 2*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - 2*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^2*(3 + 5*x)), x, 6, sqrt(1 - 2*x)/(2 + 3*x) + (68*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/sqrt(21) - 2*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^3*(3 + 5*x)), x, 7, sqrt(1 - 2*x)/(2*(2 + 3*x)^2) + (69*sqrt(1 - 2*x))/(14*(2 + 3*x)) + (793*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/7 - 10*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^4*(3 + 5*x)), x, 8, sqrt(1 - 2*x)/(3*(2 + 3*x)^3) + (52*sqrt(1 - 2*x))/(21*(2 + 3*x)^2) + (1207*sqrt(1 - 2*x))/(49*(2 + 3*x)) + (83264*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(49*sqrt(21)) - 50*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^5*(3 + 5*x)), x, 9, sqrt(1 - 2*x)/(4*(2 + 3*x)^4) + (139*sqrt(1 - 2*x))/(84*(2 + 3*x)^3) + (14555*sqrt(1 - 2*x))/(1176*(2 + 3*x)^2) + (337955*sqrt(1 - 2*x))/(2744*(2 + 3*x)) + (11656955*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(1372*sqrt(21)) - 250*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]

    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^5)/(3 + 5*x)^2, x, 7, -((172*sqrt(1 - 2*x)*(2 + 3*x)^2)/3125) + (64*sqrt(1 - 2*x)*(2 + 3*x)^3)/2625 + (11/75)*sqrt(1 - 2*x)*(2 + 3*x)^4 - (sqrt(1 - 2*x)*(2 + 3*x)^5)/(5*(3 + 5*x)) - (4*sqrt(1 - 2*x)*(10998 + 3625*x))/15625 - (328*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(15625*sqrt(55))]
    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^4)/(3 + 5*x)^2, x, 6, (12/625)*sqrt(1 - 2*x)*(2 + 3*x)^2 + (27/175)*sqrt(1 - 2*x)*(2 + 3*x)^3 - (sqrt(1 - 2*x)*(2 + 3*x)^4)/(5*(3 + 5*x)) - (3*sqrt(1 - 2*x)*(1256 + 375*x))/3125 - (262*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(3125*sqrt(55))]
    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^3)/(3 + 5*x)^2, x, 6, (-294*sqrt(1 - 2*x))/625 + (21*sqrt(1 - 2*x)*(2 + 3*x)^2)/125 - (sqrt(1 - 2*x)*(2 + 3*x)^3)/(5*(3 + 5*x)) - (196*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(625*sqrt(55))]
    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^2)/(3 + 5*x)^2, x, 5, (26/275)*sqrt(1 - 2*x) - (3/25)*(1 - 2*x)^(3/2) - (1 - 2*x)^(3/2)/(275*(3 + 5*x)) - (26*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(25*sqrt(55))]
    @test_int [(sqrt(1 - 2*x)*(2 + 3*x))/(3 + 5*x)^2, x, 4, (64*sqrt(1 - 2*x))/275 - (1 - 2*x)^(3/2)/(55*(3 + 5*x)) - (64*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(25*sqrt(55))]
    @test_int [sqrt(1 - 2*x)/(3 + 5*x)^2, x, 3, -sqrt(1 - 2*x)/(5*(3 + 5*x)) + (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(5*sqrt(55))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)*(3 + 5*x)^2), x, 6, -(sqrt(1 - 2*x)/(3 + 5*x)) - 2*sqrt(21)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) + (68*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/sqrt(55)]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^2*(3 + 5*x)^2), x, 7, (-10*sqrt(1 - 2*x))/(3 + 5*x) + sqrt(1 - 2*x)/((2 + 3*x)*(3 + 5*x)) - 138*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) + 134*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^3*(3 + 5*x)^2), x, 8, (-1045*sqrt(1 - 2*x))/(14*(3 + 5*x)) + sqrt(1 - 2*x)/(2*(2 + 3*x)^2*(3 + 5*x)) + (52*sqrt(1 - 2*x))/(7*(2 + 3*x)*(3 + 5*x)) - (7209*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/7 + 1000*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^4*(3 + 5*x)^2), x, 9, (-48645*sqrt(1 - 2*x))/(98*(3 + 5*x)) + sqrt(1 - 2*x)/(3*(2 + 3*x)^3*(3 + 5*x)) + (139*sqrt(1 - 2*x))/(42*(2 + 3*x)^2*(3 + 5*x)) + (7261*sqrt(1 - 2*x))/(147*(2 + 3*x)*(3 + 5*x)) - (335579*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/49 + 6650*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]

    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^4)/(3 + 5*x)^3, x, 6, -((21*(704 - 375*x)*sqrt(1 - 2*x))/68750) + (1428*sqrt(1 - 2*x)*(2 + 3*x)^2)/6875 - (sqrt(1 - 2*x)*(2 + 3*x)^4)/(10*(3 + 5*x)^2) - (131*sqrt(1 - 2*x)*(2 + 3*x)^3)/(550*(3 + 5*x)) - (12803*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(34375*sqrt(55))]
    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^3)/(3 + 5*x)^3, x, 5, -((sqrt(1 - 2*x)*(2 + 3*x)^3)/(10*(3 + 5*x)^2)) - (49*sqrt(1 - 2*x)*(2 + 3*x)^2)/(275*(3 + 5*x)) + (21*sqrt(1 - 2*x)*(44 + 75*x))/2750 - (1267*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(1375*sqrt(55))]
    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^2)/(3 + 5*x)^3, x, 5, (409*sqrt(1 - 2*x))/3025 - (1 - 2*x)^(3/2)/(550*(3 + 5*x)^2) - (133*(1 - 2*x)^(3/2))/(6050*(3 + 5*x)) - (409*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(275*sqrt(55))]
    @test_int [(sqrt(1 - 2*x)*(2 + 3*x))/(3 + 5*x)^3, x, 4, -(1 - 2*x)^(3/2)/(110*(3 + 5*x)^2) - (67*sqrt(1 - 2*x))/(550*(3 + 5*x)) + (67*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(275*sqrt(55))]
    @test_int [sqrt(1 - 2*x)/(3 + 5*x)^3, x, 4, -sqrt(1 - 2*x)/(10*(3 + 5*x)^2) + sqrt(1 - 2*x)/(110*(3 + 5*x)) + atanh(sqrt(5/11)*sqrt(1 - 2*x))/(55*sqrt(55))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)*(3 + 5*x)^3), x, 7, -sqrt(1 - 2*x)/(2*(3 + 5*x)^2) + (67*sqrt(1 - 2*x))/(22*(3 + 5*x)) + 6*sqrt(21)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (2243*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(11*sqrt(55))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^2*(3 + 5*x)^3), x, 8, (-15*sqrt(1 - 2*x))/(2*(3 + 5*x)^2) + sqrt(1 - 2*x)/((2 + 3*x)*(3 + 5*x)^2) + (995*sqrt(1 - 2*x))/(22*(3 + 5*x)) + 624*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (6665*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/11]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^3*(3 + 5*x)^3), x, 9, (-1045*sqrt(1 - 2*x))/(14*(3 + 5*x)^2) + sqrt(1 - 2*x)/(2*(2 + 3*x)^2*(3 + 5*x)^2) + (139*sqrt(1 - 2*x))/(14*(2 + 3*x)*(3 + 5*x)^2) + (34655*sqrt(1 - 2*x))/(77*(3 + 5*x)) + (43467*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/7 - (66325*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/11]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^4*(3 + 5*x)^3), x, 10, (-182335*sqrt(1 - 2*x))/(294*(3 + 5*x)^2) + sqrt(1 - 2*x)/(3*(2 + 3*x)^3*(3 + 5*x)^2) + (29*sqrt(1 - 2*x))/(7*(2 + 3*x)^2*(3 + 5*x)^2) + (4042*sqrt(1 - 2*x))/(49*(2 + 3*x)*(3 + 5*x)^2) + (4031135*sqrt(1 - 2*x))/(1078*(3 + 5*x)) + (2528082*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/49 - (551075*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/11]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(2+3*x)^m*(3+5*x)^n*(1-2*x)^(3/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^6*(3 + 5*x), x, 2, (-1294139*(1 - 2*x)^(5/2))/640 + (559433*(1 - 2*x)^(7/2))/128 - (564235*(1 - 2*x)^(9/2))/128 + (3658095*(1 - 2*x)^(11/2))/1408 - (1580985*(1 - 2*x)^(13/2))/1664 + (136647*(1 - 2*x)^(15/2))/640 - (59049*(1 - 2*x)^(17/2))/2176 + (3645*(1 - 2*x)^(19/2))/2432]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^5*(3 + 5*x), x, 2, (-184877*(1 - 2*x)^(5/2))/320 + (8575*(1 - 2*x)^(7/2))/8 - (173215*(1 - 2*x)^(9/2))/192 + (37485*(1 - 2*x)^(11/2))/88 - (97335*(1 - 2*x)^(13/2))/832 + (351*(1 - 2*x)^(15/2))/20 - (1215*(1 - 2*x)^(17/2))/1088]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x), x, 2, (-26411*(1 - 2*x)^(5/2))/160 + (8183*(1 - 2*x)^(7/2))/32 - (8281*(1 - 2*x)^(9/2))/48 + (10773*(1 - 2*x)^(11/2))/176 - (4671*(1 - 2*x)^(13/2))/416 + (27*(1 - 2*x)^(15/2))/32]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x), x, 2, (-3773*(1 - 2*x)^(5/2))/80 + (469*(1 - 2*x)^(7/2))/8 - (119*(1 - 2*x)^(9/2))/4 + (621*(1 - 2*x)^(11/2))/88 - (135*(1 - 2*x)^(13/2))/208]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x), x, 2, (-539*(1 - 2*x)^(5/2))/40 + (101*(1 - 2*x)^(7/2))/8 - (103*(1 - 2*x)^(9/2))/24 + (45*(1 - 2*x)^(11/2))/88]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x), x, 2, (-77*(1 - 2*x)^(5/2))/20 + (17*(1 - 2*x)^(7/2))/7 - (5*(1 - 2*x)^(9/2))/12]
    @test_int [(1 - 2*x)^(3/2)*(3 + 5*x), x, 2, (-11*(1 - 2*x)^(5/2))/10 + (5*(1 - 2*x)^(7/2))/14]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x), x, 5, (-14*sqrt(1 - 2*x))/27 - (2*(1 - 2*x)^(3/2))/27 - (1 - 2*x)^(5/2)/3 + (14*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/27]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x)^2, x, 5, (76*sqrt(1 - 2*x))/27 + (76*(1 - 2*x)^(3/2))/189 + (1 - 2*x)^(5/2)/(21*(2 + 3*x)) - (76*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/27]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x)^3, x, 5, (-71*sqrt(1 - 2*x))/63 + (1 - 2*x)^(5/2)/(42*(2 + 3*x)^2) - (71*(1 - 2*x)^(3/2))/(126*(2 + 3*x)) + (71*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(9*sqrt(21))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x)^4, x, 5, (1 - 2*x)^(5/2)/(63*(2 + 3*x)^3) - (52*(1 - 2*x)^(3/2))/(189*(2 + 3*x)^2) + (52*sqrt(1 - 2*x))/(189*(2 + 3*x)) - (104*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(189*sqrt(21))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x)^5, x, 6, (1 - 2*x)^(5/2)/(84*(2 + 3*x)^4) - (137*(1 - 2*x)^(3/2))/(756*(2 + 3*x)^3) + (137*sqrt(1 - 2*x))/(1512*(2 + 3*x)^2) - (137*sqrt(1 - 2*x))/(10584*(2 + 3*x)) - (137*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(5292*sqrt(21))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x))/(2 + 3*x)^6, x, 7, (1 - 2*x)^(5/2)/(105*(2 + 3*x)^5) - (17*(1 - 2*x)^(3/2))/(126*(2 + 3*x)^4) + (17*sqrt(1 - 2*x))/(378*(2 + 3*x)^3) - (17*sqrt(1 - 2*x))/(5292*(2 + 3*x)^2) - (17*sqrt(1 - 2*x))/(12348*(2 + 3*x)) - (17*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(6174*sqrt(21))]

    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x)^2, x, 2, (-290521*(1 - 2*x)^(5/2))/320 + (54439*(1 - 2*x)^(7/2))/32 - (832951*(1 - 2*x)^(9/2))/576 + (121359*(1 - 2*x)^(11/2))/176 - (159111*(1 - 2*x)^(13/2))/832 + (927*(1 - 2*x)^(15/2))/32 - (2025*(1 - 2*x)^(17/2))/1088]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^2, x, 2, (-41503*(1 - 2*x)^(5/2))/160 + (13013*(1 - 2*x)^(7/2))/32 - (39977*(1 - 2*x)^(9/2))/144 + (17541*(1 - 2*x)^(11/2))/176 - (7695*(1 - 2*x)^(13/2))/416 + (45*(1 - 2*x)^(15/2))/32]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^2, x, 2, (-5929*(1 - 2*x)^(5/2))/80 + (187*(1 - 2*x)^(7/2))/2 - (3467*(1 - 2*x)^(9/2))/72 + (255*(1 - 2*x)^(11/2))/22 - (225*(1 - 2*x)^(13/2))/208]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^2, x, 2, (-847*(1 - 2*x)^(5/2))/40 + (1133*(1 - 2*x)^(7/2))/56 - (505*(1 - 2*x)^(9/2))/72 + (75*(1 - 2*x)^(11/2))/88]
    @test_int [(1 - 2*x)^(3/2)*(3 + 5*x)^2, x, 2, (-121*(1 - 2*x)^(5/2))/20 + (55*(1 - 2*x)^(7/2))/14 - (25*(1 - 2*x)^(9/2))/36]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x), x, 6, (14*sqrt(1 - 2*x))/81 + (2*(1 - 2*x)^(3/2))/81 - (31*(1 - 2*x)^(5/2))/18 + (25*(1 - 2*x)^(7/2))/42 - (14*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/81]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^2, x, 6, (-146*sqrt(1 - 2*x))/81 - (146*(1 - 2*x)^(3/2))/567 - (5*(1 - 2*x)^(5/2))/9 - (1 - 2*x)^(5/2)/(63*(2 + 3*x)) + (146*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/81]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^3, x, 6, (2873*sqrt(1 - 2*x))/567 + (2873*(1 - 2*x)^(3/2))/3969 - (1 - 2*x)^(5/2)/(126*(2 + 3*x)^2) + (47*(1 - 2*x)^(5/2))/(294*(2 + 3*x)) - (2873*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(81*sqrt(21))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^4, x, 6, (-7559*sqrt(1 - 2*x))/3969 - (1 - 2*x)^(5/2)/(189*(2 + 3*x)^3) + (209*(1 - 2*x)^(5/2))/(2646*(2 + 3*x)^2) - (7559*(1 - 2*x)^(3/2))/(7938*(2 + 3*x)) + (7559*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(567*sqrt(21))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^5, x, 6, -(1 - 2*x)^(5/2)/(252*(2 + 3*x)^4) + (277*(1 - 2*x)^(5/2))/(5292*(2 + 3*x)^3) - (14423*(1 - 2*x)^(3/2))/(31752*(2 + 3*x)^2) + (14423*sqrt(1 - 2*x))/(31752*(2 + 3*x)) - (14423*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(15876*sqrt(21))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^6, x, 7, -(1 - 2*x)^(5/2)/(315*(2 + 3*x)^5) + (23*(1 - 2*x)^(5/2))/(588*(2 + 3*x)^4) - (4693*(1 - 2*x)^(3/2))/(15876*(2 + 3*x)^3) + (4693*sqrt(1 - 2*x))/(31752*(2 + 3*x)^2) - (4693*sqrt(1 - 2*x))/(222264*(2 + 3*x)) - (4693*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(111132*sqrt(21))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^7, x, 8, -(1 - 2*x)^(5/2)/(378*(2 + 3*x)^6) + (59*(1 - 2*x)^(5/2))/(1890*(2 + 3*x)^5) - (991*(1 - 2*x)^(3/2))/(4536*(2 + 3*x)^4) + (991*sqrt(1 - 2*x))/(13608*(2 + 3*x)^3) - (991*sqrt(1 - 2*x))/(190512*(2 + 3*x)^2) - (991*sqrt(1 - 2*x))/(444528*(2 + 3*x)) - (991*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(222264*sqrt(21))]

    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x)^3, x, 2, (-3195731*(1 - 2*x)^(5/2))/640 + (1405173*(1 - 2*x)^(7/2))/128 - (4324397*(1 - 2*x)^(9/2))/384 + (9504551*(1 - 2*x)^(11/2))/1408 - (4177401*(1 - 2*x)^(13/2))/1664 + (73431*(1 - 2*x)^(15/2))/128 - (161325*(1 - 2*x)^(17/2))/2176 + (10125*(1 - 2*x)^(19/2))/2432]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^3, x, 2, (-456533*(1 - 2*x)^(5/2))/320 + (43197*(1 - 2*x)^(7/2))/16 - (444983*(1 - 2*x)^(9/2))/192 + (98209*(1 - 2*x)^(11/2))/88 - (260055*(1 - 2*x)^(13/2))/832 + (765*(1 - 2*x)^(15/2))/16 - (3375*(1 - 2*x)^(17/2))/1088]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^3, x, 2, (-65219*(1 - 2*x)^(5/2))/160 + (20691*(1 - 2*x)^(7/2))/32 - (21439*(1 - 2*x)^(9/2))/48 + (28555*(1 - 2*x)^(11/2))/176 - (975*(1 - 2*x)^(13/2))/32 + (75*(1 - 2*x)^(15/2))/32]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^3, x, 2, (-9317*(1 - 2*x)^(5/2))/80 + (8349*(1 - 2*x)^(7/2))/56 - (935*(1 - 2*x)^(9/2))/12 + (1675*(1 - 2*x)^(11/2))/88 - (375*(1 - 2*x)^(13/2))/208]
    @test_int [(1 - 2*x)^(3/2)*(3 + 5*x)^3, x, 2, (-1331*(1 - 2*x)^(5/2))/40 + (1815*(1 - 2*x)^(7/2))/56 - (275*(1 - 2*x)^(9/2))/24 + (125*(1 - 2*x)^(11/2))/88]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x), x, 6, (-14*sqrt(1 - 2*x))/243 - (2*(1 - 2*x)^(3/2))/243 - (1027*(1 - 2*x)^(5/2))/108 + (400*(1 - 2*x)^(7/2))/63 - (125*(1 - 2*x)^(9/2))/108 + (14*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/243]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^2, x, 6, (8/9)*sqrt(1 - 2*x) + (5/7)*(1 - 2*x)^(3/2)*(3 + 5*x)^2 - ((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(3*(2 + 3*x)) - (10/63)*(1 - 2*x)^(3/2)*(22 + 27*x) - (8/9)*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^3, x, 6, (-(31/3))*sqrt(1 - 2*x)*(3 + 5*x)^2 - ((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(6*(2 + 3*x)^2) + (6*sqrt(1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x) + (1/54)*sqrt(1 - 2*x)*(367 + 1715*x) + (887*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(27*sqrt(21))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^4, x, 6, (251*sqrt(1 - 2*x)*(3 + 5*x)^2)/(63*(2 + 3*x)) - ((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(9*(2 + 3*x)^3) + (2*sqrt(1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^2 - (5/567)*sqrt(1 - 2*x)*(2323 + 7265*x) - (36038*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(567*sqrt(21))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^5, x, 6, (13*sqrt(1 - 2*x)*(3 + 5*x)^2)/(56*(2 + 3*x)^2) - ((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(12*(2 + 3*x)^4) + (sqrt(1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^3 - (sqrt(1 - 2*x)*(18187 + 26775*x))/(1176*(2 + 3*x)) + (13243*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(588*sqrt(21))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^6, x, 6, -((67*sqrt(1 - 2*x)*(3 + 5*x)^2)/(315*(2 + 3*x)^3)) - ((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(15*(2 + 3*x)^5) + (3*sqrt(1 - 2*x)*(3 + 5*x)^3)/(5*(2 + 3*x)^4) - (2*sqrt(1 - 2*x)*(9529 + 15074*x))/(9261*(2 + 3*x)^2) - (13892*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(9261*sqrt(21))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^7, x, 7, -((15313*sqrt(1 - 2*x))/(444528*(2 + 3*x))) - (653*sqrt(1 - 2*x)*(3 + 5*x)^2)/(2520*(2 + 3*x)^4) - ((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(18*(2 + 3*x)^6) + (2*sqrt(1 - 2*x)*(3 + 5*x)^3)/(5*(2 + 3*x)^5) - (sqrt(1 - 2*x)*(413424 + 664915*x))/(317520*(2 + 3*x)^3) - (15313*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(222264*sqrt(21))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^8, x, 8, -((4369*sqrt(1 - 2*x))/(518616*(2 + 3*x)^2)) - (4369*sqrt(1 - 2*x))/(1210104*(2 + 3*x)) - (173*sqrt(1 - 2*x)*(3 + 5*x)^2)/(735*(2 + 3*x)^5) - ((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(21*(2 + 3*x)^7) + (2*sqrt(1 - 2*x)*(3 + 5*x)^3)/(7*(2 + 3*x)^6) - (sqrt(1 - 2*x)*(146585 + 237807*x))/(185220*(2 + 3*x)^4) - (4369*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(605052*sqrt(21))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^6)/(3 + 5*x), x, 6, (22*sqrt(1 - 2*x))/390625 + (2*(1 - 2*x)^(3/2))/234375 - (167115051*(1 - 2*x)^(5/2))/2500000 + (70752609*(1 - 2*x)^(7/2))/700000 - (665817*(1 - 2*x)^(9/2))/10000 + (507627*(1 - 2*x)^(11/2))/22000 - (43011*(1 - 2*x)^(13/2))/10400 + (243*(1 - 2*x)^(15/2))/800 - (22*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/390625]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^5)/(3 + 5*x), x, 6, (22*sqrt(1 - 2*x))/78125 + (2*(1 - 2*x)^(3/2))/46875 - (4774713*(1 - 2*x)^(5/2))/250000 + (806121*(1 - 2*x)^(7/2))/35000 - (5673*(1 - 2*x)^(9/2))/500 + (5751*(1 - 2*x)^(11/2))/2200 - (243*(1 - 2*x)^(13/2))/1040 - (22*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/78125]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^4)/(3 + 5*x), x, 6, (22*sqrt(1 - 2*x))/15625 + (2*(1 - 2*x)^(3/2))/9375 - (136419*(1 - 2*x)^(5/2))/25000 + (34371*(1 - 2*x)^(7/2))/7000 - (321*(1 - 2*x)^(9/2))/200 + (81*(1 - 2*x)^(11/2))/440 - (22*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/15625]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^3)/(3 + 5*x), x, 6, (22*sqrt(1 - 2*x))/3125 + (2*(1 - 2*x)^(3/2))/1875 - (3897*(1 - 2*x)^(5/2))/2500 + (162*(1 - 2*x)^(7/2))/175 - (3*(1 - 2*x)^(9/2))/20 - (22*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/3125]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^2)/(3 + 5*x), x, 6, (22*sqrt(1 - 2*x))/625 + (2*(1 - 2*x)^(3/2))/375 - (111*(1 - 2*x)^(5/2))/250 + (9*(1 - 2*x)^(7/2))/70 - (22*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/625]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x))/(3 + 5*x), x, 5, (22*sqrt(1 - 2*x))/125 + (2*(1 - 2*x)^(3/2))/75 - (3*(1 - 2*x)^(5/2))/25 - (22*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/125]
    @test_int [(1 - 2*x)^(3/2)/(3 + 5*x), x, 4, (22*sqrt(1 - 2*x))/25 + (2*(1 - 2*x)^(3/2))/15 - (22*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/25]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)*(3 + 5*x)), x, 6, (-4*sqrt(1 - 2*x))/15 + (14*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/3 - (22*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/5]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^2*(3 + 5*x)), x, 6, (7*sqrt(1 - 2*x))/(3*(2 + 3*x)) + (64*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/3 - 22*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^3*(3 + 5*x)), x, 7, (7*sqrt(1 - 2*x))/(6*(2 + 3*x)^2) + (65*sqrt(1 - 2*x))/(6*(2 + 3*x)) + (2243*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(3*sqrt(21)) - 22*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^4*(3 + 5*x)), x, 8, (7*sqrt(1 - 2*x))/(9*(2 + 3*x)^3) + (49*sqrt(1 - 2*x))/(9*(2 + 3*x)^2) + (1138*sqrt(1 - 2*x))/(21*(2 + 3*x)) + (78506*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(21*sqrt(21)) - 110*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^5*(3 + 5*x)), x, 9, (7*sqrt(1 - 2*x))/(12*(2 + 3*x)^4) + (131*sqrt(1 - 2*x))/(36*(2 + 3*x)^3) + (13723*sqrt(1 - 2*x))/(504*(2 + 3*x)^2) + (318643*sqrt(1 - 2*x))/(1176*(2 + 3*x)) + (10990843*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(588*sqrt(21)) - 550*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^6*(3 + 5*x)), x, 10, (7*sqrt(1 - 2*x))/(15*(2 + 3*x)^5) + (41*sqrt(1 - 2*x))/(15*(2 + 3*x)^4) + (5732*sqrt(1 - 2*x))/(315*(2 + 3*x)^3) + (120077*sqrt(1 - 2*x))/(882*(2 + 3*x)^2) + (2788127*sqrt(1 - 2*x))/(2058*(2 + 3*x)) + (96169877*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(1029*sqrt(21)) - 2750*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]

    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^5)/(3 + 5*x)^2, x, 8, (324*sqrt(1 - 2*x))/78125 - (4016*(1 - 2*x)^(3/2)*(2 + 3*x)^2)/48125 + (38*(1 - 2*x)^(3/2)*(2 + 3*x)^3)/4125 + (39/275)*(1 - 2*x)^(3/2)*(2 + 3*x)^4 - ((1 - 2*x)^(3/2)*(2 + 3*x)^5)/(5*(3 + 5*x)) - (2*(1 - 2*x)^(3/2)*(298462 + 204777*x))/515625 - (324*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/78125]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^4)/(3 + 5*x)^2, x, 7, (258*sqrt(1 - 2*x))/15625 - (2/875)*(1 - 2*x)^(3/2)*(2 + 3*x)^2 + (11/75)*(1 - 2*x)^(3/2)*(2 + 3*x)^3 - ((1 - 2*x)^(3/2)*(2 + 3*x)^4)/(5*(3 + 5*x)) - ((1 - 2*x)^(3/2)*(5678 + 3663*x))/9375 - (258*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/15625]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^3)/(3 + 5*x)^2, x, 6, (192*sqrt(1 - 2*x))/3125 + (27/175)*(1 - 2*x)^(3/2)*(2 + 3*x)^2 - ((1 - 2*x)^(3/2)*(2 + 3*x)^3)/(5*(3 + 5*x)) - (6/625)*(1 - 2*x)^(3/2)*(29 + 9*x) - (192*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/3125]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^2)/(3 + 5*x)^2, x, 6, (126*sqrt(1 - 2*x))/625 + (42*(1 - 2*x)^(3/2))/1375 - (9*(1 - 2*x)^(5/2))/125 - (1 - 2*x)^(5/2)/(275*(3 + 5*x)) - (126*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/625]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x))/(3 + 5*x)^2, x, 5, (12*sqrt(1 - 2*x))/25 + (4*(1 - 2*x)^(3/2))/55 - (1 - 2*x)^(5/2)/(55*(3 + 5*x)) - (12*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/25]
    @test_int [(1 - 2*x)^(3/2)/(3 + 5*x)^2, x, 4, (-6*sqrt(1 - 2*x))/25 - (1 - 2*x)^(3/2)/(5*(3 + 5*x)) + (6*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/25]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)*(3 + 5*x)^2), x, 6, (-11*sqrt(1 - 2*x))/(5*(3 + 5*x)) - 14*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) + (72*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/5]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^2*(3 + 5*x)^2), x, 7, (-68*sqrt(1 - 2*x))/(3*(3 + 5*x)) + (7*sqrt(1 - 2*x))/(3*(2 + 3*x)*(3 + 5*x)) - 134*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) + 138*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^3*(3 + 5*x)^2), x, 8, (-335*sqrt(1 - 2*x))/(2*(3 + 5*x)) + (7*sqrt(1 - 2*x))/(6*(2 + 3*x)^2*(3 + 5*x)) + (50*sqrt(1 - 2*x))/(3*(2 + 3*x)*(3 + 5*x)) - 2311*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) + 204*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^4*(3 + 5*x)^2), x, 9, (-46555*sqrt(1 - 2*x))/(42*(3 + 5*x)) + (7*sqrt(1 - 2*x))/(9*(2 + 3*x)^3*(3 + 5*x)) + (133*sqrt(1 - 2*x))/(18*(2 + 3*x)^2*(3 + 5*x)) + (6949*sqrt(1 - 2*x))/(63*(2 + 3*x)*(3 + 5*x)) - (321161*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(7*sqrt(21)) + 1350*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^5*(3 + 5*x)^2), x, 10, (-8110915*sqrt(1 - 2*x))/(1176*(3 + 5*x)) + (7*sqrt(1 - 2*x))/(12*(2 + 3*x)^4*(3 + 5*x)) + (83*sqrt(1 - 2*x))/(18*(2 + 3*x)^3*(3 + 5*x)) + (23173*sqrt(1 - 2*x))/(504*(2 + 3*x)^2*(3 + 5*x)) + (302668*sqrt(1 - 2*x))/(441*(2 + 3*x)*(3 + 5*x)) - (55953383*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(196*sqrt(21)) + 8400*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]

    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^4)/(3 + 5*x)^3, x, 7, (1404*sqrt(1 - 2*x)*(2 + 3*x)^2)/3125 + (2643*sqrt(1 - 2*x)*(2 + 3*x)^3)/1750 - ((1 - 2*x)^(3/2)*(2 + 3*x)^4)/(10*(3 + 5*x)^2) - (129*sqrt(1 - 2*x)*(2 + 3*x)^4)/(50*(3 + 5*x)) + (9*sqrt(1 - 2*x)*(32 + 1375*x))/31250 - (12279*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(15625*sqrt(55))]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^3)/(3 + 5*x)^3, x, 6, (693/625)*sqrt(1 - 2*x)*(2 + 3*x)^2 - ((1 - 2*x)^(3/2)*(2 + 3*x)^3)/(10*(3 + 5*x)^2) - (48*sqrt(1 - 2*x)*(2 + 3*x)^3)/(25*(3 + 5*x)) + (63*sqrt(1 - 2*x)*(92 + 125*x))/6250 - (5943*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(3125*sqrt(55))]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^2)/(3 + 5*x)^3, x, 6, (357*sqrt(1 - 2*x))/1375 + (119*(1 - 2*x)^(3/2))/3025 - (1 - 2*x)^(5/2)/(550*(3 + 5*x)^2) - (131*(1 - 2*x)^(5/2))/(6050*(3 + 5*x)) - (357*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(125*sqrt(55))]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x))/(3 + 5*x)^3, x, 5, (-39*sqrt(1 - 2*x))/275 - (1 - 2*x)^(5/2)/(110*(3 + 5*x)^2) - (13*(1 - 2*x)^(3/2))/(110*(3 + 5*x)) + (39*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(25*sqrt(55))]
    @test_int [(1 - 2*x)^(3/2)/(3 + 5*x)^3, x, 4, -(1 - 2*x)^(3/2)/(10*(3 + 5*x)^2) + (3*sqrt(1 - 2*x))/(50*(3 + 5*x)) - (3*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(25*sqrt(55))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)*(3 + 5*x)^3), x, 7, (-11*sqrt(1 - 2*x))/(10*(3 + 5*x)^2) + (71*sqrt(1 - 2*x))/(10*(3 + 5*x)) + 14*sqrt(21)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (2379*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(5*sqrt(55))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^2*(3 + 5*x)^3), x, 8, (-103*sqrt(1 - 2*x))/(6*(3 + 5*x)^2) + (7*sqrt(1 - 2*x))/(3*(2 + 3*x)*(3 + 5*x)^2) + (207*sqrt(1 - 2*x))/(2*(3 + 5*x)) + 204*sqrt(21)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (6933*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/sqrt(55)]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^3*(3 + 5*x)^3), x, 9, (-1015*sqrt(1 - 2*x))/(6*(3 + 5*x)^2) + (7*sqrt(1 - 2*x))/(6*(2 + 3*x)^2*(3 + 5*x)^2) + (45*sqrt(1 - 2*x))/(2*(2 + 3*x)*(3 + 5*x)^2) + (1020*sqrt(1 - 2*x))/(3 + 5*x) + 14073*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - 13665*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^4*(3 + 5*x)^3), x, 10, (-176065*sqrt(1 - 2*x))/(126*(3 + 5*x)^2) + (7*sqrt(1 - 2*x))/(9*(2 + 3*x)^3*(3 + 5*x)^2) + (28*sqrt(1 - 2*x))/(3*(2 + 3*x)^2*(3 + 5*x)^2) + (1301*sqrt(1 - 2*x))/(7*(2 + 3*x)*(3 + 5*x)^2) + (117955*sqrt(1 - 2*x))/(14*(3 + 5*x)) + (813716*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/7 - 112875*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(2+3*x)^m*(3+5*x)^n*(1-2*x)^(5/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^6*(3 + 5*x), x, 2, (-184877*(1 - 2*x)^(7/2))/128 + (3916031*(1 - 2*x)^(9/2))/1152 - (5078115*(1 - 2*x)^(11/2))/1408 + (3658095*(1 - 2*x)^(13/2))/1664 - (105399*(1 - 2*x)^(15/2))/128 + (409941*(1 - 2*x)^(17/2))/2176 - (59049*(1 - 2*x)^(19/2))/2432 + (1215*(1 - 2*x)^(21/2))/896]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^5*(3 + 5*x), x, 2, (-26411*(1 - 2*x)^(7/2))/64 + (60025*(1 - 2*x)^(9/2))/72 - (519645*(1 - 2*x)^(11/2))/704 + (37485*(1 - 2*x)^(13/2))/104 - (6489*(1 - 2*x)^(15/2))/64 + (1053*(1 - 2*x)^(17/2))/68 - (1215*(1 - 2*x)^(19/2))/1216]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^4*(3 + 5*x), x, 2, (-3773*(1 - 2*x)^(7/2))/32 + (57281*(1 - 2*x)^(9/2))/288 - (24843*(1 - 2*x)^(11/2))/176 + (10773*(1 - 2*x)^(13/2))/208 - (1557*(1 - 2*x)^(15/2))/160 + (405*(1 - 2*x)^(17/2))/544]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x), x, 2, (-539*(1 - 2*x)^(7/2))/16 + (3283*(1 - 2*x)^(9/2))/72 - (1071*(1 - 2*x)^(11/2))/44 + (621*(1 - 2*x)^(13/2))/104 - (9*(1 - 2*x)^(15/2))/16]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x), x, 2, (-77*(1 - 2*x)^(7/2))/8 + (707*(1 - 2*x)^(9/2))/72 - (309*(1 - 2*x)^(11/2))/88 + (45*(1 - 2*x)^(13/2))/104]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x), x, 2, (-11*(1 - 2*x)^(7/2))/4 + (17*(1 - 2*x)^(9/2))/9 - (15*(1 - 2*x)^(11/2))/44]
    @test_int [(1 - 2*x)^(5/2)*(3 + 5*x), x, 2, (-11*(1 - 2*x)^(7/2))/14 + (5*(1 - 2*x)^(9/2))/18]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x), x, 6, (-98*sqrt(1 - 2*x))/81 - (14*(1 - 2*x)^(3/2))/81 - (2*(1 - 2*x)^(5/2))/45 - (5*(1 - 2*x)^(7/2))/21 + (98*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/81]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^2, x, 6, (560*sqrt(1 - 2*x))/81 + (80*(1 - 2*x)^(3/2))/81 + (16*(1 - 2*x)^(5/2))/63 + (1 - 2*x)^(7/2)/(21*(2 + 3*x)) - (560*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/81]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^3, x, 6, (-365*sqrt(1 - 2*x))/81 - (365*(1 - 2*x)^(3/2))/567 + (1 - 2*x)^(7/2)/(42*(2 + 3*x)^2) - (73*(1 - 2*x)^(5/2))/(126*(2 + 3*x)) + (365*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/81]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^4, x, 6, (530*sqrt(1 - 2*x))/567 + (1 - 2*x)^(7/2)/(63*(2 + 3*x)^3) - (53*(1 - 2*x)^(5/2))/(189*(2 + 3*x)^2) + (265*(1 - 2*x)^(3/2))/(567*(2 + 3*x)) - (530*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(81*sqrt(21))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^5, x, 6, (1 - 2*x)^(7/2)/(84*(2 + 3*x)^4) - (139*(1 - 2*x)^(5/2))/(756*(2 + 3*x)^3) + (695*(1 - 2*x)^(3/2))/(4536*(2 + 3*x)^2) - (695*sqrt(1 - 2*x))/(4536*(2 + 3*x)) + (695*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(2268*sqrt(21))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^6, x, 7, (1 - 2*x)^(7/2)/(105*(2 + 3*x)^5) - (43*(1 - 2*x)^(5/2))/(315*(2 + 3*x)^4) + (43*(1 - 2*x)^(3/2))/(567*(2 + 3*x)^3) - (43*sqrt(1 - 2*x))/(1134*(2 + 3*x)^2) + (43*sqrt(1 - 2*x))/(7938*(2 + 3*x)) + (43*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(3969*sqrt(21))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x))/(2 + 3*x)^7, x, 8, (1 - 2*x)^(7/2)/(126*(2 + 3*x)^6) - (41*(1 - 2*x)^(5/2))/(378*(2 + 3*x)^5) + (205*(1 - 2*x)^(3/2))/(4536*(2 + 3*x)^4) - (205*sqrt(1 - 2*x))/(13608*(2 + 3*x)^3) + (205*sqrt(1 - 2*x))/(190512*(2 + 3*x)^2) + (205*sqrt(1 - 2*x))/(444528*(2 + 3*x)) + (205*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(222264*sqrt(21))]

    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^4*(3 + 5*x)^2, x, 2, (-41503*(1 - 2*x)^(7/2))/64 + (381073*(1 - 2*x)^(9/2))/288 - (832951*(1 - 2*x)^(11/2))/704 + (121359*(1 - 2*x)^(13/2))/208 - (53037*(1 - 2*x)^(15/2))/320 + (13905*(1 - 2*x)^(17/2))/544 - (2025*(1 - 2*x)^(19/2))/1216]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^2, x, 2, (-5929*(1 - 2*x)^(7/2))/32 + (91091*(1 - 2*x)^(9/2))/288 - (39977*(1 - 2*x)^(11/2))/176 + (17541*(1 - 2*x)^(13/2))/208 - (513*(1 - 2*x)^(15/2))/32 + (675*(1 - 2*x)^(17/2))/544]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^2, x, 2, (-847*(1 - 2*x)^(7/2))/16 + (1309*(1 - 2*x)^(9/2))/18 - (3467*(1 - 2*x)^(11/2))/88 + (255*(1 - 2*x)^(13/2))/26 - (15*(1 - 2*x)^(15/2))/16]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^2, x, 2, (-121*(1 - 2*x)^(7/2))/8 + (1133*(1 - 2*x)^(9/2))/72 - (505*(1 - 2*x)^(11/2))/88 + (75*(1 - 2*x)^(13/2))/104]
    @test_int [(1 - 2*x)^(5/2)*(3 + 5*x)^2, x, 2, (-121*(1 - 2*x)^(7/2))/28 + (55*(1 - 2*x)^(9/2))/18 - (25*(1 - 2*x)^(11/2))/44]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x), x, 7, (98*sqrt(1 - 2*x))/243 + (14*(1 - 2*x)^(3/2))/243 + (2*(1 - 2*x)^(5/2))/135 - (155*(1 - 2*x)^(7/2))/126 + (25*(1 - 2*x)^(9/2))/54 - (98*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/243]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^2, x, 7, (-350*sqrt(1 - 2*x))/81 - (50*(1 - 2*x)^(3/2))/81 - (10*(1 - 2*x)^(5/2))/63 - (25*(1 - 2*x)^(7/2))/63 - (1 - 2*x)^(7/2)/(63*(2 + 3*x)) + (350*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/81]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^3, x, 7, (1055*sqrt(1 - 2*x))/81 + (1055*(1 - 2*x)^(3/2))/567 + (211*(1 - 2*x)^(5/2))/441 - (1 - 2*x)^(7/2)/(126*(2 + 3*x)^2) + (143*(1 - 2*x)^(7/2))/(882*(2 + 3*x)) - (1055*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/81]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^4, x, 7, (-4435*sqrt(1 - 2*x))/567 - (4435*(1 - 2*x)^(3/2))/3969 - (1 - 2*x)^(7/2)/(189*(2 + 3*x)^3) + (211*(1 - 2*x)^(7/2))/(2646*(2 + 3*x)^2) - (887*(1 - 2*x)^(5/2))/(882*(2 + 3*x)) + (4435*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(81*sqrt(21))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^5, x, 7, (24965*sqrt(1 - 2*x))/15876 - (1 - 2*x)^(7/2)/(252*(2 + 3*x)^4) + (31*(1 - 2*x)^(7/2))/(588*(2 + 3*x)^3) - (4993*(1 - 2*x)^(5/2))/(10584*(2 + 3*x)^2) + (24965*(1 - 2*x)^(3/2))/(31752*(2 + 3*x)) - (24965*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(2268*sqrt(21))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^6, x, 7, -(1 - 2*x)^(7/2)/(315*(2 + 3*x)^5) + (347*(1 - 2*x)^(7/2))/(8820*(2 + 3*x)^4) - (8051*(1 - 2*x)^(5/2))/(26460*(2 + 3*x)^3) + (8051*(1 - 2*x)^(3/2))/(31752*(2 + 3*x)^2) - (8051*sqrt(1 - 2*x))/(31752*(2 + 3*x)) + (8051*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(15876*sqrt(21))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^7, x, 8, -(1 - 2*x)^(7/2)/(378*(2 + 3*x)^6) + (83*(1 - 2*x)^(7/2))/(2646*(2 + 3*x)^5) - (263*(1 - 2*x)^(5/2))/(1176*(2 + 3*x)^4) + (1315*(1 - 2*x)^(3/2))/(10584*(2 + 3*x)^3) - (1315*sqrt(1 - 2*x))/(21168*(2 + 3*x)^2) + (1315*sqrt(1 - 2*x))/(148176*(2 + 3*x)) + (1315*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(74088*sqrt(21))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^2)/(2 + 3*x)^8, x, 9, -(1 - 2*x)^(7/2)/(441*(2 + 3*x)^7) + (23*(1 - 2*x)^(7/2))/(882*(2 + 3*x)^6) - (467*(1 - 2*x)^(5/2))/(2646*(2 + 3*x)^5) + (2335*(1 - 2*x)^(3/2))/(31752*(2 + 3*x)^4) - (2335*sqrt(1 - 2*x))/(95256*(2 + 3*x)^3) + (2335*sqrt(1 - 2*x))/(1333584*(2 + 3*x)^2) + (2335*sqrt(1 - 2*x))/(3111696*(2 + 3*x)) + (2335*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(1555848*sqrt(21))]

    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^4*(3 + 5*x)^3, x, 2, (-456533*(1 - 2*x)^(7/2))/128 + (3278737*(1 - 2*x)^(9/2))/384 - (1179381*(1 - 2*x)^(11/2))/128 + (9504551*(1 - 2*x)^(13/2))/1664 - (1392467*(1 - 2*x)^(15/2))/640 + (1101465*(1 - 2*x)^(17/2))/2176 - (161325*(1 - 2*x)^(19/2))/2432 + (3375*(1 - 2*x)^(21/2))/896]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^3, x, 2, (-65219*(1 - 2*x)^(7/2))/64 + (100793*(1 - 2*x)^(9/2))/48 - (121359*(1 - 2*x)^(11/2))/64 + (98209*(1 - 2*x)^(13/2))/104 - (17337*(1 - 2*x)^(15/2))/64 + (675*(1 - 2*x)^(17/2))/16 - (3375*(1 - 2*x)^(19/2))/1216]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^3, x, 2, (-9317*(1 - 2*x)^(7/2))/32 + (16093*(1 - 2*x)^(9/2))/32 - (5847*(1 - 2*x)^(11/2))/16 + (28555*(1 - 2*x)^(13/2))/208 - (845*(1 - 2*x)^(15/2))/32 + (1125*(1 - 2*x)^(17/2))/544]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^3, x, 2, (-1331*(1 - 2*x)^(7/2))/16 + (2783*(1 - 2*x)^(9/2))/24 - (255*(1 - 2*x)^(11/2))/4 + (1675*(1 - 2*x)^(13/2))/104 - (25*(1 - 2*x)^(15/2))/16]
    @test_int [(1 - 2*x)^(5/2)*(3 + 5*x)^3, x, 2, (-1331*(1 - 2*x)^(7/2))/56 + (605*(1 - 2*x)^(9/2))/24 - (75*(1 - 2*x)^(11/2))/8 + (125*(1 - 2*x)^(13/2))/104]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x), x, 7, (-98*sqrt(1 - 2*x))/729 - (14*(1 - 2*x)^(3/2))/729 - (2*(1 - 2*x)^(5/2))/405 - (5135*(1 - 2*x)^(7/2))/756 + (400*(1 - 2*x)^(9/2))/81 - (125*(1 - 2*x)^(11/2))/132 + (98*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/729]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^2, x, 8, (1540/729)*sqrt(1 - 2*x) + (220/729)*(1 - 2*x)^(3/2) + (55/81)*(1 - 2*x)^(5/2)*(3 + 5*x)^2 - ((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(3*(2 + 3*x)) - (22/567)*(1 - 2*x)^(5/2)*(69 + 100*x) - (1540/729)*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^3, x, 8, (-(935/81))*sqrt(1 - 2*x) - (220/21)*(1 - 2*x)^(3/2)*(3 + 5*x)^2 - ((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(6*(2 + 3*x)^2) + (55*(1 - 2*x)^(3/2)*(3 + 5*x)^3)/(9*(2 + 3*x)) + (55*(1 - 2*x)^(3/2)*(209 + 603*x))/1134 + (935/81)*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^4, x, 8, (1441/27)*sqrt(1 - 2*x)*(3 + 5*x)^2 - ((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(9*(2 + 3*x)^3) + (55*(1 - 2*x)^(3/2)*(3 + 5*x)^3)/(27*(2 + 3*x)^2) - (275*sqrt(1 - 2*x)*(3 + 5*x)^3)/(9*(2 + 3*x)) - (22/243)*sqrt(1 - 2*x)*(578 + 1885*x) - (41360*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(243*sqrt(21))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^5, x, 8, -((2255*sqrt(1 - 2*x)*(3 + 5*x)^2)/(378*(2 + 3*x))) - ((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(12*(2 + 3*x)^4) + (55*(1 - 2*x)^(3/2)*(3 + 5*x)^3)/(54*(2 + 3*x)^3) - (55*sqrt(1 - 2*x)*(3 + 5*x)^3)/(24*(2 + 3*x)^2) + (275*sqrt(1 - 2*x)*(1123 + 4595*x))/13608 + (645865*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(6804*sqrt(21))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^6, x, 8, -((209*sqrt(1 - 2*x)*(3 + 5*x)^2)/(756*(2 + 3*x)^2)) - ((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(15*(2 + 3*x)^5) + (11*(1 - 2*x)^(3/2)*(3 + 5*x)^3)/(18*(2 + 3*x)^4) + (11*sqrt(1 - 2*x)*(3 + 5*x)^3)/(9*(2 + 3*x)^3) - (11*sqrt(1 - 2*x)*(3911 + 6475*x))/(15876*(2 + 3*x)) - (146971*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(7938*sqrt(21))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^7, x, 10, -((121*(1 - 2*x)^(3/2))/(4536*(2 + 3*x)^4)) + (33275*(1 - 2*x)^(3/2))/(95256*(2 + 3*x)^3) - (559625*sqrt(1 - 2*x))/(190512*(2 + 3*x)^2) + (559625*sqrt(1 - 2*x))/(1333584*(2 + 3*x)) - ((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(18*(2 + 3*x)^6) + (11*(1 - 2*x)^(3/2)*(3 + 5*x)^3)/(27*(2 + 3*x)^5) + (559625*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(666792*sqrt(21))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^8, x, 9, (33935*sqrt(1 - 2*x))/(2333772*(2 + 3*x)) - (3223*sqrt(1 - 2*x)*(3 + 5*x)^2)/(2646*(2 + 3*x)^4) - ((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(21*(2 + 3*x)^7) + (55*(1 - 2*x)^(3/2)*(3 + 5*x)^3)/(189*(2 + 3*x)^6) + (11*sqrt(1 - 2*x)*(3 + 5*x)^3)/(7*(2 + 3*x)^5) - (11*sqrt(1 - 2*x)*(187704 + 301765*x))/(333396*(2 + 3*x)^3) + (33935*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(1166886*sqrt(21))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^4)/(3 + 5*x), x, 7, (242*sqrt(1 - 2*x))/78125 + (22*(1 - 2*x)^(3/2))/46875 + (2*(1 - 2*x)^(5/2))/15625 - (136419*(1 - 2*x)^(7/2))/35000 + (3819*(1 - 2*x)^(9/2))/1000 - (2889*(1 - 2*x)^(11/2))/2200 + (81*(1 - 2*x)^(13/2))/520 - (242*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/78125]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(3 + 5*x), x, 7, (242*sqrt(1 - 2*x))/15625 + (22*(1 - 2*x)^(3/2))/9375 + (2*(1 - 2*x)^(5/2))/3125 - (3897*(1 - 2*x)^(7/2))/3500 + (18*(1 - 2*x)^(9/2))/25 - (27*(1 - 2*x)^(11/2))/220 - (242*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/15625]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^2)/(3 + 5*x), x, 7, (242*sqrt(1 - 2*x))/3125 + (22*(1 - 2*x)^(3/2))/1875 + (2*(1 - 2*x)^(5/2))/625 - (111*(1 - 2*x)^(7/2))/350 + (1 - 2*x)^(9/2)/10 - (242*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/3125]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x))/(3 + 5*x), x, 6, (242*sqrt(1 - 2*x))/625 + (22*(1 - 2*x)^(3/2))/375 + (2*(1 - 2*x)^(5/2))/125 - (3*(1 - 2*x)^(7/2))/35 - (242*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/625]
    @test_int [(1 - 2*x)^(5/2)/(3 + 5*x), x, 5, (242*sqrt(1 - 2*x))/125 + (22*(1 - 2*x)^(3/2))/75 + (2*(1 - 2*x)^(5/2))/25 - (242*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/125]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)*(3 + 5*x)), x, 7, (-272*sqrt(1 - 2*x))/225 - (4*(1 - 2*x)^(3/2))/45 + (98*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/9 - (242*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/25]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^2*(3 + 5*x)), x, 7, (26*sqrt(1 - 2*x))/15 + (7*(1 - 2*x)^(3/2))/(3*(2 + 3*x)) + (140*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/3 - (242*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/5]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^3*(3 + 5*x)), x, 7, (7*(1 - 2*x)^(3/2))/(6*(2 + 3*x)^2) + (49*sqrt(1 - 2*x))/(2*(2 + 3*x)) + 235*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - 242*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^4*(3 + 5*x)), x, 8, (7*(1 - 2*x)^(3/2))/(9*(2 + 3*x)^3) + (112*sqrt(1 - 2*x))/(9*(2 + 3*x)^2) + (1073*sqrt(1 - 2*x))/(9*(2 + 3*x)) + (74020*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(9*sqrt(21)) - 242*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^5*(3 + 5*x)), x, 9, (7*(1 - 2*x)^(3/2))/(12*(2 + 3*x)^4) + (301*sqrt(1 - 2*x))/(36*(2 + 3*x)^3) + (4313*sqrt(1 - 2*x))/(72*(2 + 3*x)^2) + (100145*sqrt(1 - 2*x))/(168*(2 + 3*x)) + (3454265*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(84*sqrt(21)) - 1210*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^6*(3 + 5*x)), x, 10, (7*(1 - 2*x)^(3/2))/(15*(2 + 3*x)^5) + (63*sqrt(1 - 2*x))/(10*(2 + 3*x)^4) + (1201*sqrt(1 - 2*x))/(30*(2 + 3*x)^3) + (25159*sqrt(1 - 2*x))/(84*(2 + 3*x)^2) + (584179*sqrt(1 - 2*x))/(196*(2 + 3*x)) + (20149879*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(98*sqrt(21)) - 6050*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^7*(3 + 5*x)), x, 11, (7*(1 - 2*x)^(3/2))/(18*(2 + 3*x)^6) + (91*sqrt(1 - 2*x))/(18*(2 + 3*x)^5) + (2165*sqrt(1 - 2*x))/(72*(2 + 3*x)^4) + (302651*sqrt(1 - 2*x))/(1512*(2 + 3*x)^3) + (31700335*sqrt(1 - 2*x))/(21168*(2 + 3*x)^2) + (736065535*sqrt(1 - 2*x))/(49392*(2 + 3*x)) + (25388847535*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(24696*sqrt(21)) - 30250*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]

    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^4)/(3 + 5*x)^2, x, 8, (2794*sqrt(1 - 2*x))/78125 + (254*(1 - 2*x)^(3/2))/46875 - (32*(1 - 2*x)^(5/2)*(2 + 3*x)^2)/4125 + (39/275)*(1 - 2*x)^(5/2)*(2 + 3*x)^3 - ((1 - 2*x)^(5/2)*(2 + 3*x)^4)/(5*(3 + 5*x)) - ((1 - 2*x)^(5/2)*(1347116 + 1110975*x))/3609375 - (2794*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/78125]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(3 + 5*x)^2, x, 7, (2068*sqrt(1 - 2*x))/15625 + (188*(1 - 2*x)^(3/2))/9375 + (11/75)*(1 - 2*x)^(5/2)*(2 + 3*x)^2 - ((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(5*(3 + 5*x)) - (2*(1 - 2*x)^(5/2)*(6191 + 2850*x))/65625 - (2068*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/15625]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^2)/(3 + 5*x)^2, x, 7, (1342*sqrt(1 - 2*x))/3125 + (122*(1 - 2*x)^(3/2))/1875 + (122*(1 - 2*x)^(5/2))/6875 - (9*(1 - 2*x)^(7/2))/175 - (1 - 2*x)^(7/2)/(275*(3 + 5*x)) - (1342*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/3125]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x))/(3 + 5*x)^2, x, 6, (616*sqrt(1 - 2*x))/625 + (56*(1 - 2*x)^(3/2))/375 + (56*(1 - 2*x)^(5/2))/1375 - (1 - 2*x)^(7/2)/(55*(3 + 5*x)) - (616*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/625]
    @test_int [(1 - 2*x)^(5/2)/(3 + 5*x)^2, x, 5, (-22*sqrt(1 - 2*x))/25 - (2*(1 - 2*x)^(3/2))/15 - (1 - 2*x)^(5/2)/(5*(3 + 5*x)) + (22*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/25]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)*(3 + 5*x)^2), x, 7, (-58*sqrt(1 - 2*x))/75 - (11*(1 - 2*x)^(3/2))/(5*(3 + 5*x)) - (98*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/3 + (836*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/25]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^2*(3 + 5*x)^2), x, 7, (-748*sqrt(1 - 2*x))/(15*(3 + 5*x)) + (7*(1 - 2*x)^(3/2))/(3*(2 + 3*x)*(3 + 5*x)) - (910*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/3 + (1562*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/5]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^3*(3 + 5*x)^2), x, 8, (-6763*sqrt(1 - 2*x))/(18*(3 + 5*x)) + (7*(1 - 2*x)^(3/2))/(6*(2 + 3*x)^2*(3 + 5*x)) + (343*sqrt(1 - 2*x))/(9*(2 + 3*x)*(3 + 5*x)) - (6665*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/3 + 2288*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^4*(3 + 5*x)^2), x, 9, (-44545*sqrt(1 - 2*x))/(18*(3 + 5*x)) + (7*(1 - 2*x)^(3/2))/(9*(2 + 3*x)^3*(3 + 5*x)) + (917*sqrt(1 - 2*x))/(54*(2 + 3*x)^2*(3 + 5*x)) + (6649*sqrt(1 - 2*x))/(27*(2 + 3*x)*(3 + 5*x)) - (307295*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(3*sqrt(21)) + 3014*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^5*(3 + 5*x)^2), x, 10, (-7738475*sqrt(1 - 2*x))/(504*(3 + 5*x)) + (7*(1 - 2*x)^(3/2))/(12*(2 + 3*x)^4*(3 + 5*x)) + (287*sqrt(1 - 2*x))/(27*(2 + 3*x)^3*(3 + 5*x)) + (22109*sqrt(1 - 2*x))/(216*(2 + 3*x)^2*(3 + 5*x)) + (288770*sqrt(1 - 2*x))/(189*(2 + 3*x)*(3 + 5*x)) - (53384095*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(84*sqrt(21)) + 18700*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^6*(3 + 5*x)^2), x, 11, (-323422735*sqrt(1 - 2*x))/(3528*(3 + 5*x)) + (7*(1 - 2*x)^(3/2))/(15*(2 + 3*x)^5*(3 + 5*x)) + (1379*sqrt(1 - 2*x))/(180*(2 + 3*x)^4*(3 + 5*x)) + (16549*sqrt(1 - 2*x))/(270*(2 + 3*x)^3*(3 + 5*x)) + (924025*sqrt(1 - 2*x))/(1512*(2 + 3*x)^2*(3 + 5*x)) + (12068887*sqrt(1 - 2*x))/(1323*(2 + 3*x)*(3 + 5*x)) - (2231141147*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(588*sqrt(21)) + 111650*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]

    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^4)/(3 + 5*x)^3, x, 8, (11763*sqrt(1 - 2*x))/78125 + (1903*(1 - 2*x)^(3/2)*(2 + 3*x)^2)/4375 + (1117/750)*(1 - 2*x)^(3/2)*(2 + 3*x)^3 - ((1 - 2*x)^(5/2)*(2 + 3*x)^4)/(10*(3 + 5*x)^2) - (127*(1 - 2*x)^(3/2)*(2 + 3*x)^4)/(50*(3 + 5*x)) + ((1 - 2*x)^(3/2)*(734 + 24939*x))/93750 - (11763*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/78125]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(3 + 5*x)^3, x, 7, (5559*sqrt(1 - 2*x))/15625 + (954/875)*(1 - 2*x)^(3/2)*(2 + 3*x)^2 - ((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(10*(3 + 5*x)^2) - (47*(1 - 2*x)^(3/2)*(2 + 3*x)^3)/(25*(3 + 5*x)) + (3*(1 - 2*x)^(3/2)*(1618 + 2403*x))/6250 - (5559*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/15625]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^2)/(3 + 5*x)^3, x, 7, (1533*sqrt(1 - 2*x))/3125 + (511*(1 - 2*x)^(3/2))/6875 + (1533*(1 - 2*x)^(5/2))/75625 - (1 - 2*x)^(7/2)/(550*(3 + 5*x)^2) - (129*(1 - 2*x)^(7/2))/(6050*(3 + 5*x)) - (1533*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/3125]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x))/(3 + 5*x)^3, x, 6, (-63*sqrt(1 - 2*x))/125 - (21*(1 - 2*x)^(3/2))/275 - (1 - 2*x)^(7/2)/(110*(3 + 5*x)^2) - (63*(1 - 2*x)^(5/2))/(550*(3 + 5*x)) + (63*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/125]
    @test_int [(1 - 2*x)^(5/2)/(3 + 5*x)^3, x, 5, (3*sqrt(1 - 2*x))/25 - (1 - 2*x)^(5/2)/(10*(3 + 5*x)^2) + (1 - 2*x)^(3/2)/(10*(3 + 5*x)) - (3*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/25]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)*(3 + 5*x)^3), x, 7, (-11*(1 - 2*x)^(3/2))/(10*(3 + 5*x)^2) + (803*sqrt(1 - 2*x))/(50*(3 + 5*x)) + 98*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (2523*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/25]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^2*(3 + 5*x)^3), x, 8, (-1133*sqrt(1 - 2*x))/(30*(3 + 5*x)^2) + (7*(1 - 2*x)^(3/2))/(3*(2 + 3*x)*(3 + 5*x)^2) + (7103*sqrt(1 - 2*x))/(30*(3 + 5*x)) + 1400*sqrt(7/3)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (7209*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/5]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^3*(3 + 5*x)^3), x, 9, (-6899*sqrt(1 - 2*x))/(18*(3 + 5*x)^2) + (7*(1 - 2*x)^(3/2))/(6*(2 + 3*x)^2*(3 + 5*x)^2) + (931*sqrt(1 - 2*x))/(18*(2 + 3*x)*(3 + 5*x)^2) + (2311*sqrt(1 - 2*x))/(3 + 5*x) + 4555*sqrt(21)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - 14073*sqrt(11/5)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^4*(3 + 5*x)^3), x, 10, (-169975*sqrt(1 - 2*x))/(54*(3 + 5*x)^2) + (7*(1 - 2*x)^(3/2))/(9*(2 + 3*x)^3*(3 + 5*x)^2) + (581*sqrt(1 - 2*x))/(27*(2 + 3*x)^2*(3 + 5*x)^2) + (1256*sqrt(1 - 2*x))/(3*(2 + 3*x)*(3 + 5*x)^2) + (113875*sqrt(1 - 2*x))/(6*(3 + 5*x)) + (785570*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/sqrt(21) - 23115*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^5*(3 + 5*x)^3), x, 11, (-8836825*sqrt(1 - 2*x))/(378*(3 + 5*x)^2) + (7*(1 - 2*x)^(3/2))/(12*(2 + 3*x)^4*(3 + 5*x)^2) + (1393*sqrt(1 - 2*x))/(108*(2 + 3*x)^3*(3 + 5*x)^2) + (11243*sqrt(1 - 2*x))/(72*(2 + 3*x)^2*(3 + 5*x)^2) + (522385*sqrt(1 - 2*x))/(168*(2 + 3*x)*(3 + 5*x)^2) + (23680975*sqrt(1 - 2*x))/(168*(3 + 5*x)) + (163363895*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(28*sqrt(21)) - 171675*sqrt(55)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(2+3*x)^m*(3+5*x)^n / (1-2*x)^(1/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [((2 + 3*x)^5*(3 + 5*x))/sqrt(1 - 2*x), x, 2, (-184877*sqrt(1 - 2*x))/64 + (60025*(1 - 2*x)^(3/2))/24 - (103929*(1 - 2*x)^(5/2))/64 + (5355*(1 - 2*x)^(7/2))/8 - (10815*(1 - 2*x)^(9/2))/64 + (1053*(1 - 2*x)^(11/2))/44 - (1215*(1 - 2*x)^(13/2))/832]
    @test_int [((2 + 3*x)^4*(3 + 5*x))/sqrt(1 - 2*x), x, 2, (-26411*sqrt(1 - 2*x))/32 + (57281*(1 - 2*x)^(3/2))/96 - (24843*(1 - 2*x)^(5/2))/80 + (1539*(1 - 2*x)^(7/2))/16 - (519*(1 - 2*x)^(9/2))/32 + (405*(1 - 2*x)^(11/2))/352]
    @test_int [((2 + 3*x)^3*(3 + 5*x))/sqrt(1 - 2*x), x, 2, (-3773*sqrt(1 - 2*x))/16 + (3283*(1 - 2*x)^(3/2))/24 - (1071*(1 - 2*x)^(5/2))/20 + (621*(1 - 2*x)^(7/2))/56 - (15*(1 - 2*x)^(9/2))/16]
    @test_int [((2 + 3*x)^2*(3 + 5*x))/sqrt(1 - 2*x), x, 2, (-539*sqrt(1 - 2*x))/8 + (707*(1 - 2*x)^(3/2))/24 - (309*(1 - 2*x)^(5/2))/40 + (45*(1 - 2*x)^(7/2))/56]
    @test_int [((2 + 3*x)*(3 + 5*x))/sqrt(1 - 2*x), x, 2, (-77*sqrt(1 - 2*x))/4 + (17*(1 - 2*x)^(3/2))/3 - (3*(1 - 2*x)^(5/2))/4]
    @test_int [(3 + 5*x)/sqrt(1 - 2*x), x, 2, (-11*sqrt(1 - 2*x))/2 + (5*(1 - 2*x)^(3/2))/6]
    @test_int [(3 + 5*x)/(sqrt(1 - 2*x)*(2 + 3*x)), x, 3, (-5*sqrt(1 - 2*x))/3 + (2*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(3*sqrt(21))]
    @test_int [(3 + 5*x)/(sqrt(1 - 2*x)*(2 + 3*x)^2), x, 3, sqrt(1 - 2*x)/(21*(2 + 3*x)) - (68*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(21*sqrt(21))]
    @test_int [(3 + 5*x)/(sqrt(1 - 2*x)*(2 + 3*x)^3), x, 4, sqrt(1 - 2*x)/(42*(2 + 3*x)^2) - (67*sqrt(1 - 2*x))/(294*(2 + 3*x)) - (67*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(147*sqrt(21))]
    @test_int [(3 + 5*x)/(sqrt(1 - 2*x)*(2 + 3*x)^4), x, 5, sqrt(1 - 2*x)/(63*(2 + 3*x)^3) - (50*sqrt(1 - 2*x))/(441*(2 + 3*x)^2) - (50*sqrt(1 - 2*x))/(1029*(2 + 3*x)) - (100*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(1029*sqrt(21))]
    @test_int [(3 + 5*x)/(sqrt(1 - 2*x)*(2 + 3*x)^5), x, 6, sqrt(1 - 2*x)/(84*(2 + 3*x)^4) - (19*sqrt(1 - 2*x))/(252*(2 + 3*x)^3) - (95*sqrt(1 - 2*x))/(3528*(2 + 3*x)^2) - (95*sqrt(1 - 2*x))/(8232*(2 + 3*x)) - (95*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(4116*sqrt(21))]

    @test_int [((2 + 3*x)^5*(3 + 5*x)^2)/sqrt(1 - 2*x), x, 2, (-2033647*sqrt(1 - 2*x))/128 + (6206585*(1 - 2*x)^(3/2))/384 - (1623419*(1 - 2*x)^(5/2))/128 + (842415*(1 - 2*x)^(7/2))/128 - (285565*(1 - 2*x)^(9/2))/128 + (672003*(1 - 2*x)^(11/2))/1408 - (97605*(1 - 2*x)^(13/2))/1664 + (405*(1 - 2*x)^(15/2))/128]
    @test_int [((2 + 3*x)^4*(3 + 5*x)^2)/sqrt(1 - 2*x), x, 2, (-290521*sqrt(1 - 2*x))/64 + (381073*(1 - 2*x)^(3/2))/96 - (832951*(1 - 2*x)^(5/2))/320 + (17337*(1 - 2*x)^(7/2))/16 - (17679*(1 - 2*x)^(9/2))/64 + (13905*(1 - 2*x)^(11/2))/352 - (2025*(1 - 2*x)^(13/2))/832]
    @test_int [((2 + 3*x)^3*(3 + 5*x)^2)/sqrt(1 - 2*x), x, 2, (-41503*sqrt(1 - 2*x))/32 + (91091*(1 - 2*x)^(3/2))/96 - (39977*(1 - 2*x)^(5/2))/80 + (17541*(1 - 2*x)^(7/2))/112 - (855*(1 - 2*x)^(9/2))/32 + (675*(1 - 2*x)^(11/2))/352]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^2)/sqrt(1 - 2*x), x, 2, (-5929*sqrt(1 - 2*x))/16 + (1309*(1 - 2*x)^(3/2))/6 - (3467*(1 - 2*x)^(5/2))/40 + (255*(1 - 2*x)^(7/2))/14 - (25*(1 - 2*x)^(9/2))/16]
    @test_int [((2 + 3*x)*(3 + 5*x)^2)/sqrt(1 - 2*x), x, 2, (-847*sqrt(1 - 2*x))/8 + (1133*(1 - 2*x)^(3/2))/24 - (101*(1 - 2*x)^(5/2))/8 + (75*(1 - 2*x)^(7/2))/56]
    @test_int [(3 + 5*x)^2/sqrt(1 - 2*x), x, 2, (-121*sqrt(1 - 2*x))/4 + (55*(1 - 2*x)^(3/2))/6 - (5*(1 - 2*x)^(5/2))/4]
    @test_int [(3 + 5*x)^2/(sqrt(1 - 2*x)*(2 + 3*x)), x, 4, (-155*sqrt(1 - 2*x))/18 + (25*(1 - 2*x)^(3/2))/18 - (2*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(9*sqrt(21))]
    @test_int [(3 + 5*x)^2/(sqrt(1 - 2*x)*(2 + 3*x)^2), x, 4, (-25*sqrt(1 - 2*x))/9 - sqrt(1 - 2*x)/(63*(2 + 3*x)) + (46*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(21*sqrt(21))]
    @test_int [(3 + 5*x)^2/(sqrt(1 - 2*x)*(2 + 3*x)^3), x, 4, -sqrt(1 - 2*x)/(126*(2 + 3*x)^2) + (137*sqrt(1 - 2*x))/(882*(2 + 3*x)) - (257*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(49*sqrt(21))]
    @test_int [(3 + 5*x)^2/(sqrt(1 - 2*x)*(2 + 3*x)^4), x, 5, -sqrt(1 - 2*x)/(189*(2 + 3*x)^3) + (205*sqrt(1 - 2*x))/(2646*(2 + 3*x)^2) - (2245*sqrt(1 - 2*x))/(6174*(2 + 3*x)) - (2245*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(3087*sqrt(21))]
    @test_int [(3 + 5*x)^2/(sqrt(1 - 2*x)*(2 + 3*x)^5), x, 6, -sqrt(1 - 2*x)/(252*(2 + 3*x)^4) + (13*sqrt(1 - 2*x))/(252*(2 + 3*x)^3) - (635*sqrt(1 - 2*x))/(3528*(2 + 3*x)^2) - (635*sqrt(1 - 2*x))/(8232*(2 + 3*x)) - (635*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(4116*sqrt(21))]
    @test_int [(3 + 5*x)^2/(sqrt(1 - 2*x)*(2 + 3*x)^6), x, 7, -sqrt(1 - 2*x)/(315*(2 + 3*x)^5) + (341*sqrt(1 - 2*x))/(8820*(2 + 3*x)^4) - (117*sqrt(1 - 2*x))/(980*(2 + 3*x)^3) - (117*sqrt(1 - 2*x))/(2744*(2 + 3*x)^2) - (351*sqrt(1 - 2*x))/(19208*(2 + 3*x)) - (117*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/9604]

    @test_int [((2 + 3*x)^4*(3 + 5*x)^3)/sqrt(1 - 2*x), x, 2, (-3195731*sqrt(1 - 2*x))/128 + (3278737*(1 - 2*x)^(3/2))/128 - (12973191*(1 - 2*x)^(5/2))/640 + (1357793*(1 - 2*x)^(7/2))/128 - (1392467*(1 - 2*x)^(9/2))/384 + (1101465*(1 - 2*x)^(11/2))/1408 - (161325*(1 - 2*x)^(13/2))/1664 + (675*(1 - 2*x)^(15/2))/128]
    @test_int [((2 + 3*x)^3*(3 + 5*x)^3)/sqrt(1 - 2*x), x, 2, (-456533*sqrt(1 - 2*x))/64 + (100793*(1 - 2*x)^(3/2))/16 - (1334949*(1 - 2*x)^(5/2))/320 + (98209*(1 - 2*x)^(7/2))/56 - (28895*(1 - 2*x)^(9/2))/64 + (11475*(1 - 2*x)^(11/2))/176 - (3375*(1 - 2*x)^(13/2))/832]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^3)/sqrt(1 - 2*x), x, 2, (-65219*sqrt(1 - 2*x))/32 + (48279*(1 - 2*x)^(3/2))/32 - (64317*(1 - 2*x)^(5/2))/80 + (28555*(1 - 2*x)^(7/2))/112 - (4225*(1 - 2*x)^(9/2))/96 + (1125*(1 - 2*x)^(11/2))/352]
    @test_int [((2 + 3*x)*(3 + 5*x)^3)/sqrt(1 - 2*x), x, 2, (-9317*sqrt(1 - 2*x))/16 + (2783*(1 - 2*x)^(3/2))/8 - (561*(1 - 2*x)^(5/2))/4 + (1675*(1 - 2*x)^(7/2))/56 - (125*(1 - 2*x)^(9/2))/48]
    @test_int [(3 + 5*x)^3/sqrt(1 - 2*x), x, 2, (-1331*sqrt(1 - 2*x))/8 + (605*(1 - 2*x)^(3/2))/8 - (165*(1 - 2*x)^(5/2))/8 + (125*(1 - 2*x)^(7/2))/56]
    @test_int [(3 + 5*x)^3/(sqrt(1 - 2*x)*(2 + 3*x)), x, 4, (-5135*sqrt(1 - 2*x))/108 + (400*(1 - 2*x)^(3/2))/27 - (25*(1 - 2*x)^(5/2))/12 + (2*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(27*sqrt(21))]
    @test_int [(3 + 5*x)^3/(sqrt(1 - 2*x)*(2 + 3*x)^2), x, 4, (sqrt(1 - 2*x)*(3 + 5*x)^2)/(21*(2 + 3*x)) - (10/189)*sqrt(1 - 2*x)*(214 + 95*x) - (208*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(189*sqrt(21))]
    @test_int [(3 + 5*x)^3/(sqrt(1 - 2*x)*(2 + 3*x)^3), x, 4, (sqrt(1 - 2*x)*(3 + 5*x)^2)/(42*(2 + 3*x)^2) - (sqrt(1 - 2*x)*(8329 + 12425*x))/(882*(2 + 3*x)) + (2381*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(441*sqrt(21))]
    @test_int [(3 + 5*x)^3/(sqrt(1 - 2*x)*(2 + 3*x)^4), x, 4, (sqrt(1 - 2*x)*(3 + 5*x)^2)/(63*(2 + 3*x)^3) + (5*sqrt(1 - 2*x)*(1205 + 1867*x))/(9261*(2 + 3*x)^2) - (78710*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(9261*sqrt(21))]
    @test_int [(3 + 5*x)^3/(sqrt(1 - 2*x)*(2 + 3*x)^5), x, 5, -((42995*sqrt(1 - 2*x))/(74088*(2 + 3*x))) + (sqrt(1 - 2*x)*(3 + 5*x)^2)/(84*(2 + 3*x)^4) + (sqrt(1 - 2*x)*(3168 + 4955*x))/(10584*(2 + 3*x)^3) - (42995*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(37044*sqrt(21))]
    @test_int [(3 + 5*x)^3/(sqrt(1 - 2*x)*(2 + 3*x)^6), x, 6, -((5293*sqrt(1 - 2*x))/(18522*(2 + 3*x)^2)) - (5293*sqrt(1 - 2*x))/(43218*(2 + 3*x)) + (sqrt(1 - 2*x)*(3 + 5*x)^2)/(105*(2 + 3*x)^5) + (sqrt(1 - 2*x)*(1255 + 1971*x))/(6615*(2 + 3*x)^4) - (5293*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(21609*sqrt(21))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(a + b*x)^2/((c + d*x)^2*sqrt(e + f*x)), x, 4, (2*b^2*sqrt(e + f*x))/(d^2*f) - ((b*c - a*d)^2*sqrt(e + f*x))/(d^2*(d*e - c*f)*(c + d*x)) + ((b*c - a*d)*(4*b*d*e - 3*b*c*f - a*d*f)*atanh((sqrt(d)*sqrt(e + f*x))/sqrt(d*e - c*f)))/(d^(5/2)*(d*e - c*f)^(3/2))]

    @test_int [(2 + 3*x)^5/(sqrt(1 - 2*x)*(3 + 5*x)), x, 4, (-4774713*sqrt(1 - 2*x))/50000 + (268707*(1 - 2*x)^(3/2))/5000 - (51057*(1 - 2*x)^(5/2))/2500 + (5751*(1 - 2*x)^(7/2))/1400 - (27*(1 - 2*x)^(9/2))/80 - (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(3125*sqrt(55))]
    @test_int [(2 + 3*x)^4/(sqrt(1 - 2*x)*(3 + 5*x)), x, 4, (-136419*sqrt(1 - 2*x))/5000 + (11457*(1 - 2*x)^(3/2))/1000 - (2889*(1 - 2*x)^(5/2))/1000 + (81*(1 - 2*x)^(7/2))/280 - (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(625*sqrt(55))]
    @test_int [(2 + 3*x)^3/(sqrt(1 - 2*x)*(3 + 5*x)), x, 4, (-3897*sqrt(1 - 2*x))/500 + (54*(1 - 2*x)^(3/2))/25 - (27*(1 - 2*x)^(5/2))/100 - (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(125*sqrt(55))]
    @test_int [(2 + 3*x)^2/(sqrt(1 - 2*x)*(3 + 5*x)), x, 4, (-111*sqrt(1 - 2*x))/50 + (3*(1 - 2*x)^(3/2))/10 - (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(25*sqrt(55))]
    @test_int [(2 + 3*x)/(sqrt(1 - 2*x)*(3 + 5*x)), x, 3, (-3*sqrt(1 - 2*x))/5 - (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(5*sqrt(55))]
    @test_int [1/(sqrt(1 - 2*x)*(3 + 5*x)), x, 2, (-2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/sqrt(55)]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)), x, 5, 2*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - 2*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)), x, 6, (3*sqrt(1 - 2*x))/(7*(2 + 3*x)) + (72*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/7 - 10*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)), x, 7, (3*sqrt(1 - 2*x))/(14*(2 + 3*x)^2) + (219*sqrt(1 - 2*x))/(98*(2 + 3*x)) + (2523*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/49 - 50*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)), x, 8, sqrt(1 - 2*x)/(7*(2 + 3*x)^3) + (55*sqrt(1 - 2*x))/(49*(2 + 3*x)^2) + (3840*sqrt(1 - 2*x))/(343*(2 + 3*x)) + (88310*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/343 - 250*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)), x, 9, (3*sqrt(1 - 2*x))/(28*(2 + 3*x)^4) + (3*sqrt(1 - 2*x))/(4*(2 + 3*x)^3) + (45*sqrt(1 - 2*x))/(8*(2 + 3*x)^2) + (3135*sqrt(1 - 2*x))/(56*(2 + 3*x)) + (36045*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/28 - 1250*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]

    @test_int [(2 + 3*x)^6/(sqrt(1 - 2*x)*(3 + 5*x)^2), x, 7, -((26352*sqrt(1 - 2*x)*(2 + 3*x)^2)/34375) - (1717*sqrt(1 - 2*x)*(2 + 3*x)^3)/9625 - (8/275)*sqrt(1 - 2*x)*(2 + 3*x)^4 - (sqrt(1 - 2*x)*(2 + 3*x)^5)/(55*(3 + 5*x)) - (3*sqrt(1 - 2*x)*(1847824 + 615875*x))/171875 - (398*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(171875*sqrt(55))]
    @test_int [(2 + 3*x)^5/(sqrt(1 - 2*x)*(3 + 5*x)^2), x, 6, -((1668*sqrt(1 - 2*x)*(2 + 3*x)^2)/6875) - (78*sqrt(1 - 2*x)*(2 + 3*x)^3)/1925 - (sqrt(1 - 2*x)*(2 + 3*x)^4)/(55*(3 + 5*x)) - (6*sqrt(1 - 2*x)*(59708 + 19875*x))/34375 - (332*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(34375*sqrt(55))]
    @test_int [(2 + 3*x)^4/(sqrt(1 - 2*x)*(3 + 5*x)^2), x, 5, -((84*sqrt(1 - 2*x)*(2 + 3*x)^2)/1375) - (sqrt(1 - 2*x)*(2 + 3*x)^3)/(55*(3 + 5*x)) - (21*sqrt(1 - 2*x)*(1144 + 375*x))/6875 - (266*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(6875*sqrt(55))]
    @test_int [(2 + 3*x)^3/(sqrt(1 - 2*x)*(3 + 5*x)^2), x, 4, (-(6/55))*sqrt(1 - 2*x)*(11 + 3*x) - (sqrt(1 - 2*x)*(2 + 3*x)^2)/(55*(3 + 5*x)) - (8*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(55*sqrt(55))]
    @test_int [(2 + 3*x)^2/(sqrt(1 - 2*x)*(3 + 5*x)^2), x, 4, (-9*sqrt(1 - 2*x))/25 - sqrt(1 - 2*x)/(275*(3 + 5*x)) - (134*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(275*sqrt(55))]
    @test_int [(2 + 3*x)/(sqrt(1 - 2*x)*(3 + 5*x)^2), x, 3, -sqrt(1 - 2*x)/(55*(3 + 5*x)) - (68*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(55*sqrt(55))]
    @test_int [1/(sqrt(1 - 2*x)*(3 + 5*x)^2), x, 3, -sqrt(1 - 2*x)/(11*(3 + 5*x)) - (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(11*sqrt(55))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^2), x, 6, (-5*sqrt(1 - 2*x))/(11*(3 + 5*x)) - 6*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) + (64*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/11]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^2), x, 7, (-340*sqrt(1 - 2*x))/(77*(3 + 5*x)) + (3*sqrt(1 - 2*x))/(7*(2 + 3*x)*(3 + 5*x)) - (426*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/7 + (650*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/11]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^2), x, 8, (-35845*sqrt(1 - 2*x))/(1078*(3 + 5*x)) + (3*sqrt(1 - 2*x))/(14*(2 + 3*x)^2*(3 + 5*x)) + (162*sqrt(1 - 2*x))/(49*(2 + 3*x)*(3 + 5*x)) - (22479*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/49 + (4900*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/11]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^2), x, 9, (-1676975*sqrt(1 - 2*x))/(7546*(3 + 5*x)) + sqrt(1 - 2*x)/(7*(2 + 3*x)^3*(3 + 5*x)) + (145*sqrt(1 - 2*x))/(98*(2 + 3*x)^2*(3 + 5*x)) + (7585*sqrt(1 - 2*x))/(343*(2 + 3*x)*(3 + 5*x)) - (1051695*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/343 + (32750*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/11]

    @test_int [(2 + 3*x)^6/(sqrt(1 - 2*x)*(3 + 5*x)^3), x, 7, -((56556*sqrt(1 - 2*x)*(2 + 3*x)^2)/378125) - (927*sqrt(1 - 2*x)*(2 + 3*x)^3)/211750 - (sqrt(1 - 2*x)*(2 + 3*x)^5)/(110*(3 + 5*x)^2) - (117*sqrt(1 - 2*x)*(2 + 3*x)^4)/(3025*(3 + 5*x)) - (9*sqrt(1 - 2*x)*(2815648 + 934875*x))/3781250 - (33069*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(1890625*sqrt(55))]
    @test_int [(2 + 3*x)^5/(sqrt(1 - 2*x)*(3 + 5*x)^3), x, 6, -((1512*sqrt(1 - 2*x)*(2 + 3*x)^2)/75625) - (sqrt(1 - 2*x)*(2 + 3*x)^4)/(110*(3 + 5*x)^2) - (201*sqrt(1 - 2*x)*(2 + 3*x)^3)/(6050*(3 + 5*x)) - (189*sqrt(1 - 2*x)*(8976 + 2875*x))/756250 - (22113*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(378125*sqrt(55))]
    @test_int [(2 + 3*x)^4/(sqrt(1 - 2*x)*(3 + 5*x)^3), x, 5, -((sqrt(1 - 2*x)*(2 + 3*x)^3)/(110*(3 + 5*x)^2)) - (84*sqrt(1 - 2*x)*(2 + 3*x)^2)/(3025*(3 + 5*x)) - (63*sqrt(1 - 2*x)*(352 + 75*x))/30250 - (2667*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(15125*sqrt(55))]
    @test_int [(2 + 3*x)^3/(sqrt(1 - 2*x)*(3 + 5*x)^3), x, 4, -((sqrt(1 - 2*x)*(2 + 3*x)^2)/(110*(3 + 5*x)^2)) - (9*sqrt(1 - 2*x)*(432 + 715*x))/(6050*(3 + 5*x)) - (1347*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(3025*sqrt(55))]
    @test_int [(2 + 3*x)^2/(sqrt(1 - 2*x)*(3 + 5*x)^3), x, 4, -sqrt(1 - 2*x)/(550*(3 + 5*x)^2) - (27*sqrt(1 - 2*x))/(1210*(3 + 5*x)) - (2313*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(3025*sqrt(55))]
    @test_int [(2 + 3*x)/(sqrt(1 - 2*x)*(3 + 5*x)^3), x, 4, -sqrt(1 - 2*x)/(110*(3 + 5*x)^2) - (69*sqrt(1 - 2*x))/(1210*(3 + 5*x)) - (69*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(605*sqrt(55))]
    @test_int [1/(sqrt(1 - 2*x)*(3 + 5*x)^3), x, 4, -sqrt(1 - 2*x)/(22*(3 + 5*x)^2) - (3*sqrt(1 - 2*x))/(242*(3 + 5*x)) - (3*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(121*sqrt(55))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^3), x, 7, (-5*sqrt(1 - 2*x))/(22*(3 + 5*x)^2) + (315*sqrt(1 - 2*x))/(242*(3 + 5*x)) + 18*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (2115*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/121]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^3), x, 8, (-505*sqrt(1 - 2*x))/(154*(3 + 5*x)^2) + (3*sqrt(1 - 2*x))/(7*(2 + 3*x)*(3 + 5*x)^2) + (33465*sqrt(1 - 2*x))/(1694*(3 + 5*x)) + (1908*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/7 - (32025*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/121]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^3), x, 9, (-35495*sqrt(1 - 2*x))/(1078*(3 + 5*x)^2) + (3*sqrt(1 - 2*x))/(14*(2 + 3*x)^2*(3 + 5*x)^2) + (429*sqrt(1 - 2*x))/(98*(2 + 3*x)*(3 + 5*x)^2) + (1177080*sqrt(1 - 2*x))/(5929*(3 + 5*x)) + (134217*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/49 - (321825*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/121]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^3), x, 10, (-2076675*sqrt(1 - 2*x))/(7546*(3 + 5*x)^2) + sqrt(1 - 2*x)/(7*(2 + 3*x)^3*(3 + 5*x)^2) + (90*sqrt(1 - 2*x))/(49*(2 + 3*x)^2*(3 + 5*x)^2) + (12555*sqrt(1 - 2*x))/(343*(2 + 3*x)*(3 + 5*x)^2) + (137735775*sqrt(1 - 2*x))/(83006*(3 + 5*x)) + (7852680*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/343 - (2689875*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/121]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(2+3*x)^m*(3+5*x)^n / (1-2*x)^(3/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [((2 + 3*x)^7*(3 + 5*x))/(1 - 2*x)^(3/2), x, 2, 9058973/(256*sqrt(1 - 2*x)) + (15647317*sqrt(1 - 2*x))/128 - (7882483*(1 - 2*x)^(3/2))/128 + (4084101*(1 - 2*x)^(5/2))/128 - (787185*(1 - 2*x)^(7/2))/64 + (422919*(1 - 2*x)^(9/2))/128 - (821583*(1 - 2*x)^(11/2))/1408 + (101331*(1 - 2*x)^(13/2))/1664 - (729*(1 - 2*x)^(15/2))/256]
    @test_int [((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x)^(3/2), x, 2, 1294139/(128*sqrt(1 - 2*x)) + (3916031*sqrt(1 - 2*x))/128 - (1692705*(1 - 2*x)^(3/2))/128 + (731619*(1 - 2*x)^(5/2))/128 - (225855*(1 - 2*x)^(7/2))/128 + (45549*(1 - 2*x)^(9/2))/128 - (59049*(1 - 2*x)^(11/2))/1408 + (3645*(1 - 2*x)^(13/2))/1664]
    @test_int [((2 + 3*x)^5*(3 + 5*x))/(1 - 2*x)^(3/2), x, 2, 184877/(64*sqrt(1 - 2*x)) + (60025*sqrt(1 - 2*x))/8 - (173215*(1 - 2*x)^(3/2))/64 + (7497*(1 - 2*x)^(5/2))/8 - (13905*(1 - 2*x)^(7/2))/64 + (117*(1 - 2*x)^(9/2))/4 - (1215*(1 - 2*x)^(11/2))/704]
    @test_int [((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x)^(3/2), x, 2, 26411/(32*sqrt(1 - 2*x)) + (57281*sqrt(1 - 2*x))/32 - (8281*(1 - 2*x)^(3/2))/16 + (10773*(1 - 2*x)^(5/2))/80 - (4671*(1 - 2*x)^(7/2))/224 + (45*(1 - 2*x)^(9/2))/32]
    @test_int [((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x)^(3/2), x, 2, 3773/(16*sqrt(1 - 2*x)) + (3283*sqrt(1 - 2*x))/8 - (357*(1 - 2*x)^(3/2))/4 + (621*(1 - 2*x)^(5/2))/40 - (135*(1 - 2*x)^(7/2))/112]
    @test_int [((2 + 3*x)^2*(3 + 5*x))/(1 - 2*x)^(3/2), x, 2, 539/(8*sqrt(1 - 2*x)) + (707*sqrt(1 - 2*x))/8 - (103*(1 - 2*x)^(3/2))/8 + (9*(1 - 2*x)^(5/2))/8]
    @test_int [((2 + 3*x)*(3 + 5*x))/(1 - 2*x)^(3/2), x, 2, 77/(4*sqrt(1 - 2*x)) + 17*sqrt(1 - 2*x) - (5*(1 - 2*x)^(3/2))/4]
    @test_int [(3 + 5*x)/(1 - 2*x)^(3/2), x, 2, 11/(2*sqrt(1 - 2*x)) + (5*sqrt(1 - 2*x))/2]
    @test_int [(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)), x, 3, 11/(7*sqrt(1 - 2*x)) + (2*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(7*sqrt(21))]
    @test_int [(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^2), x, 4, 64/(147*sqrt(1 - 2*x)) + 1/(21*sqrt(1 - 2*x)*(2 + 3*x)) - (64*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(49*sqrt(21))]
    @test_int [(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^3), x, 5, 65/(343*sqrt(1 - 2*x)) + 1/(42*sqrt(1 - 2*x)*(2 + 3*x)^2) - 65/(294*sqrt(1 - 2*x)*(2 + 3*x)) - (65/343)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x))]
    @test_int [(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^4), x, 6, 10/(147*sqrt(1 - 2*x)) + 1/(63*sqrt(1 - 2*x)*(2 + 3*x)^3) - 1/(9*sqrt(1 - 2*x)*(2 + 3*x)^2) - 5/(63*sqrt(1 - 2*x)*(2 + 3*x)) - (10*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(49*sqrt(21))]
    @test_int [(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^5), x, 7, 655/(28812*sqrt(1 - 2*x)) + 1/(84*sqrt(1 - 2*x)*(2 + 3*x)^4) - 131/(1764*sqrt(1 - 2*x)*(2 + 3*x)^3) - 131/(3528*sqrt(1 - 2*x)*(2 + 3*x)^2) - 655/(24696*sqrt(1 - 2*x)*(2 + 3*x)) - (655*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(9604*sqrt(21))]
    @test_int [(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^6), x, 8, 123/(16807*sqrt(1 - 2*x)) + 1/(105*sqrt(1 - 2*x)*(2 + 3*x)^5) - 41/(735*sqrt(1 - 2*x)*(2 + 3*x)^4) - 41/(1715*sqrt(1 - 2*x)*(2 + 3*x)^3) - 41/(3430*sqrt(1 - 2*x)*(2 + 3*x)^2) - 41/(4802*sqrt(1 - 2*x)*(2 + 3*x)) - (123*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/16807]

    @test_int [((2 + 3*x)^5*(3 + 5*x)^2)/(1 - 2*x)^(3/2), x, 2, 2033647/(128*sqrt(1 - 2*x)) + (6206585*sqrt(1 - 2*x))/128 - (8117095*(1 - 2*x)^(3/2))/384 + (1179381*(1 - 2*x)^(5/2))/128 - (367155*(1 - 2*x)^(7/2))/128 + (74667*(1 - 2*x)^(9/2))/128 - (97605*(1 - 2*x)^(11/2))/1408 + (6075*(1 - 2*x)^(13/2))/1664]
    @test_int [((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^(3/2), x, 2, 290521/(64*sqrt(1 - 2*x)) + (381073*sqrt(1 - 2*x))/32 - (832951*(1 - 2*x)^(3/2))/192 + (121359*(1 - 2*x)^(5/2))/80 - (159111*(1 - 2*x)^(7/2))/448 + (1545*(1 - 2*x)^(9/2))/32 - (2025*(1 - 2*x)^(11/2))/704]
    @test_int [((2 + 3*x)^3*(3 + 5*x)^2)/(1 - 2*x)^(3/2), x, 2, 41503/(32*sqrt(1 - 2*x)) + (91091*sqrt(1 - 2*x))/32 - (39977*(1 - 2*x)^(3/2))/48 + (17541*(1 - 2*x)^(5/2))/80 - (7695*(1 - 2*x)^(7/2))/224 + (75*(1 - 2*x)^(9/2))/32]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x)^(3/2), x, 2, 5929/(16*sqrt(1 - 2*x)) + (1309*sqrt(1 - 2*x))/2 - (3467*(1 - 2*x)^(3/2))/24 + (51*(1 - 2*x)^(5/2))/2 - (225*(1 - 2*x)^(7/2))/112]
    @test_int [((2 + 3*x)*(3 + 5*x)^2)/(1 - 2*x)^(3/2), x, 2, 847/(8*sqrt(1 - 2*x)) + (1133*sqrt(1 - 2*x))/8 - (505*(1 - 2*x)^(3/2))/24 + (15*(1 - 2*x)^(5/2))/8]
    @test_int [(3 + 5*x)^2/(1 - 2*x)^(3/2), x, 2, 121/(4*sqrt(1 - 2*x)) + (55*sqrt(1 - 2*x))/2 - (25*(1 - 2*x)^(3/2))/12]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^(3/2)*(2 + 3*x)), x, 4, 121/(14*sqrt(1 - 2*x)) + (25*sqrt(1 - 2*x))/6 - (2*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(21*sqrt(21))]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^(3/2)*(2 + 3*x)^2), x, 4, 121/(14*sqrt(1 - 2*x)*(2 + 3*x)) - (1091*sqrt(1 - 2*x))/(294*(2 + 3*x)) + (134*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(147*sqrt(21))]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^(3/2)*(2 + 3*x)^3), x, 5, 121/(14*sqrt(1 - 2*x)*(2 + 3*x)^2) - (545*sqrt(1 - 2*x))/(147*(2 + 3*x)^2) - (2045*sqrt(1 - 2*x))/(2058*(2 + 3*x)) - (2045*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(1029*sqrt(21))]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^(3/2)*(2 + 3*x)^4), x, 6, 121/(14*sqrt(1 - 2*x)*(2 + 3*x)^3) - (467*sqrt(1 - 2*x))/(126*(2 + 3*x)^3) - (905*sqrt(1 - 2*x))/(882*(2 + 3*x)^2) - (905*sqrt(1 - 2*x))/(2058*(2 + 3*x)) - (905*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(1029*sqrt(21))]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^(3/2)*(2 + 3*x)^5), x, 7, 121/(14*sqrt(1 - 2*x)*(2 + 3*x)^4) - (2179*sqrt(1 - 2*x))/(588*(2 + 3*x)^4) - (1829*sqrt(1 - 2*x))/(1764*(2 + 3*x)^3) - (9145*sqrt(1 - 2*x))/(24696*(2 + 3*x)^2) - (9145*sqrt(1 - 2*x))/(57624*(2 + 3*x)) - (9145*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(28812*sqrt(21))]

    @test_int [((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x)^(3/2), x, 2, 3195731/(128*sqrt(1 - 2*x)) + (9836211*sqrt(1 - 2*x))/128 - (4324397*(1 - 2*x)^(3/2))/128 + (9504551*(1 - 2*x)^(5/2))/640 - (4177401*(1 - 2*x)^(7/2))/896 + (122385*(1 - 2*x)^(9/2))/128 - (161325*(1 - 2*x)^(11/2))/1408 + (10125*(1 - 2*x)^(13/2))/1664]
    @test_int [((2 + 3*x)^3*(3 + 5*x)^3)/(1 - 2*x)^(3/2), x, 2, 456533/(64*sqrt(1 - 2*x)) + (302379*sqrt(1 - 2*x))/16 - (444983*(1 - 2*x)^(3/2))/64 + (98209*(1 - 2*x)^(5/2))/40 - (260055*(1 - 2*x)^(7/2))/448 + (1275*(1 - 2*x)^(9/2))/16 - (3375*(1 - 2*x)^(11/2))/704]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^3)/(1 - 2*x)^(3/2), x, 2, 65219/(32*sqrt(1 - 2*x)) + (144837*sqrt(1 - 2*x))/32 - (21439*(1 - 2*x)^(3/2))/16 + (5711*(1 - 2*x)^(5/2))/16 - (12675*(1 - 2*x)^(7/2))/224 + (125*(1 - 2*x)^(9/2))/32]
    @test_int [((2 + 3*x)*(3 + 5*x)^3)/(1 - 2*x)^(3/2), x, 2, 9317/(16*sqrt(1 - 2*x)) + (8349*sqrt(1 - 2*x))/8 - (935*(1 - 2*x)^(3/2))/4 + (335*(1 - 2*x)^(5/2))/8 - (375*(1 - 2*x)^(7/2))/112]
    @test_int [(3 + 5*x)^3/(1 - 2*x)^(3/2), x, 2, 1331/(8*sqrt(1 - 2*x)) + (1815*sqrt(1 - 2*x))/8 - (275*(1 - 2*x)^(3/2))/8 + (25*(1 - 2*x)^(5/2))/8]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^(3/2)*(2 + 3*x)), x, 6, 1331/(28*sqrt(1 - 2*x)) + (400*sqrt(1 - 2*x))/9 - (125*(1 - 2*x)^(3/2))/36 + (2*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(63*sqrt(21))]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^(3/2)*(2 + 3*x)^2), x, 4, (11*(3 + 5*x)^2)/(7*sqrt(1 - 2*x)*(2 + 3*x)) + (2*sqrt(1 - 2*x)*(1978 + 2975*x))/(147*(2 + 3*x)) - (68*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(147*sqrt(21))]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^(3/2)*(2 + 3*x)^3), x, 4, (11*(3 + 5*x)^2)/(7*sqrt(1 - 2*x)*(2 + 3*x)^2) + (5*sqrt(1 - 2*x)*(541 + 857*x))/(2058*(2 + 3*x)^2) + (2245*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(1029*sqrt(21))]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^(3/2)*(2 + 3*x)^4), x, 5, -((4660*sqrt(1 - 2*x))/(3087*(2 + 3*x))) + (11*(3 + 5*x)^2)/(7*sqrt(1 - 2*x)*(2 + 3*x)^3) + (2*sqrt(1 - 2*x)*(297 + 470*x))/(441*(2 + 3*x)^3) - (9320*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(3087*sqrt(21))]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^(3/2)*(2 + 3*x)^5), x, 6, -((39185*sqrt(1 - 2*x))/(24696*(2 + 3*x)^2)) - (39185*sqrt(1 - 2*x))/(57624*(2 + 3*x)) + (11*(3 + 5*x)^2)/(7*sqrt(1 - 2*x)*(2 + 3*x)^4) + (sqrt(1 - 2*x)*(2395 + 3789*x))/(1764*(2 + 3*x)^4) - (39185*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(28812*sqrt(21))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(2 + 3*x)^6/((1 - 2*x)^(3/2)*(3 + 5*x)), x, 12, 117649/(352*sqrt(1 - 2*x)) + (70752609*sqrt(1 - 2*x))/100000 - (1997451*(1 - 2*x)^(3/2))/10000 + (507627*(1 - 2*x)^(5/2))/10000 - (43011*(1 - 2*x)^(7/2))/5600 + (81*(1 - 2*x)^(9/2))/160 - (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(34375*sqrt(55))]
    @test_int [(2 + 3*x)^5/((1 - 2*x)^(3/2)*(3 + 5*x)), x, 10, 16807/(176*sqrt(1 - 2*x)) + (806121*sqrt(1 - 2*x))/5000 - (17019*(1 - 2*x)^(3/2))/500 + (5751*(1 - 2*x)^(5/2))/1000 - (243*(1 - 2*x)^(7/2))/560 - (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(6875*sqrt(55))]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^(3/2)*(3 + 5*x)), x, 8, 2401/(88*sqrt(1 - 2*x)) + (34371*sqrt(1 - 2*x))/1000 - (963*(1 - 2*x)^(3/2))/200 + (81*(1 - 2*x)^(5/2))/200 - (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(1375*sqrt(55))]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)), x, 6, 343/(44*sqrt(1 - 2*x)) + (162*sqrt(1 - 2*x))/25 - (9*(1 - 2*x)^(3/2))/20 - (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(275*sqrt(55))]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^(3/2)*(3 + 5*x)), x, 4, 49/(22*sqrt(1 - 2*x)) + (9*sqrt(1 - 2*x))/10 - (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(55*sqrt(55))]
    @test_int [(2 + 3*x)/((1 - 2*x)^(3/2)*(3 + 5*x)), x, 3, 7/(11*sqrt(1 - 2*x)) - (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(11*sqrt(55))]
    @test_int [1/((1 - 2*x)^(3/2)*(3 + 5*x)), x, 3, 2/(11*sqrt(1 - 2*x)) - (2*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/11]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)), x, 6, 4/(77*sqrt(1 - 2*x)) + (6*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/7 - (10*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/11]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)), x, 7, -(58/(539*sqrt(1 - 2*x))) + 3/(7*sqrt(1 - 2*x)*(2 + 3*x)) + (228/49)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (50/11)*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)), x, 8, -(2525/(3773*sqrt(1 - 2*x))) + 3/(14*sqrt(1 - 2*x)*(2 + 3*x)^2) + 225/(98*sqrt(1 - 2*x)*(2 + 3*x)) + (8025/343)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (250/11)*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x)), x, 9, -(12790/(3773*sqrt(1 - 2*x))) + 1/(7*sqrt(1 - 2*x)*(2 + 3*x)^3) + 8/(7*sqrt(1 - 2*x)*(2 + 3*x)^2) + 565/(49*sqrt(1 - 2*x)*(2 + 3*x)) + (40140/343)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (1250/11)*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]

    @test_int [(2 + 3*x)^6/((1 - 2*x)^(3/2)*(3 + 5*x)^2), x, 7, (217152*sqrt(1 - 2*x)*(2 + 3*x)^2)/75625 + (14517*sqrt(1 - 2*x)*(2 + 3*x)^3)/21175 - (36*sqrt(1 - 2*x)*(2 + 3*x)^4)/(605*(3 + 5*x)) + (7*(2 + 3*x)^5)/(11*sqrt(1 - 2*x)*(3 + 5*x)) + (9*sqrt(1 - 2*x)*(5065808 + 1688625*x))/378125 - (402*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(378125*sqrt(55))]
    @test_int [(2 + 3*x)^5/((1 - 2*x)^(3/2)*(3 + 5*x)^2), x, 6, (10836*sqrt(1 - 2*x)*(2 + 3*x)^2)/15125 - (36*sqrt(1 - 2*x)*(2 + 3*x)^3)/(605*(3 + 5*x)) + (7*(2 + 3*x)^4)/(11*sqrt(1 - 2*x)*(3 + 5*x)) + (504*sqrt(1 - 2*x)*(4499 + 1500*x))/75625 - (336*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(75625*sqrt(55))]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^(3/2)*(3 + 5*x)^2), x, 5, -((36*sqrt(1 - 2*x)*(2 + 3*x)^2)/(605*(3 + 5*x))) + (7*(2 + 3*x)^3)/(11*sqrt(1 - 2*x)*(3 + 5*x)) + (27*sqrt(1 - 2*x)*(792 + 265*x))/3025 - (54*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(3025*sqrt(55))]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)^2), x, 4, (7*(2 + 3*x)^2)/(11*sqrt(1 - 2*x)*(3 + 5*x)) + (18*sqrt(1 - 2*x)*(559 + 935*x))/(3025*(3 + 5*x)) - (204*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(3025*sqrt(55))]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^(3/2)*(3 + 5*x)^2), x, 4, 49/(22*sqrt(1 - 2*x)*(3 + 5*x)) - (1227*sqrt(1 - 2*x))/(1210*(3 + 5*x)) - (138*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(605*sqrt(55))]
    @test_int [(2 + 3*x)/((1 - 2*x)^(3/2)*(3 + 5*x)^2), x, 4, 72/(605*sqrt(1 - 2*x)) - 1/(55*sqrt(1 - 2*x)*(3 + 5*x)) - (72*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(121*sqrt(55))]
    @test_int [1/((1 - 2*x)^(3/2)*(3 + 5*x)^2), x, 4, 6/(121*sqrt(1 - 2*x)) - 1/(11*sqrt(1 - 2*x)*(3 + 5*x)) - (6/121)*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^2), x, 7, 78/(847*sqrt(1 - 2*x)) - 5/(11*sqrt(1 - 2*x)*(3 + 5*x)) - (18/7)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) + (300/121)*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^2), x, 8, 4644/(5929*sqrt(1 - 2*x)) - 340/(77*sqrt(1 - 2*x)*(3 + 5*x)) + 3/(7*sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)) - (1314/49)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) + (3150/121)*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^2), x, 9, 245865/(41503*sqrt(1 - 2*x)) - 36175/(1078*sqrt(1 - 2*x)*(3 + 5*x)) + 3/(14*sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)) + 165/(49*sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)) - (70065/343)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) + (24000/121)*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]

    @test_int [(2 + 3*x)^6/((1 - 2*x)^(3/2)*(3 + 5*x)^3), x, 7, (377748*sqrt(1 - 2*x)*(2 + 3*x)^2)/831875 - (71*sqrt(1 - 2*x)*(2 + 3*x)^4)/(1210*(3 + 5*x)^2) + (7*(2 + 3*x)^5)/(11*sqrt(1 - 2*x)*(3 + 5*x)^2) - (2721*sqrt(1 - 2*x)*(2 + 3*x)^3)/(66550*(3 + 5*x)) + (63*sqrt(1 - 2*x)*(2492512 + 831375*x))/8318750 - (33873*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(4159375*sqrt(55))]
    @test_int [(2 + 3*x)^5/((1 - 2*x)^(3/2)*(3 + 5*x)^3), x, 6, -((71*sqrt(1 - 2*x)*(2 + 3*x)^3)/(1210*(3 + 5*x)^2)) + (7*(2 + 3*x)^4)/(11*sqrt(1 - 2*x)*(3 + 5*x)^2) - (1344*sqrt(1 - 2*x)*(2 + 3*x)^2)/(33275*(3 + 5*x)) + (441*sqrt(1 - 2*x)*(3344 + 1125*x))/332750 - (4557*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(166375*sqrt(55))]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^(3/2)*(3 + 5*x)^3), x, 5, -((71*sqrt(1 - 2*x)*(2 + 3*x)^2)/(1210*(3 + 5*x)^2)) + (7*(2 + 3*x)^3)/(11*sqrt(1 - 2*x)*(3 + 5*x)^2) + (9*sqrt(1 - 2*x)*(3044 + 5093*x))/(13310*(3 + 5*x)) - (111*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(1331*sqrt(55))]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)^3), x, 4, (7*(2 + 3*x)^2)/(11*sqrt(1 - 2*x)*(3 + 5*x)^2) - (sqrt(1 - 2*x)*(15676 + 24825*x))/(66550*(3 + 5*x)^2) - (7143*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(33275*sqrt(55))]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^(3/2)*(3 + 5*x)^3), x, 5, 49/(22*sqrt(1 - 2*x)*(3 + 5*x)^2) - (613*sqrt(1 - 2*x))/(605*(3 + 5*x)^2) - (2589*sqrt(1 - 2*x))/(13310*(3 + 5*x)) - (2589*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(6655*sqrt(55))]
    @test_int [(2 + 3*x)/((1 - 2*x)^(3/2)*(3 + 5*x)^3), x, 5, 213/(6655*sqrt(1 - 2*x)) - 1/(110*sqrt(1 - 2*x)*(3 + 5*x)^2) - 71/(1210*sqrt(1 - 2*x)*(3 + 5*x)) - (213*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(1331*sqrt(55))]
    @test_int [1/((1 - 2*x)^(3/2)*(3 + 5*x)^3), x, 5, 15/(1331*sqrt(1 - 2*x)) - 1/(22*sqrt(1 - 2*x)*(3 + 5*x)^2) - 5/(242*sqrt(1 - 2*x)*(3 + 5*x)) - (15*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/1331]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^3), x, 8, -(2049/(9317*sqrt(1 - 2*x))) - 5/(22*sqrt(1 - 2*x)*(3 + 5*x)^2) + 305/(242*sqrt(1 - 2*x)*(3 + 5*x)) + (54/7)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (9975*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/1331]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^3), x, 9, -(224967/(65219*sqrt(1 - 2*x))) - 505/(154*sqrt(1 - 2*x)*(3 + 5*x)^2) + 3/(7*sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^2) + 33115/(1694*sqrt(1 - 2*x)*(3 + 5*x)) + (5832/49)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (153825*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/1331]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^3), x, 10, -(15987390/(456533*sqrt(1 - 2*x))) - 35825/(1078*sqrt(1 - 2*x)*(3 + 5*x)^2) + 3/(14*sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^2) + 435/(98*sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^2) + 1176400/(5929*sqrt(1 - 2*x)*(3 + 5*x)) + (414315/343)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (1561125*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/1331]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(2+3*x)^m*(3+5*x)^n / (1-2*x)^(5/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [((2 + 3*x)^5*(3 + 5*x))/(1 - 2*x)^(5/2), x, 2, 184877/(192*(1 - 2*x)^(3/2)) - 60025/(8*sqrt(1 - 2*x)) - (519645*sqrt(1 - 2*x))/64 + (12495*(1 - 2*x)^(3/2))/8 - (19467*(1 - 2*x)^(5/2))/64 + (1053*(1 - 2*x)^(7/2))/28 - (135*(1 - 2*x)^(9/2))/64]
    @test_int [((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x)^(5/2), x, 2, 26411/(96*(1 - 2*x)^(3/2)) - 57281/(32*sqrt(1 - 2*x)) - (24843*sqrt(1 - 2*x))/16 + (3591*(1 - 2*x)^(3/2))/16 - (4671*(1 - 2*x)^(5/2))/160 + (405*(1 - 2*x)^(7/2))/224]
    @test_int [((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x)^(5/2), x, 2, 3773/(48*(1 - 2*x)^(3/2)) - 3283/(8*sqrt(1 - 2*x)) - (1071*sqrt(1 - 2*x))/4 + (207*(1 - 2*x)^(3/2))/8 - (27*(1 - 2*x)^(5/2))/16]
    @test_int [((2 + 3*x)^2*(3 + 5*x))/(1 - 2*x)^(5/2), x, 2, 539/(24*(1 - 2*x)^(3/2)) - 707/(8*sqrt(1 - 2*x)) - (309*sqrt(1 - 2*x))/8 + (15*(1 - 2*x)^(3/2))/8]
    @test_int [((2 + 3*x)*(3 + 5*x))/(1 - 2*x)^(5/2), x, 2, 77/(12*(1 - 2*x)^(3/2)) - 17/sqrt(1 - 2*x) - (15*sqrt(1 - 2*x))/4]
    @test_int [(3 + 5*x)/(1 - 2*x)^(5/2), x, 2, 11/(6*(1 - 2*x)^(3/2)) - 5/(2*sqrt(1 - 2*x))]
    @test_int [(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)), x, 4, 11/(21*(1 - 2*x)^(3/2)) - 2/(49*sqrt(1 - 2*x)) + (2*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/49]
    @test_int [(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^2), x, 5, 20/(147*(1 - 2*x)^(3/2)) + 60/(343*sqrt(1 - 2*x)) + 1/(21*(1 - 2*x)^(3/2)*(2 + 3*x)) - (60*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/343]
    @test_int [(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^3), x, 6, 5/(49*(1 - 2*x)^(3/2)) + 45/(343*sqrt(1 - 2*x)) + 1/(42*(1 - 2*x)^(3/2)*(2 + 3*x)^2) - 3/(14*(1 - 2*x)^(3/2)*(2 + 3*x)) - (45*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/343]
    @test_int [(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^4), x, 7, 160/(3087*(1 - 2*x)^(3/2)) + 160/(2401*sqrt(1 - 2*x)) + 1/(63*(1 - 2*x)^(3/2)*(2 + 3*x)^3) - 16/(147*(1 - 2*x)^(3/2)*(2 + 3*x)^2) - 16/(147*(1 - 2*x)^(3/2)*(2 + 3*x)) - (160*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/2401]
    @test_int [(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^5), x, 8, 215/(9604*(1 - 2*x)^(3/2)) + 1935/(67228*sqrt(1 - 2*x)) + 1/(84*(1 - 2*x)^(3/2)*(2 + 3*x)^4) - 43/(588*(1 - 2*x)^(3/2)*(2 + 3*x)^3) - 129/(2744*(1 - 2*x)^(3/2)*(2 + 3*x)^2) - 129/(2744*(1 - 2*x)^(3/2)*(2 + 3*x)) - (1935*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/67228]

    @test_int [((2 + 3*x)^5*(3 + 5*x)^2)/(1 - 2*x)^(5/2), x, 2, 2033647/(384*(1 - 2*x)^(3/2)) - 6206585/(128*sqrt(1 - 2*x)) - (8117095*sqrt(1 - 2*x))/128 + (1965635*(1 - 2*x)^(3/2))/128 - (514017*(1 - 2*x)^(5/2))/128 + (672003*(1 - 2*x)^(7/2))/896 - (10845*(1 - 2*x)^(9/2))/128 + (6075*(1 - 2*x)^(11/2))/1408]
    @test_int [((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^(5/2), x, 2, 290521/(192*(1 - 2*x)^(3/2)) - 381073/(32*sqrt(1 - 2*x)) - (832951*sqrt(1 - 2*x))/64 + (40453*(1 - 2*x)^(3/2))/16 - (159111*(1 - 2*x)^(5/2))/320 + (13905*(1 - 2*x)^(7/2))/224 - (225*(1 - 2*x)^(9/2))/64]
    @test_int [((2 + 3*x)^3*(3 + 5*x)^2)/(1 - 2*x)^(5/2), x, 2, 41503/(96*(1 - 2*x)^(3/2)) - 91091/(32*sqrt(1 - 2*x)) - (39977*sqrt(1 - 2*x))/16 + (5847*(1 - 2*x)^(3/2))/16 - (1539*(1 - 2*x)^(5/2))/32 + (675*(1 - 2*x)^(7/2))/224]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x)^(5/2), x, 2, 5929/(48*(1 - 2*x)^(3/2)) - 1309/(2*sqrt(1 - 2*x)) - (3467*sqrt(1 - 2*x))/8 + (85*(1 - 2*x)^(3/2))/2 - (45*(1 - 2*x)^(5/2))/16]
    @test_int [((2 + 3*x)*(3 + 5*x)^2)/(1 - 2*x)^(5/2), x, 2, 847/(24*(1 - 2*x)^(3/2)) - 1133/(8*sqrt(1 - 2*x)) - (505*sqrt(1 - 2*x))/8 + (25*(1 - 2*x)^(3/2))/8]
    @test_int [(3 + 5*x)^2/(1 - 2*x)^(5/2), x, 2, 121/(12*(1 - 2*x)^(3/2)) - 55/(2*sqrt(1 - 2*x)) - (25*sqrt(1 - 2*x))/4]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)), x, 4, 121/(42*(1 - 2*x)^(3/2)) - 407/(98*sqrt(1 - 2*x)) - (2*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(49*sqrt(21))]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)^2), x, 5, -130/(1029*sqrt(1 - 2*x)) + 121/(42*(1 - 2*x)^(3/2)*(2 + 3*x)) - 365/(294*sqrt(1 - 2*x)*(2 + 3*x)) + (130*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(343*sqrt(21))]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)^3), x, 6, 85/(343*sqrt(1 - 2*x)) + 121/(42*(1 - 2*x)^(3/2)*(2 + 3*x)^2) - 26/(21*sqrt(1 - 2*x)*(2 + 3*x)^2) - 85/(294*sqrt(1 - 2*x)*(2 + 3*x)) - (85/343)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x))]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)^4), x, 7, 1415/(7203*sqrt(1 - 2*x)) + 121/(42*(1 - 2*x)^(3/2)*(2 + 3*x)^3) - 1091/(882*sqrt(1 - 2*x)*(2 + 3*x)^3) - 283/(882*sqrt(1 - 2*x)*(2 + 3*x)^2) - 1415/(6174*sqrt(1 - 2*x)*(2 + 3*x)) - (1415*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(2401*sqrt(21))]
    @test_int [(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)^5), x, 8, 20465/(201684*sqrt(1 - 2*x)) + 121/(42*(1 - 2*x)^(3/2)*(2 + 3*x)^4) - 727/(588*sqrt(1 - 2*x)*(2 + 3*x)^4) - 4093/(12348*sqrt(1 - 2*x)*(2 + 3*x)^3) - 4093/(24696*sqrt(1 - 2*x)*(2 + 3*x)^2) - 20465/(172872*sqrt(1 - 2*x)*(2 + 3*x)) - (20465*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(67228*sqrt(21))]

    @test_int [((2 + 3*x)^5*(3 + 5*x)^3)/(1 - 2*x)^(5/2), x, 2, 22370117/(768*(1 - 2*x)^(3/2)) - 39220335/(128*sqrt(1 - 2*x)) - (60160485*sqrt(1 - 2*x))/128 + (52725715*(1 - 2*x)^(3/2))/384 - (2887773*(1 - 2*x)^(5/2))/64 + (10121229*(1 - 2*x)^(7/2))/896 - (246315*(1 - 2*x)^(9/2))/128 + (277425*(1 - 2*x)^(11/2))/1408 - (30375*(1 - 2*x)^(13/2))/3328]
    @test_int [((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x)^(5/2), x, 2, 3195731/(384*(1 - 2*x)^(3/2)) - 9836211/(128*sqrt(1 - 2*x)) - (12973191*sqrt(1 - 2*x))/128 + (9504551*(1 - 2*x)^(3/2))/384 - (4177401*(1 - 2*x)^(5/2))/640 + (1101465*(1 - 2*x)^(7/2))/896 - (17925*(1 - 2*x)^(9/2))/128 + (10125*(1 - 2*x)^(11/2))/1408]
    @test_int [((2 + 3*x)^3*(3 + 5*x)^3)/(1 - 2*x)^(5/2), x, 2, 456533/(192*(1 - 2*x)^(3/2)) - 302379/(16*sqrt(1 - 2*x)) - (1334949*sqrt(1 - 2*x))/64 + (98209*(1 - 2*x)^(3/2))/24 - (52011*(1 - 2*x)^(5/2))/64 + (11475*(1 - 2*x)^(7/2))/112 - (375*(1 - 2*x)^(9/2))/64]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^3)/(1 - 2*x)^(5/2), x, 2, 65219/(96*(1 - 2*x)^(3/2)) - 144837/(32*sqrt(1 - 2*x)) - (64317*sqrt(1 - 2*x))/16 + (28555*(1 - 2*x)^(3/2))/48 - (2535*(1 - 2*x)^(5/2))/32 + (1125*(1 - 2*x)^(7/2))/224]
    @test_int [((2 + 3*x)*(3 + 5*x)^3)/(1 - 2*x)^(5/2), x, 2, 9317/(48*(1 - 2*x)^(3/2)) - 8349/(8*sqrt(1 - 2*x)) - (2805*sqrt(1 - 2*x))/4 + (1675*(1 - 2*x)^(3/2))/24 - (75*(1 - 2*x)^(5/2))/16]
    @test_int [(3 + 5*x)^3/(1 - 2*x)^(5/2), x, 2, 1331/(24*(1 - 2*x)^(3/2)) - 1815/(8*sqrt(1 - 2*x)) - (825*sqrt(1 - 2*x))/8 + (125*(1 - 2*x)^(3/2))/24]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)), x, 4, 1331/(84*(1 - 2*x)^(3/2)) - 2178/(49*sqrt(1 - 2*x)) - (125*sqrt(1 - 2*x))/12 + (2*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(147*sqrt(21))]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)^2), x, 4, (11*(3 + 5*x)^2)/(21*(1 - 2*x)^(3/2)*(2 + 3*x)) - (10*(969 + 1450*x))/(1029*sqrt(1 - 2*x)*(2 + 3*x)) - (200*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(1029*sqrt(21))]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)^3), x, 5, (905*sqrt(1 - 2*x))/(2058*(2 + 3*x)) + (11*(3 + 5*x)^2)/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^2) - (487 + 720*x)/(294*sqrt(1 - 2*x)*(2 + 3*x)^2) + (905*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(1029*sqrt(21))]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)^4), x, 6, -((3755*sqrt(1 - 2*x))/(3087*(2 + 3*x)^2)) - (3755*sqrt(1 - 2*x))/(7203*(2 + 3*x)) + (11*(3 + 5*x)^2)/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^3) + (2*(1346 + 2027*x))/(441*sqrt(1 - 2*x)*(2 + 3*x)^3) - (7510*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(7203*sqrt(21))]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)^5), x, 7, -((35527*sqrt(1 - 2*x))/(12348*(2 + 3*x)^3)) - (177635*sqrt(1 - 2*x))/(172872*(2 + 3*x)^2) - (177635*sqrt(1 - 2*x))/(403368*(2 + 3*x)) + (11*(3 + 5*x)^2)/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^4) + (57069 + 85754*x)/(4116*sqrt(1 - 2*x)*(2 + 3*x)^4) - (177635*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(201684*sqrt(21))]
    @test_int [(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)^6), x, 8, -((163474*sqrt(1 - 2*x))/(36015*(2 + 3*x)^4)) - (163474*sqrt(1 - 2*x))/(108045*(2 + 3*x)^3) - (81737*sqrt(1 - 2*x))/(151263*(2 + 3*x)^2) - (81737*sqrt(1 - 2*x))/(352947*(2 + 3*x)) + (11*(3 + 5*x)^2)/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^5) + (2*(55633 + 83544*x))/(5145*sqrt(1 - 2*x)*(2 + 3*x)^5) - (163474*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/(352947*sqrt(21))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(2 + 3*x)^6/((1 - 2*x)^(5/2)*(3 + 5*x)), x, 10, 117649/(1056*(1 - 2*x)^(3/2)) - 2739541/(3872*sqrt(1 - 2*x)) - (5992353*sqrt(1 - 2*x))/10000 + (169209*(1 - 2*x)^(3/2))/2000 - (43011*(1 - 2*x)^(5/2))/4000 + (729*(1 - 2*x)^(7/2))/1120 - (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(75625*sqrt(55))]
    @test_int [(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)), x, 8, 16807/(528*(1 - 2*x)^(3/2)) - 156065/(968*sqrt(1 - 2*x)) - (51057*sqrt(1 - 2*x))/500 + (1917*(1 - 2*x)^(3/2))/200 - (243*(1 - 2*x)^(5/2))/400 - (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(15125*sqrt(55))]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^(5/2)*(3 + 5*x)), x, 6, 2401/(264*(1 - 2*x)^(3/2)) - 33271/(968*sqrt(1 - 2*x)) - (2889*sqrt(1 - 2*x))/200 + (27*(1 - 2*x)^(3/2))/40 - (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(3025*sqrt(55))]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^(5/2)*(3 + 5*x)), x, 4, 343/(132*(1 - 2*x)^(3/2)) - 784/(121*sqrt(1 - 2*x)) - (27*sqrt(1 - 2*x))/20 - (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(605*sqrt(55))]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^(5/2)*(3 + 5*x)), x, 4, 49/(66*(1 - 2*x)^(3/2)) - 217/(242*sqrt(1 - 2*x)) - (2*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(121*sqrt(55))]
    @test_int [(2 + 3*x)/((1 - 2*x)^(5/2)*(3 + 5*x)), x, 4, 7/(33*(1 - 2*x)^(3/2)) + 2/(121*sqrt(1 - 2*x)) - (2*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/121]
    @test_int [1/((1 - 2*x)^(5/2)*(3 + 5*x)), x, 4, 2/(33*(1 - 2*x)^(3/2)) + 10/(121*sqrt(1 - 2*x)) - (10*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/121]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)), x, 7, 4/(231*(1 - 2*x)^(3/2)) + 272/(5929*sqrt(1 - 2*x)) + (18*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/49 - (50*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/121]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)), x, 8, -(190/(1617*(1 - 2*x)^(3/2))) - 1370/(41503*sqrt(1 - 2*x)) + 3/(7*(1 - 2*x)^(3/2)*(2 + 3*x)) + (720/343)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (250/121)*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)), x, 9, -(1115/(1617*(1 - 2*x)^(3/2))) - 12295/(41503*sqrt(1 - 2*x)) + 3/(14*(1 - 2*x)^(3/2)*(2 + 3*x)^2) + 33/(14*(1 - 2*x)^(3/2)*(2 + 3*x)) + (3645/343)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (1250/121)*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^4*(3 + 5*x)), x, 10, -(39520/(11319*(1 - 2*x)^(3/2))) - 446660/(290521*sqrt(1 - 2*x)) + 1/(7*(1 - 2*x)^(3/2)*(2 + 3*x)^3) + 57/(49*(1 - 2*x)^(3/2)*(2 + 3*x)^2) + 582/(49*(1 - 2*x)^(3/2)*(2 + 3*x)) + (127710*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)))/2401 - (6250/121)*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x))]

    @test_int [(2 + 3*x)^6/((1 - 2*x)^(5/2)*(3 + 5*x)^2), x, 7, -((463344*sqrt(1 - 2*x)*(2 + 3*x)^2)/166375) - (10283*(2 + 3*x)^3)/(6655*sqrt(1 - 2*x)) - (38*(2 + 3*x)^4)/(1815*sqrt(1 - 2*x)*(3 + 5*x)) + (7*(2 + 3*x)^5)/(33*(1 - 2*x)^(3/2)*(3 + 5*x)) - (21*sqrt(1 - 2*x)*(4633904 + 1544625*x))/831875 - (406*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(831875*sqrt(55))]
    @test_int [(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)^2), x, 6, -((7588*(2 + 3*x)^2)/(6655*sqrt(1 - 2*x))) - (38*(2 + 3*x)^3)/(1815*sqrt(1 - 2*x)*(3 + 5*x)) + (7*(2 + 3*x)^4)/(33*(1 - 2*x)^(3/2)*(3 + 5*x)) - (6*sqrt(1 - 2*x)*(114092 + 38025*x))/33275 - (68*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(33275*sqrt(55))]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^(5/2)*(3 + 5*x)^2), x, 5, -((3*(40912 - 24739*x))/(33275*sqrt(1 - 2*x))) - (38*(2 + 3*x)^2)/(1815*sqrt(1 - 2*x)*(3 + 5*x)) + (7*(2 + 3*x)^3)/(33*(1 - 2*x)^(3/2)*(3 + 5*x)) - (274*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(33275*sqrt(55))]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^(5/2)*(3 + 5*x)^2), x, 4, (7*(2 + 3*x)^2)/(33*(1 - 2*x)^(3/2)*(3 + 5*x)) - (2*(10309 + 17112*x))/(19965*sqrt(1 - 2*x)*(3 + 5*x)) - (208*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(6655*sqrt(55))]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^(5/2)*(3 + 5*x)^2), x, 5, 142/(6655*sqrt(1 - 2*x)) + 49/(66*(1 - 2*x)^(3/2)*(3 + 5*x)) - 1231/(3630*sqrt(1 - 2*x)*(3 + 5*x)) - (142*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(1331*sqrt(55))]
    @test_int [(2 + 3*x)/((1 - 2*x)^(5/2)*(3 + 5*x)^2), x, 5, 76/(1815*(1 - 2*x)^(3/2)) + 76/(1331*sqrt(1 - 2*x)) - 1/(55*(1 - 2*x)^(3/2)*(3 + 5*x)) - (76*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/1331]
    @test_int [1/((1 - 2*x)^(5/2)*(3 + 5*x)^2), x, 5, 10/(363*(1 - 2*x)^(3/2)) + 50/(1331*sqrt(1 - 2*x)) - 1/(11*(1 - 2*x)^(3/2)*(3 + 5*x)) - (50*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/1331]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^2), x, 8, 218/(2541*(1 - 2*x)^(3/2)) + 3274/(65219*sqrt(1 - 2*x)) - 5/(11*(1 - 2*x)^(3/2)*(3 + 5*x)) - (54/49)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) + (1400*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/1331]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^2), x, 9, 13900/(17787*(1 - 2*x)^(3/2)) + 159800/(456533*sqrt(1 - 2*x)) - 340/(77*(1 - 2*x)^(3/2)*(3 + 5*x)) + 3/(7*(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)) - (4050/343)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) + (15250*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/1331]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^2), x, 10, 15185/(2541*(1 - 2*x)^(3/2)) + 172105/(65219*sqrt(1 - 2*x)) - 745/(22*(1 - 2*x)^(3/2)*(3 + 5*x)) + 3/(14*(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)) + 24/(7*(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)) - (4455/49)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) + (117500*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/1331]

    @test_int [(2 + 3*x)^6/((1 - 2*x)^(5/2)*(3 + 5*x)^3), x, 7, -((256172*(2 + 3*x)^2)/(366025*sqrt(1 - 2*x))) - (73*(2 + 3*x)^4)/(3630*sqrt(1 - 2*x)*(3 + 5*x)^2) + (7*(2 + 3*x)^5)/(33*(1 - 2*x)^(3/2)*(3 + 5*x)^2) - (3269*(2 + 3*x)^3)/(199650*sqrt(1 - 2*x)*(3 + 5*x)) - (21*sqrt(1 - 2*x)*(2211616 + 736875*x))/3660250 - (6937*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(1830125*sqrt(55))]
    @test_int [(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)^3), x, 6, -((3*(544568 - 333311*x))/(732050*sqrt(1 - 2*x))) - (73*(2 + 3*x)^3)/(3630*sqrt(1 - 2*x)*(3 + 5*x)^2) + (7*(2 + 3*x)^4)/(33*(1 - 2*x)^(3/2)*(3 + 5*x)^2) - (317*(2 + 3*x)^2)/(19965*sqrt(1 - 2*x)*(3 + 5*x)) - (4693*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(366025*sqrt(55))]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^(5/2)*(3 + 5*x)^3), x, 5, -((73*(2 + 3*x)^2)/(3630*sqrt(1 - 2*x)*(3 + 5*x)^2)) + (7*(2 + 3*x)^3)/(33*(1 - 2*x)^(3/2)*(3 + 5*x)^2) - (1287116 + 2133933*x)/(2196150*sqrt(1 - 2*x)*(3 + 5*x)) - (14423*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(366025*sqrt(55))]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^(5/2)*(3 + 5*x)^3), x, 5, (7*(2 + 3*x)^2)/(33*(1 - 2*x)^(3/2)*(3 + 5*x)^2) - (7559*sqrt(1 - 2*x))/(146410*(3 + 5*x)) + (10217 + 17296*x)/(39930*sqrt(1 - 2*x)*(3 + 5*x)^2) - (7559*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(73205*sqrt(55))]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^(5/2)*(3 + 5*x)^3), x, 6, 2873/(73205*sqrt(1 - 2*x)) + 49/(66*(1 - 2*x)^(3/2)*(3 + 5*x)^2) - 614/(1815*sqrt(1 - 2*x)*(3 + 5*x)^2) - 2873/(39930*sqrt(1 - 2*x)*(3 + 5*x)) - (2873*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/(14641*sqrt(55))]
    @test_int [(2 + 3*x)/((1 - 2*x)^(5/2)*(3 + 5*x)^3), x, 6, 73/(3993*(1 - 2*x)^(3/2)) + 365/(14641*sqrt(1 - 2*x)) - 1/(110*(1 - 2*x)^(3/2)*(3 + 5*x)^2) - 73/(1210*(1 - 2*x)^(3/2)*(3 + 5*x)) - (365*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/14641]
    @test_int [1/((1 - 2*x)^(5/2)*(3 + 5*x)^3), x, 6, 35/(3993*(1 - 2*x)^(3/2)) + 175/(14641*sqrt(1 - 2*x)) - 1/(22*(1 - 2*x)^(3/2)*(3 + 5*x)^2) - 7/(242*(1 - 2*x)^(3/2)*(3 + 5*x)) - (175*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/14641]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^3), x, 9, -(5969/(27951*(1 - 2*x)^(3/2))) - 65167/(717409*sqrt(1 - 2*x)) - 5/(22*(1 - 2*x)^(3/2)*(3 + 5*x)^2) + 295/(242*(1 - 2*x)^(3/2)*(3 + 5*x)) + (162/49)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (47075*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/14641]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^3), x, 10, -(667615/(195657*(1 - 2*x)^(3/2))) - 7554245/(5021863*sqrt(1 - 2*x)) - 505/(154*(1 - 2*x)^(3/2)*(3 + 5*x)^2) + 3/(7*(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^2) + 32765/(1694*(1 - 2*x)^(3/2)*(3 + 5*x)) + (17820/343)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (738625*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/14641]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^3), x, 11, -(6845810/(195657*(1 - 2*x)^(3/2))) - 77527480/(5021863*sqrt(1 - 2*x)) - 5165/(154*(1 - 2*x)^(3/2)*(3 + 5*x)^2) + 3/(14*(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^2) + 9/(2*(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^2) + 167960/(847*(1 - 2*x)^(3/2)*(3 + 5*x)) + (182655/343)*sqrt(3/7)*atanh(sqrt(3/7)*sqrt(1 - 2*x)) - (7570625*sqrt(5/11)*atanh(sqrt(5/11)*sqrt(1 - 2*x)))/14641]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^(n/2)*(e+f*x)^(p/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^(m/2)*(A+B*x)*(d+e*x)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=m>0=#

    @test_int [sqrt(a + b*x)*(A + B*x)*(d + e*x)^(5/2), x, 8, -((b*d - a*e)^3*(3*b*B*d - 10*A*b*e + 7*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(128*b^4*e^2) - ((b*d - a*e)^2*(3*b*B*d - 10*A*b*e + 7*a*B*e)*(a + b*x)^(3/2)*sqrt(d + e*x))/(64*b^4*e) - ((b*d - a*e)*(3*b*B*d - 10*A*b*e + 7*a*B*e)*(a + b*x)^(3/2)*(d + e*x)^(3/2))/(48*b^3*e) - ((3*b*B*d - 10*A*b*e + 7*a*B*e)*(a + b*x)^(3/2)*(d + e*x)^(5/2))/(40*b^2*e) + (B*(a + b*x)^(3/2)*(d + e*x)^(7/2))/(5*b*e) + ((b*d - a*e)^4*(3*b*B*d - 10*A*b*e + 7*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(128*b^(9/2)*e^(5/2))]
    @test_int [sqrt(a + b*x)*(A + B*x)*(d + e*x)^(3/2), x, 7, -((b*d - a*e)^2*(3*b*B*d - 8*A*b*e + 5*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(64*b^3*e^2) - ((b*d - a*e)*(3*b*B*d - 8*A*b*e + 5*a*B*e)*(a + b*x)^(3/2)*sqrt(d + e*x))/(32*b^3*e) - ((3*b*B*d - 8*A*b*e + 5*a*B*e)*(a + b*x)^(3/2)*(d + e*x)^(3/2))/(24*b^2*e) + (B*(a + b*x)^(3/2)*(d + e*x)^(5/2))/(4*b*e) + ((b*d - a*e)^3*(3*b*B*d - 8*A*b*e + 5*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(64*b^(7/2)*e^(5/2))]
    @test_int [sqrt(a + b*x)*(A + B*x)*sqrt(d + e*x), x, 6, ((b*d - a*e)*(2*A*b*e - B*(b*d + a*e))*sqrt(a + b*x)*sqrt(d + e*x))/(8*b^2*e^2) + ((2*A*b*e - B*(b*d + a*e))*(a + b*x)^(3/2)*sqrt(d + e*x))/(4*b^2*e) + (B*(a + b*x)^(3/2)*(d + e*x)^(3/2))/(3*b*e) - ((b*d - a*e)^2*(2*A*b*e - B*(b*d + a*e))*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(8*b^(5/2)*e^(5/2))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/sqrt(d + e*x), x, 5, -((3*b*B*d - 4*A*b*e + a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(4*b*e^2) + (B*(a + b*x)^(3/2)*sqrt(d + e*x))/(2*b*e) + ((b*d - a*e)*(3*b*B*d - 4*A*b*e + a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(4*b^(3/2)*e^(5/2))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/(d + e*x)^(3/2), x, 5, (-2*(B*d - A*e)*(a + b*x)^(3/2))/(e*(b*d - a*e)*sqrt(d + e*x)) + ((3*b*B*d - 2*A*b*e - a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(e^2*(b*d - a*e)) - ((3*b*B*d - 2*A*b*e - a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(sqrt(b)*e^(5/2))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/(d + e*x)^(5/2), x, 5, (-2*(B*d - A*e)*(a + b*x)^(3/2))/(3*e*(b*d - a*e)*(d + e*x)^(3/2)) - (2*B*sqrt(a + b*x))/(e^2*sqrt(d + e*x)) + (2*sqrt(b)*B*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/e^(5/2)]
    @test_int [(sqrt(a + b*x)*(A + B*x))/(d + e*x)^(7/2), x, 2, (-2*(B*d - A*e)*(a + b*x)^(3/2))/(5*e*(b*d - a*e)*(d + e*x)^(5/2)) + (2*(3*b*B*d + 2*A*b*e - 5*a*B*e)*(a + b*x)^(3/2))/(15*e*(b*d - a*e)^2*(d + e*x)^(3/2))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/(d + e*x)^(9/2), x, 3, (-2*(B*d - A*e)*(a + b*x)^(3/2))/(7*e*(b*d - a*e)*(d + e*x)^(7/2)) + (2*(3*b*B*d + 4*A*b*e - 7*a*B*e)*(a + b*x)^(3/2))/(35*e*(b*d - a*e)^2*(d + e*x)^(5/2)) + (4*b*(3*b*B*d + 4*A*b*e - 7*a*B*e)*(a + b*x)^(3/2))/(105*e*(b*d - a*e)^3*(d + e*x)^(3/2))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/(d + e*x)^(11/2), x, 4, (-2*(B*d - A*e)*(a + b*x)^(3/2))/(9*e*(b*d - a*e)*(d + e*x)^(9/2)) + (2*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^(3/2))/(21*e*(b*d - a*e)^2*(d + e*x)^(7/2)) + (8*b*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^(3/2))/(105*e*(b*d - a*e)^3*(d + e*x)^(5/2)) + (16*b^2*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^(3/2))/(315*e*(b*d - a*e)^4*(d + e*x)^(3/2))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/(d + e*x)^(13/2), x, 5, (-2*(B*d - A*e)*(a + b*x)^(3/2))/(11*e*(b*d - a*e)*(d + e*x)^(11/2)) + (2*(3*b*B*d + 8*A*b*e - 11*a*B*e)*(a + b*x)^(3/2))/(99*e*(b*d - a*e)^2*(d + e*x)^(9/2)) + (4*b*(3*b*B*d + 8*A*b*e - 11*a*B*e)*(a + b*x)^(3/2))/(231*e*(b*d - a*e)^3*(d + e*x)^(7/2)) + (16*b^2*(3*b*B*d + 8*A*b*e - 11*a*B*e)*(a + b*x)^(3/2))/(1155*e*(b*d - a*e)^4*(d + e*x)^(5/2)) + (32*b^3*(3*b*B*d + 8*A*b*e - 11*a*B*e)*(a + b*x)^(3/2))/(3465*e*(b*d - a*e)^5*(d + e*x)^(3/2))]
    @test_int [(sqrt(a + b*x)*(A + B*x))/(d + e*x)^(15/2), x, 6, (-2*(B*d - A*e)*(a + b*x)^(3/2))/(13*e*(b*d - a*e)*(d + e*x)^(13/2)) + (2*(3*b*B*d + 10*A*b*e - 13*a*B*e)*(a + b*x)^(3/2))/(143*e*(b*d - a*e)^2*(d + e*x)^(11/2)) + (16*b*(3*b*B*d + 10*A*b*e - 13*a*B*e)*(a + b*x)^(3/2))/(1287*e*(b*d - a*e)^3*(d + e*x)^(9/2)) + (32*b^2*(3*b*B*d + 10*A*b*e - 13*a*B*e)*(a + b*x)^(3/2))/(3003*e*(b*d - a*e)^4*(d + e*x)^(7/2)) + (128*b^3*(3*b*B*d + 10*A*b*e - 13*a*B*e)*(a + b*x)^(3/2))/(15015*e*(b*d - a*e)^5*(d + e*x)^(5/2)) + (256*b^4*(3*b*B*d + 10*A*b*e - 13*a*B*e)*(a + b*x)^(3/2))/(45045*e*(b*d - a*e)^6*(d + e*x)^(3/2))]

    @test_int [(a + b*x)^(3/2)*(A + B*x)*(d + e*x)^(5/2), x, 9, ((b*d - a*e)^4*(5*b*B*d - 12*A*b*e + 7*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(512*b^4*e^3) - ((b*d - a*e)^3*(5*b*B*d - 12*A*b*e + 7*a*B*e)*(a + b*x)^(3/2)*sqrt(d + e*x))/(768*b^4*e^2) - ((b*d - a*e)^2*(5*b*B*d - 12*A*b*e + 7*a*B*e)*(a + b*x)^(5/2)*sqrt(d + e*x))/(192*b^4*e) - ((b*d - a*e)*(5*b*B*d - 12*A*b*e + 7*a*B*e)*(a + b*x)^(5/2)*(d + e*x)^(3/2))/(96*b^3*e) - ((5*b*B*d - 12*A*b*e + 7*a*B*e)*(a + b*x)^(5/2)*(d + e*x)^(5/2))/(60*b^2*e) + (B*(a + b*x)^(5/2)*(d + e*x)^(7/2))/(6*b*e) - ((b*d - a*e)^5*(5*b*B*d - 12*A*b*e + 7*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(512*b^(9/2)*e^(7/2))]
    @test_int [(a + b*x)^(3/2)*(A + B*x)*(d + e*x)^(3/2), x, 8, -((3*(b*d - a*e)^3*(2*A*b*e - B*(b*d + a*e))*sqrt(a + b*x)*sqrt(d + e*x))/(128*b^3*e^3)) + ((b*d - a*e)^2*(2*A*b*e - B*(b*d + a*e))*(a + b*x)^(3/2)*sqrt(d + e*x))/(64*b^3*e^2) + ((b*d - a*e)*(2*A*b*e - B*(b*d + a*e))*(a + b*x)^(5/2)*sqrt(d + e*x))/(16*b^3*e) + ((2*A*b*e - B*(b*d + a*e))*(a + b*x)^(5/2)*(d + e*x)^(3/2))/(8*b^2*e) + (B*(a + b*x)^(5/2)*(d + e*x)^(5/2))/(5*b*e) + (3*(b*d - a*e)^4*(2*A*b*e - B*(b*d + a*e))*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(128*b^(7/2)*e^(7/2))]
    @test_int [(a + b*x)^(3/2)*(A + B*x)*sqrt(d + e*x), x, 7, ((b*d - a*e)^2*(5*b*B*d - 8*A*b*e + 3*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(64*b^2*e^3) - ((b*d - a*e)*(5*b*B*d - 8*A*b*e + 3*a*B*e)*(a + b*x)^(3/2)*sqrt(d + e*x))/(96*b^2*e^2) - ((5*b*B*d - 8*A*b*e + 3*a*B*e)*(a + b*x)^(5/2)*sqrt(d + e*x))/(24*b^2*e) + (B*(a + b*x)^(5/2)*(d + e*x)^(3/2))/(4*b*e) - ((b*d - a*e)^3*(5*b*B*d - 8*A*b*e + 3*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(64*b^(5/2)*e^(7/2))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/sqrt(d + e*x), x, 6, ((b*d - a*e)*(5*b*B*d - 6*A*b*e + a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(8*b*e^3) - ((5*b*B*d - 6*A*b*e + a*B*e)*(a + b*x)^(3/2)*sqrt(d + e*x))/(12*b*e^2) + (B*(a + b*x)^(5/2)*sqrt(d + e*x))/(3*b*e) - ((b*d - a*e)^2*(5*b*B*d - 6*A*b*e + a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(8*b^(3/2)*e^(7/2))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(3/2), x, 6, (-2*(B*d - A*e)*(a + b*x)^(5/2))/(e*(b*d - a*e)*sqrt(d + e*x)) - (3*(5*b*B*d - 4*A*b*e - a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(4*e^3) + ((5*b*B*d - 4*A*b*e - a*B*e)*(a + b*x)^(3/2)*sqrt(d + e*x))/(2*e^2*(b*d - a*e)) + (3*(b*d - a*e)*(5*b*B*d - 4*A*b*e - a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(4*sqrt(b)*e^(7/2))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(5/2), x, 6, (-2*(B*d - A*e)*(a + b*x)^(5/2))/(3*e*(b*d - a*e)*(d + e*x)^(3/2)) - (2*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(a + b*x)^(3/2))/(3*e^2*(b*d - a*e)*sqrt(d + e*x)) + (b*(5*b*B*d - 2*A*b*e - 3*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(e^3*(b*d - a*e)) - (sqrt(b)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/e^(7/2)]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(7/2), x, 6, (-2*(B*d - A*e)*(a + b*x)^(5/2))/(5*e*(b*d - a*e)*(d + e*x)^(5/2)) - (2*B*(a + b*x)^(3/2))/(3*e^2*(d + e*x)^(3/2)) - (2*b*B*sqrt(a + b*x))/(e^3*sqrt(d + e*x)) + (2*b^(3/2)*B*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/e^(7/2)]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(9/2), x, 2, (-2*(B*d - A*e)*(a + b*x)^(5/2))/(7*e*(b*d - a*e)*(d + e*x)^(7/2)) + (2*(5*b*B*d + 2*A*b*e - 7*a*B*e)*(a + b*x)^(5/2))/(35*e*(b*d - a*e)^2*(d + e*x)^(5/2))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(11/2), x, 3, (-2*(B*d - A*e)*(a + b*x)^(5/2))/(9*e*(b*d - a*e)*(d + e*x)^(9/2)) + (2*(5*b*B*d + 4*A*b*e - 9*a*B*e)*(a + b*x)^(5/2))/(63*e*(b*d - a*e)^2*(d + e*x)^(7/2)) + (4*b*(5*b*B*d + 4*A*b*e - 9*a*B*e)*(a + b*x)^(5/2))/(315*e*(b*d - a*e)^3*(d + e*x)^(5/2))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(13/2), x, 4, (-2*(B*d - A*e)*(a + b*x)^(5/2))/(11*e*(b*d - a*e)*(d + e*x)^(11/2)) + (2*(5*b*B*d + 6*A*b*e - 11*a*B*e)*(a + b*x)^(5/2))/(99*e*(b*d - a*e)^2*(d + e*x)^(9/2)) + (8*b*(5*b*B*d + 6*A*b*e - 11*a*B*e)*(a + b*x)^(5/2))/(693*e*(b*d - a*e)^3*(d + e*x)^(7/2)) + (16*b^2*(5*b*B*d + 6*A*b*e - 11*a*B*e)*(a + b*x)^(5/2))/(3465*e*(b*d - a*e)^4*(d + e*x)^(5/2))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(15/2), x, 5, (-2*(B*d - A*e)*(a + b*x)^(5/2))/(13*e*(b*d - a*e)*(d + e*x)^(13/2)) + (2*(5*b*B*d + 8*A*b*e - 13*a*B*e)*(a + b*x)^(5/2))/(143*e*(b*d - a*e)^2*(d + e*x)^(11/2)) + (4*b*(5*b*B*d + 8*A*b*e - 13*a*B*e)*(a + b*x)^(5/2))/(429*e*(b*d - a*e)^3*(d + e*x)^(9/2)) + (16*b^2*(5*b*B*d + 8*A*b*e - 13*a*B*e)*(a + b*x)^(5/2))/(3003*e*(b*d - a*e)^4*(d + e*x)^(7/2)) + (32*b^3*(5*b*B*d + 8*A*b*e - 13*a*B*e)*(a + b*x)^(5/2))/(15015*e*(b*d - a*e)^5*(d + e*x)^(5/2))]
    @test_int [((a + b*x)^(3/2)*(A + B*x))/(d + e*x)^(17/2), x, 6, (-2*(B*d - A*e)*(a + b*x)^(5/2))/(15*e*(b*d - a*e)*(d + e*x)^(15/2)) + (2*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^(5/2))/(39*e*(b*d - a*e)^2*(d + e*x)^(13/2)) + (16*b*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^(5/2))/(429*e*(b*d - a*e)^3*(d + e*x)^(11/2)) + (32*b^2*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^(5/2))/(1287*e*(b*d - a*e)^4*(d + e*x)^(9/2)) + (128*b^3*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^(5/2))/(9009*e*(b*d - a*e)^5*(d + e*x)^(7/2)) + (256*b^4*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^(5/2))/(45045*e*(b*d - a*e)^6*(d + e*x)^(5/2))]

    @test_int [(a + b*x)^(5/2)*(A + B*x)*(d + e*x)^(5/2), x, 10, (5*(b*d - a*e)^5*(2*A*b*e - B*(b*d + a*e))*sqrt(a + b*x)*sqrt(d + e*x))/(1024*b^4*e^4) - (5*(b*d - a*e)^4*(2*A*b*e - B*(b*d + a*e))*(a + b*x)^(3/2)*sqrt(d + e*x))/(1536*b^4*e^3) + ((b*d - a*e)^3*(2*A*b*e - B*(b*d + a*e))*(a + b*x)^(5/2)*sqrt(d + e*x))/(384*b^4*e^2) + ((b*d - a*e)^2*(2*A*b*e - B*(b*d + a*e))*(a + b*x)^(7/2)*sqrt(d + e*x))/(64*b^4*e) + ((b*d - a*e)*(2*A*b*e - B*(b*d + a*e))*(a + b*x)^(7/2)*(d + e*x)^(3/2))/(24*b^3*e) + ((2*A*b*e - B*(b*d + a*e))*(a + b*x)^(7/2)*(d + e*x)^(5/2))/(12*b^2*e) + (B*(a + b*x)^(7/2)*(d + e*x)^(7/2))/(7*b*e) - (5*(b*d - a*e)^6*(2*A*b*e - B*(b*d + a*e))*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(1024*b^(9/2)*e^(9/2))]
    @test_int [(a + b*x)^(5/2)*(A + B*x)*(d + e*x)^(3/2), x, 9, -((b*d - a*e)^4*(7*b*B*d - 12*A*b*e + 5*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(512*b^3*e^4) + ((b*d - a*e)^3*(7*b*B*d - 12*A*b*e + 5*a*B*e)*(a + b*x)^(3/2)*sqrt(d + e*x))/(768*b^3*e^3) - ((b*d - a*e)^2*(7*b*B*d - 12*A*b*e + 5*a*B*e)*(a + b*x)^(5/2)*sqrt(d + e*x))/(960*b^3*e^2) - ((b*d - a*e)*(7*b*B*d - 12*A*b*e + 5*a*B*e)*(a + b*x)^(7/2)*sqrt(d + e*x))/(160*b^3*e) - ((7*b*B*d - 12*A*b*e + 5*a*B*e)*(a + b*x)^(7/2)*(d + e*x)^(3/2))/(60*b^2*e) + (B*(a + b*x)^(7/2)*(d + e*x)^(5/2))/(6*b*e) + ((b*d - a*e)^5*(7*b*B*d - 12*A*b*e + 5*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(512*b^(7/2)*e^(9/2))]
    @test_int [(a + b*x)^(5/2)*(A + B*x)*sqrt(d + e*x), x, 8, -((b*d - a*e)^3*(7*b*B*d - 10*A*b*e + 3*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(128*b^2*e^4) + ((b*d - a*e)^2*(7*b*B*d - 10*A*b*e + 3*a*B*e)*(a + b*x)^(3/2)*sqrt(d + e*x))/(192*b^2*e^3) - ((b*d - a*e)*(7*b*B*d - 10*A*b*e + 3*a*B*e)*(a + b*x)^(5/2)*sqrt(d + e*x))/(240*b^2*e^2) - ((7*b*B*d - 10*A*b*e + 3*a*B*e)*(a + b*x)^(7/2)*sqrt(d + e*x))/(40*b^2*e) + (B*(a + b*x)^(7/2)*(d + e*x)^(3/2))/(5*b*e) + ((b*d - a*e)^4*(7*b*B*d - 10*A*b*e + 3*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(128*b^(5/2)*e^(9/2))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/sqrt(d + e*x), x, 7, (-5*(b*d - a*e)^2*(7*b*B*d - 8*A*b*e + a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(64*b*e^4) + (5*(b*d - a*e)*(7*b*B*d - 8*A*b*e + a*B*e)*(a + b*x)^(3/2)*sqrt(d + e*x))/(96*b*e^3) - ((7*b*B*d - 8*A*b*e + a*B*e)*(a + b*x)^(5/2)*sqrt(d + e*x))/(24*b*e^2) + (B*(a + b*x)^(7/2)*sqrt(d + e*x))/(4*b*e) + (5*(b*d - a*e)^3*(7*b*B*d - 8*A*b*e + a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(64*b^(3/2)*e^(9/2))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(3/2), x, 7, (-2*(B*d - A*e)*(a + b*x)^(7/2))/(e*(b*d - a*e)*sqrt(d + e*x)) + (5*(b*d - a*e)*(7*b*B*d - 6*A*b*e - a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(8*e^4) - (5*(7*b*B*d - 6*A*b*e - a*B*e)*(a + b*x)^(3/2)*sqrt(d + e*x))/(12*e^3) + ((7*b*B*d - 6*A*b*e - a*B*e)*(a + b*x)^(5/2)*sqrt(d + e*x))/(3*e^2*(b*d - a*e)) - (5*(b*d - a*e)^2*(7*b*B*d - 6*A*b*e - a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(8*sqrt(b)*e^(9/2))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(5/2), x, 7, (-2*(B*d - A*e)*(a + b*x)^(7/2))/(3*e*(b*d - a*e)*(d + e*x)^(3/2)) - (2*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(a + b*x)^(5/2))/(3*e^2*(b*d - a*e)*sqrt(d + e*x)) - (5*b*(7*b*B*d - 4*A*b*e - 3*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(4*e^4) + (5*b*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(a + b*x)^(3/2)*sqrt(d + e*x))/(6*e^3*(b*d - a*e)) + (5*sqrt(b)*(b*d - a*e)*(7*b*B*d - 4*A*b*e - 3*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(4*e^(9/2))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(7/2), x, 7, (-2*(B*d - A*e)*(a + b*x)^(7/2))/(5*e*(b*d - a*e)*(d + e*x)^(5/2)) - (2*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(a + b*x)^(5/2))/(15*e^2*(b*d - a*e)*(d + e*x)^(3/2)) - (2*b*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(a + b*x)^(3/2))/(3*e^3*(b*d - a*e)*sqrt(d + e*x)) + (b^2*(7*b*B*d - 2*A*b*e - 5*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(e^4*(b*d - a*e)) - (b^(3/2)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/e^(9/2)]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(9/2), x, 7, (-2*(B*d - A*e)*(a + b*x)^(7/2))/(7*e*(b*d - a*e)*(d + e*x)^(7/2)) - (2*B*(a + b*x)^(5/2))/(5*e^2*(d + e*x)^(5/2)) - (2*b*B*(a + b*x)^(3/2))/(3*e^3*(d + e*x)^(3/2)) - (2*b^2*B*sqrt(a + b*x))/(e^4*sqrt(d + e*x)) + (2*b^(5/2)*B*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/e^(9/2)]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(11/2), x, 2, (-2*(B*d - A*e)*(a + b*x)^(7/2))/(9*e*(b*d - a*e)*(d + e*x)^(9/2)) + (2*(7*b*B*d + 2*A*b*e - 9*a*B*e)*(a + b*x)^(7/2))/(63*e*(b*d - a*e)^2*(d + e*x)^(7/2))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(13/2), x, 3, (-2*(B*d - A*e)*(a + b*x)^(7/2))/(11*e*(b*d - a*e)*(d + e*x)^(11/2)) + (2*(7*b*B*d + 4*A*b*e - 11*a*B*e)*(a + b*x)^(7/2))/(99*e*(b*d - a*e)^2*(d + e*x)^(9/2)) + (4*b*(7*b*B*d + 4*A*b*e - 11*a*B*e)*(a + b*x)^(7/2))/(693*e*(b*d - a*e)^3*(d + e*x)^(7/2))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(15/2), x, 4, (-2*(B*d - A*e)*(a + b*x)^(7/2))/(13*e*(b*d - a*e)*(d + e*x)^(13/2)) + (2*(7*b*B*d + 6*A*b*e - 13*a*B*e)*(a + b*x)^(7/2))/(143*e*(b*d - a*e)^2*(d + e*x)^(11/2)) + (8*b*(7*b*B*d + 6*A*b*e - 13*a*B*e)*(a + b*x)^(7/2))/(1287*e*(b*d - a*e)^3*(d + e*x)^(9/2)) + (16*b^2*(7*b*B*d + 6*A*b*e - 13*a*B*e)*(a + b*x)^(7/2))/(9009*e*(b*d - a*e)^4*(d + e*x)^(7/2))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(17/2), x, 5, (-2*(B*d - A*e)*(a + b*x)^(7/2))/(15*e*(b*d - a*e)*(d + e*x)^(15/2)) + (2*(7*b*B*d + 8*A*b*e - 15*a*B*e)*(a + b*x)^(7/2))/(195*e*(b*d - a*e)^2*(d + e*x)^(13/2)) + (4*b*(7*b*B*d + 8*A*b*e - 15*a*B*e)*(a + b*x)^(7/2))/(715*e*(b*d - a*e)^3*(d + e*x)^(11/2)) + (16*b^2*(7*b*B*d + 8*A*b*e - 15*a*B*e)*(a + b*x)^(7/2))/(6435*e*(b*d - a*e)^4*(d + e*x)^(9/2)) + (32*b^3*(7*b*B*d + 8*A*b*e - 15*a*B*e)*(a + b*x)^(7/2))/(45045*e*(b*d - a*e)^5*(d + e*x)^(7/2))]
    @test_int [((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(19/2), x, 6, (-2*(B*d - A*e)*(a + b*x)^(7/2))/(17*e*(b*d - a*e)*(d + e*x)^(17/2)) + (2*(7*b*B*d + 10*A*b*e - 17*a*B*e)*(a + b*x)^(7/2))/(255*e*(b*d - a*e)^2*(d + e*x)^(15/2)) + (16*b*(7*b*B*d + 10*A*b*e - 17*a*B*e)*(a + b*x)^(7/2))/(3315*e*(b*d - a*e)^3*(d + e*x)^(13/2)) + (32*b^2*(7*b*B*d + 10*A*b*e - 17*a*B*e)*(a + b*x)^(7/2))/(12155*e*(b*d - a*e)^4*(d + e*x)^(11/2)) + (128*b^3*(7*b*B*d + 10*A*b*e - 17*a*B*e)*(a + b*x)^(7/2))/(109395*e*(b*d - a*e)^5*(d + e*x)^(9/2)) + (256*b^4*(7*b*B*d + 10*A*b*e - 17*a*B*e)*(a + b*x)^(7/2))/(765765*e*(b*d - a*e)^6*(d + e*x)^(7/2))]

    #= ::Subsubsection::Closed:: =#
    #=m<0=#

    @test_int [((A + B*x)*(d + e*x)^(5/2))/sqrt(a + b*x), x, 7, (-5*(b*d - a*e)^2*(b*B*d - 8*A*b*e + 7*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(64*b^4*e) - (5*(b*d - a*e)*(b*B*d - 8*A*b*e + 7*a*B*e)*sqrt(a + b*x)*(d + e*x)^(3/2))/(96*b^3*e) - ((b*B*d - 8*A*b*e + 7*a*B*e)*sqrt(a + b*x)*(d + e*x)^(5/2))/(24*b^2*e) + (B*sqrt(a + b*x)*(d + e*x)^(7/2))/(4*b*e) - (5*(b*d - a*e)^3*(b*B*d - 8*A*b*e + 7*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(64*b^(9/2)*e^(3/2))]
    @test_int [((A + B*x)*(d + e*x)^(3/2))/sqrt(a + b*x), x, 6, -((b*d - a*e)*(b*B*d - 6*A*b*e + 5*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(8*b^3*e) - ((b*B*d - 6*A*b*e + 5*a*B*e)*sqrt(a + b*x)*(d + e*x)^(3/2))/(12*b^2*e) + (B*sqrt(a + b*x)*(d + e*x)^(5/2))/(3*b*e) - ((b*d - a*e)^2*(b*B*d - 6*A*b*e + 5*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(8*b^(7/2)*e^(3/2))]
    @test_int [((A + B*x)*sqrt(d + e*x))/sqrt(a + b*x), x, 5, -((b*B*d - 4*A*b*e + 3*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(4*b^2*e) + (B*sqrt(a + b*x)*(d + e*x)^(3/2))/(2*b*e) - ((b*d - a*e)*(b*B*d - 4*A*b*e + 3*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(4*b^(5/2)*e^(3/2))]
    @test_int [(A + B*x)/(sqrt(a + b*x)*sqrt(d + e*x)), x, 4, (B*sqrt(a + b*x)*sqrt(d + e*x))/(b*e) + ((2*A*b*e - B*(b*d + a*e))*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(b^(3/2)*e^(3/2))]
    @test_int [(A + B*x)/(sqrt(a + b*x)*(d + e*x)^(3/2)), x, 4, (-2*(B*d - A*e)*sqrt(a + b*x))/(e*(b*d - a*e)*sqrt(d + e*x)) + (2*B*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(sqrt(b)*e^(3/2))]
    @test_int [(A + B*x)/(sqrt(a + b*x)*(d + e*x)^(5/2)), x, 2, (-2*(B*d - A*e)*sqrt(a + b*x))/(3*e*(b*d - a*e)*(d + e*x)^(3/2)) + (2*(b*B*d + 2*A*b*e - 3*a*B*e)*sqrt(a + b*x))/(3*e*(b*d - a*e)^2*sqrt(d + e*x))]
    @test_int [(A + B*x)/(sqrt(a + b*x)*(d + e*x)^(7/2)), x, 3, (-2*(B*d - A*e)*sqrt(a + b*x))/(5*e*(b*d - a*e)*(d + e*x)^(5/2)) + (2*(b*B*d + 4*A*b*e - 5*a*B*e)*sqrt(a + b*x))/(15*e*(b*d - a*e)^2*(d + e*x)^(3/2)) + (4*b*(b*B*d + 4*A*b*e - 5*a*B*e)*sqrt(a + b*x))/(15*e*(b*d - a*e)^3*sqrt(d + e*x))]
    @test_int [(A + B*x)/(sqrt(a + b*x)*(d + e*x)^(9/2)), x, 4, (-2*(B*d - A*e)*sqrt(a + b*x))/(7*e*(b*d - a*e)*(d + e*x)^(7/2)) + (2*(b*B*d + 6*A*b*e - 7*a*B*e)*sqrt(a + b*x))/(35*e*(b*d - a*e)^2*(d + e*x)^(5/2)) + (8*b*(b*B*d + 6*A*b*e - 7*a*B*e)*sqrt(a + b*x))/(105*e*(b*d - a*e)^3*(d + e*x)^(3/2)) + (16*b^2*(b*B*d + 6*A*b*e - 7*a*B*e)*sqrt(a + b*x))/(105*e*(b*d - a*e)^4*sqrt(d + e*x))]
    @test_int [(A + B*x)/(sqrt(a + b*x)*(d + e*x)^(11/2)), x, 5, (-2*(B*d - A*e)*sqrt(a + b*x))/(9*e*(b*d - a*e)*(d + e*x)^(9/2)) + (2*(b*B*d + 8*A*b*e - 9*a*B*e)*sqrt(a + b*x))/(63*e*(b*d - a*e)^2*(d + e*x)^(7/2)) + (4*b*(b*B*d + 8*A*b*e - 9*a*B*e)*sqrt(a + b*x))/(105*e*(b*d - a*e)^3*(d + e*x)^(5/2)) + (16*b^2*(b*B*d + 8*A*b*e - 9*a*B*e)*sqrt(a + b*x))/(315*e*(b*d - a*e)^4*(d + e*x)^(3/2)) + (32*b^3*(b*B*d + 8*A*b*e - 9*a*B*e)*sqrt(a + b*x))/(315*e*(b*d - a*e)^5*sqrt(d + e*x))]

    @test_int [((A + B*x)*(d + e*x)^(5/2))/(a + b*x)^(3/2), x, 7, (5*(b*d - a*e)*(b*B*d + 6*A*b*e - 7*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(8*b^4) + (5*(b*B*d + 6*A*b*e - 7*a*B*e)*sqrt(a + b*x)*(d + e*x)^(3/2))/(12*b^3) + ((b*B*d + 6*A*b*e - 7*a*B*e)*sqrt(a + b*x)*(d + e*x)^(5/2))/(3*b^2*(b*d - a*e)) - (2*(A*b - a*B)*(d + e*x)^(7/2))/(b*(b*d - a*e)*sqrt(a + b*x)) + (5*(b*d - a*e)^2*(b*B*d + 6*A*b*e - 7*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(8*b^(9/2)*sqrt(e))]
    @test_int [((A + B*x)*(d + e*x)^(3/2))/(a + b*x)^(3/2), x, 6, (3*(b*B*d + 4*A*b*e - 5*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(4*b^3) + ((b*B*d + 4*A*b*e - 5*a*B*e)*sqrt(a + b*x)*(d + e*x)^(3/2))/(2*b^2*(b*d - a*e)) - (2*(A*b - a*B)*(d + e*x)^(5/2))/(b*(b*d - a*e)*sqrt(a + b*x)) + (3*(b*d - a*e)*(b*B*d + 4*A*b*e - 5*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(4*b^(7/2)*sqrt(e))]
    @test_int [((A + B*x)*sqrt(d + e*x))/(a + b*x)^(3/2), x, 5, ((b*B*d + 2*A*b*e - 3*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(b^2*(b*d - a*e)) - (2*(A*b - a*B)*(d + e*x)^(3/2))/(b*(b*d - a*e)*sqrt(a + b*x)) + ((b*B*d + 2*A*b*e - 3*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(b^(5/2)*sqrt(e))]
    @test_int [(A + B*x)/((a + b*x)^(3/2)*sqrt(d + e*x)), x, 4, (-2*(A*b - a*B)*sqrt(d + e*x))/(b*(b*d - a*e)*sqrt(a + b*x)) + (2*B*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(b^(3/2)*sqrt(e))]
    @test_int [(A + B*x)/((a + b*x)^(3/2)*(d + e*x)^(3/2)), x, 2, -((2*(B*d - A*e))/(e*(b*d - a*e)*sqrt(a + b*x)*sqrt(d + e*x))) + (2*(b*B*d - 2*A*b*e + a*B*e)*sqrt(d + e*x))/(e*(b*d - a*e)^2*sqrt(a + b*x))]
    @test_int [(A + B*x)/((a + b*x)^(3/2)*(d + e*x)^(5/2)), x, 3, (-2*(A*b - a*B))/(b*(b*d - a*e)*sqrt(a + b*x)*(d + e*x)^(3/2)) + (2*(b*B*d - 4*A*b*e + 3*a*B*e)*sqrt(a + b*x))/(3*b*(b*d - a*e)^2*(d + e*x)^(3/2)) + (4*(b*B*d - 4*A*b*e + 3*a*B*e)*sqrt(a + b*x))/(3*(b*d - a*e)^3*sqrt(d + e*x))]
    @test_int [(A + B*x)/((a + b*x)^(3/2)*(d + e*x)^(7/2)), x, 4, (-2*(A*b - a*B))/(b*(b*d - a*e)*sqrt(a + b*x)*(d + e*x)^(5/2)) + (2*(b*B*d - 6*A*b*e + 5*a*B*e)*sqrt(a + b*x))/(5*b*(b*d - a*e)^2*(d + e*x)^(5/2)) + (8*(b*B*d - 6*A*b*e + 5*a*B*e)*sqrt(a + b*x))/(15*(b*d - a*e)^3*(d + e*x)^(3/2)) + (16*b*(b*B*d - 6*A*b*e + 5*a*B*e)*sqrt(a + b*x))/(15*(b*d - a*e)^4*sqrt(d + e*x))]
    @test_int [(A + B*x)/((a + b*x)^(3/2)*(d + e*x)^(9/2)), x, 5, (-2*(A*b - a*B))/(b*(b*d - a*e)*sqrt(a + b*x)*(d + e*x)^(7/2)) + (2*(b*B*d - 8*A*b*e + 7*a*B*e)*sqrt(a + b*x))/(7*b*(b*d - a*e)^2*(d + e*x)^(7/2)) + (12*(b*B*d - 8*A*b*e + 7*a*B*e)*sqrt(a + b*x))/(35*(b*d - a*e)^3*(d + e*x)^(5/2)) + (16*b*(b*B*d - 8*A*b*e + 7*a*B*e)*sqrt(a + b*x))/(35*(b*d - a*e)^4*(d + e*x)^(3/2)) + (32*b^2*(b*B*d - 8*A*b*e + 7*a*B*e)*sqrt(a + b*x))/(35*(b*d - a*e)^5*sqrt(d + e*x))]

    @test_int [((A + B*x)*(d + e*x)^(7/2))/(a + b*x)^(5/2), x, 8, (35*e*(b*d - a*e)*(b*B*d + 2*A*b*e - 3*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(8*b^5) + (35*e*(b*B*d + 2*A*b*e - 3*a*B*e)*sqrt(a + b*x)*(d + e*x)^(3/2))/(12*b^4) + (7*e*(b*B*d + 2*A*b*e - 3*a*B*e)*sqrt(a + b*x)*(d + e*x)^(5/2))/(3*b^3*(b*d - a*e)) - (2*(b*B*d + 2*A*b*e - 3*a*B*e)*(d + e*x)^(7/2))/(b^2*(b*d - a*e)*sqrt(a + b*x)) - (2*(A*b - a*B)*(d + e*x)^(9/2))/(3*b*(b*d - a*e)*(a + b*x)^(3/2)) + (35*sqrt(e)*(b*d - a*e)^2*(b*B*d + 2*A*b*e - 3*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(8*b^(11/2))]
    @test_int [((A + B*x)*(d + e*x)^(5/2))/(a + b*x)^(5/2), x, 7, (5*e*(3*b*B*d + 4*A*b*e - 7*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(4*b^4) + (5*e*(3*b*B*d + 4*A*b*e - 7*a*B*e)*sqrt(a + b*x)*(d + e*x)^(3/2))/(6*b^3*(b*d - a*e)) - (2*(3*b*B*d + 4*A*b*e - 7*a*B*e)*(d + e*x)^(5/2))/(3*b^2*(b*d - a*e)*sqrt(a + b*x)) - (2*(A*b - a*B)*(d + e*x)^(7/2))/(3*b*(b*d - a*e)*(a + b*x)^(3/2)) + (5*sqrt(e)*(b*d - a*e)*(3*b*B*d + 4*A*b*e - 7*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/(4*b^(9/2))]
    @test_int [((A + B*x)*(d + e*x)^(3/2))/(a + b*x)^(5/2), x, 6, (e*(3*b*B*d + 2*A*b*e - 5*a*B*e)*sqrt(a + b*x)*sqrt(d + e*x))/(b^3*(b*d - a*e)) - (2*(3*b*B*d + 2*A*b*e - 5*a*B*e)*(d + e*x)^(3/2))/(3*b^2*(b*d - a*e)*sqrt(a + b*x)) - (2*(A*b - a*B)*(d + e*x)^(5/2))/(3*b*(b*d - a*e)*(a + b*x)^(3/2)) + (sqrt(e)*(3*b*B*d + 2*A*b*e - 5*a*B*e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/b^(7/2)]
    @test_int [((A + B*x)*sqrt(d + e*x))/(a + b*x)^(5/2), x, 5, (-2*B*sqrt(d + e*x))/(b^2*sqrt(a + b*x)) - (2*(A*b - a*B)*(d + e*x)^(3/2))/(3*b*(b*d - a*e)*(a + b*x)^(3/2)) + (2*B*sqrt(e)*atanh((sqrt(e)*sqrt(a + b*x))/(sqrt(b)*sqrt(d + e*x))))/b^(5/2)]
    @test_int [(A + B*x)/((a + b*x)^(5/2)*sqrt(d + e*x)), x, 2, (-2*(A*b - a*B)*sqrt(d + e*x))/(3*b*(b*d - a*e)*(a + b*x)^(3/2)) - (2*(3*b*B*d - 2*A*b*e - a*B*e)*sqrt(d + e*x))/(3*b*(b*d - a*e)^2*sqrt(a + b*x))]
    @test_int [(A + B*x)/((a + b*x)^(5/2)*(d + e*x)^(3/2)), x, 3, -((2*(B*d - A*e))/(e*(b*d - a*e)*(a + b*x)^(3/2)*sqrt(d + e*x))) + (2*(3*b*B*d - 4*A*b*e + a*B*e)*sqrt(d + e*x))/(3*e*(b*d - a*e)^2*(a + b*x)^(3/2)) - (4*(3*b*B*d - 4*A*b*e + a*B*e)*sqrt(d + e*x))/(3*(b*d - a*e)^3*sqrt(a + b*x))]
    @test_int [(A + B*x)/((a + b*x)^(5/2)*(d + e*x)^(5/2)), x, 4, -((2*(B*d - A*e))/(3*e*(b*d - a*e)*(a + b*x)^(3/2)*(d + e*x)^(3/2))) + (2*(b*B*d - 2*A*b*e + a*B*e))/(3*e*(b*d - a*e)^2*(a + b*x)^(3/2)*sqrt(d + e*x)) - (8*(b*B*d - 2*A*b*e + a*B*e))/(3*(b*d - a*e)^3*sqrt(a + b*x)*sqrt(d + e*x)) - (16*e*(b*B*d - 2*A*b*e + a*B*e)*sqrt(a + b*x))/(3*(b*d - a*e)^4*sqrt(d + e*x))]
    @test_int [(A + B*x)/((a + b*x)^(5/2)*(d + e*x)^(7/2)), x, 5, (-2*(A*b - a*B))/(3*b*(b*d - a*e)*(a + b*x)^(3/2)*(d + e*x)^(5/2)) - (2*(3*b*B*d - 8*A*b*e + 5*a*B*e))/(3*b*(b*d - a*e)^2*sqrt(a + b*x)*(d + e*x)^(5/2)) - (4*e*(3*b*B*d - 8*A*b*e + 5*a*B*e)*sqrt(a + b*x))/(5*b*(b*d - a*e)^3*(d + e*x)^(5/2)) - (16*e*(3*b*B*d - 8*A*b*e + 5*a*B*e)*sqrt(a + b*x))/(15*(b*d - a*e)^4*(d + e*x)^(3/2)) - (32*b*e*(3*b*B*d - 8*A*b*e + 5*a*B*e)*sqrt(a + b*x))/(15*(b*d - a*e)^5*sqrt(d + e*x))]
    @test_int [(A + B*x)/((a + b*x)^(5/2)*(d + e*x)^(9/2)), x, 6, (-2*(A*b - a*B))/(3*b*(b*d - a*e)*(a + b*x)^(3/2)*(d + e*x)^(7/2)) - (2*(3*b*B*d - 10*A*b*e + 7*a*B*e))/(3*b*(b*d - a*e)^2*sqrt(a + b*x)*(d + e*x)^(7/2)) - (16*e*(3*b*B*d - 10*A*b*e + 7*a*B*e)*sqrt(a + b*x))/(21*b*(b*d - a*e)^3*(d + e*x)^(7/2)) - (32*e*(3*b*B*d - 10*A*b*e + 7*a*B*e)*sqrt(a + b*x))/(35*(b*d - a*e)^4*(d + e*x)^(5/2)) - (128*b*e*(3*b*B*d - 10*A*b*e + 7*a*B*e)*sqrt(a + b*x))/(105*(b*d - a*e)^5*(d + e*x)^(3/2)) - (256*b^2*e*(3*b*B*d - 10*A*b*e + 7*a*B*e)*sqrt(a + b*x))/(105*(b*d - a*e)^6*sqrt(d + e*x))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^(n/2)*(e+f*x)^(1/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^4*sqrt(3 + 5*x), x, 7, (374762311*sqrt(1 - 2*x)*sqrt(3 + 5*x))/51200000 - (34069301*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/5120000 - (333*(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2))/2000 - (1/20)*(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(3/2) - (7*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)*(231223 + 140652*x))/640000 + (4122385421*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(51200000*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^3*sqrt(3 + 5*x), x, 6, (3558401*sqrt(1 - 2*x)*sqrt(3 + 5*x))/1280000 - (323491*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/128000 - (3/50)*(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2) - (21*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)*(731 + 444*x))/16000 + (39142411*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(1280000*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x), x, 6, (14443*sqrt(1 - 2*x)*sqrt(3 + 5*x))/12800 - (1313*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/1280 - (37*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/160 - (3*(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(3/2))/40 + (158873*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(12800*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)*sqrt(3 + 5*x), x, 5, (407*sqrt(1 - 2*x)*sqrt(3 + 5*x))/800 - (37*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/80 - ((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/10 + (4477*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(800*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*sqrt(3 + 5*x), x, 4, (11*sqrt(1 - 2*x)*sqrt(3 + 5*x))/40 - ((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/4 + (121*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(40*sqrt(10))]
    @test_int [(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2 + 3*x), x, 6, (sqrt(1 - 2*x)*sqrt(3 + 5*x))/3 + (37*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(9*sqrt(10)) + (2*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/9]
    @test_int [(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2 + 3*x)^2, x, 6, -(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3*(2 + 3*x)) - (2*sqrt(10)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/9 - (37*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(9*sqrt(7))]
    @test_int [(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2 + 3*x)^3, x, 4, (-11*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(28*(2 + 3*x)) + (sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(2*(2 + 3*x)^2) - (121*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(28*sqrt(7))]
    @test_int [(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2 + 3*x)^4, x, 5, (-407*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(392*(2 + 3*x)) + ((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(7*(2 + 3*x)^3) + (37*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(28*(2 + 3*x)^2) - (4477*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(392*sqrt(7))]
    @test_int [(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2 + 3*x)^5, x, 7, -(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(12*(2 + 3*x)^4) + (37*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(504*(2 + 3*x)^3) + (6005*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(14112*(2 + 3*x)^2) + (625115*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(197568*(2 + 3*x)) - (794365*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(21952*sqrt(7))]
    @test_int [(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2 + 3*x)^6, x, 8, -(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(15*(2 + 3*x)^5) + (37*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(840*(2 + 3*x)^4) + (403*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1680*(2 + 3*x)^3) + (14023*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(9408*(2 + 3*x)^2) + (1466281*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(131712*(2 + 3*x)) - (5591773*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(43904*sqrt(7))]
    @test_int [(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2 + 3*x)^7, x, 9, -(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(18*(2 + 3*x)^6) + (37*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1260*(2 + 3*x)^5) + (10921*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(70560*(2 + 3*x)^4) + (126799*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(141120*(2 + 3*x)^3) + (4429459*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(790272*(2 + 3*x)^2) + (463266973*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(11063808*(2 + 3*x)) - (588912203*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(1229312*sqrt(7))]

    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^(3/2), x, 8, (6384004649*sqrt(1 - 2*x)*sqrt(3 + 5*x))/204800000 - (580364059*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/20480000 - (52760369*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/7680000 - (403*(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2))/2800 - (3/70)*(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(5/2) - ((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)*(1480103 + 874608*x))/640000 + (70224051139*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(204800000*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^(3/2), x, 7, (115431701*sqrt(1 - 2*x)*sqrt(3 + 5*x))/10240000 - (10493791*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/1024000 - (953981*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/384000 - (1/20)*(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2) - (7*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)*(3821 + 2256*x))/32000 + (1269748711*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(10240000*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^(3/2), x, 7, (1089847*sqrt(1 - 2*x)*sqrt(3 + 5*x))/256000 - (99077*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/25600 - (9007*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/9600 - (153*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/800 - (3*(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(5/2))/50 + (11988317*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(256000*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^(3/2), x, 6, (21901*sqrt(1 - 2*x)*sqrt(3 + 5*x))/12800 - (1991*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/1280 - (181*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/480 - (3*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/40 + (240911*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(12800*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(3 + 5*x)^(3/2), x, 5, (121*sqrt(1 - 2*x)*sqrt(3 + 5*x))/160 - (11*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/16 - ((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/6 + (1331*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(160*sqrt(10))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(2 + 3*x), x, 7, (-41*sqrt(1 - 2*x)*sqrt(3 + 5*x))/72 + (sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/6 + (793*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(216*sqrt(10)) - (2*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/27]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(2 + 3*x)^2, x, 7, (10*sqrt(1 - 2*x)*sqrt(3 + 5*x))/9 - (sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(3*(2 + 3*x)) + (41*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/27 + (107*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(27*sqrt(7))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(2 + 3*x)^3, x, 7, (-107*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(252*(2 + 3*x)) - (sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(6*(2 + 3*x)^2) - (10*sqrt(10)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/27 - (4091*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(756*sqrt(7))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(2 + 3*x)^4, x, 5, (-121*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(392*(2 + 3*x)) - (11*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(84*(2 + 3*x)^2) + (sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(3*(2 + 3*x)^3) - (1331*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(392*sqrt(7))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(2 + 3*x)^5, x, 6, (-13915*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(21952*(2 + 3*x)) - (1265*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(4704*(2 + 3*x)^2) + (3*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(28*(2 + 3*x)^4) + (115*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(168*(2 + 3*x)^3) - (153065*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(21952*sqrt(7))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(2 + 3*x)^6, x, 8, (-107*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2520*(2 + 3*x)^4) + (641*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(15120*(2 + 3*x)^3) + (17981*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(84672*(2 + 3*x)^2) + (1852307*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1185408*(2 + 3*x)) - (sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(15*(2 + 3*x)^5) - (783959*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(43904*sqrt(7))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(2 + 3*x)^7, x, 9, (-107*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3780*(2 + 3*x)^5) + (4619*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(211680*(2 + 3*x)^4) + (42461*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(423360*(2 + 3*x)^3) + (1460201*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2370816*(2 + 3*x)^2) + (152571047*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(33191424*(2 + 3*x)) - (sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(18*(2 + 3*x)^6) - (64645339*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(1229312*sqrt(7))]

    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^(5/2), x, 9, (180773237579*sqrt(1 - 2*x)*sqrt(3 + 5*x))/1310720000 - (16433930689*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/131072000 - (1493993699*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/49152000 - (135817609*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/20480000 - (1419*(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(7/2))/11200 - (3/80)*(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(7/2) - (3*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2)*(899099 + 522420*x))/1280000 + (1988505613369*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(1310720000*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^(5/2), x, 8, (394818523*sqrt(1 - 2*x)*sqrt(3 + 5*x))/8192000 - (35892593*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/819200 - (3262963*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/307200 - (296633*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/128000 - (3/70)*(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(7/2) - (3*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2)*(1963 + 1140*x))/8000 + (4343003753*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(8192000*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^(5/2), x, 8, (1422839*sqrt(1 - 2*x)*sqrt(3 + 5*x))/81920 - (129349*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/8192 - (11759*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/3072 - (1069*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/1280 - (13*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2))/80 - ((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(7/2))/20 + (15651229*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(81920*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^(5/2), x, 7, (334081*sqrt(1 - 2*x)*sqrt(3 + 5*x))/51200 - (30371*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/5120 - (2761*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/1920 - (251*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/800 - (3*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2))/50 + (3674891*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(51200*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(3 + 5*x)^(5/2), x, 6, (1331*sqrt(1 - 2*x)*sqrt(3 + 5*x))/512 - (605*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/256 - (55*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/96 - ((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/8 + (14641*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(512*sqrt(10))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(2 + 3*x), x, 8, (-925*sqrt(1 - 2*x)*sqrt(3 + 5*x))/864 - (5*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/24 + (sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/9 + (6553*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/2592 + (2*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/81]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(2 + 3*x)^2, x, 8, (-95*sqrt(1 - 2*x)*sqrt(3 + 5*x))/72 + (5*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/6 - (sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(3*(2 + 3*x)) + (155*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/216 - (59*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(27*sqrt(7))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(2 + 3*x)^3, x, 8, (215*sqrt(1 - 2*x)*sqrt(3 + 5*x))/84 - (59*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(84*(2 + 3*x)) - (sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(6*(2 + 3*x)^2) + (25*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/9 + (2119*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(252*sqrt(7))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(2 + 3*x)^4, x, 8, (-6401*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(10584*(2 + 3*x)) - (59*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(252*(2 + 3*x)^2) - (sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(9*(2 + 3*x)^3) - (50*sqrt(10)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/81 - (250433*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(31752*sqrt(7))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(2 + 3*x)^5, x, 6, (-6655*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(21952*(2 + 3*x)) - (605*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(4704*(2 + 3*x)^2) - (11*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(168*(2 + 3*x)^3) + (sqrt(1 - 2*x)*(3 + 5*x)^(7/2))/(4*(2 + 3*x)^4) - (73205*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(21952*sqrt(7))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(2 + 3*x)^6, x, 7, (-22627*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(43904*(2 + 3*x)) - (2057*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(9408*(2 + 3*x)^2) - (187*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(1680*(2 + 3*x)^3) + (3*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2))/(35*(2 + 3*x)^5) + (17*sqrt(1 - 2*x)*(3 + 5*x)^(7/2))/(40*(2 + 3*x)^4) - (248897*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(43904*sqrt(7))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(2 + 3*x)^7, x, 9, (-6533*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(211680*(2 + 3*x)^4) + (47279*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1270080*(2 + 3*x)^3) + (1057139*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(7112448*(2 + 3*x)^2) + (106751933*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(99574272*(2 + 3*x)) - (59*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(1260*(2 + 3*x)^5) - (sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(18*(2 + 3*x)^6) - (15036307*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(1229312*sqrt(7))]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(2 + 3*x)^8, x, 10, (-6577*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(370440*(2 + 3*x)^5) + (369409*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(20744640*(2 + 3*x)^4) + (2524471*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(41489280*(2 + 3*x)^3) + (84539611*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(232339968*(2 + 3*x)^2) + (8818415317*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3252759552*(2 + 3*x)) - (59*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(1764*(2 + 3*x)^6) - (sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(21*(2 + 3*x)^7) - (3735929329*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(120472576*sqrt(7))]

    @test_int [sqrt(a + b*x)/(sqrt(c + d*x)*(e + f*x)), x, 7, (2*sqrt(b)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(sqrt(d)*f) - (2*sqrt(b*e - a*f)*atanh((sqrt(d*e - c*f)*sqrt(a + b*x))/(sqrt(b*e - a*f)*sqrt(c + d*x))))/(f*sqrt(d*e - c*f))]
    @test_int [sqrt(c + d*x)/(sqrt(a + b*x)*(e + f*x)), x, 7, (2*sqrt(d)*atanh((sqrt(d)*sqrt(a + b*x))/(sqrt(b)*sqrt(c + d*x))))/(sqrt(b)*f) - (2*sqrt(d*e - c*f)*atanh((sqrt(d*e - c*f)*sqrt(a + b*x))/(sqrt(b*e - a*f)*sqrt(c + d*x))))/(f*sqrt(b*e - a*f))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^3/sqrt(3 + 5*x), x, 5, (47761*sqrt(1 - 2*x)*sqrt(3 + 5*x))/64000 - (3/40)*(1 - 2*x)^(3/2)*(2 + 3*x)^2*sqrt(3 + 5*x) - (21*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)*(335 + 216*x))/6400 + (525371*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(64000*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^2/sqrt(3 + 5*x), x, 5, (277*sqrt(1 - 2*x)*sqrt(3 + 5*x))/800 - (23*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/80 - ((1 - 2*x)^(3/2)*(2 + 3*x)*sqrt(3 + 5*x))/10 + (3047*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(800*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^1/sqrt(3 + 5*x), x, 4, (41*sqrt(1 - 2*x)*sqrt(3 + 5*x))/200 - (3*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/20 + (451*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(200*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^0/sqrt(3 + 5*x), x, 3, (sqrt(1 - 2*x)*sqrt(3 + 5*x))/5 + (11*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(5*sqrt(10))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^1*sqrt(3 + 5*x)), x, 6, (-2*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/3 - (2*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/3]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^2*sqrt(3 + 5*x)), x, 3, (sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2 + 3*x) - (11*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/sqrt(7)]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^3*sqrt(3 + 5*x)), x, 4, (3*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(14*(2 + 3*x)^2) + (107*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(28*(2 + 3*x)) - (1177*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(28*sqrt(7))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^4*sqrt(3 + 5*x)), x, 6, (sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3*(2 + 3*x)^3) + (173*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(84*(2 + 3*x)^2) + (18083*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1176*(2 + 3*x)) - (68959*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(392*sqrt(7))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^5*sqrt(3 + 5*x)), x, 7, (sqrt(1 - 2*x)*sqrt(3 + 5*x))/(4*(2 + 3*x)^4) + (81*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(56*(2 + 3*x)^3) + (14145*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1568*(2 + 3*x)^2) + (1479375*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(21952*(2 + 3*x)) - (16925425*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(21952*sqrt(7))]

    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^3/(3 + 5*x)^(3/2), x, 5, -((2*sqrt(1 - 2*x)*(2 + 3*x)^3)/(5*sqrt(3 + 5*x))) - (7*(73 - 60*x)*sqrt(1 - 2*x)*sqrt(3 + 5*x))/4000 + (7/25)*sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x) + (10409*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(4000*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^2/(3 + 5*x)^(3/2), x, 5, (-2*(1 - 2*x)^(3/2))/(275*sqrt(3 + 5*x)) + (317*sqrt(1 - 2*x)*sqrt(3 + 5*x))/2200 - (9*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/100 + (317*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(200*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^1/(3 + 5*x)^(3/2), x, 4, (-2*(1 - 2*x)^(3/2))/(55*sqrt(3 + 5*x)) + (29*sqrt(1 - 2*x)*sqrt(3 + 5*x))/275 + (29*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(25*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^0/(3 + 5*x)^(3/2), x, 3, (-2*sqrt(1 - 2*x))/(5*sqrt(3 + 5*x)) - (2*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/5]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^1*(3 + 5*x)^(3/2)), x, 3, (-2*sqrt(1 - 2*x))/sqrt(3 + 5*x) + 2*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x)))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^2*(3 + 5*x)^(3/2)), x, 4, (-103*sqrt(1 - 2*x))/(7*sqrt(3 + 5*x)) + (3*(1 - 2*x)^(3/2))/(7*(2 + 3*x)*sqrt(3 + 5*x)) + (103*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/sqrt(7)]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^3*(3 + 5*x)^(3/2)), x, 6, (-2615*sqrt(1 - 2*x))/(28*sqrt(3 + 5*x)) + sqrt(1 - 2*x)/(2*(2 + 3*x)^2*sqrt(3 + 5*x)) + (173*sqrt(1 - 2*x))/(28*(2 + 3*x)*sqrt(3 + 5*x)) + (17951*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(28*sqrt(7))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^4*(3 + 5*x)^(3/2)), x, 7, (-639565*sqrt(1 - 2*x))/(1176*sqrt(3 + 5*x)) + sqrt(1 - 2*x)/(3*(2 + 3*x)^3*sqrt(3 + 5*x)) + (81*sqrt(1 - 2*x))/(28*(2 + 3*x)^2*sqrt(3 + 5*x)) + (14101*sqrt(1 - 2*x))/(392*(2 + 3*x)*sqrt(3 + 5*x)) + (1463447*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(392*sqrt(7))]

    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^4/(3 + 5*x)^(5/2), x, 6, -((2*sqrt(1 - 2*x)*(2 + 3*x)^4)/(15*(3 + 5*x)^(3/2))) - (524*sqrt(1 - 2*x)*(2 + 3*x)^3)/(825*sqrt(3 + 5*x)) + (623*sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x))/1375 + (7*sqrt(1 - 2*x)*sqrt(3 + 5*x)*(2563 + 8940*x))/220000 + (35511*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(20000*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^3/(3 + 5*x)^(5/2), x, 5, -((2*sqrt(1 - 2*x)*(2 + 3*x)^3)/(15*(3 + 5*x)^(3/2))) - (392*sqrt(1 - 2*x)*(2 + 3*x)^2)/(825*sqrt(3 + 5*x)) + (7*sqrt(1 - 2*x)*sqrt(3 + 5*x)*(1243 + 1740*x))/11000 + (1071*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(1000*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^2/(3 + 5*x)^(5/2), x, 5, (-2*(1 - 2*x)^(3/2))/(825*(3 + 5*x)^(3/2)) - (12*(1 - 2*x)^(3/2))/(275*sqrt(3 + 5*x)) + (3*sqrt(1 - 2*x)*sqrt(3 + 5*x))/55 + (3*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(5*sqrt(10))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^1/(3 + 5*x)^(5/2), x, 4, (-2*(1 - 2*x)^(3/2))/(165*(3 + 5*x)^(3/2)) - (6*sqrt(1 - 2*x))/(25*sqrt(3 + 5*x)) - (6*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/25]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^0/(3 + 5*x)^(5/2), x, 1, (-2*(1 - 2*x)^(3/2))/(33*(3 + 5*x)^(3/2))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^1*(3 + 5*x)^(5/2)), x, 4, (-10*(1 - 2*x)^(3/2))/(33*(3 + 5*x)^(3/2)) + (6*sqrt(1 - 2*x))/sqrt(3 + 5*x) - 6*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x)))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^2*(3 + 5*x)^(5/2)), x, 6, (-25*sqrt(1 - 2*x))/(3*(3 + 5*x)^(3/2)) + sqrt(1 - 2*x)/((2 + 3*x)*(3 + 5*x)^(3/2)) + (2495*sqrt(1 - 2*x))/(33*sqrt(3 + 5*x)) - (519*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/sqrt(7)]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^3*(3 + 5*x)^(5/2)), x, 7, (-6095*sqrt(1 - 2*x))/(84*(3 + 5*x)^(3/2)) + sqrt(1 - 2*x)/(2*(2 + 3*x)^2*(3 + 5*x)^(3/2)) + (243*sqrt(1 - 2*x))/(28*(2 + 3*x)*(3 + 5*x)^(3/2)) + (608185*sqrt(1 - 2*x))/(924*sqrt(3 + 5*x)) - (126513*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(28*sqrt(7))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^4*(3 + 5*x)^(5/2)), x, 8, (-638165*sqrt(1 - 2*x))/(1176*(3 + 5*x)^(3/2)) + sqrt(1 - 2*x)/(3*(2 + 3*x)^3*(3 + 5*x)^(3/2)) + (313*sqrt(1 - 2*x))/(84*(2 + 3*x)^2*(3 + 5*x)^(3/2)) + (25441*sqrt(1 - 2*x))/(392*(2 + 3*x)*(3 + 5*x)^(3/2)) + (63678595*sqrt(1 - 2*x))/(12936*sqrt(3 + 5*x)) - (13246251*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(392*sqrt(7))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^(n/2)*(e+f*x)^(3/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^3*sqrt(3 + 5*x), x, 7, (41137943*sqrt(1 - 2*x)*sqrt(3 + 5*x))/25600000 + (3739813*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/7680000 - (339983*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/384000 - (1/20)*(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2) - ((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)*(88987 + 63120*x))/160000 + (452517373*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(25600000*sqrt(10))]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^2*sqrt(3 + 5*x), x, 7, (498883*sqrt(1 - 2*x)*sqrt(3 + 5*x))/640000 + (45353*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/192000 - (4123*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/9600 - (567*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/4000 - (3*(1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^(3/2))/50 + (5487713*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(640000*sqrt(10))]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)*sqrt(3 + 5*x), x, 6, (2783*sqrt(1 - 2*x)*sqrt(3 + 5*x))/6400 + (253*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/1920 - (23*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/96 - (3*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/40 + (30613*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(6400*sqrt(10))]
    @test_int [(1 - 2*x)^(3/2)*sqrt(3 + 5*x), x, 5, (121*sqrt(1 - 2*x)*sqrt(3 + 5*x))/400 + (11*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/120 - ((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/6 + (1331*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(400*sqrt(10))]
    @test_int [((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(2 + 3*x), x, 7, (107*sqrt(1 - 2*x)*sqrt(3 + 5*x))/180 + ((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/6 + (4091*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(540*sqrt(10)) + (14*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/27]
    @test_int [((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(2 + 3*x)^2, x, 7, (-4*sqrt(1 - 2*x)*sqrt(3 + 5*x))/9 - ((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(3*(2 + 3*x)) - (107*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/27 - (41*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/27]
    @test_int [((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(2 + 3*x)^3, x, 7, -((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(6*(2 + 3*x)^2) + (41*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(36*(2 + 3*x)) + (4*sqrt(10)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/27 - (793*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(108*sqrt(7))]
    @test_int [((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(2 + 3*x)^4, x, 5, (-121*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(56*(2 + 3*x)) + ((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(3*(2 + 3*x)^3) + (11*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(4*(2 + 3*x)^2) - (1331*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(56*sqrt(7))]
    @test_int [((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(2 + 3*x)^5, x, 6, (-21901*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3136*(2 + 3*x)) + (3*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(28*(2 + 3*x)^4) + (181*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(168*(2 + 3*x)^3) + (1991*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(224*(2 + 3*x)^2) - (240911*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(3136*sqrt(7))]
    @test_int [((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(2 + 3*x)^6, x, 8, -((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(15*(2 + 3*x)^5) + (41*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(360*(2 + 3*x)^4) + (7723*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(15120*(2 + 3*x)^3) + (270463*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(84672*(2 + 3*x)^2) + (28291441*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1185408*(2 + 3*x)) - (11988317*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(43904*sqrt(7))]

    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(3/2), x, 8, (565404807*sqrt(1 - 2*x)*sqrt(3 + 5*x))/102400000 + (17133479*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/10240000 - (1557589*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/512000 - (141599*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/128000 - (3/70)*(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2) - (3*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)*(49829 + 33300*x))/280000 + (6219452877*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(102400000*sqrt(10))]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2), x, 8, (12382293*sqrt(1 - 2*x)*sqrt(3 + 5*x))/5120000 + (375221*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/512000 - (34111*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/25600 - (3101*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/6400 - (259*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/2000 - ((1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^(5/2))/20 + (136205223*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(5120000*sqrt(10))]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(3/2), x, 7, (147741*sqrt(1 - 2*x)*sqrt(3 + 5*x))/128000 + (4477*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/12800 - (407*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/640 - (37*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/160 - (3*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/50 + (1625151*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(128000*sqrt(10))]
    @test_int [(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2), x, 6, (3993*sqrt(1 - 2*x)*sqrt(3 + 5*x))/6400 + (121*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/640 - (11*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/32 - ((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/8 + (43923*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(6400*sqrt(10))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x), x, 8, (-1781*sqrt(1 - 2*x)*sqrt(3 + 5*x))/2160 + (37*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/180 + ((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/9 + (19573*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(6480*sqrt(10)) - (14*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/81]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^2, x, 8, (107*sqrt(1 - 2*x)*sqrt(3 + 5*x))/36 - (sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/3 - ((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(3*(2 + 3*x)) + (1649*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(108*sqrt(10)) + (37*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/27]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^3, x, 8, (-205*sqrt(1 - 2*x)*sqrt(3 + 5*x))/36 - ((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(6*(2 + 3*x)^2) + (37*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(12*(2 + 3*x)) - (37*sqrt(10)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/27 - (1649*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(108*sqrt(7))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^4, x, 8, (-661*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1512*(2 + 3*x)) - ((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(9*(2 + 3*x)^3) + (37*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(36*(2 + 3*x)^2) + (20*sqrt(10)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/81 - (19573*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(4536*sqrt(7))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^5, x, 6, (-3993*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3136*(2 + 3*x)) - (121*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(224*(2 + 3*x)^2) + ((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(4*(2 + 3*x)^4) + (11*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(8*(2 + 3*x)^3) - (43923*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(3136*sqrt(7))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^6, x, 7, (-147741*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(43904*(2 + 3*x)) - (4477*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(3136*(2 + 3*x)^2) + (3*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(35*(2 + 3*x)^5) + (37*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(56*(2 + 3*x)^4) + (407*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(112*(2 + 3*x)^3) - (1625151*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(43904*sqrt(7))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^7, x, 9, (-7591*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(30240*(2 + 3*x)^4) + (37333*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(181440*(2 + 3*x)^3) + (1316353*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1016064*(2 + 3*x)^2) + (137752591*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(14224896*(2 + 3*x)) - ((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(18*(2 + 3*x)^6) + (37*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(180*(2 + 3*x)^5) - (19457889*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(175616*sqrt(7))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^8, x, 10, (-9901*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(52920*(2 + 3*x)^5) + (341917*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2963520*(2 + 3*x)^4) + (4014523*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(5927040*(2 + 3*x)^3) + (140331343*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(33191424*(2 + 3*x)^2) + (14677525921*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(464679936*(2 + 3*x)) - ((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(21*(2 + 3*x)^7) + (37*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(252*(2 + 3*x)^6) - (6219452877*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(17210368*sqrt(7))]

    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(5/2), x, 9, (13441711767*sqrt(1 - 2*x)*sqrt(3 + 5*x))/655360000 + (407324599*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/65536000 - (37029509*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/3276800 - (3366319*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/819200 - (306029*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/256000 - (3/80)*(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^(7/2) - (9*(1 - 2*x)^(5/2)*(3 + 5*x)^(7/2)*(25043 + 16120*x))/448000 + (147858829437*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(655360000*sqrt(10))]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2), x, 9, (34391709*sqrt(1 - 2*x)*sqrt(3 + 5*x))/4096000 + (1042173*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/409600 - (94743*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/20480 - (8613*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/5120 - (783*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/1600 - (47*(1 - 2*x)^(5/2)*(3 + 5*x)^(7/2))/400 - (3*(1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^(7/2))/70 + (378308799*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(4096000*sqrt(10))]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(5/2), x, 8, (746691*sqrt(1 - 2*x)*sqrt(3 + 5*x))/204800 + (22627*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/20480 - (2057*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/1024 - (187*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/256 - (17*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/80 - ((1 - 2*x)^(5/2)*(3 + 5*x)^(7/2))/20 + (8213601*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(204800*sqrt(10))]
    @test_int [(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2), x, 7, (43923*sqrt(1 - 2*x)*sqrt(3 + 5*x))/25600 + (1331*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/2560 - (121*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/128 - (11*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/32 - ((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/10 + (483153*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(25600*sqrt(10))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x), x, 9, (-15863*sqrt(1 - 2*x)*sqrt(3 + 5*x))/20736 - (53*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/192 + (23*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/216 + ((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/12 + (648919*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(62208*sqrt(10)) + (14*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/243]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^2, x, 9, (-3065*sqrt(1 - 2*x)*sqrt(3 + 5*x))/1296 + (25*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/12 - (8*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/27 - ((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(3*(2 + 3*x)) - (43*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/3888 - (181*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/243]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^3, x, 9, (185*sqrt(1 - 2*x)*sqrt(3 + 5*x))/27 - (35*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/4 - ((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(6*(2 + 3*x)^2) + (181*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(36*(2 + 3*x)) + (1945*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/324 + (6829*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(324*sqrt(7))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^4, x, 9, (-39745*sqrt(1 - 2*x)*sqrt(3 + 5*x))/4536 + (331*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(168*(2 + 3*x)) - ((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(9*(2 + 3*x)^3) + (181*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(108*(2 + 3*x)^2) - (575*sqrt(10)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/243 - (326717*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(13608*sqrt(7))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^5, x, 9, (-77269*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(254016*(2 + 3*x)) - (871*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(6048*(2 + 3*x)^2) - ((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(12*(2 + 3*x)^4) + (181*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(216*(2 + 3*x)^3) + (100*sqrt(10)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/243 - (1922677*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(762048*sqrt(7))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^6, x, 7, (-43923*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(43904*(2 + 3*x)) - (1331*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(3136*(2 + 3*x)^2) - (121*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(560*(2 + 3*x)^3) + ((1 - 2*x)^(3/2)*(3 + 5*x)^(7/2))/(5*(2 + 3*x)^5) + (33*sqrt(1 - 2*x)*(3 + 5*x)^(7/2))/(40*(2 + 3*x)^4) - (483153*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(43904*sqrt(7))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^7, x, 8, (-395307*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(175616*(2 + 3*x)) - (11979*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(12544*(2 + 3*x)^2) - (1089*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(2240*(2 + 3*x)^3) + ((1 - 2*x)^(5/2)*(3 + 5*x)^(7/2))/(14*(2 + 3*x)^6) + (9*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2))/(20*(2 + 3*x)^5) + (297*sqrt(1 - 2*x)*(3 + 5*x)^(7/2))/(160*(2 + 3*x)^4) - (4348377*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(175616*sqrt(7))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^8, x, 10, (-1289227*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(8890560*(2 + 3*x)^4) + (6249601*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(53343360*(2 + 3*x)^3) + (224018941*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(298722816*(2 + 3*x)^2) + (23466191827*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(4182119424*(2 + 3*x)) - (12421*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(52920*(2 + 3*x)^5) - ((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(21*(2 + 3*x)^7) + (181*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(756*(2 + 3*x)^6) - (1104970911*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(17210368*sqrt(7))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^3)/sqrt(3 + 5*x), x, 6, (1695309*sqrt(1 - 2*x)*sqrt(3 + 5*x))/3200000 + (51373*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/320000 - (3/50)*(1 - 2*x)^(5/2)*(2 + 3*x)^2*sqrt(3 + 5*x) - (3*(1 - 2*x)^(5/2)*sqrt(3 + 5*x)*(14629 + 11580*x))/80000 + (18648399*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(3200000*sqrt(10))]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^2)/sqrt(3 + 5*x), x, 6, (9933*sqrt(1 - 2*x)*sqrt(3 + 5*x))/32000 + (301*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/3200 - (119*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/800 - (3*(1 - 2*x)^(5/2)*(2 + 3*x)*sqrt(3 + 5*x))/40 + (109263*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(32000*sqrt(10))]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x))/sqrt(3 + 5*x), x, 5, (99*sqrt(1 - 2*x)*sqrt(3 + 5*x))/400 + (3*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/40 - ((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/10 + (1089*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(400*sqrt(10))]
    @test_int [(1 - 2*x)^(3/2)/sqrt(3 + 5*x), x, 4, (33*sqrt(1 - 2*x)*sqrt(3 + 5*x))/100 + ((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/10 + (363*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(100*sqrt(10))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)*sqrt(3 + 5*x)), x, 6, (-2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/15 - (103*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/45 - (14*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/9]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^2*sqrt(3 + 5*x)), x, 6, (7*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3*(2 + 3*x)) + (4*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/9 - (29*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/9]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^3*sqrt(3 + 5*x)), x, 4, ((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(2*(2 + 3*x)^2) + (33*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(4*(2 + 3*x)) - (363*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(4*sqrt(7))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^4*sqrt(3 + 5*x)), x, 5, ((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(7*(2 + 3*x)^3) + (59*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(28*(2 + 3*x)^2) + (1947*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(56*(2 + 3*x)) - (21417*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(56*sqrt(7))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^5*sqrt(3 + 5*x)), x, 7, (7*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(12*(2 + 3*x)^4) + (227*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(72*(2 + 3*x)^3) + (39667*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2016*(2 + 3*x)^2) + (4148797*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(28224*(2 + 3*x)) - (5274027*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(3136*sqrt(7))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^6*sqrt(3 + 5*x)), x, 8, (7*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(15*(2 + 3*x)^5) + (293*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(120*(2 + 3*x)^4) + (23909*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1680*(2 + 3*x)^3) + (835409*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(9408*(2 + 3*x)^2) + (87374783*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(131712*(2 + 3*x)) - (333216939*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(43904*sqrt(7))]

    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^3)/(3 + 5*x)^(3/2), x, 6, -((2*(1 - 2*x)^(3/2)*(2 + 3*x)^3)/(5*sqrt(3 + 5*x))) + (35511*sqrt(1 - 2*x)*sqrt(3 + 5*x))/160000 - (63*(35 - 8*x)*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/16000 + (27/100)*(1 - 2*x)^(3/2)*(2 + 3*x)^2*sqrt(3 + 5*x) + (390621*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(160000*sqrt(10))]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^2)/(3 + 5*x)^(3/2), x, 6, (-2*(1 - 2*x)^(5/2))/(275*sqrt(3 + 5*x)) + (357*sqrt(1 - 2*x)*sqrt(3 + 5*x))/2000 + (119*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/2200 - (3*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/50 + (3927*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(2000*sqrt(10))]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x))/(3 + 5*x)^(3/2), x, 5, (-2*(1 - 2*x)^(5/2))/(55*sqrt(3 + 5*x)) + (3*sqrt(1 - 2*x)*sqrt(3 + 5*x))/20 + ((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/22 + (33*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(20*sqrt(10))]
    @test_int [(1 - 2*x)^(3/2)/(3 + 5*x)^(3/2), x, 4, (-2*(1 - 2*x)^(3/2))/(5*sqrt(3 + 5*x)) - (6*sqrt(1 - 2*x)*sqrt(3 + 5*x))/25 - (33*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/25]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)*(3 + 5*x)^(3/2)), x, 6, (-22*sqrt(1 - 2*x))/(5*sqrt(3 + 5*x)) + (4*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/15 + (14*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/3]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^2*(3 + 5*x)^(3/2)), x, 4, (-33*sqrt(1 - 2*x))/sqrt(3 + 5*x) + (1 - 2*x)^(3/2)/((2 + 3*x)*sqrt(3 + 5*x)) + 33*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x)))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^3*(3 + 5*x)^(3/2)), x, 5, (-5709*sqrt(1 - 2*x))/(28*sqrt(3 + 5*x)) + (3*(1 - 2*x)^(5/2))/(14*(2 + 3*x)^2*sqrt(3 + 5*x)) + (173*(1 - 2*x)^(3/2))/(28*(2 + 3*x)*sqrt(3 + 5*x)) + (5709*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(4*sqrt(7))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^4*(3 + 5*x)^(3/2)), x, 7, (-608185*sqrt(1 - 2*x))/(504*sqrt(3 + 5*x)) + (7*sqrt(1 - 2*x))/(9*(2 + 3*x)^3*sqrt(3 + 5*x)) + (77*sqrt(1 - 2*x))/(12*(2 + 3*x)^2*sqrt(3 + 5*x)) + (13409*sqrt(1 - 2*x))/(168*(2 + 3*x)*sqrt(3 + 5*x)) + (463881*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(56*sqrt(7))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^5*(3 + 5*x)^(3/2)), x, 8, (-63678595*sqrt(1 - 2*x))/(9408*sqrt(3 + 5*x)) + (7*sqrt(1 - 2*x))/(12*(2 + 3*x)^4*sqrt(3 + 5*x)) + (33*sqrt(1 - 2*x))/(8*(2 + 3*x)^3*sqrt(3 + 5*x)) + (8063*sqrt(1 - 2*x))/(224*(2 + 3*x)^2*sqrt(3 + 5*x)) + (1403963*sqrt(1 - 2*x))/(3136*(2 + 3*x)*sqrt(3 + 5*x)) + (145708761*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(3136*sqrt(7))]

    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^3)/(3 + 5*x)^(5/2), x, 6, -((2*(1 - 2*x)^(3/2)*(2 + 3*x)^3)/(15*(3 + 5*x)^(3/2))) - (128*sqrt(1 - 2*x)*(2 + 3*x)^3)/(25*sqrt(3 + 5*x)) + (378/125)*sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x) + (21*sqrt(1 - 2*x)*sqrt(3 + 5*x)*(853 + 1140*x))/10000 + (13153*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(10000*sqrt(10))]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^2)/(3 + 5*x)^(5/2), x, 6, (-2*(1 - 2*x)^(5/2))/(825*(3 + 5*x)^(3/2)) - (388*(1 - 2*x)^(5/2))/(9075*sqrt(3 + 5*x)) + (343*sqrt(1 - 2*x)*sqrt(3 + 5*x))/5500 + (343*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/18150 + (343*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(500*sqrt(10))]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x))/(3 + 5*x)^(5/2), x, 5, (-2*(1 - 2*x)^(5/2))/(165*(3 + 5*x)^(3/2)) - (38*(1 - 2*x)^(3/2))/(165*sqrt(3 + 5*x)) - (38*sqrt(1 - 2*x)*sqrt(3 + 5*x))/275 - (19*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/25]
    @test_int [(1 - 2*x)^(3/2)/(3 + 5*x)^(5/2), x, 4, (-2*(1 - 2*x)^(3/2))/(15*(3 + 5*x)^(3/2)) + (4*sqrt(1 - 2*x))/(25*sqrt(3 + 5*x)) + (4*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/25]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)*(3 + 5*x)^(5/2)), x, 4, (-2*(1 - 2*x)^(3/2))/(3*(3 + 5*x)^(3/2)) + (14*sqrt(1 - 2*x))/sqrt(3 + 5*x) - 14*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x)))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^2*(3 + 5*x)^(5/2)), x, 5, (-169*(1 - 2*x)^(3/2))/(21*(3 + 5*x)^(3/2)) + (3*(1 - 2*x)^(5/2))/(7*(2 + 3*x)*(3 + 5*x)^(3/2)) + (169*sqrt(1 - 2*x))/sqrt(3 + 5*x) - 169*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x)))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^3*(3 + 5*x)^(5/2)), x, 7, (-655*sqrt(1 - 2*x))/(4*(3 + 5*x)^(3/2)) + (7*sqrt(1 - 2*x))/(6*(2 + 3*x)^2*(3 + 5*x)^(3/2)) + (235*sqrt(1 - 2*x))/(12*(2 + 3*x)*(3 + 5*x)^(3/2)) + (17825*sqrt(1 - 2*x))/(12*sqrt(3 + 5*x)) - (40787*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(4*sqrt(7))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^4*(3 + 5*x)^(5/2)), x, 8, (-204595*sqrt(1 - 2*x))/(168*(3 + 5*x)^(3/2)) + (7*sqrt(1 - 2*x))/(9*(2 + 3*x)^3*(3 + 5*x)^(3/2)) + (301*sqrt(1 - 2*x))/(36*(2 + 3*x)^2*(3 + 5*x)^(3/2)) + (24469*sqrt(1 - 2*x))/(168*(2 + 3*x)*(3 + 5*x)^(3/2)) + (618645*sqrt(1 - 2*x))/(56*sqrt(3 + 5*x)) - (4246733*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(56*sqrt(7))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^(n/2)*(e+f*x)^(5/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^3*sqrt(3 + 5*x), x, 8, (339629939*sqrt(1 - 2*x)*sqrt(3 + 5*x))/256000000 + (30875449*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/76800000 + (2806859*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/19200000 - (255169*(1 - 2*x)^(7/2)*sqrt(3 + 5*x))/640000 - (3/70)*(1 - 2*x)^(7/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2) - (3*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2)*(33857 + 26700*x))/280000 + (3735929329*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(256000000*sqrt(10))]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^2*sqrt(3 + 5*x), x, 8, (9568559*sqrt(1 - 2*x)*sqrt(3 + 5*x))/12800000 + (869869*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/3840000 + (79079*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/960000 - (7189*(1 - 2*x)^(7/2)*sqrt(3 + 5*x))/32000 - (193*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/2000 - ((1 - 2*x)^(7/2)*(2 + 3*x)*(3 + 5*x)^(3/2))/20 + (105254149*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(12800000*sqrt(10))]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)*sqrt(3 + 5*x), x, 7, (158389*sqrt(1 - 2*x)*sqrt(3 + 5*x))/320000 + (14399*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/96000 + (1309*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/24000 - (119*(1 - 2*x)^(7/2)*sqrt(3 + 5*x))/800 - (3*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/50 + (1742279*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(320000*sqrt(10))]
    @test_int [(1 - 2*x)^(5/2)*sqrt(3 + 5*x), x, 6, (1331*sqrt(1 - 2*x)*sqrt(3 + 5*x))/3200 + (121*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/960 + (11*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/240 - ((1 - 2*x)^(7/2)*sqrt(3 + 5*x))/8 + (14641*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(3200*sqrt(10))]
    @test_int [((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(2 + 3*x), x, 8, (6401*sqrt(1 - 2*x)*sqrt(3 + 5*x))/5400 + (59*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/180 + ((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/9 + (250433*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(16200*sqrt(10)) + (98*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/81]
    @test_int [((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(2 + 3*x)^2, x, 8, (-43*sqrt(1 - 2*x)*sqrt(3 + 5*x))/30 - ((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/3 - ((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(3*(2 + 3*x)) - (2119*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(90*sqrt(10)) - (35*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/9]
    @test_int [((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(2 + 3*x)^3, x, 8, (19*sqrt(1 - 2*x)*sqrt(3 + 5*x))/18 - ((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(6*(2 + 3*x)^2) + (5*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(4*(2 + 3*x)) + (118*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/27 - (155*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/108]
    @test_int [((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(2 + 3*x)^4, x, 8, -((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(9*(2 + 3*x)^3) + (5*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(12*(2 + 3*x)^2) + (925*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(216*(2 + 3*x)) - (8*sqrt(10)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/81 - (32765*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(648*sqrt(7))]
    @test_int [((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(2 + 3*x)^5, x, 6, (-6655*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(448*(2 + 3*x)) + ((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(4*(2 + 3*x)^4) + (55*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(24*(2 + 3*x)^3) + (605*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(32*(2 + 3*x)^2) - (73205*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(448*sqrt(7))]
    @test_int [((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(2 + 3*x)^6, x, 7, (-334081*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(6272*(2 + 3*x)) + (3*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/(35*(2 + 3*x)^5) + (251*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(280*(2 + 3*x)^4) + (2761*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(336*(2 + 3*x)^3) + (30371*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(448*(2 + 3*x)^2) - (3674891*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(6272*sqrt(7))]
    @test_int [((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(2 + 3*x)^7, x, 9, -((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(18*(2 + 3*x)^6) + ((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(12*(2 + 3*x)^5) + (647*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(864*(2 + 3*x)^4) + (151621*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(36288*(2 + 3*x)^3) + (26486645*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1016064*(2 + 3*x)^2) + (2770202075*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(14224896*(2 + 3*x)) - (391280725*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(175616*sqrt(7))]

    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^(3/2), x, 9, (32302687197*sqrt(1 - 2*x)*sqrt(3 + 5*x))/8192000000 + (978869309*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/819200000 + (88988119*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/204800000 - (24269487*(1 - 2*x)^(7/2)*sqrt(3 + 5*x))/20480000 - (735439*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/1280000 - (3/80)*(1 - 2*x)^(7/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2) - (9*(1 - 2*x)^(7/2)*(3 + 5*x)^(5/2)*(18399 + 13480*x))/448000 + (355329559167*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(8192000000*sqrt(10))]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2), x, 9, (100451901*sqrt(1 - 2*x)*sqrt(3 + 5*x))/51200000 + (3043997*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/5120000 + (276727*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/1280000 - (75471*(1 - 2*x)^(7/2)*sqrt(3 + 5*x))/128000 - (2287*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/8000 - (263*(1 - 2*x)^(7/2)*(3 + 5*x)^(5/2))/2800 - (3*(1 - 2*x)^(7/2)*(2 + 3*x)*(3 + 5*x)^(5/2))/70 + (1104970911*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(51200000*sqrt(10))]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^(3/2), x, 8, (2767149*sqrt(1 - 2*x)*sqrt(3 + 5*x))/2560000 + (83853*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/256000 + (7623*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/64000 - (2079*(1 - 2*x)^(7/2)*sqrt(3 + 5*x))/6400 - (63*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/400 - ((1 - 2*x)^(7/2)*(3 + 5*x)^(5/2))/20 + (30438639*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(2560000*sqrt(10))]
    @test_int [(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2), x, 7, (43923*sqrt(1 - 2*x)*sqrt(3 + 5*x))/64000 + (1331*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/6400 + (121*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/1600 - (33*(1 - 2*x)^(7/2)*sqrt(3 + 5*x))/160 - ((1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/10 + (483153*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(64000*sqrt(10))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x), x, 9, (-390869*sqrt(1 - 2*x)*sqrt(3 + 5*x))/259200 + (7093*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/21600 + (181*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/1080 + ((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/12 + (1922677*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(777600*sqrt(10)) - (98*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/243]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^2, x, 9, (24251*sqrt(1 - 2*x)*sqrt(3 + 5*x))/3240 - (247*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/270 - (8*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/27 - ((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(3*(2 + 3*x)) + (326717*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(9720*sqrt(10)) + (805*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/243]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^3, x, 9, (-1649*sqrt(1 - 2*x)*sqrt(3 + 5*x))/108 + (41*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/18 - ((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(6*(2 + 3*x)^2) + (115*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(36*(2 + 3*x)) - (6829*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(162*sqrt(10)) - (1945*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/324]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^4, x, 9, (-845*sqrt(1 - 2*x)*sqrt(3 + 5*x))/648 - ((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(9*(2 + 3*x)^3) + (115*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(108*(2 + 3*x)^2) + (365*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(216*(2 + 3*x)) + (362*sqrt(10)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/243 + (215*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(1944*sqrt(7))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^5, x, 9, (-97235*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(36288*(2 + 3*x)) - ((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(12*(2 + 3*x)^4) + (115*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(216*(2 + 3*x)^3) + (2675*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(864*(2 + 3*x)^2) - (40*sqrt(10)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/243 - (3244595*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(108864*sqrt(7))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^6, x, 7, (-43923*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(6272*(2 + 3*x)) - (1331*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(448*(2 + 3*x)^2) + ((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(5*(2 + 3*x)^5) + (11*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(8*(2 + 3*x)^4) + (121*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(16*(2 + 3*x)^3) - (483153*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(6272*sqrt(7))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^7, x, 8, (-3733455*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(175616*(2 + 3*x)) - (113135*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(12544*(2 + 3*x)^2) + ((1 - 2*x)^(7/2)*(3 + 5*x)^(5/2))/(14*(2 + 3*x)^6) + (17*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(28*(2 + 3*x)^5) + (935*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(224*(2 + 3*x)^4) + (10285*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(448*(2 + 3*x)^3) - (41068005*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(175616*sqrt(7))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^8, x, 10, (-443563*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(254016*(2 + 3*x)^4) + (2199649*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1524096*(2 + 3*x)^3) + (384136145*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(42674688*(2 + 3*x)^2) + (40175505215*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(597445632*(2 + 3*x)) - ((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(21*(2 + 3*x)^7) + (115*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(756*(2 + 3*x)^6) + (1921*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(1512*(2 + 3*x)^5) - (1891543995*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(2458624*sqrt(7))]

    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^(5/2), x, 10, (84729414253*sqrt(1 - 2*x)*sqrt(3 + 5*x))/6553600000 + (7702674023*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/1966080000 + (700243093*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/491520000 - (63658463*(1 - 2*x)^(7/2)*sqrt(3 + 5*x))/16384000 - (5787133*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/3072000 - (526103*(1 - 2*x)^(7/2)*(3 + 5*x)^(5/2))/768000 - (1/30)*(1 - 2*x)^(7/2)*(2 + 3*x)^2*(3 + 5*x)^(7/2) - ((1 - 2*x)^(7/2)*(3 + 5*x)^(7/2)*(245011 + 170940*x))/672000 + (932023556783*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(6553600000*sqrt(10))]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2), x, 10, (1939215091*sqrt(1 - 2*x)*sqrt(3 + 5*x))/327680000 + (176292281*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/98304000 + (16026571*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/24576000 - (1456961*(1 - 2*x)^(7/2)*sqrt(3 + 5*x))/819200 - (132451*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/153600 - (12041*(1 - 2*x)^(7/2)*(3 + 5*x)^(5/2))/38400 - (999*(1 - 2*x)^(7/2)*(3 + 5*x)^(7/2))/11200 - (3*(1 - 2*x)^(7/2)*(2 + 3*x)*(3 + 5*x)^(7/2))/80 + (21331366001*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(327680000*sqrt(10))]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^(5/2), x, 9, (5958887*sqrt(1 - 2*x)*sqrt(3 + 5*x))/2048000 + (541717*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/614400 + (49247*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/153600 - (4477*(1 - 2*x)^(7/2)*sqrt(3 + 5*x))/5120 - (407*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/960 - (37*(1 - 2*x)^(7/2)*(3 + 5*x)^(5/2))/240 - (3*(1 - 2*x)^(7/2)*(3 + 5*x)^(7/2))/70 + (65547757*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(2048000*sqrt(10))]
    @test_int [(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2), x, 8, (161051*sqrt(1 - 2*x)*sqrt(3 + 5*x))/102400 + (14641*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/30720 + (1331*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/7680 - (121*(1 - 2*x)^(7/2)*sqrt(3 + 5*x))/256 - (11*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/48 - ((1 - 2*x)^(7/2)*(3 + 5*x)^(5/2))/12 + (1771561*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(102400*sqrt(10))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x), x, 10, (-1994287*sqrt(1 - 2*x)*sqrt(3 + 5*x))/3110400 - (14557*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/28800 + (4783*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/32400 + (37*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/360 + ((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/15 + (109715471*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(9331200*sqrt(10)) + (98*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/729]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^2, x, 10, (-155777*sqrt(1 - 2*x)*sqrt(3 + 5*x))/31104 + (1453*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/288 - (247*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/324 - (5*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/18 - ((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(3*(2 + 3*x)) - (660959*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(93312*sqrt(10)) - (1295*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/729]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^3, x, 10, (34145*sqrt(1 - 2*x)*sqrt(3 + 5*x))/1944 - (785*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/36 + (575*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/162 - ((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(6*(2 + 3*x)^2) + (185*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(36*(2 + 3*x)) + (81733*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/5832 + (21935*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/2916]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^4, x, 10, (-48625*sqrt(1 - 2*x)*sqrt(3 + 5*x))/1944 + (2075*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/72 - ((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(9*(2 + 3*x)^3) + (185*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(108*(2 + 3*x)^2) - (10385*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(648*(2 + 3*x)) - (21935*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/1458 - (408665*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(5832*sqrt(7))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^5, x, 10, (249575*sqrt(1 - 2*x)*sqrt(3 + 5*x))/108864 - (3485*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(4032*(2 + 3*x)) - ((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(12*(2 + 3*x)^4) + (185*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(216*(2 + 3*x)^3) + (1165*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(2592*(2 + 3*x)^2) + (1850*sqrt(10)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/729 + (3304795*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(326592*sqrt(7))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^6, x, 10, (-3248687*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1524096*(2 + 3*x)) - (32453*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(36288*(2 + 3*x)^2) - ((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(15*(2 + 3*x)^5) + (37*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(72*(2 + 3*x)^4) + (2543*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(1296*(2 + 3*x)^3) - (200*sqrt(10)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/729 - (109715471*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(4572288*sqrt(7))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^7, x, 8, (-805255*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(175616*(2 + 3*x)) - (73205*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(37632*(2 + 3*x)^2) - (1331*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(1344*(2 + 3*x)^3) + ((1 - 2*x)^(5/2)*(3 + 5*x)^(7/2))/(6*(2 + 3*x)^6) + (11*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2))/(12*(2 + 3*x)^5) + (121*sqrt(1 - 2*x)*(3 + 5*x)^(7/2))/(32*(2 + 3*x)^4) - (8857805*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(175616*sqrt(7))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^8, x, 9, (-29794435*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2458624*(2 + 3*x)) - (2708585*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(526848*(2 + 3*x)^2) - (49247*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(18816*(2 + 3*x)^3) + (3*(1 - 2*x)^(7/2)*(3 + 5*x)^(7/2))/(49*(2 + 3*x)^7) + (37*(1 - 2*x)^(5/2)*(3 + 5*x)^(7/2))/(84*(2 + 3*x)^6) + (407*(1 - 2*x)^(3/2)*(3 + 5*x)^(7/2))/(168*(2 + 3*x)^5) + (4477*sqrt(1 - 2*x)*(3 + 5*x)^(7/2))/(448*(2 + 3*x)^4) - (327738785*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(2458624*sqrt(7))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^9, x, 11, (-75045071*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(85349376*(2 + 3*x)^4) + (372439373*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(512096256*(2 + 3*x)^3) + (64983635965*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(14338695168*(2 + 3*x)^2) + (6796051494355*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(200741732352*(2 + 3*x)) - (720833*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(508032*(2 + 3*x)^5) - ((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(24*(2 + 3*x)^8) + (185*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(1008*(2 + 3*x)^7) + (47365*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(36288*(2 + 3*x)^6) - (106656830005*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(275365888*sqrt(7))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^4)/sqrt(3 + 5*x), x, 8, (1152712429*sqrt(1 - 2*x)*sqrt(3 + 5*x))/1280000000 + (104792039*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/384000000 + (9526549*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/96000000 - (271*(1 - 2*x)^(7/2)*(2 + 3*x)^2*sqrt(3 + 5*x))/2800 - (3/70)*(1 - 2*x)^(7/2)*(2 + 3*x)^3*sqrt(3 + 5*x) - ((1 - 2*x)^(7/2)*sqrt(3 + 5*x)*(12923401 + 11603280*x))/22400000 + (12679836719*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(1280000000*sqrt(10))]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^3)/sqrt(3 + 5*x), x, 7, (33455653*sqrt(1 - 2*x)*sqrt(3 + 5*x))/64000000 + (3041423*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/19200000 + (276493*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/4800000 - (1/20)*(1 - 2*x)^(7/2)*(2 + 3*x)^2*sqrt(3 + 5*x) - ((1 - 2*x)^(7/2)*sqrt(3 + 5*x)*(52951 + 47280*x))/160000 + (368012183*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(64000000*sqrt(10))]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^2)/sqrt(3 + 5*x), x, 7, (593747*sqrt(1 - 2*x)*sqrt(3 + 5*x))/1600000 + (53977*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/480000 + (4907*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/120000 - (369*(1 - 2*x)^(7/2)*sqrt(3 + 5*x))/4000 - (3*(1 - 2*x)^(7/2)*(2 + 3*x)*sqrt(3 + 5*x))/50 + (6531217*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(1600000*sqrt(10))]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x))/sqrt(3 + 5*x), x, 6, (5929*sqrt(1 - 2*x)*sqrt(3 + 5*x))/16000 + (539*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/4800 + (49*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/1200 - (3*(1 - 2*x)^(7/2)*sqrt(3 + 5*x))/40 + (65219*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(16000*sqrt(10))]
    @test_int [(1 - 2*x)^(5/2)/sqrt(3 + 5*x), x, 5, (121*sqrt(1 - 2*x)*sqrt(3 + 5*x))/200 + (11*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/60 + ((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/15 + (1331*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(200*sqrt(10))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)*sqrt(3 + 5*x)), x, 7, (-239*sqrt(1 - 2*x)*sqrt(3 + 5*x))/450 - ((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/15 - (17687*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(1350*sqrt(10)) - (98*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/27]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^2*sqrt(3 + 5*x)), x, 7, (74*sqrt(1 - 2*x)*sqrt(3 + 5*x))/45 + (7*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(3*(2 + 3*x)) + (346*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/135 - (175*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/27]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^3*sqrt(3 + 5*x)), x, 7, (7*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(6*(2 + 3*x)^2) + (637*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(36*(2 + 3*x)) - (8*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/27 - (3035*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/108]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^4*sqrt(3 + 5*x)), x, 5, ((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(3*(2 + 3*x)^3) + (55*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(12*(2 + 3*x)^2) + (605*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(8*(2 + 3*x)) - (6655*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(8*sqrt(7))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^5*sqrt(3 + 5*x)), x, 6, (3*(1 - 2*x)^(7/2)*sqrt(3 + 5*x))/(28*(2 + 3*x)^4) + (247*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(168*(2 + 3*x)^3) + (13585*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(672*(2 + 3*x)^2) + (149435*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(448*(2 + 3*x)) - (1643785*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(448*sqrt(7))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^6*sqrt(3 + 5*x)), x, 8, (7*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(15*(2 + 3*x)^5) + (2023*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(360*(2 + 3*x)^4) + (67187*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2160*(2 + 3*x)^3) + (2347559*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(12096*(2 + 3*x)^2) + (245529161*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(169344*(2 + 3*x)) - (104040277*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(6272*sqrt(7))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^7*sqrt(3 + 5*x)), x, 9, (7*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(18*(2 + 3*x)^6) + (497*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(108*(2 + 3*x)^5) + (21199*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(864*(2 + 3*x)^4) + (1729615*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(12096*(2 + 3*x)^3) + (302171615*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(338688*(2 + 3*x)^2) + (31603880465*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(4741632*(2 + 3*x)) - (13391796605*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(175616*sqrt(7))]

    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^4)/(3 + 5*x)^(3/2), x, 8, -((2*(1 - 2*x)^(5/2)*(2 + 3*x)^4)/(5*sqrt(3 + 5*x))) + (118054167*sqrt(1 - 2*x)*sqrt(3 + 5*x))/320000000 + (3577399*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/32000000 + (111*(1 - 2*x)^(5/2)*(2 + 3*x)^2*sqrt(3 + 5*x))/5000 + (13/50)*(1 - 2*x)^(5/2)*(2 + 3*x)^3*sqrt(3 + 5*x) - ((1 - 2*x)^(5/2)*sqrt(3 + 5*x)*(2725981 + 1990620*x))/8000000 + (1298595837*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(320000000*sqrt(10))]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(3 + 5*x)^(3/2), x, 7, -((2*(1 - 2*x)^(5/2)*(2 + 3*x)^3)/(5*sqrt(3 + 5*x))) + (2210901*sqrt(1 - 2*x)*sqrt(3 + 5*x))/8000000 + (66997*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/800000 - (9*(2127 - 460*x)*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/200000 + (33/125)*(1 - 2*x)^(5/2)*(2 + 3*x)^2*sqrt(3 + 5*x) + (24319911*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(8000000*sqrt(10))]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^2)/(3 + 5*x)^(3/2), x, 7, (-2*(1 - 2*x)^(7/2))/(275*sqrt(3 + 5*x)) + (21483*sqrt(1 - 2*x)*sqrt(3 + 5*x))/80000 + (651*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/8000 + (651*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/22000 - (9*(1 - 2*x)^(7/2)*sqrt(3 + 5*x))/200 + (236313*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(80000*sqrt(10))]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x))/(3 + 5*x)^(3/2), x, 6, (-2*(1 - 2*x)^(7/2))/(55*sqrt(3 + 5*x)) + (231*sqrt(1 - 2*x)*sqrt(3 + 5*x))/1000 + (7*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/100 + (7*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/275 + (2541*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(1000*sqrt(10))]
    @test_int [(1 - 2*x)^(5/2)/(3 + 5*x)^(3/2), x, 5, (-2*(1 - 2*x)^(5/2))/(5*sqrt(3 + 5*x)) - (33*sqrt(1 - 2*x)*sqrt(3 + 5*x))/50 - ((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/5 - (363*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(50*sqrt(10))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)*(3 + 5*x)^(3/2)), x, 7, (-22*(1 - 2*x)^(3/2))/(5*sqrt(3 + 5*x)) - (128*sqrt(1 - 2*x)*sqrt(3 + 5*x))/75 + (338*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/225 + (98*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/9]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^2*(3 + 5*x)^(3/2)), x, 7, (-1111*sqrt(1 - 2*x))/(15*sqrt(3 + 5*x)) + (7*(1 - 2*x)^(3/2))/(3*(2 + 3*x)*sqrt(3 + 5*x)) - (8*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/45 + (665*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/9]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^3*(3 + 5*x)^(3/2)), x, 5, (-1815*sqrt(1 - 2*x))/(4*sqrt(3 + 5*x)) + (1 - 2*x)^(5/2)/(2*(2 + 3*x)^2*sqrt(3 + 5*x)) + (55*(1 - 2*x)^(3/2))/(4*(2 + 3*x)*sqrt(3 + 5*x)) + (1815*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/4]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^4*(3 + 5*x)^(3/2)), x, 6, (-147015*sqrt(1 - 2*x))/(56*sqrt(3 + 5*x)) + (1 - 2*x)^(7/2)/(7*(2 + 3*x)^3*sqrt(3 + 5*x)) + (81*(1 - 2*x)^(5/2))/(28*(2 + 3*x)^2*sqrt(3 + 5*x)) + (4455*(1 - 2*x)^(3/2))/(56*(2 + 3*x)*sqrt(3 + 5*x)) + (147015*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(8*sqrt(7))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^5*(3 + 5*x)^(3/2)), x, 8, (-181304825*sqrt(1 - 2*x))/(12096*sqrt(3 + 5*x)) + (7*(1 - 2*x)^(3/2))/(12*(2 + 3*x)^4*sqrt(3 + 5*x)) + (2051*sqrt(1 - 2*x))/(216*(2 + 3*x)^3*sqrt(3 + 5*x)) + (22957*sqrt(1 - 2*x))/(288*(2 + 3*x)^2*sqrt(3 + 5*x)) + (3997345*sqrt(1 - 2*x))/(4032*(2 + 3*x)*sqrt(3 + 5*x)) + (46095555*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(448*sqrt(7))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^6*(3 + 5*x)^(3/2)), x, 9, (-4639661185*sqrt(1 - 2*x))/(56448*sqrt(3 + 5*x)) + (7*(1 - 2*x)^(3/2))/(15*(2 + 3*x)^5*sqrt(3 + 5*x)) + (2513*sqrt(1 - 2*x))/(360*(2 + 3*x)^4*sqrt(3 + 5*x)) + (12023*sqrt(1 - 2*x))/(240*(2 + 3*x)^3*sqrt(3 + 5*x)) + (587477*sqrt(1 - 2*x))/(1344*(2 + 3*x)^2*sqrt(3 + 5*x)) + (102293609*sqrt(1 - 2*x))/(18816*(2 + 3*x)*sqrt(3 + 5*x)) + (3538809681*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(6272*sqrt(7))]

    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^4)/(3 + 5*x)^(5/2), x, 8, -((2*(1 - 2*x)^(5/2)*(2 + 3*x)^4)/(15*(3 + 5*x)^(3/2))) - (508*(1 - 2*x)^(3/2)*(2 + 3*x)^4)/(75*sqrt(3 + 5*x)) + (8026963*sqrt(1 - 2*x)*sqrt(3 + 5*x))/40000000 + (23991*(1 - 2*x)^(3/2)*(2 + 3*x)^2*sqrt(3 + 5*x))/25000 + (2514/625)*(1 - 2*x)^(3/2)*(2 + 3*x)^3*sqrt(3 + 5*x) + (21*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)*(64435 + 118392*x))/4000000 + (88296593*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(40000000*sqrt(10))]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(3 + 5*x)^(5/2), x, 7, -((2*(1 - 2*x)^(5/2)*(2 + 3*x)^3)/(15*(3 + 5*x)^(3/2))) - (376*(1 - 2*x)^(3/2)*(2 + 3*x)^3)/(75*sqrt(3 + 5*x)) + (69713*sqrt(1 - 2*x)*sqrt(3 + 5*x))/400000 + (741/250)*(1 - 2*x)^(3/2)*(2 + 3*x)^2*sqrt(3 + 5*x) + (21*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)*(3185 + 4392*x))/40000 + (766843*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(400000*sqrt(10))]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^2)/(3 + 5*x)^(5/2), x, 7, (-2*(1 - 2*x)^(7/2))/(825*(3 + 5*x)^(3/2)) - (76*(1 - 2*x)^(7/2))/(1815*sqrt(3 + 5*x)) + (329*sqrt(1 - 2*x)*sqrt(3 + 5*x))/5000 + (329*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/16500 + (329*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/45375 + (3619*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(5000*sqrt(10))]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x))/(3 + 5*x)^(5/2), x, 6, (-2*(1 - 2*x)^(7/2))/(165*(3 + 5*x)^(3/2)) - (182*(1 - 2*x)^(5/2))/(825*sqrt(3 + 5*x)) - (91*sqrt(1 - 2*x)*sqrt(3 + 5*x))/250 - (91*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/825 - (1001*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(250*sqrt(10))]
    @test_int [(1 - 2*x)^(5/2)/(3 + 5*x)^(5/2), x, 5, (-2*(1 - 2*x)^(5/2))/(15*(3 + 5*x)^(3/2)) + (4*(1 - 2*x)^(3/2))/(15*sqrt(3 + 5*x)) + (4*sqrt(1 - 2*x)*sqrt(3 + 5*x))/25 + (22*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/25]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)*(3 + 5*x)^(5/2)), x, 7, (-22*(1 - 2*x)^(3/2))/(15*(3 + 5*x)^(3/2)) + (814*sqrt(1 - 2*x))/(25*sqrt(3 + 5*x)) - (8*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/75 - (98*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/3]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^2*(3 + 5*x)^(5/2)), x, 5, (-55*(1 - 2*x)^(3/2))/(3*(3 + 5*x)^(3/2)) + (1 - 2*x)^(5/2)/((2 + 3*x)*(3 + 5*x)^(3/2)) + (385*sqrt(1 - 2*x))/sqrt(3 + 5*x) - 385*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x)))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^3*(3 + 5*x)^(5/2)), x, 6, (-13145*(1 - 2*x)^(3/2))/(84*(3 + 5*x)^(3/2)) + (3*(1 - 2*x)^(7/2))/(14*(2 + 3*x)^2*(3 + 5*x)^(3/2)) + (239*(1 - 2*x)^(5/2))/(28*(2 + 3*x)*(3 + 5*x)^(3/2)) + (13145*sqrt(1 - 2*x))/(4*sqrt(3 + 5*x)) - (13145*sqrt(7)*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/4]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^4*(3 + 5*x)^(5/2)), x, 8, (-196735*sqrt(1 - 2*x))/(72*(3 + 5*x)^(3/2)) + (7*(1 - 2*x)^(3/2))/(9*(2 + 3*x)^3*(3 + 5*x)^(3/2)) + (77*sqrt(1 - 2*x))/(4*(2 + 3*x)^2*(3 + 5*x)^(3/2)) + (7843*sqrt(1 - 2*x))/(24*(2 + 3*x)*(3 + 5*x)^(3/2)) + (1784635*sqrt(1 - 2*x))/(72*sqrt(3 + 5*x)) - (1361195*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(8*sqrt(7))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^5*(3 + 5*x)^(5/2)), x, 9, (-25024175*sqrt(1 - 2*x))/(1344*(3 + 5*x)^(3/2)) + (7*(1 - 2*x)^(3/2))/(12*(2 + 3*x)^4*(3 + 5*x)^(3/2)) + (847*sqrt(1 - 2*x))/(72*(2 + 3*x)^3*(3 + 5*x)^(3/2)) + (36817*sqrt(1 - 2*x))/(288*(2 + 3*x)^2*(3 + 5*x)^(3/2)) + (2992825*sqrt(1 - 2*x))/(1344*(2 + 3*x)*(3 + 5*x)^(3/2)) + (227000875*sqrt(1 - 2*x))/(1344*sqrt(3 + 5*x)) - (519421265*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(448*sqrt(7))]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^6*(3 + 5*x)^(5/2)), x, 10, (-754386765*sqrt(1 - 2*x))/(6272*(3 + 5*x)^(3/2)) + (7*(1 - 2*x)^(3/2))/(15*(2 + 3*x)^5*(3 + 5*x)^(3/2)) + (1001*sqrt(1 - 2*x))/(120*(2 + 3*x)^4*(3 + 5*x)^(3/2)) + (53009*sqrt(1 - 2*x))/(720*(2 + 3*x)^3*(3 + 5*x)^(3/2)) + (3329689*sqrt(1 - 2*x))/(4032*(2 + 3*x)^2*(3 + 5*x)^(3/2)) + (270667969*sqrt(1 - 2*x))/(18816*(2 + 3*x)*(3 + 5*x)^(3/2)) + (20529722435*sqrt(1 - 2*x))/(18816*sqrt(3 + 5*x)) - (46975917593*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(6272*sqrt(7))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^(n/2) / (e+f*x)^(1/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [((2 + 3*x)^4*sqrt(3 + 5*x))/sqrt(1 - 2*x), x, 6, -((97032047*sqrt(1 - 2*x)*sqrt(3 + 5*x))/2560000) - (987*sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^(3/2))/4000 - (3/50)*sqrt(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^(3/2) - (21*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)*(194923 + 92040*x))/640000 + (1067352517*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(2560000*sqrt(10))]
    @test_int [((2 + 3*x)^3*sqrt(3 + 5*x))/sqrt(1 - 2*x), x, 5, -((61547*sqrt(1 - 2*x)*sqrt(3 + 5*x))/5120) - (3/40)*sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^(3/2) - (3*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)*(865 + 408*x))/1280 + (677017*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(5120*sqrt(10))]
    @test_int [((2 + 3*x)^2*sqrt(3 + 5*x))/sqrt(1 - 2*x), x, 5, (-6269*sqrt(1 - 2*x)*sqrt(3 + 5*x))/1600 - (181*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/400 - (sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^(3/2))/10 + (68959*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(1600*sqrt(10))]
    @test_int [((2 + 3*x)*sqrt(3 + 5*x))/sqrt(1 - 2*x), x, 4, (-107*sqrt(1 - 2*x)*sqrt(3 + 5*x))/80 - (3*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/20 + (1177*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(80*sqrt(10))]
    @test_int [sqrt(3 + 5*x)/sqrt(1 - 2*x), x, 3, -(sqrt(1 - 2*x)*sqrt(3 + 5*x))/2 + (11*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(2*sqrt(10))]
    @test_int [sqrt(3 + 5*x)/(sqrt(1 - 2*x)*(2 + 3*x)), x, 6, (sqrt(10)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/3 + (2*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(3*sqrt(7))]
    @test_int [sqrt(3 + 5*x)/(sqrt(1 - 2*x)*(2 + 3*x)^2), x, 3, -(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(7*(2 + 3*x)) - (11*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(7*sqrt(7))]
    @test_int [sqrt(3 + 5*x)/(sqrt(1 - 2*x)*(2 + 3*x)^3), x, 4, (-41*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(196*(2 + 3*x)) + (3*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(14*(2 + 3*x)^2) - (451*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(196*sqrt(7))]
    @test_int [sqrt(3 + 5*x)/(sqrt(1 - 2*x)*(2 + 3*x)^4), x, 6, -(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(21*(2 + 3*x)^3) + (25*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(588*(2 + 3*x)^2) + (3895*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(8232*(2 + 3*x)) - (15235*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(2744*sqrt(7))]
    @test_int [sqrt(3 + 5*x)/(sqrt(1 - 2*x)*(2 + 3*x)^5), x, 7, -(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(28*(2 + 3*x)^4) + (sqrt(1 - 2*x)*sqrt(3 + 5*x))/(56*(2 + 3*x)^3) + (305*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1568*(2 + 3*x)^2) + (32735*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(21952*(2 + 3*x)) - (375265*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(21952*sqrt(7))]

    @test_int [((2 + 3*x)^3*(3 + 5*x)^(3/2))/sqrt(1 - 2*x), x, 6, -((30292449*sqrt(1 - 2*x)*sqrt(3 + 5*x))/512000) - (917953*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/128000 - (3/50)*sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^(5/2) - (3*sqrt(1 - 2*x)*(3 + 5*x)^(5/2)*(7889 + 3900*x))/16000 + (333216939*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(512000*sqrt(10))]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^(3/2))/sqrt(1 - 2*x), x, 6, (-479457*sqrt(1 - 2*x)*sqrt(3 + 5*x))/25600 - (14529*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/6400 - (251*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/800 - (3*sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^(5/2))/40 + (5274027*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(25600*sqrt(10))]
    @test_int [((2 + 3*x)*(3 + 5*x)^(3/2))/sqrt(1 - 2*x), x, 5, (-1947*sqrt(1 - 2*x)*sqrt(3 + 5*x))/320 - (59*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/80 - (sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/10 + (21417*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(320*sqrt(10))]
    @test_int [(3 + 5*x)^(3/2)/sqrt(1 - 2*x), x, 4, (-33*sqrt(1 - 2*x)*sqrt(3 + 5*x))/16 - (sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/4 + (363*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(16*sqrt(10))]
    @test_int [(3 + 5*x)^(3/2)/(sqrt(1 - 2*x)*(2 + 3*x)), x, 6, (-5*sqrt(1 - 2*x)*sqrt(3 + 5*x))/6 + (29*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/18 - (2*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(9*sqrt(7))]
    @test_int [(3 + 5*x)^(3/2)/(sqrt(1 - 2*x)*(2 + 3*x)^2), x, 6, (sqrt(1 - 2*x)*sqrt(3 + 5*x))/(21*(2 + 3*x)) + (5*sqrt(10)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/9 + (103*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(63*sqrt(7))]
    @test_int [(3 + 5*x)^(3/2)/(sqrt(1 - 2*x)*(2 + 3*x)^3), x, 4, (-33*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(196*(2 + 3*x)) - (sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(14*(2 + 3*x)^2) - (363*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(196*sqrt(7))]
    @test_int [(3 + 5*x)^(3/2)/(sqrt(1 - 2*x)*(2 + 3*x)^4), x, 5, (-495*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2744*(2 + 3*x)) - (15*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(196*(2 + 3*x)^2) + (sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(7*(2 + 3*x)^3) - (5445*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(2744*sqrt(7))]
    @test_int [(3 + 5*x)^(3/2)/(sqrt(1 - 2*x)*(2 + 3*x)^5), x, 7, (sqrt(1 - 2*x)*sqrt(3 + 5*x))/(84*(2 + 3*x)^4) - (43*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(504*(2 + 3*x)^3) + (85*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(14112*(2 + 3*x)^2) + (57595*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(197568*(2 + 3*x)) - (78045*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(21952*sqrt(7))]
    @test_int [(3 + 5*x)^(3/2)/(sqrt(1 - 2*x)*(2 + 3*x)^6), x, 8, (sqrt(1 - 2*x)*sqrt(3 + 5*x))/(105*(2 + 3*x)^5) - (367*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(5880*(2 + 3*x)^4) - (73*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(11760*(2 + 3*x)^3) + (6107*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(65856*(2 + 3*x)^2) + (694229*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(921984*(2 + 3*x)) - (2664057*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(307328*sqrt(7))]

    @test_int [((2 + 3*x)^3*(3 + 5*x)^(5/2))/sqrt(1 - 2*x), x, 7, -((243487211*sqrt(1 - 2*x)*sqrt(3 + 5*x))/819200) - (22135201*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/614400 - (2012291*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/384000 - (1/20)*sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^(7/2) - (sqrt(1 - 2*x)*(3 + 5*x)^(7/2)*(37439 + 18960*x))/32000 + (2678359321*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(819200*sqrt(10))]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^(5/2))/sqrt(1 - 2*x), x, 7, (-9458207*sqrt(1 - 2*x)*sqrt(3 + 5*x))/102400 - (859837*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/76800 - (78167*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/48000 - (963*sqrt(1 - 2*x)*(3 + 5*x)^(7/2))/4000 - (3*sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^(7/2))/50 + (104040277*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(102400*sqrt(10))]
    @test_int [((2 + 3*x)*(3 + 5*x)^(5/2))/sqrt(1 - 2*x), x, 6, (-29887*sqrt(1 - 2*x)*sqrt(3 + 5*x))/1024 - (2717*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/768 - (247*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/480 - (3*sqrt(1 - 2*x)*(3 + 5*x)^(7/2))/40 + (328757*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(1024*sqrt(10))]
    @test_int [(3 + 5*x)^(5/2)/sqrt(1 - 2*x), x, 5, (-605*sqrt(1 - 2*x)*sqrt(3 + 5*x))/64 - (55*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/48 - (sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/6 + (1331*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/64]
    @test_int [(3 + 5*x)^(5/2)/(sqrt(1 - 2*x)*(2 + 3*x)), x, 7, (-455*sqrt(1 - 2*x)*sqrt(3 + 5*x))/144 - (5*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/12 + (3035*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/432 + (2*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(27*sqrt(7))]
    @test_int [(3 + 5*x)^(5/2)/(sqrt(1 - 2*x)*(2 + 3*x)^2), x, 7, (-185*sqrt(1 - 2*x)*sqrt(3 + 5*x))/126 + (sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(21*(2 + 3*x)) + (125*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/54 - (173*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(189*sqrt(7))]
    @test_int [(3 + 5*x)^(5/2)/(sqrt(1 - 2*x)*(2 + 3*x)^3), x, 7, (239*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1764*(2 + 3*x)) + (sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(42*(2 + 3*x)^2) + (25*sqrt(10)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/27 + (17687*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(5292*sqrt(7))]
    @test_int [(3 + 5*x)^(5/2)/(sqrt(1 - 2*x)*(2 + 3*x)^4), x, 5, (-605*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2744*(2 + 3*x)) - (55*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(588*(2 + 3*x)^2) - (sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(21*(2 + 3*x)^3) - (6655*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(2744*sqrt(7))]
    @test_int [(3 + 5*x)^(5/2)/(sqrt(1 - 2*x)*(2 + 3*x)^5), x, 6, (-605*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3136*(2 + 3*x)) - (55*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(672*(2 + 3*x)^2) - (sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(24*(2 + 3*x)^3) + (3*sqrt(1 - 2*x)*(3 + 5*x)^(7/2))/(28*(2 + 3*x)^4) - (6655*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(3136*sqrt(7))]
    @test_int [(3 + 5*x)^(5/2)/(sqrt(1 - 2*x)*(2 + 3*x)^6), x, 8, (437*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(17640*(2 + 3*x)^4) - (14831*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(105840*(2 + 3*x)^3) - (12371*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(592704*(2 + 3*x)^2) + (1948963*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(8297856*(2 + 3*x)) + (sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(105*(2 + 3*x)^5) - (933031*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(307328*sqrt(7))]
    @test_int [(3 + 5*x)^(5/2)/(sqrt(1 - 2*x)*(2 + 3*x)^7), x, 9, (503*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(26460*(2 + 3*x)^5) - (149951*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1481760*(2 + 3*x)^4) - (71369*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2963520*(2 + 3*x)^3) + (958171*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(16595712*(2 + 3*x)^2) + (122343637*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(232339968*(2 + 3*x)) + (sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(126*(2 + 3*x)^6) - (52573169*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(8605184*sqrt(7))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(2 + 3*x)^4/(sqrt(1 - 2*x)*sqrt(3 + 5*x)), x, 5, (-(259/800))*sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x) - (3/40)*sqrt(1 - 2*x)*(2 + 3*x)^3*sqrt(3 + 5*x) - (7*sqrt(1 - 2*x)*sqrt(3 + 5*x)*(187559 + 77820*x))/128000 + (10866247*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(128000*sqrt(10))]
    @test_int [(2 + 3*x)^3/(sqrt(1 - 2*x)*sqrt(3 + 5*x)), x, 4, (-(1/10))*sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x) - (sqrt(1 - 2*x)*sqrt(3 + 5*x)*(5363 + 2220*x))/1600 + (44437*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(1600*sqrt(10))]
    @test_int [(2 + 3*x)^2/(sqrt(1 - 2*x)*sqrt(3 + 5*x)), x, 4, (-333*sqrt(1 - 2*x)*sqrt(3 + 5*x))/400 - (3*sqrt(1 - 2*x)*(2 + 3*x)*sqrt(3 + 5*x))/20 + (3827*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(400*sqrt(10))]
    @test_int [(2 + 3*x)/(sqrt(1 - 2*x)*sqrt(3 + 5*x)), x, 3, (-3*sqrt(1 - 2*x)*sqrt(3 + 5*x))/10 + (37*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(10*sqrt(10))]
    @test_int [1/(sqrt(1 - 2*x)*sqrt(3 + 5*x)), x, 2, sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)*sqrt(3 + 5*x)), x, 2, (-2*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/sqrt(7)]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x)), x, 3, (3*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(7*(2 + 3*x)) - (37*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(7*sqrt(7))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^3*sqrt(3 + 5*x)), x, 5, (3*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(14*(2 + 3*x)^2) + (333*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(196*(2 + 3*x)) - (3827*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(196*sqrt(7))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^4*sqrt(3 + 5*x)), x, 6, (sqrt(1 - 2*x)*sqrt(3 + 5*x))/(7*(2 + 3*x)^3) + (185*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(196*(2 + 3*x)^2) + (19415*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2744*(2 + 3*x)) - (222185*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(2744*sqrt(7))]

    @test_int [(2 + 3*x)^4/(sqrt(1 - 2*x)*(3 + 5*x)^(3/2)), x, 5, -((2*sqrt(1 - 2*x)*(2 + 3*x)^3)/(55*sqrt(3 + 5*x))) - (21/550)*sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x) - (21*sqrt(1 - 2*x)*sqrt(3 + 5*x)*(8987 + 3660*x))/88000 + (143283*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(8000*sqrt(10))]
    @test_int [(2 + 3*x)^3/(sqrt(1 - 2*x)*(3 + 5*x)^(3/2)), x, 4, -((2*sqrt(1 - 2*x)*(2 + 3*x)^2)/(55*sqrt(3 + 5*x))) - (3*sqrt(1 - 2*x)*sqrt(3 + 5*x)*(979 + 300*x))/4400 + (2493*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(400*sqrt(10))]
    @test_int [(2 + 3*x)^2/(sqrt(1 - 2*x)*(3 + 5*x)^(3/2)), x, 4, (-2*sqrt(1 - 2*x))/(275*sqrt(3 + 5*x)) - (9*sqrt(1 - 2*x)*sqrt(3 + 5*x))/50 + (123*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(50*sqrt(10))]
    @test_int [(2 + 3*x)/(sqrt(1 - 2*x)*(3 + 5*x)^(3/2)), x, 3, (-2*sqrt(1 - 2*x))/(55*sqrt(3 + 5*x)) + (3*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/5]
    @test_int [1/(sqrt(1 - 2*x)*(3 + 5*x)^(3/2)), x, 1, (-2*sqrt(1 - 2*x))/(11*sqrt(3 + 5*x))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^(3/2)), x, 3, (-10*sqrt(1 - 2*x))/(11*sqrt(3 + 5*x)) + (6*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/sqrt(7)]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^(3/2)), x, 5, (-515*sqrt(1 - 2*x))/(77*sqrt(3 + 5*x)) + (3*sqrt(1 - 2*x))/(7*(2 + 3*x)*sqrt(3 + 5*x)) + (321*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(7*sqrt(7))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^(3/2)), x, 6, (-90415*sqrt(1 - 2*x))/(2156*sqrt(3 + 5*x)) + (3*sqrt(1 - 2*x))/(14*(2 + 3*x)^2*sqrt(3 + 5*x)) + (543*sqrt(1 - 2*x))/(196*(2 + 3*x)*sqrt(3 + 5*x)) + (56421*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(196*sqrt(7))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^(3/2)), x, 7, (-7396875*sqrt(1 - 2*x))/(30184*sqrt(3 + 5*x)) + sqrt(1 - 2*x)/(7*(2 + 3*x)^3*sqrt(3 + 5*x)) + (255*sqrt(1 - 2*x))/(196*(2 + 3*x)^2*sqrt(3 + 5*x)) + (44475*sqrt(1 - 2*x))/(2744*(2 + 3*x)*sqrt(3 + 5*x)) + (4616025*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(2744*sqrt(7))]

    @test_int [(2 + 3*x)^5/(sqrt(1 - 2*x)*(3 + 5*x)^(5/2)), x, 6, -((2*sqrt(1 - 2*x)*(2 + 3*x)^4)/(165*(3 + 5*x)^(3/2))) - (734*sqrt(1 - 2*x)*(2 + 3*x)^3)/(9075*sqrt(3 + 5*x)) + (511*sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x))/30250 - (7*sqrt(1 - 2*x)*sqrt(3 + 5*x)*(938509 + 366420*x))/4840000 + (462357*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(40000*sqrt(10))]
    @test_int [(2 + 3*x)^4/(sqrt(1 - 2*x)*(3 + 5*x)^(5/2)), x, 5, -((2*sqrt(1 - 2*x)*(2 + 3*x)^3)/(165*(3 + 5*x)^(3/2))) - (602*sqrt(1 - 2*x)*(2 + 3*x)^2)/(9075*sqrt(3 + 5*x)) - (7*sqrt(1 - 2*x)*sqrt(3 + 5*x)*(12199 + 1020*x))/242000 + (8127*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(2000*sqrt(10))]
    @test_int [(2 + 3*x)^3/(sqrt(1 - 2*x)*(3 + 5*x)^(5/2)), x, 4, -((2*sqrt(1 - 2*x)*(2 + 3*x)^2)/(165*(3 + 5*x)^(3/2))) - (sqrt(1 - 2*x)*(5831 + 9405*x))/(18150*sqrt(3 + 5*x)) + (81*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(50*sqrt(10))]
    @test_int [(2 + 3*x)^2/(sqrt(1 - 2*x)*(3 + 5*x)^(5/2)), x, 4, (-2*sqrt(1 - 2*x))/(825*(3 + 5*x)^(3/2)) - (404*sqrt(1 - 2*x))/(9075*sqrt(3 + 5*x)) + (9*sqrt(2/5)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/25]
    @test_int [(2 + 3*x)/(sqrt(1 - 2*x)*(3 + 5*x)^(5/2)), x, 2, (-2*sqrt(1 - 2*x))/(165*(3 + 5*x)^(3/2)) - (206*sqrt(1 - 2*x))/(1815*sqrt(3 + 5*x))]
    @test_int [1/(sqrt(1 - 2*x)*(3 + 5*x)^(5/2)), x, 2, (-2*sqrt(1 - 2*x))/(33*(3 + 5*x)^(3/2)) - (8*sqrt(1 - 2*x))/(363*sqrt(3 + 5*x))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^(5/2)), x, 5, (-10*sqrt(1 - 2*x))/(33*(3 + 5*x)^(3/2)) + (950*sqrt(1 - 2*x))/(363*sqrt(3 + 5*x)) - (18*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/sqrt(7)]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^(5/2)), x, 6, (-845*sqrt(1 - 2*x))/(231*(3 + 5*x)^(3/2)) + (3*sqrt(1 - 2*x))/(7*(2 + 3*x)*(3 + 5*x)^(3/2)) + (84235*sqrt(1 - 2*x))/(2541*sqrt(3 + 5*x)) - (1593*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(7*sqrt(7))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^(5/2)), x, 7, (-207895*sqrt(1 - 2*x))/(6468*(3 + 5*x)^(3/2)) + (3*sqrt(1 - 2*x))/(14*(2 + 3*x)^2*(3 + 5*x)^(3/2)) + (753*sqrt(1 - 2*x))/(196*(2 + 3*x)*(3 + 5*x)^(3/2)) + (20743985*sqrt(1 - 2*x))/(71148*sqrt(3 + 5*x)) - (392283*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(196*sqrt(7))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^(5/2)), x, 8, (-21891025*sqrt(1 - 2*x))/(90552*(3 + 5*x)^(3/2)) + sqrt(1 - 2*x)/(7*(2 + 3*x)^3*(3 + 5*x)^(3/2)) + (325*sqrt(1 - 2*x))/(196*(2 + 3*x)^2*(3 + 5*x)^(3/2)) + (79335*sqrt(1 - 2*x))/(2744*(2 + 3*x)*(3 + 5*x)^(3/2)) + (2184369575*sqrt(1 - 2*x))/(996072*sqrt(3 + 5*x)) - (41307885*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(2744*sqrt(7))]

    @test_int [1/(sqrt(a + b*x)*sqrt(2*b*e - a*f + b*f*x)*(e + f*x)), x, 2, atan((sqrt(f)*sqrt(a + b*x)*sqrt(2*b*e - a*f + b*f*x))/(b*e - a*f))/(sqrt(f)*(b*e - a*f))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^(n/2) / (e+f*x)^(3/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [((2 + 3*x)^5*sqrt(3 + 5*x))/(1 - 2*x)^(3/2), x, 7, (847637*sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x))/32000 + (10389*sqrt(1 - 2*x)*(2 + 3*x)^3*sqrt(3 + 5*x))/1600 + (33/20)*sqrt(1 - 2*x)*(2 + 3*x)^4*sqrt(3 + 5*x) + ((2 + 3*x)^5*sqrt(3 + 5*x))/sqrt(1 - 2*x) + (49*sqrt(1 - 2*x)*sqrt(3 + 5*x)*(87394471 + 36265980*x))/5120000 - (35439958001*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(5120000*sqrt(10))]
    @test_int [((2 + 3*x)^4*sqrt(3 + 5*x))/(1 - 2*x)^(3/2), x, 6, (2203/320)*sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x) + (27/16)*sqrt(1 - 2*x)*(2 + 3*x)^3*sqrt(3 + 5*x) + ((2 + 3*x)^4*sqrt(3 + 5*x))/sqrt(1 - 2*x) + (sqrt(1 - 2*x)*sqrt(3 + 5*x)*(11129753 + 4618500*x))/51200 - (92108287*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(51200*sqrt(10))]
    @test_int [((2 + 3*x)^3*sqrt(3 + 5*x))/(1 - 2*x)^(3/2), x, 5, (7/4)*sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x) + ((2 + 3*x)^3*sqrt(3 + 5*x))/sqrt(1 - 2*x) + (sqrt(1 - 2*x)*sqrt(3 + 5*x)*(176833 + 73380*x))/3200 - (1463447*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(3200*sqrt(10))]
    @test_int [((2 + 3*x)^2*sqrt(3 + 5*x))/(1 - 2*x)^(3/2), x, 5, (17951*sqrt(1 - 2*x)*sqrt(3 + 5*x))/1760 + (49*(3 + 5*x)^(3/2))/(22*sqrt(1 - 2*x)) + (9*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/40 - (17951*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(160*sqrt(10))]
    @test_int [((2 + 3*x)*sqrt(3 + 5*x))/(1 - 2*x)^(3/2), x, 4, (103*sqrt(1 - 2*x)*sqrt(3 + 5*x))/44 + (7*(3 + 5*x)^(3/2))/(11*sqrt(1 - 2*x)) - (103*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(4*sqrt(10))]
    @test_int [sqrt(3 + 5*x)/(1 - 2*x)^(3/2), x, 3, sqrt(3 + 5*x)/sqrt(1 - 2*x) - sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x))]
    @test_int [sqrt(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)), x, 3, (2*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)) + (2*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(7*sqrt(7))]
    @test_int [sqrt(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^2), x, 4, (-29*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(539*(2 + 3*x)) + (4*(3 + 5*x)^(3/2))/(77*sqrt(1 - 2*x)*(2 + 3*x)) - (29*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(49*sqrt(7))]
    @test_int [sqrt(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^3), x, 6, (2*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)*(2 + 3*x)^2) - (15*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(98*(2 + 3*x)^2) + (15*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1372*(2 + 3*x)) - (1585*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(1372*sqrt(7))]
    @test_int [sqrt(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^4), x, 7, (2*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)*(2 + 3*x)^3) - (sqrt(1 - 2*x)*sqrt(3 + 5*x))/(7*(2 + 3*x)^3) - (5*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(196*(2 + 3*x)^2) + (565*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2744*(2 + 3*x)) - (7435*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(2744*sqrt(7))]
    @test_int [sqrt(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^5), x, 8, (2*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)*(2 + 3*x)^4) - (27*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(196*(2 + 3*x)^4) - (13*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(392*(2 + 3*x)^3) + (835*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(10976*(2 + 3*x)^2) + (107245*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(153664*(2 + 3*x)) - (1244755*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(153664*sqrt(7))]

    @test_int [((2 + 3*x)^4*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2), x, 7, (1018114917*sqrt(1 - 2*x)*sqrt(3 + 5*x))/1024000 + (10377*sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^(3/2))/1600 + (33/20)*sqrt(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^(3/2) + ((2 + 3*x)^4*(3 + 5*x)^(3/2))/sqrt(1 - 2*x) + (9*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)*(4772357 + 2253560*x))/256000 - (11199264087*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(1024000*sqrt(10))]
    @test_int [((2 + 3*x)^3*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2), x, 6, (13246251*sqrt(1 - 2*x)*sqrt(3 + 5*x))/51200 + (27/16)*sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^(3/2) + ((2 + 3*x)^3*(3 + 5*x)^(3/2))/sqrt(1 - 2*x) + (9*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)*(62091 + 29320*x))/12800 - (145708761*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(51200*sqrt(10))]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2), x, 6, (42171*sqrt(1 - 2*x)*sqrt(3 + 5*x))/640 + (14057*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/1760 + (49*(3 + 5*x)^(5/2))/(22*sqrt(1 - 2*x)) + (3*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/20 - (463881*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(640*sqrt(10))]
    @test_int [((2 + 3*x)*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2), x, 5, (519*sqrt(1 - 2*x)*sqrt(3 + 5*x))/32 + (173*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/88 + (7*(3 + 5*x)^(5/2))/(11*sqrt(1 - 2*x)) - (5709*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(32*sqrt(10))]
    @test_int [(3 + 5*x)^(3/2)/(1 - 2*x)^(3/2), x, 4, (15*sqrt(1 - 2*x)*sqrt(3 + 5*x))/4 + (3 + 5*x)^(3/2)/sqrt(1 - 2*x) - (33*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/4]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)), x, 6, (11*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)) - (5*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/3 - (2*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(21*sqrt(7))]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^2), x, 4, (3*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(49*(2 + 3*x)) + (2*(3 + 5*x)^(3/2))/(7*sqrt(1 - 2*x)*(2 + 3*x)) + (33*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(49*sqrt(7))]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^3), x, 5, (-75*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1372*(2 + 3*x)) - (25*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(1078*(2 + 3*x)^2) + (4*(3 + 5*x)^(5/2))/(77*sqrt(1 - 2*x)*(2 + 3*x)^2) - (825*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(1372*sqrt(7))]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^4), x, 7, (11*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)*(2 + 3*x)^3) - (2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3*(2 + 3*x)^3) - (145*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(588*(2 + 3*x)^2) - (415*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(8232*(2 + 3*x)) - (2805*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(2744*sqrt(7))]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^5), x, 8, (11*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)*(2 + 3*x)^4) - (131*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(196*(2 + 3*x)^4) - (89*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(392*(2 + 3*x)^3) - (745*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(10976*(2 + 3*x)^2) + (16985*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(153664*(2 + 3*x)) - (279015*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(153664*sqrt(7))]

    @test_int [((2 + 3*x)^4*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2), x, 8, (9738340821*sqrt(1 - 2*x)*sqrt(3 + 5*x))/1638400 + (295101237*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/409600 + (999/160)*sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^(5/2) + (13/8)*sqrt(1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^(5/2) + ((2 + 3*x)^4*(3 + 5*x)^(5/2))/sqrt(1 - 2*x) + (sqrt(1 - 2*x)*(3 + 5*x)^(5/2)*(7611023 + 3765060*x))/51200 - (107121749031*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(1638400*sqrt(10))]
    @test_int [((2 + 3*x)^3*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2), x, 7, (321709971*sqrt(1 - 2*x)*sqrt(3 + 5*x))/204800 + (9748787*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/51200 + (33/20)*sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^(5/2) + ((2 + 3*x)^3*(3 + 5*x)^(5/2))/sqrt(1 - 2*x) + (9*sqrt(1 - 2*x)*(3 + 5*x)^(5/2)*(27937 + 13820*x))/6400 - (3538809681*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(204800*sqrt(10))]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2), x, 7, (838101*sqrt(1 - 2*x)*sqrt(3 + 5*x))/2048 + (25397*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/512 + (25397*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/3520 + (49*(3 + 5*x)^(7/2))/(22*sqrt(1 - 2*x)) + (9*sqrt(1 - 2*x)*(3 + 5*x)^(7/2))/80 - (9219111*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(2048*sqrt(10))]
    @test_int [((2 + 3*x)*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2), x, 6, (13365*sqrt(1 - 2*x)*sqrt(3 + 5*x))/128 + (405*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/32 + (81*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/44 + (7*(3 + 5*x)^(7/2))/(11*sqrt(1 - 2*x)) - (29403*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/128]
    @test_int [(3 + 5*x)^(5/2)/(1 - 2*x)^(3/2), x, 5, (825*sqrt(1 - 2*x)*sqrt(3 + 5*x))/32 + (25*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/8 + (3 + 5*x)^(5/2)/sqrt(1 - 2*x) - (1815*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/32]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)), x, 7, (505*sqrt(1 - 2*x)*sqrt(3 + 5*x))/84 + (11*(3 + 5*x)^(3/2))/(7*sqrt(1 - 2*x)) - (475*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/36 + (2*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(63*sqrt(7))]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^2), x, 7, (32*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(147*(2 + 3*x)) + (11*(3 + 5*x)^(3/2))/(7*sqrt(1 - 2*x)*(2 + 3*x)) - (25*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/9 - (169*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(441*sqrt(7))]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^3), x, 5, (165*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1372*(2 + 3*x)) + (5*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(98*(2 + 3*x)^2) + (2*(3 + 5*x)^(5/2))/(7*sqrt(1 - 2*x)*(2 + 3*x)^2) + (1815*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(1372*sqrt(7))]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^4), x, 6, (-165*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2744*(2 + 3*x)) - (5*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(196*(2 + 3*x)^2) - (sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(77*(2 + 3*x)^3) + (4*(3 + 5*x)^(7/2))/(77*sqrt(1 - 2*x)*(2 + 3*x)^3) - (1815*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(2744*sqrt(7))]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^5), x, 8, (131*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(588*(2 + 3*x)^4) - (3653*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3528*(2 + 3*x)^3) - (38365*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(98784*(2 + 3*x)^2) - (167155*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1382976*(2 + 3*x)) + (11*(3 + 5*x)^(3/2))/(7*sqrt(1 - 2*x)*(2 + 3*x)^4) - (168795*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(153664*sqrt(7))]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^6), x, 9, (164*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(735*(2 + 3*x)^5) - (42863*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(41160*(2 + 3*x)^4) - (29297*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(82320*(2 + 3*x)^3) - (55277*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(460992*(2 + 3*x)^2) + (426781*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(6453888*(2 + 3*x)) + (11*(3 + 5*x)^(3/2))/(7*sqrt(1 - 2*x)*(2 + 3*x)^5) - (3474273*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(2151296*sqrt(7))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(2 + 3*x)^5/((1 - 2*x)^(3/2)*sqrt(3 + 5*x)), x, 6, (76587*sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x))/17600 + (939/880)*sqrt(1 - 2*x)*(2 + 3*x)^3*sqrt(3 + 5*x) + (7*(2 + 3*x)^4*sqrt(3 + 5*x))/(11*sqrt(1 - 2*x)) + (21*sqrt(1 - 2*x)*sqrt(3 + 5*x)*(18424549 + 7645620*x))/2816000 - (291096141*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(256000*sqrt(10))]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^(3/2)*sqrt(3 + 5*x)), x, 5, (243/220)*sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x) + (7*(2 + 3*x)^3*sqrt(3 + 5*x))/(11*sqrt(1 - 2*x)) + (9*sqrt(1 - 2*x)*sqrt(3 + 5*x)*(27269 + 11316*x))/7040 - (184641*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(640*sqrt(10))]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^(3/2)*sqrt(3 + 5*x)), x, 4, (7*(2 + 3*x)^2*sqrt(3 + 5*x))/(11*sqrt(1 - 2*x)) + (3*sqrt(1 - 2*x)*sqrt(3 + 5*x)*(25003 + 10380*x))/8800 - (56421*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(800*sqrt(10))]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^(3/2)*sqrt(3 + 5*x)), x, 4, (49*sqrt(3 + 5*x))/(22*sqrt(1 - 2*x)) + (9*sqrt(1 - 2*x)*sqrt(3 + 5*x))/20 - (321*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(20*sqrt(10))]
    @test_int [(2 + 3*x)/((1 - 2*x)^(3/2)*sqrt(3 + 5*x)), x, 3, (7*sqrt(3 + 5*x))/(11*sqrt(1 - 2*x)) - (3*asin(sqrt(2/11)*sqrt(3 + 5*x)))/sqrt(10)]
    @test_int [1/((1 - 2*x)^(3/2)*sqrt(3 + 5*x)), x, 1, (2*sqrt(3 + 5*x))/(11*sqrt(1 - 2*x))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)*sqrt(3 + 5*x)), x, 3, (4*sqrt(3 + 5*x))/(77*sqrt(1 - 2*x)) - (6*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(7*sqrt(7))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*sqrt(3 + 5*x)), x, 5, -((58*sqrt(3 + 5*x))/(539*sqrt(1 - 2*x))) + (3*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)*(2 + 3*x)) - (123*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(49*sqrt(7))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*sqrt(3 + 5*x)), x, 6, -((3895*sqrt(3 + 5*x))/(7546*sqrt(1 - 2*x))) + (3*sqrt(3 + 5*x))/(14*sqrt(1 - 2*x)*(2 + 3*x)^2) + (345*sqrt(3 + 5*x))/(196*sqrt(1 - 2*x)*(2 + 3*x)) - (12465*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(1372*sqrt(7))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^4*sqrt(3 + 5*x)), x, 7, -((32735*sqrt(3 + 5*x))/(15092*sqrt(1 - 2*x))) + sqrt(3 + 5*x)/(7*sqrt(1 - 2*x)*(2 + 3*x)^3) + (27*sqrt(3 + 5*x))/(28*sqrt(1 - 2*x)*(2 + 3*x)^2) + (2865*sqrt(3 + 5*x))/(392*sqrt(1 - 2*x)*(2 + 3*x)) - (102345*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(2744*sqrt(7))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^5*sqrt(3 + 5*x)), x, 8, -((7986105*sqrt(3 + 5*x))/(845152*sqrt(1 - 2*x))) + (3*sqrt(3 + 5*x))/(28*sqrt(1 - 2*x)*(2 + 3*x)^4) + (263*sqrt(3 + 5*x))/(392*sqrt(1 - 2*x)*(2 + 3*x)^3) + (6621*sqrt(3 + 5*x))/(1568*sqrt(1 - 2*x)*(2 + 3*x)^2) + (698295*sqrt(3 + 5*x))/(21952*sqrt(1 - 2*x)*(2 + 3*x)) - (24922335*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(153664*sqrt(7))]

    @test_int [(2 + 3*x)^5/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)), x, 6, -((37*sqrt(1 - 2*x)*(2 + 3*x)^3)/(605*sqrt(3 + 5*x))) + (7*(2 + 3*x)^4)/(11*sqrt(1 - 2*x)*sqrt(3 + 5*x)) + (8463*sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x))/12100 + (21*sqrt(1 - 2*x)*sqrt(3 + 5*x)*(2027201 + 841380*x))/1936000 - (2911419*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(16000*sqrt(10))]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)), x, 5, -((37*sqrt(1 - 2*x)*(2 + 3*x)^2)/(605*sqrt(3 + 5*x))) + (7*(2 + 3*x)^3)/(11*sqrt(1 - 2*x)*sqrt(3 + 5*x)) + (3*sqrt(1 - 2*x)*sqrt(3 + 5*x)*(173063 + 72060*x))/96800 - (35451*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(800*sqrt(10))]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)), x, 4, (7*(2 + 3*x)^2)/(11*sqrt(1 - 2*x)*sqrt(3 + 5*x)) + (sqrt(1 - 2*x)*(30443 + 50985*x))/(12100*sqrt(3 + 5*x)) - (999*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(100*sqrt(10))]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)), x, 4, 49/(22*sqrt(1 - 2*x)*sqrt(3 + 5*x)) - (1229*sqrt(1 - 2*x))/(1210*sqrt(3 + 5*x)) - (9*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(5*sqrt(10))]
    @test_int [(2 + 3*x)/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)), x, 2, -2/(55*sqrt(1 - 2*x)*sqrt(3 + 5*x)) + (74*sqrt(3 + 5*x))/(605*sqrt(1 - 2*x))]
    @test_int [1/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)), x, 2, 2/(11*sqrt(1 - 2*x)*sqrt(3 + 5*x)) - (20*sqrt(1 - 2*x))/(121*sqrt(3 + 5*x))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(3/2)), x, 5, 4/(77*sqrt(1 - 2*x)*sqrt(3 + 5*x)) - (370*sqrt(1 - 2*x))/(847*sqrt(3 + 5*x)) + (18*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(7*sqrt(7))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2)), x, 6, -(58/(539*sqrt(1 - 2*x)*sqrt(3 + 5*x))) - (17735*sqrt(1 - 2*x))/(5929*sqrt(3 + 5*x)) + 3/(7*sqrt(1 - 2*x)*(2 + 3*x)*sqrt(3 + 5*x)) + (999*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(49*sqrt(7))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(3/2)), x, 7, -(6205/(7546*sqrt(1 - 2*x)*sqrt(3 + 5*x))) - (3125575*sqrt(1 - 2*x))/(166012*sqrt(3 + 5*x)) + 3/(14*sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x)) + 555/(196*sqrt(1 - 2*x)*(2 + 3*x)*sqrt(3 + 5*x)) + (177255*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(1372*sqrt(7))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x)^(3/2)), x, 8, -(73435/(15092*sqrt(1 - 2*x)*sqrt(3 + 5*x))) - (36657025*sqrt(1 - 2*x))/(332024*sqrt(3 + 5*x)) + 1/(7*sqrt(1 - 2*x)*(2 + 3*x)^3*sqrt(3 + 5*x)) + 37/(28*sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x)) + 6525/(392*sqrt(1 - 2*x)*(2 + 3*x)*sqrt(3 + 5*x)) + (2079585*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(2744*sqrt(7))]

    @test_int [(2 + 3*x)^5/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)), x, 6, -((107*sqrt(1 - 2*x)*(2 + 3*x)^3)/(1815*(3 + 5*x)^(3/2))) + (7*(2 + 3*x)^4)/(11*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (4487*sqrt(1 - 2*x)*(2 + 3*x)^2)/(99825*sqrt(3 + 5*x)) + (7*sqrt(1 - 2*x)*sqrt(3 + 5*x)*(2571547 + 1078860*x))/5324000 - (111321*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(4000*sqrt(10))]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)), x, 5, -((107*sqrt(1 - 2*x)*(2 + 3*x)^2)/(1815*(3 + 5*x)^(3/2))) + (7*(2 + 3*x)^3)/(11*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) + (sqrt(1 - 2*x)*(627641 + 1051875*x))/(399300*sqrt(3 + 5*x)) - (621*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(100*sqrt(10))]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)), x, 4, (7*(2 + 3*x)^2)/(11*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (sqrt(1 - 2*x)*(24439 + 38770*x))/(99825*(3 + 5*x)^(3/2)) - (27*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(25*sqrt(10))]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)), x, 3, 49/(22*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (3679*sqrt(1 - 2*x))/(3630*(3 + 5*x)^(3/2)) - (4091*sqrt(1 - 2*x))/(19965*sqrt(3 + 5*x))]
    @test_int [(2 + 3*x)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)), x, 3, 7/(11*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (107*sqrt(1 - 2*x))/(363*(3 + 5*x)^(3/2)) - (428*sqrt(1 - 2*x))/(3993*sqrt(3 + 5*x))]
    @test_int [1/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)), x, 3, 2/(11*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (40*sqrt(1 - 2*x))/(363*(3 + 5*x)^(3/2)) - (160*sqrt(1 - 2*x))/(3993*sqrt(3 + 5*x))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(5/2)), x, 6, 4/(77*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (410*sqrt(1 - 2*x))/(2541*(3 + 5*x)^(3/2)) + (31030*sqrt(1 - 2*x))/(27951*sqrt(3 + 5*x)) - (54*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(7*sqrt(7))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2)), x, 7, -(58/(539*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))) - (28705*sqrt(1 - 2*x))/(17787*(3 + 5*x)^(3/2)) + 3/(7*sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^(3/2)) + (2841815*sqrt(1 - 2*x))/(195657*sqrt(3 + 5*x)) - (4887*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(49*sqrt(7))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(5/2)), x, 8, -(8515/(7546*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))) - (7090175*sqrt(1 - 2*x))/(498036*(3 + 5*x)^(3/2)) + 3/(14*sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^(3/2)) + 765/(196*sqrt(1 - 2*x)*(2 + 3*x)*(3 + 5*x)^(3/2)) + (707286025*sqrt(1 - 2*x))/(5478396*sqrt(3 + 5*x)) - (1215945*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(1372*sqrt(7))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^(n/2) / (e+f*x)^(5/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [((2 + 3*x)^4*sqrt(3 + 5*x))/(1 - 2*x)^(5/2), x, 6, (-(697/88))*sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x) - (299*(2 + 3*x)^3*sqrt(3 + 5*x))/(66*sqrt(1 - 2*x)) + ((2 + 3*x)^4*sqrt(3 + 5*x))/(3*(1 - 2*x)^(3/2)) - (sqrt(1 - 2*x)*sqrt(3 + 5*x)*(17606479 + 7306140*x))/70400 + (13246251*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(6400*sqrt(10))]
    @test_int [((2 + 3*x)^3*sqrt(3 + 5*x))/(1 - 2*x)^(5/2), x, 5, -((233*(2 + 3*x)^2*sqrt(3 + 5*x))/(66*sqrt(1 - 2*x))) + ((2 + 3*x)^3*sqrt(3 + 5*x))/(3*(1 - 2*x)^(3/2)) - (sqrt(1 - 2*x)*sqrt(3 + 5*x)*(168157 + 69780*x))/3520 + (126513*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(320*sqrt(10))]
    @test_int [((2 + 3*x)^2*sqrt(3 + 5*x))/(1 - 2*x)^(5/2), x, 5, (-519*sqrt(1 - 2*x)*sqrt(3 + 5*x))/88 + (49*(3 + 5*x)^(3/2))/(66*(1 - 2*x)^(3/2)) - (21*(3 + 5*x)^(3/2))/(11*sqrt(1 - 2*x)) + (519*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(8*sqrt(10))]
    @test_int [((2 + 3*x)*sqrt(3 + 5*x))/(1 - 2*x)^(5/2), x, 4, (-3*sqrt(3 + 5*x))/(2*sqrt(1 - 2*x)) + (7*(3 + 5*x)^(3/2))/(33*(1 - 2*x)^(3/2)) + (3*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/2]
    @test_int [sqrt(3 + 5*x)/(1 - 2*x)^(5/2), x, 1, (2*(3 + 5*x)^(3/2))/(33*(1 - 2*x)^(3/2))]
    @test_int [sqrt(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)), x, 4, (6*sqrt(3 + 5*x))/(49*sqrt(1 - 2*x)) + (4*(3 + 5*x)^(3/2))/(231*(1 - 2*x)^(3/2)) + (6*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(49*sqrt(7))]
    @test_int [sqrt(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^2), x, 6, (850*sqrt(3 + 5*x))/(11319*sqrt(1 - 2*x)) + (2*sqrt(3 + 5*x))/(21*(1 - 2*x)^(3/2)*(2 + 3*x)) - (5*sqrt(3 + 5*x))/(49*sqrt(1 - 2*x)*(2 + 3*x)) - (75*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(343*sqrt(7))]
    @test_int [sqrt(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^3), x, 7, (415*sqrt(3 + 5*x))/(22638*sqrt(1 - 2*x)) + (2*sqrt(3 + 5*x))/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^2) - sqrt(3 + 5*x)/(14*sqrt(1 - 2*x)*(2 + 3*x)^2) + (5*sqrt(3 + 5*x))/(196*sqrt(1 - 2*x)*(2 + 3*x)) - (765*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(1372*sqrt(7))]
    @test_int [sqrt(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^4), x, 8, -((16985*sqrt(3 + 5*x))/(316932*sqrt(1 - 2*x))) + (2*sqrt(3 + 5*x))/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^3) - (3*sqrt(3 + 5*x))/(49*sqrt(1 - 2*x)*(2 + 3*x)^3) - sqrt(3 + 5*x)/(196*sqrt(1 - 2*x)*(2 + 3*x)^2) + (605*sqrt(3 + 5*x))/(2744*sqrt(1 - 2*x)*(2 + 3*x)) - (25365*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(19208*sqrt(7))]

    @test_int [((2 + 3*x)^4*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2), x, 7, -((1626211523*sqrt(1 - 2*x)*sqrt(3 + 5*x))/1126400) - (3315/352)*sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^(3/2) - (123*(2 + 3*x)^3*(3 + 5*x)^(3/2))/(22*sqrt(1 - 2*x)) + ((2 + 3*x)^4*(3 + 5*x)^(3/2))/(3*(1 - 2*x)^(3/2)) - (3*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)*(22868329 + 10798680*x))/281600 + (1626211523*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(102400*sqrt(10))]
    @test_int [((2 + 3*x)^3*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2), x, 6, -((4246733*sqrt(1 - 2*x)*sqrt(3 + 5*x))/14080) - (101*(2 + 3*x)^2*(3 + 5*x)^(3/2))/(22*sqrt(1 - 2*x)) + ((2 + 3*x)^3*(3 + 5*x)^(3/2))/(3*(1 - 2*x)^(3/2)) - (3*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)*(59719 + 28200*x))/3520 + (4246733*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(1280*sqrt(10))]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2), x, 6, (-40787*sqrt(1 - 2*x)*sqrt(3 + 5*x))/704 - (40787*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/5808 + (49*(3 + 5*x)^(5/2))/(66*(1 - 2*x)^(3/2)) - (938*(3 + 5*x)^(5/2))/(363*sqrt(1 - 2*x)) + (40787*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(64*sqrt(10))]
    @test_int [((2 + 3*x)*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2), x, 5, (-845*sqrt(1 - 2*x)*sqrt(3 + 5*x))/88 - (169*(3 + 5*x)^(3/2))/(66*sqrt(1 - 2*x)) + (7*(3 + 5*x)^(5/2))/(33*(1 - 2*x)^(3/2)) + (169*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/8]
    @test_int [(3 + 5*x)^(3/2)/(1 - 2*x)^(5/2), x, 4, (-5*sqrt(3 + 5*x))/(2*sqrt(1 - 2*x)) + (3 + 5*x)^(3/2)/(3*(1 - 2*x)^(3/2)) + (5*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/2]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)), x, 4, (-2*sqrt(3 + 5*x))/(49*sqrt(1 - 2*x)) + (2*(3 + 5*x)^(3/2))/(21*(1 - 2*x)^(3/2)) - (2*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(49*sqrt(7))]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^2), x, 5, (95*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3773*(2 + 3*x)) + (190*(3 + 5*x)^(3/2))/(1617*sqrt(1 - 2*x)*(2 + 3*x)) + (4*(3 + 5*x)^(5/2))/(231*(1 - 2*x)^(3/2)*(2 + 3*x)) + (95*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(343*sqrt(7))]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^3), x, 7, (5*sqrt(3 + 5*x))/(42*sqrt(1 - 2*x)) + (11*sqrt(3 + 5*x))/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^2) - (3*sqrt(3 + 5*x))/(14*sqrt(1 - 2*x)*(2 + 3*x)^2) - (5*sqrt(3 + 5*x))/(28*sqrt(1 - 2*x)*(2 + 3*x)) - (5*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(28*sqrt(7))]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^4), x, 8, (465*sqrt(3 + 5*x))/(9604*sqrt(1 - 2*x)) + (11*sqrt(3 + 5*x))/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^3) - (32*sqrt(3 + 5*x))/(147*sqrt(1 - 2*x)*(2 + 3*x)^3) - (23*sqrt(3 + 5*x))/(196*sqrt(1 - 2*x)*(2 + 3*x)^2) - (85*sqrt(3 + 5*x))/(2744*sqrt(1 - 2*x)*(2 + 3*x)) - (9395*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(19208*sqrt(7))]

    @test_int [((2 + 3*x)^4*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2), x, 8, -((4270537963*sqrt(1 - 2*x)*sqrt(3 + 5*x))/409600) - (4270537963*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/3379200 - (4819/440)*sqrt(1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^(5/2) - (439*(2 + 3*x)^3*(3 + 5*x)^(5/2))/(66*sqrt(1 - 2*x)) + ((2 + 3*x)^4*(3 + 5*x)^(5/2))/(3*(1 - 2*x)^(3/2)) - (sqrt(1 - 2*x)*(3 + 5*x)^(5/2)*(36714139 + 18161940*x))/140800 + (46975917593*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(409600*sqrt(10))]
    @test_int [((2 + 3*x)^3*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2), x, 7, -((9444023*sqrt(1 - 2*x)*sqrt(3 + 5*x))/4096) - (9444023*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/33792 - (373*(2 + 3*x)^2*(3 + 5*x)^(5/2))/(66*sqrt(1 - 2*x)) + ((2 + 3*x)^3*(3 + 5*x)^(5/2))/(3*(1 - 2*x)^(3/2)) - (sqrt(1 - 2*x)*(3 + 5*x)^(5/2)*(81191 + 40164*x))/1408 + (103884253*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(4096*sqrt(10))]
    @test_int [((2 + 3*x)^2*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2), x, 7, (-123745*sqrt(1 - 2*x)*sqrt(3 + 5*x))/256 - (123745*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/2112 - (24749*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/2904 + (49*(3 + 5*x)^(7/2))/(66*(1 - 2*x)^(3/2)) - (1183*(3 + 5*x)^(7/2))/(363*sqrt(1 - 2*x)) + (272239*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/256]
    @test_int [((2 + 3*x)*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2), x, 6, (-5975*sqrt(1 - 2*x)*sqrt(3 + 5*x))/64 - (5975*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/528 - (239*(3 + 5*x)^(5/2))/(66*sqrt(1 - 2*x)) + (7*(3 + 5*x)^(7/2))/(33*(1 - 2*x)^(3/2)) + (13145*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/64]
    @test_int [(3 + 5*x)^(5/2)/(1 - 2*x)^(5/2), x, 5, (-125*sqrt(1 - 2*x)*sqrt(3 + 5*x))/8 - (25*(3 + 5*x)^(3/2))/(6*sqrt(1 - 2*x)) + (3 + 5*x)^(5/2)/(3*(1 - 2*x)^(3/2)) + (275*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/8]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)), x, 7, (-407*sqrt(3 + 5*x))/(98*sqrt(1 - 2*x)) + (11*(3 + 5*x)^(3/2))/(21*(1 - 2*x)^(3/2)) + (25*sqrt(5/2)*asin(sqrt(2/11)*sqrt(3 + 5*x)))/6 + (2*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(147*sqrt(7))]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^2), x, 5, (-5*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(343*(2 + 3*x)) - (10*(3 + 5*x)^(3/2))/(147*sqrt(1 - 2*x)*(2 + 3*x)) + (2*(3 + 5*x)^(5/2))/(21*(1 - 2*x)^(3/2)*(2 + 3*x)) - (55*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(343*sqrt(7))]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^3), x, 6, (65*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1372*(2 + 3*x)) + (65*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(3234*(2 + 3*x)^2) + (26*(3 + 5*x)^(5/2))/(231*sqrt(1 - 2*x)*(2 + 3*x)^2) + (4*(3 + 5*x)^(7/2))/(231*(1 - 2*x)^(3/2)*(2 + 3*x)^2) + (715*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(1372*sqrt(7))]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^4), x, 8, (15755*sqrt(3 + 5*x))/(86436*sqrt(1 - 2*x)) + (32*sqrt(3 + 5*x))/(441*sqrt(1 - 2*x)*(2 + 3*x)^3) - (187*sqrt(3 + 5*x))/(588*sqrt(1 - 2*x)*(2 + 3*x)^2) - (2365*sqrt(3 + 5*x))/(8232*sqrt(1 - 2*x)*(2 + 3*x)) + (11*(3 + 5*x)^(3/2))/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^3) - (2585*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(19208*sqrt(7))]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^5), x, 9, (139745*sqrt(3 + 5*x))/(1613472*sqrt(1 - 2*x)) + (43*sqrt(3 + 5*x))/(588*sqrt(1 - 2*x)*(2 + 3*x)^4) - (2717*sqrt(3 + 5*x))/(8232*sqrt(1 - 2*x)*(2 + 3*x)^3) - (2013*sqrt(3 + 5*x))/(10976*sqrt(1 - 2*x)*(2 + 3*x)^2) - (14135*sqrt(3 + 5*x))/(153664*sqrt(1 - 2*x)*(2 + 3*x)) + (11*(3 + 5*x)^(3/2))/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^4) - (547745*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(1075648*sqrt(7))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(2 + 3*x)^5/((1 - 2*x)^(5/2)*sqrt(3 + 5*x)), x, 6, -((23909*sqrt(1 - 2*x)*(2 + 3*x)^2*sqrt(3 + 5*x))/4840) - (2051*(2 + 3*x)^3*sqrt(3 + 5*x))/(726*sqrt(1 - 2*x)) + (7*(2 + 3*x)^4*sqrt(3 + 5*x))/(33*(1 - 2*x)^(3/2)) - (sqrt(1 - 2*x)*sqrt(3 + 5*x)*(120791143 + 50124540*x))/774400 + (8261577*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(6400*sqrt(10))]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^(5/2)*sqrt(3 + 5*x)), x, 5, -((1589*(2 + 3*x)^2*sqrt(3 + 5*x))/(726*sqrt(1 - 2*x))) + (7*(2 + 3*x)^3*sqrt(3 + 5*x))/(33*(1 - 2*x)^(3/2)) - (sqrt(1 - 2*x)*sqrt(3 + 5*x)*(5735477 + 2380020*x))/193600 + (392283*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(1600*sqrt(10))]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^(5/2)*sqrt(3 + 5*x)), x, 4, -(((95621 - 33462*x)*sqrt(3 + 5*x))/(14520*sqrt(1 - 2*x))) + (7*(2 + 3*x)^2*sqrt(3 + 5*x))/(33*(1 - 2*x)^(3/2)) + (1593*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(40*sqrt(10))]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^(5/2)*sqrt(3 + 5*x)), x, 4, (49*sqrt(3 + 5*x))/(66*(1 - 2*x)^(3/2)) - (448*sqrt(3 + 5*x))/(363*sqrt(1 - 2*x)) + (9*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(2*sqrt(10))]
    @test_int [(2 + 3*x)/((1 - 2*x)^(5/2)*sqrt(3 + 5*x)), x, 2, (7*sqrt(3 + 5*x))/(33*(1 - 2*x)^(3/2)) - (29*sqrt(3 + 5*x))/(363*sqrt(1 - 2*x))]
    @test_int [1/((1 - 2*x)^(5/2)*sqrt(3 + 5*x)), x, 2, (2*sqrt(3 + 5*x))/(33*(1 - 2*x)^(3/2)) + (20*sqrt(3 + 5*x))/(363*sqrt(1 - 2*x))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)*sqrt(3 + 5*x)), x, 5, (4*sqrt(3 + 5*x))/(231*(1 - 2*x)^(3/2)) + (676*sqrt(3 + 5*x))/(17787*sqrt(1 - 2*x)) - (18*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(49*sqrt(7))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*sqrt(3 + 5*x)), x, 6, -((190*sqrt(3 + 5*x))/(1617*(1 - 2*x)^(3/2))) - (4390*sqrt(3 + 5*x))/(124509*sqrt(1 - 2*x)) + (3*sqrt(3 + 5*x))/(7*(1 - 2*x)^(3/2)*(2 + 3*x)) - (405*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(343*sqrt(7))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*sqrt(3 + 5*x)), x, 7, -((1735*sqrt(3 + 5*x))/(3234*(1 - 2*x)^(3/2))) - (57595*sqrt(3 + 5*x))/(249018*sqrt(1 - 2*x)) + (3*sqrt(3 + 5*x))/(14*(1 - 2*x)^(3/2)*(2 + 3*x)^2) + (51*sqrt(3 + 5*x))/(28*(1 - 2*x)^(3/2)*(2 + 3*x)) - (5805*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(1372*sqrt(7))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^4*sqrt(3 + 5*x)), x, 8, -((101485*sqrt(3 + 5*x))/(45276*(1 - 2*x)^(3/2))) - (3471145*sqrt(3 + 5*x))/(3486252*sqrt(1 - 2*x)) + sqrt(3 + 5*x)/(7*(1 - 2*x)^(3/2)*(2 + 3*x)^3) + (193*sqrt(3 + 5*x))/(196*(1 - 2*x)^(3/2)*(2 + 3*x)^2) + (423*sqrt(3 + 5*x))/(56*(1 - 2*x)^(3/2)*(2 + 3*x)) - (330255*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(19208*sqrt(7))]

    @test_int [(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)), x, 6, (7723*sqrt(1 - 2*x)*(2 + 3*x)^2)/(39930*sqrt(3 + 5*x)) - (1561*(2 + 3*x)^3)/(726*sqrt(1 - 2*x)*sqrt(3 + 5*x)) + (7*(2 + 3*x)^4)/(33*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)) - (sqrt(1 - 2*x)*sqrt(3 + 5*x)*(39109961 + 16227780*x))/2129600 + (243189*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(1600*sqrt(10))]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)), x, 5, -((1099*(2 + 3*x)^2)/(726*sqrt(1 - 2*x)*sqrt(3 + 5*x))) + (7*(2 + 3*x)^3)/(33*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)) - (sqrt(1 - 2*x)*(4898747 + 8200665*x))/(798600*sqrt(3 + 5*x)) + (4887*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(200*sqrt(10))]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)), x, 4, (7*(2 + 3*x)^2)/(33*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)) - (66967 + 111311*x)/(39930*sqrt(1 - 2*x)*sqrt(3 + 5*x)) + (27*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(10*sqrt(10))]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)), x, 3, 49/(66*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)) - 1237/(3630*sqrt(1 - 2*x)*sqrt(3 + 5*x)) - (793*sqrt(3 + 5*x))/(19965*sqrt(1 - 2*x))]
    @test_int [(2 + 3*x)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)), x, 3, -2/(55*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)) + (82*sqrt(3 + 5*x))/(1815*(1 - 2*x)^(3/2)) + (164*sqrt(3 + 5*x))/(3993*sqrt(1 - 2*x))]
    @test_int [1/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)), x, 3, 2/(33*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)) + 40/(363*sqrt(1 - 2*x)*sqrt(3 + 5*x)) - (400*sqrt(1 - 2*x))/(3993*sqrt(3 + 5*x))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^(3/2)), x, 6, 4/(231*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)) + 956/(17787*sqrt(1 - 2*x)*sqrt(3 + 5*x)) - (42230*sqrt(1 - 2*x))/(195657*sqrt(3 + 5*x)) + (54*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(49*sqrt(7))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2)), x, 7, -(190/(1617*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))) - 3830/(124509*sqrt(1 - 2*x)*sqrt(3 + 5*x)) - (1840225*sqrt(1 - 2*x))/(1369599*sqrt(3 + 5*x)) + 3/(7*(1 - 2*x)^(3/2)*(2 + 3*x)*sqrt(3 + 5*x)) + (3105*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(343*sqrt(7))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^(3/2)), x, 8, -(2725/(3234*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))) - 89945/(249018*sqrt(1 - 2*x)*sqrt(3 + 5*x)) - (46307675*sqrt(1 - 2*x))/(5478396*sqrt(3 + 5*x)) + 3/(14*(1 - 2*x)^(3/2)*(2 + 3*x)^2*sqrt(3 + 5*x)) + 81/(28*(1 - 2*x)^(3/2)*(2 + 3*x)*sqrt(3 + 5*x)) + (79515*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(1372*sqrt(7))]

    @test_int [(2 + 3*x)^6/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)), x, 7, (7591*sqrt(1 - 2*x)*(2 + 3*x)^3)/(39930*(3 + 5*x)^(3/2)) - (511*(2 + 3*x)^4)/(242*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) + (7*(2 + 3*x)^5)/(33*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + (261331*sqrt(1 - 2*x)*(2 + 3*x)^2)/(2196150*sqrt(3 + 5*x)) - (7*sqrt(1 - 2*x)*sqrt(3 + 5*x)*(190406711 + 78981180*x))/117128000 + (753543*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(8000*sqrt(10))]
    @test_int [(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)), x, 6, (5281*sqrt(1 - 2*x)*(2 + 3*x)^2)/(39930*(3 + 5*x)^(3/2)) - (357*(2 + 3*x)^3)/(242*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) + (7*(2 + 3*x)^4)/(33*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) - (sqrt(1 - 2*x)*(33035947 + 55300905*x))/(8784600*sqrt(3 + 5*x)) + (2997*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(200*sqrt(10))]
    @test_int [(2 + 3*x)^4/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)), x, 5, -((203*(2 + 3*x)^2)/(242*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))) + (7*(2 + 3*x)^3)/(33*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + (sqrt(1 - 2*x)*(627287 + 991010*x))/(2196150*(3 + 5*x)^(3/2)) + (81*asin(sqrt(2/11)*sqrt(3 + 5*x)))/(50*sqrt(10))]
    @test_int [(2 + 3*x)^3/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)), x, 4, 49/(121*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (3679*sqrt(1 - 2*x))/(19965*(3 + 5*x)^(3/2)) + (2*(2 + 3*x)^3)/(33*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) - (8182*sqrt(1 - 2*x))/(219615*sqrt(3 + 5*x))]
    @test_int [(2 + 3*x)^2/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)), x, 4, 49/(66*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + 14/(121*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (1649*sqrt(1 - 2*x))/(7986*(3 + 5*x)^(3/2)) - (3298*sqrt(1 - 2*x))/(43923*sqrt(3 + 5*x))]
    @test_int [(2 + 3*x)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)), x, 4, -2/(165*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + 74/(1815*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)) + 296/(3993*sqrt(1 - 2*x)*sqrt(3 + 5*x)) - (2960*sqrt(1 - 2*x))/(43923*sqrt(3 + 5*x))]
    @test_int [1/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)), x, 4, 2/(33*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + 20/(121*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (400*sqrt(1 - 2*x))/(3993*(3 + 5*x)^(3/2)) - (1600*sqrt(1 - 2*x))/(43923*sqrt(3 + 5*x))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)*(3 + 5*x)^(5/2)), x, 7, 4/(231*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + 412/(5929*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (19130*sqrt(1 - 2*x))/(195657*(3 + 5*x)^(3/2)) + (1001590*sqrt(1 - 2*x))/(2152227*sqrt(3 + 5*x)) - (162*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(49*sqrt(7))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2)), x, 8, -(190/(1617*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))) - 1090/(41503*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (985525*sqrt(1 - 2*x))/(1369599*(3 + 5*x)^(3/2)) + 3/(7*(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(3/2)) + (95783075*sqrt(1 - 2*x))/(15065589*sqrt(3 + 5*x)) - (14985*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(343*sqrt(7))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^(5/2)), x, 9, -(3715/(3234*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))) - 40765/(83006*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (34551425*sqrt(1 - 2*x))/(5478396*(3 + 5*x)^(3/2)) + 3/(14*(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2)) + 111/(28*(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^(3/2)) + (3443814775*sqrt(1 - 2*x))/(60262356*sqrt(3 + 5*x)) - (538245*atan(sqrt(1 - 2*x)/(sqrt(7)*sqrt(3 + 5*x))))/(1372*sqrt(7))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^(m/2)*(c+d*x)^(n/2)*(e+f*x)^(p/2)=#

    @test_int [1/(sqrt(a + b*x)*sqrt(c + b*((c - 1)/a)*x)*sqrt(e + b*((e - 1)/a)*x)), x, 1, (2*sqrt(a)*Elliptic.F(asin((sqrt(1 - c)*sqrt(a + b*x))/sqrt(a)), (1 - e)/(1 - c)))/(b*sqrt(1 - c))]
    @test_int [1/(sqrt(a + b*x)*sqrt(c + d*x)*sqrt(e + (b*(e - 1)*x)/a)), x, 2, (2*sqrt(a)*sqrt((b*(c + d*x))/(b*c - a*d))*Elliptic.F(asin((sqrt(1 - e)*sqrt(a + b*x))/sqrt(a)), -((a*d)/((b*c - a*d)*(1 - e)))))/(b*sqrt(1 - e)*sqrt(c + d*x))]
    @test_int [1/(sqrt(a + b*x)*sqrt(c + d*x)*sqrt(e + f*x)), x, 3, (2*sqrt((-b)*c + a*d)*sqrt((b*(c + d*x))/(b*c - a*d))*sqrt((b*(e + f*x))/(b*e - a*f))*Elliptic.F(asin((sqrt(d)*sqrt(a + b*x))/sqrt((-b)*c + a*d)), ((b*c - a*d)*f)/(d*(b*e - a*f))))/(b*sqrt(d)*sqrt(c + d*x)*sqrt(e + f*x))]

    @test_int [sqrt(e + b*((e - 1)/a)*x)/(sqrt(a + b*x)*sqrt(c + b*((c - 1)/a)*x)), x, 1, (2*sqrt(a)*Elliptic.E(asin((sqrt(1 - c)*sqrt(a + b*x))/sqrt(a)), (1 - e)/(1 - c)))/(b*sqrt(1 - c))]
    @test_int [sqrt(c + d*x)/(sqrt(a + b*x)*sqrt(e + (b*(e - 1)*x)/a)), x, 2, (2*sqrt(a)*sqrt(c + d*x)*Elliptic.E(asin((sqrt(1 - e)*sqrt(a + b*x))/sqrt(a)), -((a*d)/((b*c - a*d)*(1 - e)))))/(b*sqrt(1 - e)*sqrt((b*(c + d*x))/(b*c - a*d)))]
    @test_int [sqrt(a + b*x)/(sqrt(e + (b*(e - 1)*x)/a)*sqrt(c + (b*(c - 1)*x)/a)), x, 2, -((2*a*sqrt(c - e)*sqrt(a + b*x)*sqrt(-(((1 - c)*(a*e - b*(1 - e)*x))/(a*(c - e))))*Elliptic.E(asin((sqrt(1 - e)*sqrt(c - (b*(1 - c)*x)/a))/sqrt(c - e)), (c - e)/(1 - e)))/(b*(1 - c)*sqrt(1 - e)*sqrt(((1 - c)*(a + b*x))/a)*sqrt(e - (b*(1 - e)*x)/a)))]
    @test_int [sqrt(e + f*x)/(sqrt(a + b*x)*sqrt(c + d*x)), x, 2, (2*sqrt((-b)*c + a*d)*sqrt((b*(c + d*x))/(b*c - a*d))*sqrt(e + f*x)*Elliptic.E(asin((sqrt(d)*sqrt(a + b*x))/sqrt((-b)*c + a*d)), ((b*c - a*d)*f)/(d*(b*e - a*f))))/(b*sqrt(d)*sqrt(c + d*x)*sqrt((b*(e + f*x))/(b*e - a*f)))]

    #= Caused*infinite*recursion*for*Rubi*4.14.9a =#
    @test_int [1/(sqrt(-c + d*x)*sqrt(c + d*x)*sqrt(e + f*x)), x, 3, (2*sqrt(c)*sqrt((c - d*x)/c)*sqrt((d*(e + f*x))/(d*e - c*f))*Elliptic.F(asin(sqrt(c + d*x)/(sqrt(2)*sqrt(c))), -((2*c*f)/(d*e - c*f))))/(d*sqrt(-c + d*x)*sqrt(e + f*x))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^(m/2)*(c+d*x)^(n/2)*(e+f*x)^(1/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x), x, 7, (-175111*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/236250 - (1244*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/13125 - (23*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/1575 + (2*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/45 - (2911577*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/590625 - (175111*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1181250]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x), x, 6, (-823*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/2625 - (27*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/875 + (2*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/35 - (55019*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/26250 - (823*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/13125]
    @test_int [sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x), x, 5, (-31*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/225 + (2*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/25 - (1159*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1125 - (31*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1125]
    @test_int [(sqrt(1 - 2*x)*sqrt(3 + 5*x))/sqrt(2 + 3*x), x, 4, (2*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/9 - (37*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/45 + (2*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/45]
    @test_int [(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2 + 3*x)^(3/2), x, 4, (-2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3*sqrt(2 + 3*x)) + (4*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3 - (2*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3]
    @test_int [(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2 + 3*x)^(5/2), x, 5, (-2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(9*(2 + 3*x)^(3/2)) + (74*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(63*sqrt(2 + 3*x)) - (74*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/63 + (4*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/63]
    @test_int [(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2 + 3*x)^(7/2), x, 6, (-2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(15*(2 + 3*x)^(5/2)) + (74*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(315*(2 + 3*x)^(3/2)) + (4636*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2205*sqrt(2 + 3*x)) - (4636*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/2205 - (124*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/2205]
    @test_int [(sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2 + 3*x)^(9/2), x, 7, (-2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(21*(2 + 3*x)^(7/2)) + (74*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(735*(2 + 3*x)^(5/2)) + (3184*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(5145*(2 + 3*x)^(3/2)) + (220076*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(36015*sqrt(2 + 3*x)) - (220076*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/36015 - (6584*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/36015]

    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2), x, 8, (-11346991*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/3898125 - (342971*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/866250 - (543*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/9625 - (23*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/2475 + (2*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/55 - (1508889271*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(7087500*sqrt(33)) - (11346991*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1771875*sqrt(33))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2), x, 7, (-160297*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/141750 - (1208*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/7875 - (3*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/175 + (2*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/45 - (5327983*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/708750 - (160297*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/708750]
    @test_int [sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2), x, 6, (-2252*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/4725 - (31*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/525 + (2*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/35 - (148831*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/47250 - (2252*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/23625]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/sqrt(2 + 3*x), x, 5, (-41*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/135 + (2*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/15 - (974*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/675 - (41*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/675]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(2 + 3*x)^(3/2), x, 5, (40*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/27 - (2*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(3*sqrt(2 + 3*x)) - (49*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/27 + (8*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/27]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(2 + 3*x)^(5/2), x, 5, (-214*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(189*sqrt(2 + 3*x)) - (2*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(9*(2 + 3*x)^(3/2)) + (494*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/189 - (214*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/189]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(2 + 3*x)^(7/2), x, 6, (-214*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(945*(2 + 3*x)^(3/2)) + (8314*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(6615*sqrt(2 + 3*x)) - (2*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(15*(2 + 3*x)^(5/2)) - (8314*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/6615 + (824*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/6615]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(2 + 3*x)^(9/2), x, 7, (-214*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2205*(2 + 3*x)^(5/2)) + (8578*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(46305*(2 + 3*x)^(3/2)) + (475592*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(324135*sqrt(2 + 3*x)) - (2*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(21*(2 + 3*x)^(7/2)) - (475592*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/324135 - (10628*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/324135]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(2 + 3*x)^(11/2), x, 8, (-214*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3969*(2 + 3*x)^(7/2)) + (8842*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(138915*(2 + 3*x)^(5/2)) + (332372*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(972405*(2 + 3*x)^(3/2)) + (22738708*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(6806835*sqrt(2 + 3*x)) - (2*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(27*(2 + 3*x)^(9/2)) - (22738708*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/6806835 - (673072*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/6806835]

    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2), x, 9, (-493825477*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/40540500 - (1865989*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/1126125 - (564731*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/2252250 - (2014*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(7/2))/53625 - (23*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(7/2))/3575 + (2*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(7/2))/65 - (16416987253*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(18427500*sqrt(33)) - (493825477*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(18427500*sqrt(33))]
    @test_int [sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2), x, 8, (-465127*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/103950 - (7031*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/11550 - (177*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/1925 - (3*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(7/2))/275 + (2*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(7/2))/55 - (30926081*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(94500*sqrt(33)) - (465127*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(47250*sqrt(33))]
    @test_int [sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2), x, 7, (-29357*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/17010 - (223*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/945 - (31*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/945 + (2*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(7/2))/45 - (488149*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/42525 - (29357*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/85050]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/sqrt(2 + 3*x), x, 6, (-131*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/189 - (sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/7 + (2*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/21 - (9013*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1890 - (131*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/945]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(2 + 3*x)^(3/2), x, 6, -(sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x)) + (4*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/3 - (2*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(3*sqrt(2 + 3*x)) - (3*sqrt(33)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5 - (sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(2 + 3*x)^(5/2), x, 6, (2470*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/567 - (118*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(63*sqrt(2 + 3*x)) - (2*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(9*(2 + 3*x)^(3/2)) - (2209*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/567 + (494*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/567]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(2 + 3*x)^(7/2), x, 6, (-12758*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(6615*sqrt(2 + 3*x)) - (118*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(315*(2 + 3*x)^(3/2)) - (2*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(15*(2 + 3*x)^(5/2)) + (31588*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/6615 - (12758*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/6615]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(2 + 3*x)^(9/2), x, 7, (-4282*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(15435*(2 + 3*x)^(3/2)) + (173482*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(108045*sqrt(2 + 3*x)) - (118*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(735*(2 + 3*x)^(5/2)) - (2*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(21*(2 + 3*x)^(7/2)) - (173482*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/108045 + (23612*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/108045]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(2 + 3*x)^(11/2), x, 8, (-12934*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(138915*(2 + 3*x)^(5/2)) + (568318*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2917215*(2 + 3*x)^(3/2)) + (27198452*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(20420505*sqrt(2 + 3*x)) - (118*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(1323*(2 + 3*x)^(7/2)) - (2*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(27*(2 + 3*x)^(9/2)) - (27198452*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/20420505 - (442868*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/20420505]
    @test_int [(sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(2 + 3*x)^(13/2), x, 9, (-13022*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(305613*(2 + 3*x)^(7/2)) + (627806*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(10696455*(2 + 3*x)^(5/2)) + (19417096*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(74875185*(2 + 3*x)^(3/2)) + (1305025844*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(524126295*sqrt(2 + 3*x)) - (118*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(2079*(2 + 3*x)^(9/2)) - (2*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(33*(2 + 3*x)^(11/2)) - (1305025844*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(47647845*sqrt(33)) - (37904696*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(47647845*sqrt(33))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [sqrt(e + f*x)/(sqrt(a + b*x)*sqrt(c + d*x)), x, 2, (2*sqrt((-b)*c + a*d)*sqrt((b*(c + d*x))/(b*c - a*d))*sqrt(e + f*x)*Elliptic.E(asin((sqrt(d)*sqrt(a + b*x))/sqrt((-b)*c + a*d)), ((b*c - a*d)*f)/(d*(b*e - a*f))))/(b*sqrt(d)*sqrt(c + d*x)*sqrt((b*(e + f*x))/(b*e - a*f)))]
    @test_int [sqrt(e + f*x)/((a + b*x)^(3/2)*sqrt(c + d*x)), x, 4, -((2*sqrt(c + d*x)*sqrt(e + f*x))/((b*c - a*d)*sqrt(a + b*x))) + (2*sqrt(f)*sqrt((-b)*e + a*f)*sqrt(c + d*x)*sqrt((b*(e + f*x))/(b*e - a*f))*Elliptic.E(asin((sqrt(f)*sqrt(a + b*x))/sqrt((-b)*e + a*f)), (d*(b*e - a*f))/((b*c - a*d)*f)))/(b*(b*c - a*d)*sqrt((b*(c + d*x))/(b*c - a*d))*sqrt(e + f*x))]

    @test_int [sqrt(1 - 2*x)/(sqrt(-3 - 5*x)*sqrt(2 + 3*x)), x, 1, (2*sqrt(7/5)*Elliptic.E(asin(sqrt(5)*sqrt(2 + 3*x)), 2/35))/3]

    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^(5/2))/sqrt(3 + 5*x), x, 6, (-859*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/4375 - (23*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/875 + (2*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/35 - (61151*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/43750 - (314*sqrt(33)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/21875]
    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^(3/2))/sqrt(3 + 5*x), x, 5, (-9*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/125 + (2*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/25 - (146*sqrt(33)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/625 - (17*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/625]
    @test_int [(sqrt(1 - 2*x)*sqrt(2 + 3*x))/sqrt(3 + 5*x), x, 4, (2*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/15 - (31*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/75 - (4*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/75]
    @test_int [sqrt(1 - 2*x)/(sqrt(2 + 3*x)*sqrt(3 + 5*x)), x, 2, (2*sqrt(7/5)*sqrt(-3 - 5*x)*Elliptic.E(asin(sqrt(5)*sqrt(2 + 3*x)), 2/35))/(3*sqrt(3 + 5*x))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^(3/2)*sqrt(3 + 5*x)), x, 3, (2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/sqrt(2 + 3*x) - 2*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33)]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^(5/2)*sqrt(3 + 5*x)), x, 5, (2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3*(2 + 3*x)^(3/2)) + (136*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(21*sqrt(2 + 3*x)) - (136*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/21 - (4*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/21]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^(7/2)*sqrt(3 + 5*x)), x, 6, (2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(5*(2 + 3*x)^(5/2)) + (92*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(35*(2 + 3*x)^(3/2)) + (6388*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(245*sqrt(2 + 3*x)) - (6388*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/245 - (64*sqrt(33)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/245]

    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^(7/2))/(3 + 5*x)^(3/2), x, 7, (-2*sqrt(1 - 2*x)*(2 + 3*x)^(7/2))/(5*sqrt(3 + 5*x)) - (2486*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/21875 + (183*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/4375 + (48*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/175 - (203179*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/218750 - (38723*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(109375*sqrt(33))]
    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^(5/2))/(3 + 5*x)^(3/2), x, 6, (-2*sqrt(1 - 2*x)*(2 + 3*x)^(5/2))/(5*sqrt(3 + 5*x)) + (13*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/625 + (36*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/125 - (1409*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3125 - (1091*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(3125*sqrt(33))]
    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^(3/2))/(3 + 5*x)^(3/2), x, 5, (-2*sqrt(1 - 2*x)*(2 + 3*x)^(3/2))/(5*sqrt(3 + 5*x)) + (8*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/25 - (19*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/125 - (106*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(125*sqrt(33))]
    @test_int [(sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3 + 5*x)^(3/2), x, 4, (-2*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(5*sqrt(3 + 5*x)) + (4*sqrt(33)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/25 - (62*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(25*sqrt(33))]
    @test_int [sqrt(1 - 2*x)/(sqrt(2 + 3*x)*(3 + 5*x)^(3/2)), x, 3, (-2*sqrt(1 - 2*x)*sqrt(2 + 3*x))/sqrt(3 + 5*x) + 2*sqrt(7/5)*Elliptic.E(asin(sqrt(5/11)*sqrt(1 - 2*x)), 33/35)]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)), x, 5, (2*sqrt(1 - 2*x))/(sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (20*sqrt(1 - 2*x)*sqrt(2 + 3*x))/sqrt(3 + 5*x) + 4*sqrt(33)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33) + (4*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/sqrt(33)]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)), x, 6, (2*sqrt(1 - 2*x))/(3*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + (92*sqrt(1 - 2*x))/(7*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (2780*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(21*sqrt(3 + 5*x)) + (556*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/7 + (184*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(7*sqrt(33))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)), x, 7, (2*sqrt(1 - 2*x))/(5*(2 + 3*x)^(5/2)*sqrt(3 + 5*x)) + (416*sqrt(1 - 2*x))/(105*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + (19268*sqrt(1 - 2*x))/(245*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (116464*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(147*sqrt(3 + 5*x)) + (116464*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/245 + (38536*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(245*sqrt(33))]

    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^(9/2))/(3 + 5*x)^(5/2), x, 8, (-2*sqrt(1 - 2*x)*(2 + 3*x)^(9/2))/(15*(3 + 5*x)^(3/2)) - (118*sqrt(1 - 2*x)*(2 + 3*x)^(7/2))/(165*sqrt(3 + 5*x)) - (12601*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/240625 + (5153*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/48125 + (958*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/1925 - (1473539*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(218750*sqrt(33)) - (31288*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(109375*sqrt(33))]
    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^(7/2))/(3 + 5*x)^(5/2), x, 7, (-2*sqrt(1 - 2*x)*(2 + 3*x)^(7/2))/(15*(3 + 5*x)^(3/2)) - (458*sqrt(1 - 2*x)*(2 + 3*x)^(5/2))/(825*sqrt(3 + 5*x)) + (2719*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/34375 + (2818*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/6875 - (47342*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(15625*sqrt(33)) - (523*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/15625]
    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^(5/2))/(3 + 5*x)^(5/2), x, 6, (-2*sqrt(1 - 2*x)*(2 + 3*x)^(5/2))/(15*(3 + 5*x)^(3/2)) - (326*sqrt(1 - 2*x)*(2 + 3*x)^(3/2))/(825*sqrt(3 + 5*x)) + (458*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/1375 - (169*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(625*sqrt(33)) - (496*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(625*sqrt(33))]
    @test_int [(sqrt(1 - 2*x)*(2 + 3*x)^(3/2))/(3 + 5*x)^(5/2), x, 5, (-2*sqrt(1 - 2*x)*(2 + 3*x)^(3/2))/(15*(3 + 5*x)^(3/2)) - (194*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(825*sqrt(3 + 5*x)) + (458*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(125*sqrt(33)) - (178*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(125*sqrt(33))]
    @test_int [(sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3 + 5*x)^(5/2), x, 5, (-2*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(15*(3 + 5*x)^(3/2)) - (62*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(165*sqrt(3 + 5*x)) + (62*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(25*sqrt(33)) + (8*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(25*sqrt(33))]
    @test_int [sqrt(1 - 2*x)/(sqrt(2 + 3*x)*(3 + 5*x)^(5/2)), x, 5, (-2*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3*(3 + 5*x)^(3/2)) + (136*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(33*sqrt(3 + 5*x)) - (136*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(5*sqrt(33)) - (4*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(5*sqrt(33))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)), x, 6, (2*sqrt(1 - 2*x))/(sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (40*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3*(3 + 5*x)^(3/2)) + (2660*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(33*sqrt(3 + 5*x)) - (532*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/sqrt(33) - (16*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/sqrt(33)]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)), x, 7, (2*sqrt(1 - 2*x))/(3*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (416*sqrt(1 - 2*x))/(21*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (2780*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(21*(3 + 5*x)^(3/2)) + (184840*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(231*sqrt(3 + 5*x)) - (36968*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(7*sqrt(33)) - (1112*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(7*sqrt(33))]
    @test_int [sqrt(1 - 2*x)/((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)), x, 8, (2*sqrt(1 - 2*x))/(5*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + (556*sqrt(1 - 2*x))/(105*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (116044*sqrt(1 - 2*x))/(735*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (155104*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(147*(3 + 5*x)^(3/2)) + (10312712*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(1617*sqrt(3 + 5*x)) - (10312712*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(245*sqrt(33)) - (310208*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(245*sqrt(33))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^(m/2)*(c+d*x)^(n/2)*(e+f*x)^(3/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x), x, 8, (-18177329*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/38981250 - (124891*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/2165625 + (1103*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/259875 + (178*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/7425 + (2*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/55 - (604915631*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(17718750*sqrt(33)) - (18177329*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(17718750*sqrt(33))]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x), x, 7, (-84134*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/354375 - (347*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/39375 + (62*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/1575 + (2*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/45 - (5684677*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3543750 - (84134*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1771875]
    @test_int [(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*sqrt(3 + 5*x), x, 6, (-2657*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/23625 + (194*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/2625 + (2*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/35 - (118898*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/118125 - (2657*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/118125]
    @test_int [((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/sqrt(2 + 3*x), x, 5, (214*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/675 + (2*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/15 - (4157*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3375 + (412*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3375]
    @test_int [((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(2 + 3*x)^(3/2), x, 5, (-2*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(3*sqrt(2 + 3*x)) - (16*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/27 + (494*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/135 - (214*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/135]
    @test_int [((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(2 + 3*x)^(5/2), x, 5, (-2*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(9*(2 + 3*x)^(3/2)) + (82*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(27*sqrt(2 + 3*x)) - (98*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/27 + (16*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/27]
    @test_int [((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(2 + 3*x)^(7/2), x, 6, (-2*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(15*(2 + 3*x)^(5/2)) + (82*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(135*(2 + 3*x)^(3/2)) + (3896*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(945*sqrt(2 + 3*x)) - (3896*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/945 - (164*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/945]
    @test_int [((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(2 + 3*x)^(9/2), x, 7, (-2*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(21*(2 + 3*x)^(7/2)) + (82*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(315*(2 + 3*x)^(5/2)) + (8516*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(6615*(2 + 3*x)^(3/2)) + (595324*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(46305*sqrt(2 + 3*x)) - (595324*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/46305 - (18016*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/46305]
    @test_int [((1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(2 + 3*x)^(11/2), x, 8, (-2*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(27*(2 + 3*x)^(9/2)) + (82*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(567*(2 + 3*x)^(7/2)) + (13136*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(19845*(2 + 3*x)^(5/2)) + (613276*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(138915*(2 + 3*x)^(3/2)) + (42623864*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(972405*sqrt(2 + 3*x)) - (42623864*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/972405 - (1282376*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/972405]

    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2), x, 9, (-776112041*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/506756250 - (11725073*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/56306250 - (18034*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/625625 + (601*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/160875 + (178*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/10725 + (2*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/65 - (51601293223*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(460687500*sqrt(33)) - (776112041*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(230343750*sqrt(33))]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2), x, 8, (-5442127*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/7796250 - (40703*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/433125 - (23*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/9625 + (62*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/2475 + (2*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/55 - (90397364*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1771875*sqrt(33)) - (5442127*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(3543750*sqrt(33))]
    @test_int [(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2), x, 7, (-76163*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/212625 - (839*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/23625 + (194*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/4725 + (2*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/45 - (4971289*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/2126250 - (76163*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1063125]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/sqrt(2 + 3*x), x, 6, (-1847*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/4725 + (74*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/525 + (2*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/21 - (29933*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/23625 - (1847*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/23625]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(3/2), x, 6, (494*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/135 - (2*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(3*sqrt(2 + 3*x)) - (8*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/15 - (2209*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/675 + (494*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/675]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(5/2), x, 6, (-1150*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/81 - (2*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(9*(2 + 3*x)^(3/2)) + (74*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(9*sqrt(2 + 3*x)) + (592*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/81 - (230*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/81]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(7/2), x, 6, (988*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(945*sqrt(2 + 3*x)) - (2*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(15*(2 + 3*x)^(5/2)) + (74*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(45*(2 + 3*x)^(3/2)) - (4418*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/945 + (988*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/945]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(9/2), x, 7, (-3632*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(6615*(2 + 3*x)^(3/2)) + (119732*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(46305*sqrt(2 + 3*x)) - (2*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(21*(2 + 3*x)^(7/2)) + (74*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(105*(2 + 3*x)^(5/2)) - (119732*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/46305 - (7388*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/46305]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(11/2), x, 8, (-8252*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(19845*(2 + 3*x)^(5/2)) + (280904*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(416745*(2 + 3*x)^(3/2)) + (19885156*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2917215*sqrt(2 + 3*x)) - (2*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(27*(2 + 3*x)^(9/2)) + (74*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(189*(2 + 3*x)^(7/2)) - (19885156*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/2917215 - (609304*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/2917215]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(13/2), x, 9, (-12872*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(43659*(2 + 3*x)^(7/2)) + (442076*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1528065*(2 + 3*x)^(5/2)) + (20799916*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(10696455*(2 + 3*x)^(3/2)) + (1446357824*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(74875185*sqrt(2 + 3*x)) - (2*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(33*(2 + 3*x)^(11/2)) + (74*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(297*(2 + 3*x)^(9/2)) - (1446357824*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(6806835*sqrt(33)) - (43537016*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(6806835*sqrt(33))]

    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2), x, 10, (-50299451003*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/9121612500 - (380132617*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/506756250 - (57509209*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/506756250 - (199721*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(7/2))/12065625 + (2503*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(7/2))/804375 + (178*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(7/2))/14625 + (2*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(7/2))/75 - (836091184171*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(2073093750*sqrt(33)) - (50299451003*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(4146187500*sqrt(33))]
    @test_int [(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2), x, 9, (-70536439*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/30405375 - (2133359*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/6756750 - (160084*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/3378375 - (67*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(7/2))/160875 + (62*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(7/2))/3575 + (2*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(7/2))/65 - (9380126059*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(55282500*sqrt(33)) - (70536439*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(13820625*sqrt(33))]
    @test_int [(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2), x, 8, (-2930159*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/2806650 - (22576*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/155925 - (2377*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/155925 + (194*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(7/2))/7425 + (2*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*(3 + 5*x)^(7/2))/55 - (97540001*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1275750*sqrt(33)) - (2930159*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1275750*sqrt(33))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/sqrt(2 + 3*x), x, 7, (-11908*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/25515 - (499*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/2835 + (46*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/567 + (2*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/27 - (886499*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/255150 - (11908*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/127575]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(3/2), x, 7, (-1061*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/567 + (202*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/63 - (2*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(3*sqrt(2 + 3*x)) - (32*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/63 - (2894*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/2835 - (1061*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/2835]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(5/2), x, 7, (2632*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/243 - (614*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/27 - (2*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(9*(2 + 3*x)^(3/2)) + (362*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(27*sqrt(2 + 3*x)) - (9587*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1215 + (2632*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1215]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(7/2), x, 7, (-43214*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/1701 + (9808*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(945*sqrt(2 + 3*x)) - (2*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(15*(2 + 3*x)^(5/2)) + (362*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(135*(2 + 3*x)^(3/2)) + (116854*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/8505 - (43214*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/8505]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(9/2), x, 7, (249448*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(138915*sqrt(2 + 3*x)) + (2108*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(6615*(2 + 3*x)^(3/2)) - (2*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(21*(2 + 3*x)^(7/2)) + (362*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(315*(2 + 3*x)^(5/2)) - (962678*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/138915 + (249448*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/138915]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(11/2), x, 8, (-558524*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1250235*(2 + 3*x)^(3/2)) + (17830424*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(8751645*sqrt(2 + 3*x)) - (1864*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(6615*(2 + 3*x)^(5/2)) - (2*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(27*(2 + 3*x)^(9/2)) + (362*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(567*(2 + 3*x)^(7/2)) - (17830424*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/8751645 - (1717916*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/8751645]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(13/2), x, 9, (-1366496*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(4584195*(2 + 3*x)^(5/2)) + (45748292*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(96268095*(2 + 3*x)^(3/2)) + (3316711588*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(673876665*sqrt(2 + 3*x)) - (13292*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(43659*(2 + 3*x)^(7/2)) - (2*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(33*(2 + 3*x)^(11/2)) + (362*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(891*(2 + 3*x)^(9/2)) - (3316711588*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(61261515*sqrt(33)) - (103970992*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(61261515*sqrt(33))]
    @test_int [((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(15/2), x, 10, (-2174468*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(11918907*(2 + 3*x)^(7/2)) + (73596464*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(417161745*(2 + 3*x)^(5/2)) + (3523482724*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2920132215*(2 + 3*x)^(3/2)) + (245282464136*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(20440925505*sqrt(2 + 3*x)) - (20992*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(81081*(2 + 3*x)^(9/2)) - (2*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(39*(2 + 3*x)^(13/2)) + (362*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(1287*(2 + 3*x)^(11/2)) - (245282464136*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1858265955*sqrt(33)) - (7391549624*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1858265955*sqrt(33))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2))/sqrt(3 + 5*x), x, 7, (-87476*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/590625 + (403*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/118125 + (178*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/4725 + (2*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/45 - (6515539*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5906250 - (104663*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/2953125]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2))/sqrt(3 + 5*x), x, 6, (-487*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/13125 + (62*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/875 + (2*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/35 - (46159*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/65625 - (2281*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/65625]
    @test_int [((1 - 2*x)^(3/2)*sqrt(2 + 3*x))/sqrt(3 + 5*x), x, 5, (194*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/1125 + (2*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/25 - (2797*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5625 - (598*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5625]
    @test_int [(1 - 2*x)^(3/2)/(sqrt(2 + 3*x)*sqrt(3 + 5*x)), x, 4, (-4*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/45 + (272*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/225 - (202*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/225]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^(3/2)*sqrt(3 + 5*x)), x, 4, (14*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3*sqrt(2 + 3*x)) - (74*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/15 + (4*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/15]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^(5/2)*sqrt(3 + 5*x)), x, 5, (14*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(9*(2 + 3*x)^(3/2)) + (124*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(9*sqrt(2 + 3*x)) - (124*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/9 - (4*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/9]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^(7/2)*sqrt(3 + 5*x)), x, 6, (14*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(15*(2 + 3*x)^(5/2)) + (256*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(45*(2 + 3*x)^(3/2)) + (17804*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(315*sqrt(2 + 3*x)) - (17804*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/315 - (536*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/315]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^(9/2)*sqrt(3 + 5*x)), x, 7, (2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3*(2 + 3*x)^(7/2)) + (388*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(105*(2 + 3*x)^(5/2)) + (18068*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(735*(2 + 3*x)^(3/2)) + (1255552*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(5145*sqrt(2 + 3*x)) - (1255552*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5145 - (37768*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5145]

    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2))/(3 + 5*x)^(3/2), x, 8, (-2*(1 - 2*x)^(3/2)*(2 + 3*x)^(7/2))/(5*sqrt(3 + 5*x)) - (12601*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/196875 + (5153*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/39375 + (958*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/1575 - (8*sqrt(1 - 2*x)*(2 + 3*x)^(7/2)*sqrt(3 + 5*x))/45 - (1473539*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1968750 - (31288*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/984375]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2))/(3 + 5*x)^(3/2), x, 7, (-2*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2))/(5*sqrt(3 + 5*x)) + (2719*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/21875 + (2818*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/4375 - (32*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/175 - (47342*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/109375 - (5753*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/109375]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2))/(3 + 5*x)^(3/2), x, 6, (-2*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2))/(5*sqrt(3 + 5*x)) + (458*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/625 - (24*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/125 - (169*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3125 - (496*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3125]
    @test_int [((1 - 2*x)^(3/2)*sqrt(2 + 3*x))/(3 + 5*x)^(3/2), x, 5, (-2*(1 - 2*x)^(3/2)*sqrt(2 + 3*x))/(5*sqrt(3 + 5*x)) - (16*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/75 + (458*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/375 - (178*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/375]
    @test_int [(1 - 2*x)^(3/2)/(sqrt(2 + 3*x)*(3 + 5*x)^(3/2)), x, 4, (-22*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(5*sqrt(3 + 5*x)) + (62*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/25 + (8*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/25]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)), x, 5, (14*sqrt(1 - 2*x))/(3*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (136*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3*sqrt(3 + 5*x)) + (136*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5 + (4*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)), x, 6, (14*sqrt(1 - 2*x))/(9*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + (88*sqrt(1 - 2*x))/(3*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (2660*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(9*sqrt(3 + 5*x)) + (532*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3 + (16*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)), x, 7, (14*sqrt(1 - 2*x))/(15*(2 + 3*x)^(5/2)*sqrt(3 + 5*x)) + (44*sqrt(1 - 2*x))/(5*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + (6116*sqrt(1 - 2*x))/(35*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (36968*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(21*sqrt(3 + 5*x)) + (36968*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/35 + (1112*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/35]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^(9/2)*(3 + 5*x)^(3/2)), x, 8, (2*sqrt(1 - 2*x))/(3*(2 + 3*x)^(7/2)*sqrt(3 + 5*x)) + (176*sqrt(1 - 2*x))/(35*(2 + 3*x)^(5/2)*sqrt(3 + 5*x)) + (12276*sqrt(1 - 2*x))/(245*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + (1706144*sqrt(1 - 2*x))/(1715*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (10312712*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(1029*sqrt(3 + 5*x)) + (10312712*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1715 + (310208*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1715]

    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2))/(3 + 5*x)^(5/2), x, 8, (-2*(1 - 2*x)^(3/2)*(2 + 3*x)^(7/2))/(15*(3 + 5*x)^(3/2)) - (6*sqrt(1 - 2*x)*(2 + 3*x)^(7/2))/sqrt(3 + 5*x) + (4801*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/21875 + (3872*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/4375 + (622*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/175 - (25643*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/109375 - (24369*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/109375]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2))/(3 + 5*x)^(5/2), x, 7, (-2*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2))/(15*(3 + 5*x)^(3/2)) - (106*sqrt(1 - 2*x)*(2 + 3*x)^(5/2))/(25*sqrt(3 + 5*x)) + (2264*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/3125 + (1558*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/625 + (1973*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/15625 - (8366*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/15625]
    @test_int [((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2))/(3 + 5*x)^(5/2), x, 6, (-2*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2))/(15*(3 + 5*x)^(3/2)) - (62*sqrt(1 - 2*x)*(2 + 3*x)^(3/2))/(25*sqrt(3 + 5*x)) + (178*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/125 + (496*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/625 - (582*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/625]
    @test_int [((1 - 2*x)^(3/2)*sqrt(2 + 3*x))/(3 + 5*x)^(5/2), x, 5, (-2*(1 - 2*x)^(3/2)*sqrt(2 + 3*x))/(15*(3 + 5*x)^(3/2)) - (18*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(25*sqrt(3 + 5*x)) + (38*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/125 + (212*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(125*sqrt(33))]
    @test_int [(1 - 2*x)^(3/2)/(sqrt(2 + 3*x)*(3 + 5*x)^(5/2)), x, 5, (-22*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(15*(3 + 5*x)^(3/2)) + (148*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(15*sqrt(3 + 5*x)) - (148*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/25 - (52*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(25*sqrt(33))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)), x, 6, (14*sqrt(1 - 2*x))/(3*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (92*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3*(3 + 5*x)^(3/2)) + (556*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3*sqrt(3 + 5*x)) - (556*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5 - (184*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(5*sqrt(33))]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)), x, 7, (14*sqrt(1 - 2*x))/(9*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (404*sqrt(1 - 2*x))/(9*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (300*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3 + 5*x)^(3/2) + (5440*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3*sqrt(3 + 5*x)) - 1088*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33) - 120*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33)]
    @test_int [(1 - 2*x)^(3/2)/((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)), x, 8, (14*sqrt(1 - 2*x))/(15*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + (536*sqrt(1 - 2*x))/(45*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (111884*sqrt(1 - 2*x))/(315*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (16616*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(7*(3 + 5*x)^(3/2)) + (301304*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(21*sqrt(3 + 5*x)) - (301304*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/35 - (33232*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/35]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^(m/2)*(c+d*x)^(n/2)*(e+f*x)^(5/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x), x, 9, (-69808931*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/168918750 - (445024*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/9384375 + (32717*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/1126125 + (34*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/2475 + (62*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/2145 + (2*(1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/65 - (1163388067*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(38390625*sqrt(33)) - (69808931*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(76781250*sqrt(33))]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x), x, 8, (-4738087*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/19490625 + (38729*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/2165625 + (2866*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/86625 + (106*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/2475 + (2*(1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/55 - (326256461*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(17718750*sqrt(33)) - (4738087*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(8859375*sqrt(33))]
    @test_int [(1 - 2*x)^(5/2)*sqrt(2 + 3*x)*sqrt(3 + 5*x), x, 7, (-110717*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/1063125 + (10214*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/118125 + (326*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/4725 + (2*(1 - 2*x)^(5/2)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/45 - (6799613*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5315625 - (110717*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5315625]
    @test_int [((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/sqrt(2 + 3*x), x, 6, (4282*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/7875 + (118*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/525 + (2*(1 - 2*x)^(5/2)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/21 - (86741*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/39375 + (11806*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/39375]
    @test_int [((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(2 + 3*x)^(3/2), x, 6, (-2*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(3*sqrt(2 + 3*x)) - (1076*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/675 - (8*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/15 + (31588*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3375 - (12758*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3375]
    @test_int [((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(2 + 3*x)^(5/2), x, 6, (-2*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(9*(2 + 3*x)^(3/2)) + (10*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(3*sqrt(2 + 3*x)) + (196*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/81 - (4418*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/405 + (988*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/405]
    @test_int [((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(2 + 3*x)^(7/2), x, 6, (-2*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(15*(2 + 3*x)^(5/2)) + (2*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(3*(2 + 3*x)^(3/2)) + (8*sqrt(1 - 2*x)*sqrt(3 + 5*x))/sqrt(2 + 3*x) - (12*sqrt(33)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5 - (4*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5]
    @test_int [((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(2 + 3*x)^(9/2), x, 7, (-2*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(21*(2 + 3*x)^(7/2)) + (2*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(7*(2 + 3*x)^(5/2)) + (524*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(189*(2 + 3*x)^(3/2)) + (36052*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1323*sqrt(2 + 3*x)) - (36052*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1323 - (1048*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1323]
    @test_int [((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(2 + 3*x)^(11/2), x, 8, (-2*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(27*(2 + 3*x)^(9/2)) + (10*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(63*(2 + 3*x)^(7/2)) + (832*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(567*(2 + 3*x)^(5/2)) + (112436*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(11907*(2 + 3*x)^(3/2)) + (7810384*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(83349*sqrt(2 + 3*x)) - (7810384*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/83349 - (234856*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/83349]
    @test_int [((1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(2 + 3*x)^(13/2), x, 9, (-2*(1 - 2*x)^(5/2)*sqrt(3 + 5*x))/(33*(2 + 3*x)^(11/2)) + (10*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(99*(2 + 3*x)^(9/2)) + (1900*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2079*(2 + 3*x)^(7/2)) + (76492*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(14553*(2 + 3*x)^(5/2)) + (3560432*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(101871*(2 + 3*x)^(3/2)) + (247408648*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(713097*sqrt(2 + 3*x)) - (247408648*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(64827*sqrt(33)) - (7442032*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(64827*sqrt(33))]

    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2), x, 10, (-13267820528*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/11402015625 - (400516993*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/2533781250 - (569519*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/28153125 + (142391*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/7239375 + (3698*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/482625 + (62*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/2925 + (2*(1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/75 - (1764163292393*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(20730937500*sqrt(33)) - (13267820528*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(5182734375*sqrt(33))]
    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2), x, 9, (-923943703*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/1520268750 - (6794792*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/84459375 + (25603*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/1876875 + (8318*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/482625 + (106*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/3575 + (2*(1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/65 - (30660308017*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(691031250*sqrt(33)) - (923943703*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(691031250*sqrt(33))]
    @test_int [(1 - 2*x)^(5/2)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2), x, 8, (-12996374*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/35083125 - (78797*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/3898125 + (30362*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/779625 + (326*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/7425 + (2*(1 - 2*x)^(5/2)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/55 - (829177897*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(31893750*sqrt(33)) - (12996374*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(15946875*sqrt(33))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/sqrt(2 + 3*x), x, 7, (-429479*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/637875 + (14318*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/70875 + (362*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/2835 + (2*(1 - 2*x)^(5/2)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/27 - (4457606*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3189375 - (429479*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3189375]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(3/2), x, 7, (124724*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/14175 - (2*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(3*sqrt(2 + 3*x)) - (2108*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/1575 - (32*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/63 - (481339*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/70875 + (124724*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/70875]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(5/2), x, 7, (-43214*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/1215 - (2*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(9*(2 + 3*x)^(3/2)) + (230*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(27*sqrt(2 + 3*x)) + (788*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/135 + (116854*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/6075 - (43214*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/6075]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(7/2), x, 7, (5264*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/243 - (2*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(15*(2 + 3*x)^(5/2)) + (46*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(27*(2 + 3*x)^(3/2)) - (316*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(27*sqrt(2 + 3*x)) - (19174*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1215 + (5264*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1215]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(9/2), x, 7, (-4244*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3969*sqrt(2 + 3*x)) - (2*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(21*(2 + 3*x)^(7/2)) + (46*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(63*(2 + 3*x)^(5/2)) + (608*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(189*(2 + 3*x)^(3/2)) - (11576*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3969 - (4244*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3969]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(11/2), x, 8, (-104036*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(35721*(2 + 3*x)^(3/2)) + (3545996*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(250047*sqrt(2 + 3*x)) - (2*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(27*(2 + 3*x)^(9/2)) + (230*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(567*(2 + 3*x)^(7/2)) + (1532*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(567*(2 + 3*x)^(5/2)) - (3545996*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/250047 - (95264*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/250047]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(13/2), x, 9, (-325796*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(130977*(2 + 3*x)^(5/2)) + (11243972*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2750517*(2 + 3*x)^(3/2)) + (780320008*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(19253619*sqrt(2 + 3*x)) - (2*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(33*(2 + 3*x)^(11/2)) + (230*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(891*(2 + 3*x)^(9/2)) + (12280*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(6237*(2 + 3*x)^(7/2)) - (780320008*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1750329*sqrt(33)) - (23441272*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1750329*sqrt(33))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^(15/2), x, 10, (-3347620*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1702701*(2 + 3*x)^(7/2)) + (23210828*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(11918907*(2 + 3*x)^(5/2)) + (1079936248*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(83432349*(2 + 3*x)^(3/2)) + (75041008472*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(584026443*sqrt(2 + 3*x)) - (2*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(39*(2 + 3*x)^(13/2)) + (230*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(1287*(2 + 3*x)^(11/2)) + (1300*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(891*(2 + 3*x)^(9/2)) - (75041008472*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(53093313*sqrt(33)) - (2257166048*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(53093313*sqrt(33))]

    @test_int [(1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2), x, 10, (-23763809947*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/13682418750 - (359748241*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/1520268750 - (26534891*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/760134375 + (364267*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(7/2))/36196875 + (8038*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(7/2))/804375 + (106*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(7/2))/4875 + (2*(1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(7/2))/75 - (1580201444291*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(12438562500*sqrt(33)) - (23763809947*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(6219281250*sqrt(33))]
    @test_int [(1 - 2*x)^(5/2)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2), x, 9, (-486785077*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/547296750 - (3872003*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/30405375 - (121031*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/30405375 + (2314*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(7/2))/111375 + (326*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*(3 + 5*x)^(7/2))/10725 + (2*(1 - 2*x)^(5/2)*sqrt(2 + 3*x)*(3 + 5*x)^(7/2))/65 - (8120161139*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(124385625*sqrt(33)) - (486785077*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(248771250*sqrt(33))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/sqrt(2 + 3*x), x, 8, (-1654421*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/4209975 - (146963*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/467775 + (9698*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/93555 + (74*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/891 + (2*(1 - 2*x)^(5/2)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/33 - (146222113*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(3827250*sqrt(33)) - (1654421*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1913625*sqrt(33))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(3/2), x, 8, (-310399*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/76545 + (64628*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/8505 - (2*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(3*sqrt(2 + 3*x)) - (2108*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/1701 - (40*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/81 - (25111*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/382725 - (310399*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/382725]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(5/2), x, 8, (135334*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/5103 - (31298*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/567 - (2*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(9*(2 + 3*x)^(3/2)) + (370*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(27*sqrt(2 + 3*x)) + (5260*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/567 - (452399*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/25515 + (135334*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/25515]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(7/2), x, 8, (-48478*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/729 + (11036*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/81 - (2*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(15*(2 + 3*x)^(5/2)) + (74*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(27*(2 + 3*x)^(3/2)) - (6464*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(81*sqrt(2 + 3*x)) + (136028*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3645 - (48478*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3645]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(9/2), x, 8, (1353340*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/35721 - (62596*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(3969*sqrt(2 + 3*x)) - (2*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(21*(2 + 3*x)^(7/2)) + (74*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(63*(2 + 3*x)^(5/2)) - (1844*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(567*(2 + 3*x)^(3/2)) - (904798*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/35721 + (270668*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/35721]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(11/2), x, 8, (-1241596*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(750141*sqrt(2 + 3*x)) - (13316*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(35721*(2 + 3*x)^(3/2)) - (2*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(27*(2 + 3*x)^(9/2)) + (370*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(567*(2 + 3*x)^(7/2)) + (2776*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(1701*(2 + 3*x)^(5/2)) - (100444*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/750141 - (1241596*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/750141]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(13/2), x, 9, (-17089252*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(8251551*(2 + 3*x)^(3/2)) + (584888452*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(57760857*sqrt(2 + 3*x)) - (55772*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(43659*(2 + 3*x)^(5/2)) - (2*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(33*(2 + 3*x)^(11/2)) + (370*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(891*(2 + 3*x)^(9/2)) + (36980*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(18711*(2 + 3*x)^(7/2)) - (584888452*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(5250987*sqrt(33)) - (13235368*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(5250987*sqrt(33))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(15/2), x, 10, (-54281308*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(35756721*(2 + 3*x)^(5/2)) + (1876198516*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(750891141*(2 + 3*x)^(3/2)) + (129922578224*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(5256237987*sqrt(2 + 3*x)) - (2622980*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(1702701*(2 + 3*x)^(7/2)) - (2*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(39*(2 + 3*x)^(13/2)) + (370*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(1287*(2 + 3*x)^(11/2)) + (60080*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(34749*(2 + 3*x)^(9/2)) - (129922578224*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(477839817*sqrt(33)) - (3894280616*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(477839817*sqrt(33))]
    @test_int [((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^(17/2), x, 11, (-112817764*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(107270163*(2 + 3*x)^(7/2)) + (3914701972*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3754455705*(2 + 3*x)^(5/2)) + (181941877952*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(26281189935*(2 + 3*x)^(3/2)) + (12641611554328*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(183968329545*sqrt(2 + 3*x)) - (1085156*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(729729*(2 + 3*x)^(9/2)) - (2*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(45*(2 + 3*x)^(15/2)) + (74*(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(351*(2 + 3*x)^(13/2)) + (16636*sqrt(1 - 2*x)*(3 + 5*x)^(5/2))/(11583*(2 + 3*x)^(11/2)) - (12641611554328*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(16724393595*sqrt(33)) - (380220959152*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(16724393595*sqrt(33))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2))/sqrt(3 + 5*x), x, 8, (-2865161*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/19490625 + (181333*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/3898125 + (4258*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/155925 + (62*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/1485 + (2*(1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/55 - (231061879*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(17718750*sqrt(33)) - (3963068*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(8859375*sqrt(33))]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2))/sqrt(3 + 5*x), x, 7, (21547*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/1771875 + (8878*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/118125 + (106*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/1575 + (2*(1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/45 - (8024546*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/8859375 - (509189*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/8859375]
    @test_int [((1 - 2*x)^(5/2)*sqrt(2 + 3*x))/sqrt(3 + 5*x), x, 6, (30922*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/118125 + (326*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/2625 + (2*(1 - 2*x)^(5/2)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/35 - (408311*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/590625 - (132824*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/590625]
    @test_int [(1 - 2*x)^(5/2)/(sqrt(2 + 3*x)*sqrt(3 + 5*x)), x, 5, (-1088*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/3375 - (4*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/75 + (53194*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/16875 - (34154*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/16875]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^(3/2)*sqrt(3 + 5*x)), x, 5, (14*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(3*sqrt(2 + 3*x)) + (428*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/135 - (8314*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/675 + (824*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/675]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^(5/2)*sqrt(3 + 5*x)), x, 5, (14*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(9*(2 + 3*x)^(3/2)) + (812*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(27*sqrt(2 + 3*x)) - (3896*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/135 - (164*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/135]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^(7/2)*sqrt(3 + 5*x)), x, 6, (14*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(15*(2 + 3*x)^(5/2)) + (1736*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(135*(2 + 3*x)^(3/2)) + (16564*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(135*sqrt(2 + 3*x)) - (16564*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/135 - (496*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/135]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^(9/2)*sqrt(3 + 5*x)), x, 7, (2*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(3*(2 + 3*x)^(7/2)) + (76*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(9*(2 + 3*x)^(5/2)) + (10124*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(189*(2 + 3*x)^(3/2)) + (703480*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1323*sqrt(2 + 3*x)) - (703480*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1323 - (21160*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1323]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^(11/2)*sqrt(3 + 5*x)), x, 8, (14*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(27*(2 + 3*x)^(9/2)) + (512*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(81*(2 + 3*x)^(7/2)) + (20420*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(567*(2 + 3*x)^(5/2)) + (950584*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3969*(2 + 3*x)^(3/2)) + (66055016*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(27783*sqrt(2 + 3*x)) - (66055016*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/27783 - (1986944*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/27783]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^(13/2)*sqrt(3 + 5*x)), x, 9, (14*(1 - 2*x)^(3/2)*sqrt(3 + 5*x))/(33*(2 + 3*x)^(11/2)) + (4508*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(891*(2 + 3*x)^(9/2)) + (171004*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(6237*(2 + 3*x)^(7/2)) + (7173272*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(43659*(2 + 3*x)^(5/2)) + (333930952*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(305613*(2 + 3*x)^(3/2)) + (23204503328*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2139291*sqrt(2 + 3*x)) - (23204503328*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(194481*sqrt(33)) - (697995152*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(194481*sqrt(33))]

    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2))/(3 + 5*x)^(3/2), x, 9, (-2*(1 - 2*x)^(5/2)*(2 + 3*x)^(7/2))/(5*sqrt(3 + 5*x)) - (703672*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/32484375 + (2020841*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/6496875 + (346636*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/259875 - (2972*sqrt(1 - 2*x)*(2 + 3*x)^(7/2)*sqrt(3 + 5*x))/7425 - (48*(1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)*sqrt(3 + 5*x))/275 - (264260033*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(29531250*sqrt(33)) - (7261561*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(14765625*sqrt(33))]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2))/(3 + 5*x)^(3/2), x, 8, (-2*(1 - 2*x)^(5/2)*(2 + 3*x)^(5/2))/(5*sqrt(3 + 5*x)) + (196499*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/590625 + (167228*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/118125 - (1972*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/4725 - (8*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/45 - (1509007*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/2953125 - (299863*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/2953125]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2))/(3 + 5*x)^(3/2), x, 7, (-2*(1 - 2*x)^(5/2)*(2 + 3*x)^(3/2))/(5*sqrt(3 + 5*x)) + (106772*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/65625 - (1972*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/4375 - (32*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/175 + (53279*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/328125 - (110014*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/328125]
    @test_int [((1 - 2*x)^(5/2)*sqrt(2 + 3*x))/(3 + 5*x)^(3/2), x, 6, (-2*(1 - 2*x)^(5/2)*sqrt(2 + 3*x))/(5*sqrt(3 + 5*x)) - (3028*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/5625 - (24*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/125 + (81164*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/28125 - (28174*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/28125]
    @test_int [(1 - 2*x)^(5/2)/(sqrt(2 + 3*x)*(3 + 5*x)^(3/2)), x, 5, (-22*(1 - 2*x)^(3/2)*sqrt(2 + 3*x))/(5*sqrt(3 + 5*x)) - (388*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/225 + (5594*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1125 + (1196*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1125]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)), x, 5, (14*(1 - 2*x)^(3/2))/(3*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (1496*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(15*sqrt(3 + 5*x)) + (4636*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/75 + (124*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/75]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)), x, 6, (14*(1 - 2*x)^(3/2))/(9*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + (1792*sqrt(1 - 2*x))/(27*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (17804*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(27*sqrt(3 + 5*x)) + (17804*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/45 + (536*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/45]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)), x, 7, (14*(1 - 2*x)^(3/2))/(15*(2 + 3*x)^(5/2)*sqrt(3 + 5*x)) + (2716*sqrt(1 - 2*x))/(135*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + (17468*sqrt(1 - 2*x))/(45*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (105584*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(27*sqrt(3 + 5*x)) + (105584*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/45 + (3176*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/45]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^(9/2)*(3 + 5*x)^(3/2)), x, 8, (2*(1 - 2*x)^(3/2))/(3*(2 + 3*x)^(7/2)*sqrt(3 + 5*x)) + (104*sqrt(1 - 2*x))/(9*(2 + 3*x)^(5/2)*sqrt(3 + 5*x)) + (2332*sqrt(1 - 2*x))/(21*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + (324104*sqrt(1 - 2*x))/(147*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (9795160*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(441*sqrt(3 + 5*x)) + (1959032*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/147 + (58928*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/147]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^(11/2)*(3 + 5*x)^(3/2)), x, 9, (14*(1 - 2*x)^(3/2))/(27*(2 + 3*x)^(9/2)*sqrt(3 + 5*x)) + (652*sqrt(1 - 2*x))/(81*(2 + 3*x)^(7/2)*sqrt(3 + 5*x)) + (11660*sqrt(1 - 2*x))/(189*(2 + 3*x)^(5/2)*sqrt(3 + 5*x)) + (813208*sqrt(1 - 2*x))/(1323*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + (113020952*sqrt(1 - 2*x))/(9261*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (3415750480*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(27783*sqrt(3 + 5*x)) + (683150096*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/9261 + (20549264*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/9261]

    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2))/(3 + 5*x)^(5/2), x, 9, (-2*(1 - 2*x)^(5/2)*(2 + 3*x)^(7/2))/(15*(3 + 5*x)^(3/2)) - (442*(1 - 2*x)^(3/2)*(2 + 3*x)^(7/2))/(75*sqrt(3 + 5*x)) + (500501*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/984375 + (373022*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/196875 + (59662*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/7875 - (524*sqrt(1 - 2*x)*(2 + 3*x)^(7/2)*sqrt(3 + 5*x))/225 - (1065118*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/4921875 - (595387*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/4921875]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2))/(3 + 5*x)^(5/2), x, 8, (-2*(1 - 2*x)^(5/2)*(2 + 3*x)^(5/2))/(15*(3 + 5*x)^(3/2)) - (62*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2))/(15*sqrt(3 + 5*x)) + (33778*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/21875 + (22866*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/4375 - (284*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/175 + (49321*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/109375 - (32836*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/109375]
    @test_int [((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2))/(3 + 5*x)^(5/2), x, 7, (-2*(1 - 2*x)^(5/2)*(2 + 3*x)^(3/2))/(15*(3 + 5*x)^(3/2)) - (178*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2))/(75*sqrt(3 + 5*x)) + (8874*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/3125 - (572*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/625 + (9206*sqrt(33)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/15625 - (7738*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/15625]
    @test_int [((1 - 2*x)^(5/2)*sqrt(2 + 3*x))/(3 + 5*x)^(5/2), x, 6, (-2*(1 - 2*x)^(5/2)*sqrt(2 + 3*x))/(15*(3 + 5*x)^(3/2)) - (46*(1 - 2*x)^(3/2)*sqrt(2 + 3*x))/(75*sqrt(3 + 5*x)) - (76*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/375 + (338*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1875 + (992*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1875]
    @test_int [(1 - 2*x)^(5/2)/(sqrt(2 + 3*x)*(3 + 5*x)^(5/2)), x, 5, (-22*(1 - 2*x)^(3/2)*sqrt(2 + 3*x))/(15*(3 + 5*x)^(3/2)) + (572*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(25*sqrt(3 + 5*x)) - (584*sqrt(33)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/125 - (68*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/125]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)), x, 6, (14*(1 - 2*x)^(3/2))/(3*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (1012*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(15*(3 + 5*x)^(3/2)) + (6388*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(15*sqrt(3 + 5*x)) - (6388*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/25 - (64*sqrt(33)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/25]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)), x, 7, (14*(1 - 2*x)^(3/2))/(9*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (308*sqrt(1 - 2*x))/(3*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (6116*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(9*(3 + 5*x)^(3/2)) + (36968*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(9*sqrt(3 + 5*x)) - (36968*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/15 - (1112*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/15]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)), x, 8, (14*(1 - 2*x)^(3/2))/(15*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + (1232*sqrt(1 - 2*x))/(45*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (35948*sqrt(1 - 2*x))/(45*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (16016*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3*(3 + 5*x)^(3/2)) + (96808*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3*sqrt(3 + 5*x)) - (96808*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5 - (2912*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5]
    @test_int [(1 - 2*x)^(5/2)/((2 + 3*x)^(9/2)*(3 + 5*x)^(5/2)), x, 9, (2*(1 - 2*x)^(3/2))/(3*(2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)) + (44*sqrt(1 - 2*x))/(3*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + (11924*sqrt(1 - 2*x))/(63*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (2488904*sqrt(1 - 2*x))/(441*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (5544440*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(147*(3 + 5*x)^(3/2)) + (11171040*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(49*sqrt(3 + 5*x)) - (2234208*sqrt(33)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/49 - (201616*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/49]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^(m/2)*(c+d*x)^(n/2) / (e+f*x)^(1/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [((2 + 3*x)^(5/2)*sqrt(3 + 5*x))/sqrt(1 - 2*x), x, 6, (-4839*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/1750 - (104*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/175 - (sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/7 - (56041*sqrt(33)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/8750 - (5057*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/8750]
    @test_int [((2 + 3*x)^(3/2)*sqrt(3 + 5*x))/sqrt(1 - 2*x), x, 5, (-23*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/25 - (sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/5 - (1597*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/250 - (8*sqrt(33)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/125]
    @test_int [(sqrt(2 + 3*x)*sqrt(3 + 5*x))/sqrt(1 - 2*x), x, 4, -(sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/3 - (34*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/15 - (sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/15]
    @test_int [sqrt(3 + 5*x)/(sqrt(1 - 2*x)*sqrt(2 + 3*x)), x, 1, -(sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))]
    @test_int [sqrt(3 + 5*x)/(sqrt(1 - 2*x)*(2 + 3*x)^(3/2)), x, 4, (-2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(7*sqrt(2 + 3*x)) + (2*sqrt(5/7)*sqrt(-3 - 5*x)*Elliptic.E(asin(sqrt(5)*sqrt(2 + 3*x)), 2/35))/(3*sqrt(3 + 5*x))]
    @test_int [sqrt(3 + 5*x)/(sqrt(1 - 2*x)*(2 + 3*x)^(5/2)), x, 5, (-2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(21*(2 + 3*x)^(3/2)) + (62*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(147*sqrt(2 + 3*x)) - (62*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/147 - (8*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/147]
    @test_int [sqrt(3 + 5*x)/(sqrt(1 - 2*x)*(2 + 3*x)^(7/2)), x, 6, (-2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(35*(2 + 3*x)^(5/2)) + (18*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(245*(2 + 3*x)^(3/2)) + (1752*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1715*sqrt(2 + 3*x)) - (584*sqrt(33)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1715 - (68*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1715]

    @test_int [((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/sqrt(1 - 2*x), x, 7, (-663409*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/47250 - (9547*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/5250 - (137*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/315 - (sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/9 - (44109377*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/472500 - (663409*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/236250]
    @test_int [((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/sqrt(1 - 2*x), x, 6, (-4721*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/1050 - (102*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/175 - (sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/7 - (78472*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/2625 - (4721*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5250]
    @test_int [(sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/sqrt(1 - 2*x), x, 5, (-67*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/45 - (sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/5 - (4451*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/450 - (67*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/225]
    @test_int [(3 + 5*x)^(3/2)/(sqrt(1 - 2*x)*sqrt(2 + 3*x)), x, 4, (-5*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/9 - (31*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/9 - (sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/9]
    @test_int [(3 + 5*x)^(3/2)/(sqrt(1 - 2*x)*(2 + 3*x)^(3/2)), x, 4, (2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(21*sqrt(2 + 3*x)) - (37*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/21 + (2*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/21]
    @test_int [(3 + 5*x)^(3/2)/(sqrt(1 - 2*x)*(2 + 3*x)^(5/2)), x, 5, (2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(63*(2 + 3*x)^(3/2)) - (272*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(441*sqrt(2 + 3*x)) + (272*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/441 - (202*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/441]
    @test_int [(3 + 5*x)^(3/2)/(sqrt(1 - 2*x)*(2 + 3*x)^(7/2)), x, 6, (2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(105*(2 + 3*x)^(5/2)) - (404*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2205*(2 + 3*x)^(3/2)) + (5594*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(15435*sqrt(2 + 3*x)) - (5594*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/15435 - (1196*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/15435]
    @test_int [(3 + 5*x)^(3/2)/(sqrt(1 - 2*x)*(2 + 3*x)^(9/2)), x, 7, (2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(147*(2 + 3*x)^(7/2)) - (536*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(5145*(2 + 3*x)^(5/2)) + (974*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(36015*(2 + 3*x)^(3/2)) + (184636*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(252105*sqrt(2 + 3*x)) - (184636*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/252105 - (9124*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/252105]

    @test_int [((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2))/sqrt(1 - 2*x), x, 9, (-2295970088*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/10135125 - (138809831*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/4504500 - (221673*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/50050 - (14303*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/12870 - (41*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/143 - (sqrt(1 - 2*x)*(2 + 3*x)^(7/2)*(3 + 5*x)^(5/2))/13 - (610627101631*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(36855000*sqrt(33)) - (2295970088*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(4606875*sqrt(33))]
    @test_int [((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/sqrt(1 - 2*x), x, 8, (-43624697*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/623700 - (329683*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/34650 - (1053*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/770 - (34*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/99 - (sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/11 - (725140729*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(141750*sqrt(33)) - (43624697*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(283500*sqrt(33))]
    @test_int [((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/sqrt(1 - 2*x), x, 7, (-62092*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/2835 - (1877*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/630 - (3*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/7 - (sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/9 - (8256877*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/56700 - (62092*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/14175]
    @test_int [(sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/sqrt(1 - 2*x), x, 6, (-2645*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/378 - (20*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/21 - (sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/7 - (17587*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/378 - (529*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/378]
    @test_int [(3 + 5*x)^(5/2)/(sqrt(1 - 2*x)*sqrt(2 + 3*x)), x, 5, (-62*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/27 - (sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/3 - (4141*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/270 - (62*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/135]
    @test_int [(3 + 5*x)^(5/2)/(sqrt(1 - 2*x)*(2 + 3*x)^(3/2)), x, 5, (-205*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/189 + (2*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(21*sqrt(2 + 3*x)) - (974*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/189 - (41*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/189]
    @test_int [(3 + 5*x)^(5/2)/(sqrt(1 - 2*x)*(2 + 3*x)^(5/2)), x, 5, (412*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1323*sqrt(2 + 3*x)) + (2*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(63*(2 + 3*x)^(3/2)) - (4157*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1323 + (412*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1323]
    @test_int [(3 + 5*x)^(5/2)/(sqrt(1 - 2*x)*(2 + 3*x)^(7/2)), x, 6, (544*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(6615*(2 + 3*x)^(3/2)) - (53194*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(46305*sqrt(2 + 3*x)) + (2*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(105*(2 + 3*x)^(5/2)) + (53194*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/46305 - (34154*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/46305]
    @test_int [(3 + 5*x)^(5/2)/(sqrt(1 - 2*x)*(2 + 3*x)^(9/2)), x, 7, (676*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(15435*(2 + 3*x)^(5/2)) - (101902*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(324135*(2 + 3*x)^(3/2)) + (816622*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2268945*sqrt(2 + 3*x)) + (2*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(147*(2 + 3*x)^(7/2)) - (816622*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/2268945 - (265648*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/2268945]
    @test_int [(3 + 5*x)^(5/2)/(sqrt(1 - 2*x)*(2 + 3*x)^(11/2)), x, 8, (808*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(27783*(2 + 3*x)^(7/2)) - (168034*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(972405*(2 + 3*x)^(5/2)) - (43094*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(6806835*(2 + 3*x)^(3/2)) + (32098184*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(47647845*sqrt(2 + 3*x)) + (2*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(189*(2 + 3*x)^(9/2)) - (32098184*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/47647845 - (2036756*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/47647845]
    @test_int [(3 + 5*x)^(5/2)/(sqrt(1 - 2*x)*(2 + 3*x)^(13/2)), x, 9, (940*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(43659*(2 + 3*x)^(9/2)) - (251590*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2139291*(2 + 3*x)^(7/2)) - (362666*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(14975037*(2 + 3*x)^(5/2)) + (11460644*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(104825259*(2 + 3*x)^(3/2)) + (924247516*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(733776813*sqrt(2 + 3*x)) + (2*sqrt(1 - 2*x)*(3 + 5*x)^(3/2))/(231*(2 + 3*x)^(11/2)) - (924247516*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(66706983*sqrt(33)) - (31704544*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(66706983*sqrt(33))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [1/(sqrt(1 + x)*sqrt(2 + x)*sqrt(3 + x)), x, 1, -2*Elliptic.F(asin(1/sqrt(3 + x)), 2)]
    @test_int [1/(sqrt(1 + x)*sqrt(2 + x)*sqrt(3 - x)), x, 1, 2*Elliptic.F(asin(sqrt(1 + x)/2), -4)]
    @test_int [1/(sqrt(1 + x)*sqrt(2 - x)*sqrt(3 + x)), x, 1, sqrt(2)*Elliptic.F(asin(sqrt(1 + x)/sqrt(3)), -(3/2))]
    @test_int [1/(sqrt(1 + x)*sqrt(2 - x)*sqrt(3 - x)), x, 1, Elliptic.F(asin(sqrt(1 + x)/sqrt(3)), 3/4)]

    @test_int [1/(sqrt(1 - x)*sqrt(2 + x)*sqrt(3 + x)), x, 1, 2*Elliptic.F(asin(sqrt(2 + x)/sqrt(3)), -3)]
    @test_int [1/(sqrt(1 - x)*sqrt(2 + x)*sqrt(3 - x)), x, 1, (2*Elliptic.F(asin(sqrt(2 + x)/sqrt(3)), 3/5))/sqrt(5)]
    @test_int [1/(sqrt(1 - x)*sqrt(2 - x)*sqrt(3 + x)), x, 1, (2*Elliptic.F(asin(sqrt(3 + x)/2), 4/5))/sqrt(5)]
    @test_int [1/(sqrt(1 - x)*sqrt(2 - x)*sqrt(3 - x)), x, 1, 2*Elliptic.F(asin(1/sqrt(3 - x)), 2)]

    @test_int [1/(sqrt(-1 + x)*sqrt(-2 + x)*sqrt(-3 + x)), x, 1, -2*Elliptic.F(asin(1/sqrt(-1 + x)), 2)]
    @test_int [1/(sqrt(-1 + x)*sqrt(-2 + x)*sqrt(-3 - x)), x, 2, -((sqrt(3 + x)*Elliptic.F(asin(2/sqrt(3 + x)), 5/4))/sqrt(-3 - x)) - (im*sqrt(3 + x)*Elliptic.K(-(1/4)))/sqrt(-3 - x), -((sqrt(3 + x)*Elliptic.F(asin(1/sqrt(3/4 + x/4)), 5/4))/sqrt(-3 - x))]
    @test_int [1/(sqrt(-1 + x)*sqrt(-2 - x)*sqrt(-3 + x)), x, 2, -((2*sqrt(2 + x)*Elliptic.F(asin(1/sqrt(2/3 + x/3)), 5/3))/(sqrt(3)*sqrt(-2 - x)))]
    @test_int [1/(sqrt(-1 + x)*sqrt(-2 - x)*sqrt(-3 - x)), x, 3, -((sqrt(2 + x)*sqrt(3 + x)*Elliptic.F(asin(2/sqrt(3 + x)), 1/4))/(sqrt(-3 - x)*sqrt(-2 - x))) + (sqrt(3 + x)*Elliptic.K(3/4))/sqrt(-3 - x) - (2*im*sqrt(2 + x)*Elliptic.K(4))/sqrt(-2 - x), -((sqrt(2 + x)*sqrt(3 + x)*Elliptic.F(asin(1/sqrt(3/4 + x/4)), 1/4))/(sqrt(-3 - x)*sqrt(-2 - x)))]

    @test_int [1/(sqrt(-1 - x)*sqrt(-2 + x)*sqrt(-3 + x)), x, 2, -((2*sqrt(1 + x)*Elliptic.F(asin(1/sqrt(1/3 + x/3)), 4/3))/(sqrt(3)*sqrt(-1 - x)))]
    @test_int [1/(sqrt(-1 - x)*sqrt(-2 + x)*sqrt(-3 - x)), x, 3, -((2*sqrt(1 + x)*sqrt(3 + x)*Elliptic.F(asin(1/sqrt(3/5 + x/5)), 2/5))/(sqrt(5)*sqrt(-3 - x)*sqrt(-1 - x)))]
    @test_int [1/(sqrt(-1 - x)*sqrt(-2 - x)*sqrt(-3 + x)), x, 3, -((2*sqrt(1 + x)*sqrt(2 + x)*Elliptic.F(asin(1/sqrt(2/5 + x/5)), 1/5))/(sqrt(5)*sqrt(-2 - x)*sqrt(-1 - x)))]
    @test_int [1/(sqrt(-1 - x)*sqrt(-2 - x)*sqrt(-3 - x)), x, 1, 2*Elliptic.F(asin(1/sqrt(-1 - x)), 2)]

    @test_int [1/((a + b*x)^(3/2)*sqrt(c + d*x)*sqrt(e + f*x)), x, 4, -((2*b*sqrt(c + d*x)*sqrt(e + f*x))/((b*c - a*d)*(b*e - a*f)*sqrt(a + b*x))) + (2*sqrt(f)*sqrt((-d)*e + c*f)*sqrt(a + b*x)*sqrt((d*(e + f*x))/(d*e - c*f))*Elliptic.E(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), -((b*(d*e - c*f))/((b*c - a*d)*f))))/((b*c - a*d)*(b*e - a*f)*sqrt(-((d*(a + b*x))/(b*c - a*d)))*sqrt(e + f*x))]
    @test_int [1/((a + b*x)^(5/2)*sqrt(c + d*x)*sqrt(e + f*x)), x, 8, -((2*b*sqrt(c + d*x)*sqrt(e + f*x))/(3*(b*c - a*d)*(b*e - a*f)*(a + b*x)^(3/2))) + (4*b*(b*d*e + b*c*f - 2*a*d*f)*sqrt(c + d*x)*sqrt(e + f*x))/(3*(b*c - a*d)^2*(b*e - a*f)^2*sqrt(a + b*x)) - (4*sqrt(d)*(b*d*e + b*c*f - 2*a*d*f)*sqrt((b*(c + d*x))/(b*c - a*d))*sqrt(e + f*x)*Elliptic.E(asin((sqrt(d)*sqrt(a + b*x))/sqrt((-b)*c + a*d)), ((b*c - a*d)*f)/(d*(b*e - a*f))))/(3*((-b)*c + a*d)^(3/2)*(b*e - a*f)^2*sqrt(c + d*x)*sqrt((b*(e + f*x))/(b*e - a*f))) + (2*sqrt(d)*(2*b*d*e + b*c*f - 3*a*d*f)*sqrt((b*(c + d*x))/(b*c - a*d))*sqrt((b*(e + f*x))/(b*e - a*f))*Elliptic.F(asin((sqrt(d)*sqrt(a + b*x))/sqrt((-b)*c + a*d)), ((b*c - a*d)*f)/(d*(b*e - a*f))))/(3*b*((-b)*c + a*d)^(3/2)*(b*e - a*f)*sqrt(c + d*x)*sqrt(e + f*x))]

    @test_int [(2 + 3*x)^(7/2)/(sqrt(1 - 2*x)*sqrt(3 + 5*x)), x, 6, (-15553*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/8750 - (333*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/875 - (3*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/35 - (270248*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/21875 - (178879*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(43750*sqrt(33))]
    @test_int [(2 + 3*x)^(5/2)/(sqrt(1 - 2*x)*sqrt(3 + 5*x)), x, 5, (-74*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/125 - (3*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/25 - (5161*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1250 - (857*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(625*sqrt(33))]
    @test_int [(2 + 3*x)^(3/2)/(sqrt(1 - 2*x)*sqrt(3 + 5*x)), x, 4, -(sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/5 - (37*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/25 - (13*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(25*sqrt(33))]
    @test_int [sqrt(2 + 3*x)/(sqrt(1 - 2*x)*sqrt(3 + 5*x)), x, 1, -(sqrt(7/5)*Elliptic.E(asin(sqrt(5/11)*sqrt(1 - 2*x)), 33/35))]
    @test_int [1/(sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x)), x, 1, (-2*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/sqrt(33)]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)), x, 3, (6*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(7*sqrt(2 + 3*x)) - 2*sqrt(5/7)*Elliptic.E(asin(sqrt(5/11)*sqrt(1 - 2*x)), 33/35)]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x)), x, 5, (2*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(7*(2 + 3*x)^(3/2)) + (148*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(49*sqrt(2 + 3*x)) - (148*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/49 - (52*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(49*sqrt(33))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^(7/2)*sqrt(3 + 5*x)), x, 6, (6*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(35*(2 + 3*x)^(5/2)) + (296*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(245*(2 + 3*x)^(3/2)) + (20644*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1715*sqrt(2 + 3*x)) - (20644*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1715 - (6856*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1715*sqrt(33))]

    @test_int [(2 + 3*x)^(7/2)/(sqrt(1 - 2*x)*(3 + 5*x)^(3/2)), x, 6, (-2*sqrt(1 - 2*x)*(2 + 3*x)^(5/2))/(55*sqrt(3 + 5*x)) - (2577*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/6875 - (69*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/1375 - (61151*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/6250 - (942*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3125]
    @test_int [(2 + 3*x)^(5/2)/(sqrt(1 - 2*x)*(3 + 5*x)^(3/2)), x, 5, (-2*sqrt(1 - 2*x)*(2 + 3*x)^(3/2))/(55*sqrt(3 + 5*x)) - (27*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/275 - (438*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/125 - (17*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/125]
    @test_int [(2 + 3*x)^(3/2)/(sqrt(1 - 2*x)*(3 + 5*x)^(3/2)), x, 4, (-2*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(55*sqrt(3 + 5*x)) - (31*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/25 - (4*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/25]
    @test_int [sqrt(2 + 3*x)/(sqrt(1 - 2*x)*(3 + 5*x)^(3/2)), x, 4, (-2*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(11*sqrt(3 + 5*x)) + (2*sqrt(7/5)*sqrt(-3 - 5*x)*Elliptic.E(asin(sqrt(5)*sqrt(2 + 3*x)), 2/35))/(11*sqrt(3 + 5*x))]
    @test_int [1/(sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)), x, 3, (-10*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(11*sqrt(3 + 5*x)) + 2*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33)]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)), x, 5, (6*sqrt(1 - 2*x))/(7*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (680*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(77*sqrt(3 + 5*x)) + (136*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/7 + (4*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/7]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)), x, 6, (2*sqrt(1 - 2*x))/(7*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + (288*sqrt(1 - 2*x))/(49*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (31940*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(539*sqrt(3 + 5*x)) + (6388*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/49 + (192*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/49]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)), x, 7, (6*sqrt(1 - 2*x))/(35*(2 + 3*x)^(5/2)*sqrt(3 + 5*x)) + (436*sqrt(1 - 2*x))/(245*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + (60684*sqrt(1 - 2*x))/(1715*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (1344984*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3773*sqrt(3 + 5*x)) + (1344984*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1715 + (40456*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1715]

    @test_int [(2 + 3*x)^(9/2)/(sqrt(1 - 2*x)*(3 + 5*x)^(5/2)), x, 7, (-2*sqrt(1 - 2*x)*(2 + 3*x)^(7/2))/(165*(3 + 5*x)^(3/2)) - (668*sqrt(1 - 2*x)*(2 + 3*x)^(5/2))/(9075*sqrt(3 + 5*x)) - (87476*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/378125 + (403*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/75625 - (6515539*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(343750*sqrt(33)) - (104663*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(171875*sqrt(33))]
    @test_int [(2 + 3*x)^(7/2)/(sqrt(1 - 2*x)*(3 + 5*x)^(5/2)), x, 6, (-2*sqrt(1 - 2*x)*(2 + 3*x)^(5/2))/(165*(3 + 5*x)^(3/2)) - (536*sqrt(1 - 2*x)*(2 + 3*x)^(3/2))/(9075*sqrt(3 + 5*x)) - (487*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/15125 - (46159*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(6875*sqrt(33)) - (2281*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(6875*sqrt(33))]
    @test_int [(2 + 3*x)^(5/2)/(sqrt(1 - 2*x)*(3 + 5*x)^(5/2)), x, 5, (-2*sqrt(1 - 2*x)*(2 + 3*x)^(3/2))/(165*(3 + 5*x)^(3/2)) - (404*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(9075*sqrt(3 + 5*x)) - (2797*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1375*sqrt(33)) - (598*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1375*sqrt(33))]
    @test_int [(2 + 3*x)^(3/2)/(sqrt(1 - 2*x)*(3 + 5*x)^(5/2)), x, 5, (-2*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(165*(3 + 5*x)^(3/2)) - (272*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(1815*sqrt(3 + 5*x)) + (272*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(275*sqrt(33)) - (202*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(275*sqrt(33))]
    @test_int [sqrt(2 + 3*x)/(sqrt(1 - 2*x)*(3 + 5*x)^(5/2)), x, 5, (-2*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(33*(3 + 5*x)^(3/2)) - (74*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(363*sqrt(3 + 5*x)) + (74*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(55*sqrt(33)) - (4*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(55*sqrt(33))]
    @test_int [1/(sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2)), x, 5, (-10*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(33*(3 + 5*x)^(3/2)) + (620*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(363*sqrt(3 + 5*x)) - (124*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(11*sqrt(33)) - (4*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(11*sqrt(33))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)), x, 6, (6*sqrt(1 - 2*x))/(7*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (1340*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(231*(3 + 5*x)^(3/2)) + (89020*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(2541*sqrt(3 + 5*x)) - (17804*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(77*sqrt(33)) - (536*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(77*sqrt(33))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)), x, 7, (2*sqrt(1 - 2*x))/(7*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (428*sqrt(1 - 2*x))/(49*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (94420*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(1617*(3 + 5*x)^(3/2)) + (6277760*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(17787*sqrt(3 + 5*x)) - (1255552*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(539*sqrt(33)) - (37768*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(539*sqrt(33))]
    @test_int [1/(sqrt(1 - 2*x)*(2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)), x, 8, (6*sqrt(1 - 2*x))/(35*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + (576*sqrt(1 - 2*x))/(245*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (120324*sqrt(1 - 2*x))/(1715*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (5307272*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(11319*(3 + 5*x)^(3/2)) + (352875016*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(124509*sqrt(3 + 5*x)) - (352875016*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(18865*sqrt(33)) - (10614544*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(18865*sqrt(33))]

    #= Resulted*in*infinite*recursion*for*Rubi*versions*prior*to*4.5.0. =#
    @test_int [sqrt(x)/(sqrt(a + 2*x)*sqrt(c + 2*x)), x, 3, (sqrt(a - c)*sqrt(x)*sqrt(-((c + 2*x)/(a - c)))*Elliptic.E(asin(sqrt(a + 2*x)/sqrt(a - c)), 1 - c/a))/(sqrt(2)*sqrt(-(x/a))*sqrt(c + 2*x))]

    #= Following*integrands*are*equal. =#
    @test_int [1/(sqrt(4 - x)*sqrt(5 - x)*sqrt(-3 + x)), x, 1, sqrt(2)*Elliptic.F(asin(sqrt(-3 + x)), 1/2)]
    @test_int [1/(sqrt(4 - x)*sqrt((5 - x)*(-3 + x))), x, 3, -2*Elliptic.F(asin(sqrt(4 - x)), -1)]
    @test_int [1/(sqrt(4 - x)*sqrt(-15 + 8*x - x^2)), x, 2, -2*Elliptic.F(asin(sqrt(4 - x)), -1)]

    #= Following*integrands*are*equal. =#
    @test_int [1/(sqrt(6 - x)*sqrt(-2 + x)*sqrt(-1 + x)), x, 1, 2*Elliptic.F(asin(sqrt(-2 + x)/2), -4)]
    @test_int [1/(sqrt((6 - x)*(-2 + x))*sqrt(-1 + x)), x, 3, -((2*Elliptic.F(asin(sqrt(6 - x)/2), 4/5))/sqrt(5))]
    @test_int [1/(sqrt(-1 + x)*sqrt(-12 + 8*x - x^2)), x, 2, -((2*Elliptic.F(asin(sqrt(6 - x)/2), 4/5))/sqrt(5))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^(m/2)*(c+d*x)^(n/2) / (e+f*x)^(3/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [((2 + 3*x)^(7/2)*sqrt(3 + 5*x))/(1 - 2*x)^(3/2), x, 7, (29293*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/875 + (2517*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/350 + (12*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/7 + ((2 + 3*x)^(7/2)*sqrt(3 + 5*x))/sqrt(1 - 2*x) + (4071079*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/17500 + (673523*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(8750*sqrt(33))]
    @test_int [((2 + 3*x)^(5/2)*sqrt(3 + 5*x))/(1 - 2*x)^(3/2), x, 6, (419*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/50 + (9*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/5 + ((2 + 3*x)^(5/2)*sqrt(3 + 5*x))/sqrt(1 - 2*x) + (7279*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/125 + (4817*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(250*sqrt(33))]
    @test_int [((2 + 3*x)^(3/2)*sqrt(3 + 5*x))/(1 - 2*x)^(3/2), x, 5, 2*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x) + ((2 + 3*x)^(3/2)*sqrt(3 + 5*x))/sqrt(1 - 2*x) + (139*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/10 + (23*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(5*sqrt(33))]
    @test_int [(sqrt(2 + 3*x)*sqrt(3 + 5*x))/(1 - 2*x)^(3/2), x, 4, (sqrt(2 + 3*x)*sqrt(3 + 5*x))/sqrt(1 - 2*x) + sqrt(33)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33) + Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33)/sqrt(33)]
    @test_int [sqrt(3 + 5*x)/((1 - 2*x)^(3/2)*sqrt(2 + 3*x)), x, 3, (2*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)) + sqrt(5/7)*Elliptic.E(asin(sqrt(5/11)*sqrt(1 - 2*x)), 33/35)]
    @test_int [sqrt(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)), x, 5, (2*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)*sqrt(2 + 3*x)) - (12*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(49*sqrt(2 + 3*x)) + (4*sqrt(33)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/49 - (62*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(49*sqrt(33))]
    @test_int [sqrt(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)), x, 6, (2*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)) - (8*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(49*(2 + 3*x)^(3/2)) + (38*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(343*sqrt(2 + 3*x)) - (38*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/343 - (212*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(343*sqrt(33))]
    @test_int [sqrt(3 + 5*x)/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)), x, 7, (2*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)) - (36*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(245*(2 + 3*x)^(5/2)) - (26*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1715*(2 + 3*x)^(3/2)) + (5636*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(12005*sqrt(2 + 3*x)) - (5636*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/12005 - (4364*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(12005*sqrt(33))]

    @test_int [((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2), x, 8, (6770629*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/31500 + (24358*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/875 + (1397*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/210 + (5*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/3 + ((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2))/sqrt(1 - 2*x) + (112543103*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/78750 + (6770629*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/157500]
    @test_int [((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2), x, 7, (9694*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/175 + (2511*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/350 + (12*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/7 + ((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/sqrt(1 - 2*x) + (1289089*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3500 + (9694*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/875]
    @test_int [((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2), x, 6, (139*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/10 + (9*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/5 + ((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/sqrt(1 - 2*x) + (4621*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/50 + (139*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/50]
    @test_int [(sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2), x, 5, (10*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/3 + (sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/sqrt(1 - 2*x) + (133*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/6 + (2*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*sqrt(2 + 3*x)), x, 4, (11*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)) + (34*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/7 + (sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/7]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)), x, 5, (11*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)*sqrt(2 + 3*x)) - (31*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(49*sqrt(2 + 3*x)) + (31*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/49 + (4*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/49]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)), x, 6, (11*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)) - (97*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(147*(2 + 3*x)^(3/2)) - (458*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1029*sqrt(2 + 3*x)) + (458*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1029 - (178*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1029]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)), x, 7, (11*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)) - (163*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(245*(2 + 3*x)^(5/2)) - (458*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1715*(2 + 3*x)^(3/2)) + (338*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(12005*sqrt(2 + 3*x)) - (338*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/12005 - (992*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/12005]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(9/2)), x, 8, (11*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)*(2 + 3*x)^(7/2)) - (229*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(343*(2 + 3*x)^(7/2)) - (2818*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(12005*(2 + 3*x)^(5/2)) - (5438*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(84035*(2 + 3*x)^(3/2)) + (189368*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(588245*sqrt(2 + 3*x)) - (189368*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/588245 - (23012*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/588245]

    @test_int [((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2), x, 9, (269045681*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/207900 + (4066493*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/23100 + (9741*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/385 + (419*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/66 + (18*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/11 + ((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2))/sqrt(1 - 2*x) + (17888580643*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(189000*sqrt(33)) + (269045681*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(94500*sqrt(33))]
    @test_int [((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2), x, 8, (1284329*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/3780 + (4853*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/105 + (93*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/14 + (5*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/3 + ((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/sqrt(1 - 2*x) + (42696881*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/18900 + (1284329*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/18900]
    @test_int [((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2), x, 7, (3683*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/42 + (167*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/14 + (12*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/7 + ((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/sqrt(1 - 2*x) + (244879*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/420 + (3683*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/210]
    @test_int [(sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2), x, 6, (397*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/18 + 3*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2) + (sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/sqrt(1 - 2*x) + (6599*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/45 + (397*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/90]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*sqrt(2 + 3*x)), x, 5, (335*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/63 + (11*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/(7*sqrt(1 - 2*x)) + (4451*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/126 + (67*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/63]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)), x, 5, (31*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(147*sqrt(2 + 3*x)) + (11*(3 + 5*x)^(3/2))/(7*sqrt(1 - 2*x)*sqrt(2 + 3*x)) + (1159*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/147 + (31*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/147]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)), x, 6, (97*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(441*(2 + 3*x)^(3/2)) - (2797*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3087*sqrt(2 + 3*x)) + (11*(3 + 5*x)^(3/2))/(7*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)) + (2797*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3087 + (598*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3087]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)), x, 7, (163*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(735*(2 + 3*x)^(5/2)) - (15601*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(15435*(2 + 3*x)^(3/2)) - (81164*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(108045*sqrt(2 + 3*x)) + (11*(3 + 5*x)^(3/2))/(7*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)) + (81164*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/108045 - (28174*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/108045]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(9/2)), x, 8, (229*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1029*(2 + 3*x)^(7/2)) - (37117*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(36015*(2 + 3*x)^(5/2)) - (106772*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(252105*(2 + 3*x)^(3/2)) - (106558*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1764735*sqrt(2 + 3*x)) + (11*(3 + 5*x)^(3/2))/(7*sqrt(1 - 2*x)*(2 + 3*x)^(7/2)) + (106558*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1764735 - (220028*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1764735]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(3/2)*(2 + 3*x)^(11/2)), x, 9, (295*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1323*(2 + 3*x)^(9/2)) - (67345*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(64827*(2 + 3*x)^(7/2)) - (167228*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(453789*(2 + 3*x)^(5/2)) - (392998*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3176523*(2 + 3*x)^(3/2)) + (6036028*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(22235661*sqrt(2 + 3*x)) + (11*(3 + 5*x)^(3/2))/(7*sqrt(1 - 2*x)*(2 + 3*x)^(9/2)) - (6036028*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/22235661 - (1199452*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/22235661]

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(2 + 3*x)^(7/2)/((1 - 2*x)^(3/2)*sqrt(3 + 5*x)), x, 6, (14517*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/2750 + (312*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/275 + (7*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/(11*sqrt(1 - 2*x)) + (168123*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1250 + (5057*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1250]
    @test_int [(2 + 3*x)^(5/2)/((1 - 2*x)^(3/2)*sqrt(3 + 5*x)), x, 5, (69*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/55 + (7*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/(11*sqrt(1 - 2*x)) + (1597*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/50 + (24*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/25]
    @test_int [(2 + 3*x)^(3/2)/((1 - 2*x)^(3/2)*sqrt(3 + 5*x)), x, 4, (7*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(11*sqrt(1 - 2*x)) + (34*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5 + (sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5]
    @test_int [sqrt(2 + 3*x)/((1 - 2*x)^(3/2)*sqrt(3 + 5*x)), x, 3, (2*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(11*sqrt(1 - 2*x)) + sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33)]
    @test_int [1/((1 - 2*x)^(3/2)*sqrt(2 + 3*x)*sqrt(3 + 5*x)), x, 4, (4*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(77*sqrt(1 - 2*x)) + (2*sqrt(5/7)*sqrt(-3 - 5*x)*Elliptic.E(asin(sqrt(5)*sqrt(2 + 3*x)), 2/35))/(11*sqrt(3 + 5*x))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)), x, 5, (4*sqrt(3 + 5*x))/(77*sqrt(1 - 2*x)*sqrt(2 + 3*x)) + (186*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(539*sqrt(2 + 3*x)) - (62*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/49 - (8*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/49]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x)), x, 6, (4*sqrt(3 + 5*x))/(77*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)) + (54*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(539*(2 + 3*x)^(3/2)) + (5256*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3773*sqrt(2 + 3*x)) - (1752*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/343 - (68*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/343]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)*sqrt(3 + 5*x)), x, 7, (4*sqrt(3 + 5*x))/(77*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)) + (138*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2695*(2 + 3*x)^(5/2)) + (10308*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(18865*(2 + 3*x)^(3/2)) + (733812*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(132055*sqrt(2 + 3*x)) - (244604*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/12005 - (7536*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/12005]

    @test_int [(2 + 3*x)^(9/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)), x, 7, (-37*sqrt(1 - 2*x)*(2 + 3*x)^(5/2))/(605*sqrt(3 + 5*x)) + (7*(2 + 3*x)^(7/2))/(11*sqrt(1 - 2*x)*sqrt(3 + 5*x)) + (502941*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/151250 + (10851*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/15125 + (2911577*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/34375 + (175111*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/68750]
    @test_int [(2 + 3*x)^(7/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)), x, 6, (-37*sqrt(1 - 2*x)*(2 + 3*x)^(3/2))/(605*sqrt(3 + 5*x)) + (7*(2 + 3*x)^(5/2))/(11*sqrt(1 - 2*x)*sqrt(3 + 5*x)) + (2388*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/3025 + (55019*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/2750 + (823*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/1375]
    @test_int [(2 + 3*x)^(5/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)), x, 5, (-37*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(605*sqrt(3 + 5*x)) + (7*(2 + 3*x)^(3/2))/(11*sqrt(1 - 2*x)*sqrt(3 + 5*x)) + (1159*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/275 + (31*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/275]
    @test_int [(2 + 3*x)^(3/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)), x, 5, (7*sqrt(2 + 3*x))/(11*sqrt(1 - 2*x)*sqrt(3 + 5*x)) - (37*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(121*sqrt(3 + 5*x)) + (37*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/55 - (2*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/55]
    @test_int [sqrt(2 + 3*x)/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)), x, 5, (2*sqrt(2 + 3*x))/(11*sqrt(1 - 2*x)*sqrt(3 + 5*x)) - (20*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(121*sqrt(3 + 5*x)) + (4*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/11 - (2*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/11]
    @test_int [1/((1 - 2*x)^(3/2)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)), x, 5, (4*sqrt(2 + 3*x))/(77*sqrt(1 - 2*x)*sqrt(3 + 5*x)) - (370*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(847*sqrt(3 + 5*x)) + (74*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/77 - (4*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/77]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)), x, 6, 4/(77*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x)) + (186*sqrt(1 - 2*x))/(539*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (23180*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(5929*sqrt(3 + 5*x)) + (4636*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/539 + (124*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/539]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)), x, 7, 4/(77*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + (54*sqrt(1 - 2*x))/(539*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + (9876*sqrt(1 - 2*x))/(3773*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (1100380*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(41503*sqrt(3 + 5*x)) + (220076*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3773 + (6584*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3773]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)), x, 8, 4/(77*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x)) + (138*sqrt(1 - 2*x))/(2695*(2 + 3*x)^(5/2)*sqrt(3 + 5*x)) + (14928*sqrt(1 - 2*x))/(18865*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + (2101332*sqrt(1 - 2*x))/(132055*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (46585232*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(290521*sqrt(3 + 5*x)) + (46585232*sqrt(3/11)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/132055 + (1400888*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/132055]

    @test_int [(2 + 3*x)^(11/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)), x, 8, (-107*sqrt(1 - 2*x)*(2 + 3*x)^(7/2))/(1815*(3 + 5*x)^(3/2)) + (7*(2 + 3*x)^(9/2))/(11*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (4553*sqrt(1 - 2*x)*(2 + 3*x)^(5/2))/(99825*sqrt(3 + 5*x)) + (17427983*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/8318750 + (380188*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/831875 + (604915631*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(3781250*sqrt(33)) + (18177329*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(3781250*sqrt(33))]
    @test_int [(2 + 3*x)^(9/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)), x, 7, (-107*sqrt(1 - 2*x)*(2 + 3*x)^(5/2))/(1815*(3 + 5*x)^(3/2)) + (7*(2 + 3*x)^(7/2))/(11*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (4421*sqrt(1 - 2*x)*(2 + 3*x)^(3/2))/(99825*sqrt(3 + 5*x)) + (83093*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/166375 + (5684677*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(151250*sqrt(33)) + (84134*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(75625*sqrt(33))]
    @test_int [(2 + 3*x)^(7/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)), x, 6, (-107*sqrt(1 - 2*x)*(2 + 3*x)^(3/2))/(1815*(3 + 5*x)^(3/2)) + (7*(2 + 3*x)^(5/2))/(11*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (4289*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(99825*sqrt(3 + 5*x)) + (118898*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(15125*sqrt(33)) + (2657*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(15125*sqrt(33))]
    @test_int [(2 + 3*x)^(5/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)), x, 6, (-107*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(1815*(3 + 5*x)^(3/2)) + (7*(2 + 3*x)^(3/2))/(11*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (4157*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(19965*sqrt(3 + 5*x)) + (4157*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(3025*sqrt(33)) - (412*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(3025*sqrt(33))]
    @test_int [(2 + 3*x)^(3/2)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)), x, 6, (7*sqrt(2 + 3*x))/(11*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (107*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(363*(3 + 5*x)^(3/2)) - (494*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3993*sqrt(3 + 5*x)) + (494*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(605*sqrt(33)) - (214*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(605*sqrt(33))]
    @test_int [sqrt(2 + 3*x)/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)), x, 6, (2*sqrt(2 + 3*x))/(11*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (40*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(363*(3 + 5*x)^(3/2)) - (490*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3993*sqrt(3 + 5*x)) + (98*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(121*sqrt(33)) - (16*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(121*sqrt(33))]
    @test_int [1/((1 - 2*x)^(3/2)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2)), x, 6, (4*sqrt(2 + 3*x))/(77*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (410*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(2541*(3 + 5*x)^(3/2)) + (19480*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(27951*sqrt(3 + 5*x)) - (3896*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(847*sqrt(33)) - (164*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(847*sqrt(33))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)), x, 7, 4/(77*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) + (186*sqrt(1 - 2*x))/(539*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (45040*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(17787*(3 + 5*x)^(3/2)) + (2976620*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(195657*sqrt(3 + 5*x)) - (595324*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(5929*sqrt(33)) - (18016*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(5929*sqrt(33))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)), x, 8, 4/(77*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (54*sqrt(1 - 2*x))/(539*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (14496*sqrt(1 - 2*x))/(3773*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (3205940*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(124509*(3 + 5*x)^(3/2)) + (213119320*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(1369599*sqrt(3 + 5*x)) - (42623864*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(41503*sqrt(33)) - (1282376*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(41503*sqrt(33))]
    @test_int [1/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)), x, 9, 4/(77*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + (138*sqrt(1 - 2*x))/(2695*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + (19548*sqrt(1 - 2*x))/(18865*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (4115652*sqrt(1 - 2*x))/(132055*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (181551856*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(871563*(3 + 5*x)^(3/2)) + (12071114168*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(9587193*sqrt(3 + 5*x)) - (12071114168*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1452605*sqrt(33)) - (363103712*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1452605*sqrt(33))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^(m/2)*(c+d*x)^(n/2) / (e+f*x)^(5/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [((2 + 3*x)^(9/2)*sqrt(3 + 5*x))/(1 - 2*x)^(5/2), x, 8, (-6478333*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/38500 - (139163*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/3850 - (1327*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/154 - (166*(2 + 3*x)^(7/2)*sqrt(3 + 5*x))/(33*sqrt(1 - 2*x)) + ((2 + 3*x)^(9/2)*sqrt(3 + 5*x))/(3*(1 - 2*x)^(3/2)) - (112543103*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(8750*sqrt(33)) - (6770629*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(17500*sqrt(33))]
    @test_int [((2 + 3*x)^(7/2)*sqrt(3 + 5*x))/(1 - 2*x)^(5/2), x, 7, (-18551*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/550 - (797*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/110 - (133*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/(33*sqrt(1 - 2*x)) + ((2 + 3*x)^(7/2)*sqrt(3 + 5*x))/(3*(1 - 2*x)^(3/2)) - (1289089*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(500*sqrt(33)) - (9694*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(125*sqrt(33))]
    @test_int [((2 + 3*x)^(5/2)*sqrt(3 + 5*x))/(1 - 2*x)^(5/2), x, 6, (-133*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/22 - (100*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/(33*sqrt(1 - 2*x)) + ((2 + 3*x)^(5/2)*sqrt(3 + 5*x))/(3*(1 - 2*x)^(3/2)) - (4621*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(10*sqrt(33)) - (139*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(10*sqrt(33))]
    @test_int [((2 + 3*x)^(3/2)*sqrt(3 + 5*x))/(1 - 2*x)^(5/2), x, 5, (-67*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(33*sqrt(1 - 2*x)) + ((2 + 3*x)^(3/2)*sqrt(3 + 5*x))/(3*(1 - 2*x)^(3/2)) - (133*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(2*sqrt(33)) - (2*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/sqrt(33)]
    @test_int [(sqrt(2 + 3*x)*sqrt(3 + 5*x))/(1 - 2*x)^(5/2), x, 5, (sqrt(2 + 3*x)*sqrt(3 + 5*x))/(3*(1 - 2*x)^(3/2)) - (68*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(231*sqrt(1 - 2*x)) - (34*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(7*sqrt(33)) - Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33)/(7*sqrt(33))]
    @test_int [sqrt(3 + 5*x)/((1 - 2*x)^(5/2)*sqrt(2 + 3*x)), x, 5, (2*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(21*(1 - 2*x)^(3/2)) + (62*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(1617*sqrt(1 - 2*x)) + (31*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(49*sqrt(33)) + (4*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(49*sqrt(33))]
    @test_int [sqrt(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)), x, 6, (2*sqrt(3 + 5*x))/(21*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)) + (194*sqrt(3 + 5*x))/(1617*sqrt(1 - 2*x)*sqrt(2 + 3*x)) - (458*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3773*sqrt(2 + 3*x)) + (458*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(343*sqrt(33)) - (178*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(343*sqrt(33))]
    @test_int [sqrt(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)), x, 7, (2*sqrt(3 + 5*x))/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)) + (326*sqrt(3 + 5*x))/(1617*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)) - (458*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(3773*(2 + 3*x)^(3/2)) + (338*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(26411*sqrt(2 + 3*x)) - (338*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(2401*sqrt(33)) - (992*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(2401*sqrt(33))]
    @test_int [sqrt(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)), x, 8, (2*sqrt(3 + 5*x))/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)) + (458*sqrt(3 + 5*x))/(1617*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)) - (2818*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(18865*(2 + 3*x)^(5/2)) - (5438*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(132055*(2 + 3*x)^(3/2)) + (189368*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(924385*sqrt(2 + 3*x)) - (189368*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(84035*sqrt(33)) - (2092*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/84035]

    @test_int [((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2), x, 8, (-2166399*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/7700 - (140289*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/3850 - (1341*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/154 - (56*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/(11*sqrt(1 - 2*x)) + ((2 + 3*x)^(7/2)*(3 + 5*x)^(3/2))/(3*(1 - 2*x)^(3/2)) - (6547351*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3500 - (722133*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3500]
    @test_int [((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2), x, 7, (-6231*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/110 - (807*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/110 - (45*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/(11*sqrt(1 - 2*x)) + ((2 + 3*x)^(5/2)*(3 + 5*x)^(3/2))/(3*(1 - 2*x)^(3/2)) - (37663*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/100 - (2077*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/50]
    @test_int [((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2), x, 6, (-225*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/22 - (34*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/(11*sqrt(1 - 2*x)) + ((2 + 3*x)^(3/2)*(3 + 5*x)^(3/2))/(3*(1 - 2*x)^(3/2)) - 68*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33) - (15*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/2]
    @test_int [(sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/(1 - 2*x)^(5/2), x, 5, (-23*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(7*sqrt(1 - 2*x)) + (sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/(3*(1 - 2*x)^(3/2)) - (139*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/14 - (23*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(7*sqrt(33))]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*sqrt(2 + 3*x)), x, 5, (11*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(21*(1 - 2*x)^(3/2)) - (74*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(147*sqrt(1 - 2*x)) - (37*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/49 - (13*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(49*sqrt(33))]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)), x, 6, (11*sqrt(3 + 5*x))/(21*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)) - (8*sqrt(3 + 5*x))/(147*sqrt(1 - 2*x)*sqrt(2 + 3*x)) - (19*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(343*sqrt(2 + 3*x)) + (19*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/343 + (106*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(343*sqrt(33))]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)), x, 7, (11*sqrt(3 + 5*x))/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)) + (58*sqrt(3 + 5*x))/(147*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)) - (89*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(343*(2 + 3*x)^(3/2)) - (496*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2401*sqrt(2 + 3*x)) + (496*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/2401 - (582*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/2401]
    @test_int [(3 + 5*x)^(3/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)), x, 8, (11*sqrt(3 + 5*x))/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)) + (124*sqrt(3 + 5*x))/(147*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)) - (779*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1715*(2 + 3*x)^(5/2)) - (2264*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(12005*(2 + 3*x)^(3/2)) - (3946*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(84035*sqrt(2 + 3*x)) + (3946*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/84035 - (16732*sqrt(3/11)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/84035]

    @test_int [((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2), x, 9, (-1313411*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/630 - (1310203*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/4620 - (6277*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/154 - (225*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/22 - (203*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/(33*sqrt(1 - 2*x)) + ((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2))/(3*(1 - 2*x)^(3/2)) - (174654791*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/12600 - (1313411*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/3150]
    @test_int [((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2), x, 8, (-12601*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/28 - (28283*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/462 - (1355*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/154 - (170*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/(33*sqrt(1 - 2*x)) + ((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/(3*(1 - 2*x)^(3/2)) - (69819*sqrt(33)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/70 - (12601*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/140]
    @test_int [((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2), x, 7, -91*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x) - (817*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/66 - (137*sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/(33*sqrt(1 - 2*x)) + ((2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/(3*(1 - 2*x)^(3/2)) - (12101*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/20 - (91*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/5]
    @test_int [(sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/(1 - 2*x)^(5/2), x, 6, (-695*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/42 - (104*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/(21*sqrt(1 - 2*x)) + (sqrt(2 + 3*x)*(3 + 5*x)^(5/2))/(3*(1 - 2*x)^(3/2)) - (4621*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/42 - (139*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/42]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*sqrt(2 + 3*x)), x, 5, (-264*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(49*sqrt(1 - 2*x)) + (11*sqrt(2 + 3*x)*(3 + 5*x)^(3/2))/(21*(1 - 2*x)^(3/2)) - (1597*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/98 - (8*sqrt(33)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/49]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)), x, 6, (-143*sqrt(3 + 5*x))/(49*sqrt(1 - 2*x)*sqrt(2 + 3*x)) + (438*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(343*sqrt(2 + 3*x)) + (11*(3 + 5*x)^(3/2))/(21*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)) - (146*sqrt(33)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/343 - (17*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/343]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)), x, 7, (-22*sqrt(3 + 5*x))/(49*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)) + (229*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1029*(2 + 3*x)^(3/2)) - (169*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(7203*sqrt(2 + 3*x)) + (11*(3 + 5*x)^(3/2))/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)) + (169*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/7203 + (496*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/7203]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)), x, 8, (99*sqrt(3 + 5*x))/(49*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)) - (1432*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1715*(2 + 3*x)^(5/2)) - (4437*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(12005*(2 + 3*x)^(3/2)) - (27618*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(84035*sqrt(2 + 3*x)) + (11*(3 + 5*x)^(3/2))/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)) + (9206*sqrt(33)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/84035 - (7738*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/84035]
    @test_int [(3 + 5*x)^(5/2)/((1 - 2*x)^(5/2)*(2 + 3*x)^(9/2)), x, 9, (220*sqrt(3 + 5*x))/(49*sqrt(1 - 2*x)*(2 + 3*x)^(7/2)) - (4545*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(2401*(2 + 3*x)^(7/2)) - (11433*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(16807*(2 + 3*x)^(5/2)) - (33778*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(117649*(2 + 3*x)^(3/2)) - (98642*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(823543*sqrt(2 + 3*x)) + (11*(3 + 5*x)^(3/2))/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)) + (98642*sqrt(11/3)*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/823543 - (65672*sqrt(11/3)*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/823543]

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(2 + 3*x)^(9/2)/((1 - 2*x)^(5/2)*sqrt(3 + 5*x)), x, 7, (-317384*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/15125 - (27271*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/6050 - (910*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/(363*sqrt(1 - 2*x)) + (7*(2 + 3*x)^(7/2)*sqrt(3 + 5*x))/(33*(1 - 2*x)^(3/2)) - (44109377*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(27500*sqrt(33)) - (663409*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(13750*sqrt(33))]
    @test_int [(2 + 3*x)^(7/2)/((1 - 2*x)^(5/2)*sqrt(3 + 5*x)), x, 6, (-4517*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/1210 - (679*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/(363*sqrt(1 - 2*x)) + (7*(2 + 3*x)^(5/2)*sqrt(3 + 5*x))/(33*(1 - 2*x)^(3/2)) - (78472*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(275*sqrt(33)) - (4721*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(550*sqrt(33))]
    @test_int [(2 + 3*x)^(5/2)/((1 - 2*x)^(5/2)*sqrt(3 + 5*x)), x, 5, (-448*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(363*sqrt(1 - 2*x)) + (7*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/(33*(1 - 2*x)^(3/2)) - (4451*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(110*sqrt(33)) - (67*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(55*sqrt(33))]
    @test_int [(2 + 3*x)^(3/2)/((1 - 2*x)^(5/2)*sqrt(3 + 5*x)), x, 5, (7*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(33*(1 - 2*x)^(3/2)) - (62*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(363*sqrt(1 - 2*x)) - (31*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(11*sqrt(33)) - Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33)/(11*sqrt(33))]
    @test_int [sqrt(2 + 3*x)/((1 - 2*x)^(5/2)*sqrt(3 + 5*x)), x, 5, (2*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(33*(1 - 2*x)^(3/2)) + (74*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(2541*sqrt(1 - 2*x)) + (37*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(77*sqrt(33)) - (2*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(77*sqrt(33))]
    @test_int [1/((1 - 2*x)^(5/2)*sqrt(2 + 3*x)*sqrt(3 + 5*x)), x, 5, (4*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(231*(1 - 2*x)^(3/2)) + (544*sqrt(2 + 3*x)*sqrt(3 + 5*x))/(17787*sqrt(1 - 2*x)) + (272*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(539*sqrt(33)) - (202*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(539*sqrt(33))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)), x, 6, (4*sqrt(3 + 5*x))/(231*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)) + (808*sqrt(3 + 5*x))/(17787*sqrt(1 - 2*x)*sqrt(2 + 3*x)) + (5594*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(41503*sqrt(2 + 3*x)) - (5594*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(3773*sqrt(33)) - (1196*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(3773*sqrt(33))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x)), x, 7, (4*sqrt(3 + 5*x))/(231*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)) + (1072*sqrt(3 + 5*x))/(17787*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)) + (974*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(41503*(2 + 3*x)^(3/2)) + (184636*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(290521*sqrt(2 + 3*x)) - (184636*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(26411*sqrt(33)) - (9124*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(26411*sqrt(33))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)*sqrt(3 + 5*x)), x, 8, (4*sqrt(3 + 5*x))/(231*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)) + (1336*sqrt(3 + 5*x))/(17787*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)) - (806*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(207515*(2 + 3*x)^(5/2)) + (349904*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(1452605*(2 + 3*x)^(3/2)) + (26062156*sqrt(1 - 2*x)*sqrt(3 + 5*x))/(10168235*sqrt(2 + 3*x)) - (26062156*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(924385*sqrt(33)) - (837304*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(924385*sqrt(33))]

    @test_int [(2 + 3*x)^(11/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)), x, 8, (4439*sqrt(1 - 2*x)*(2 + 3*x)^(5/2))/(19965*sqrt(3 + 5*x)) - (896*(2 + 3*x)^(7/2))/(363*sqrt(1 - 2*x)*sqrt(3 + 5*x)) + (7*(2 + 3*x)^(9/2))/(33*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)) - (21713939*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/1663750 - (932783*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/332750 - (1508889271*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1512500*sqrt(33)) - (11346991*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(378125*sqrt(33))]
    @test_int [(2 + 3*x)^(9/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)), x, 7, (3284*sqrt(1 - 2*x)*(2 + 3*x)^(3/2))/(19965*sqrt(3 + 5*x)) - (665*(2 + 3*x)^(5/2))/(363*sqrt(1 - 2*x)*sqrt(3 + 5*x)) + (7*(2 + 3*x)^(7/2))/(33*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)) - (153319*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/66550 - (5327983*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(30250*sqrt(33)) - (160297*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(30250*sqrt(33))]
    @test_int [(2 + 3*x)^(7/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)), x, 6, (2129*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(19965*sqrt(3 + 5*x)) - (434*(2 + 3*x)^(3/2))/(363*sqrt(1 - 2*x)*sqrt(3 + 5*x)) + (7*(2 + 3*x)^(5/2))/(33*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)) - (148831*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(6050*sqrt(33)) - (2252*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(3025*sqrt(33))]
    @test_int [(2 + 3*x)^(5/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)), x, 6, (-203*sqrt(2 + 3*x))/(363*sqrt(1 - 2*x)*sqrt(3 + 5*x)) + (974*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3993*sqrt(3 + 5*x)) + (7*(2 + 3*x)^(3/2))/(33*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)) - (974*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(605*sqrt(33)) - (41*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(605*sqrt(33))]
    @test_int [(2 + 3*x)^(3/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)), x, 6, (7*sqrt(2 + 3*x))/(33*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)) + (8*sqrt(2 + 3*x))/(363*sqrt(1 - 2*x)*sqrt(3 + 5*x)) - (245*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3993*sqrt(3 + 5*x)) + (49*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(121*sqrt(33)) - (8*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(121*sqrt(33))]
    @test_int [sqrt(2 + 3*x)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)), x, 6, (2*sqrt(2 + 3*x))/(33*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)) + (214*sqrt(2 + 3*x))/(2541*sqrt(1 - 2*x)*sqrt(3 + 5*x)) - (2470*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(27951*sqrt(3 + 5*x)) + (494*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(847*sqrt(33)) - (214*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(847*sqrt(33))]
    @test_int [1/((1 - 2*x)^(5/2)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)), x, 6, (4*sqrt(2 + 3*x))/(231*(1 - 2*x)^(3/2)*sqrt(3 + 5*x)) + (824*sqrt(2 + 3*x))/(17787*sqrt(1 - 2*x)*sqrt(3 + 5*x)) - (41570*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(195657*sqrt(3 + 5*x)) + (8314*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(5929*sqrt(33)) - (824*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(5929*sqrt(33))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)), x, 7, 4/(231*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*sqrt(3 + 5*x)) + 1088/(17787*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x)) + (5314*sqrt(1 - 2*x))/(41503*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (2377960*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(1369599*sqrt(3 + 5*x)) + (475592*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(41503*sqrt(33)) + (10628*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(41503*sqrt(33))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)), x, 8, 4/(231*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + 1352/(17787*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + (694*sqrt(1 - 2*x))/(41503*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + (336536*sqrt(1 - 2*x))/(290521*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (113693540*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(9587193*sqrt(3 + 5*x)) + (22738708*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(290521*sqrt(33)) + (673072*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(290521*sqrt(33))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)), x, 9, 4/(231*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x)) + 1616/(17787*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*sqrt(3 + 5*x)) - (2206*sqrt(1 - 2*x))/(207515*(2 + 3*x)^(5/2)*sqrt(3 + 5*x)) + (499564*sqrt(1 - 2*x))/(1452605*(2 + 3*x)^(3/2)*sqrt(3 + 5*x)) + (72709316*sqrt(1 - 2*x))/(10168235*sqrt(2 + 3*x)*sqrt(3 + 5*x)) - (4839325048*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(67110351*sqrt(3 + 5*x)) + (4839325048*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(10168235*sqrt(33)) + (145418632*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(10168235*sqrt(33))]

    @test_int [(2 + 3*x)^(13/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)), x, 9, (4373*sqrt(1 - 2*x)*(2 + 3*x)^(7/2))/(19965*(3 + 5*x)^(3/2)) - (294*(2 + 3*x)^(9/2))/(121*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) + (7*(2 + 3*x)^(11/2))/(33*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + (150812*sqrt(1 - 2*x)*(2 + 3*x)^(5/2))/(1098075*sqrt(3 + 5*x)) - (371279941*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/45753125 - (31887029*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*sqrt(3 + 5*x))/18301250 - (51601293223*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(83187500*sqrt(33)) - (776112041*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(41593750*sqrt(33))]
    @test_int [(2 + 3*x)^(11/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)), x, 8, (3218*sqrt(1 - 2*x)*(2 + 3*x)^(5/2))/(19965*(3 + 5*x)^(3/2)) - (217*(2 + 3*x)^(7/2))/(121*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) + (7*(2 + 3*x)^(9/2))/(33*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + (110519*sqrt(1 - 2*x)*(2 + 3*x)^(3/2))/(1098075*sqrt(3 + 5*x)) - (5199979*sqrt(1 - 2*x)*sqrt(2 + 3*x)*sqrt(3 + 5*x))/3660250 - (90397364*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(831875*sqrt(33)) - (5442127*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1663750*sqrt(33))]
    @test_int [(2 + 3*x)^(9/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)), x, 7, (2063*sqrt(1 - 2*x)*(2 + 3*x)^(3/2))/(19965*(3 + 5*x)^(3/2)) - (140*(2 + 3*x)^(5/2))/(121*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) + (7*(2 + 3*x)^(7/2))/(33*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + (70226*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(1098075*sqrt(3 + 5*x)) - (4971289*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(332750*sqrt(33)) - (76163*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(166375*sqrt(33))]
    @test_int [(2 + 3*x)^(7/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)), x, 7, (908*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(19965*(3 + 5*x)^(3/2)) - (63*(2 + 3*x)^(3/2))/(121*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) + (7*(2 + 3*x)^(5/2))/(33*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + (29933*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(219615*sqrt(3 + 5*x)) - (29933*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(33275*sqrt(33)) - (1847*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(33275*sqrt(33))]
    @test_int [(2 + 3*x)^(5/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)), x, 7, (14*sqrt(2 + 3*x))/(121*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (247*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3993*(3 + 5*x)^(3/2)) + (7*(2 + 3*x)^(3/2))/(33*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) - (2209*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(43923*sqrt(3 + 5*x)) + (2209*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(6655*sqrt(33)) - (494*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(6655*sqrt(33))]
    @test_int [(2 + 3*x)^(3/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)), x, 7, (7*sqrt(2 + 3*x))/(33*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + (26*sqrt(2 + 3*x))/(121*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (575*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(3993*(3 + 5*x)^(3/2)) - (2960*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(43923*sqrt(3 + 5*x)) + (592*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1331*sqrt(33)) - (230*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(1331*sqrt(33))]
    @test_int [sqrt(2 + 3*x)/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)), x, 7, (2*sqrt(2 + 3*x))/(33*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + (118*sqrt(2 + 3*x))/(847*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (2470*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(27951*(3 + 5*x)^(3/2)) - (22090*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(307461*sqrt(3 + 5*x)) + (4418*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(9317*sqrt(33)) - (988*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(9317*sqrt(33))]
    @test_int [1/((1 - 2*x)^(5/2)*sqrt(2 + 3*x)*(3 + 5*x)^(5/2)), x, 7, (4*sqrt(2 + 3*x))/(231*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)) + (368*sqrt(2 + 3*x))/(5929*sqrt(1 - 2*x)*(3 + 5*x)^(3/2)) - (18470*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(195657*(3 + 5*x)^(3/2)) + (598660*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(2152227*sqrt(3 + 5*x)) - (119732*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(65219*sqrt(33)) - (7388*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(65219*sqrt(33))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2)), x, 8, 4/(231*(1 - 2*x)^(3/2)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) + 456/(5929*sqrt(1 - 2*x)*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) + (5034*sqrt(1 - 2*x))/(41503*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (1523260*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(1369599*(3 + 5*x)^(3/2)) + (99425780*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(15065589*sqrt(3 + 5*x)) - (19885156*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(456533*sqrt(33)) - (609304*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(456533*sqrt(33))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2)), x, 9, 4/(231*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + 544/(5929*sqrt(1 - 2*x)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (414*sqrt(1 - 2*x))/(41503*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (488436*sqrt(1 - 2*x))/(290521*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (108842540*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(9587193*(3 + 5*x)^(3/2)) + (7231789120*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(105459123*sqrt(3 + 5*x)) - (1446357824*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(3195731*sqrt(33)) - (43537016*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(3195731*sqrt(33))]
    @test_int [1/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)), x, 10, 4/(231*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + 632/(5929*sqrt(1 - 2*x)*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) - (3606*sqrt(1 - 2*x))/(207515*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + (649224*sqrt(1 - 2*x))/(1452605*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (140700876*sqrt(1 - 2*x))/(10168235*sqrt(2 + 3*x)*(3 + 5*x)^(3/2)) - (6208896328*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(67110351*(3 + 5*x)^(3/2)) + (412810345784*sqrt(1 - 2*x)*sqrt(2 + 3*x))/(738213861*sqrt(3 + 5*x)) - (412810345784*Elliptic.E(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(111850585*sqrt(33)) - (12417792656*Elliptic.F(asin(sqrt(3/7)*sqrt(1 - 2*x)), 35/33))/(111850585*sqrt(33))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^(m/3)*(c+d*x)^(n/3)*(e+f*x)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^(1/3)*(c+d*x)^(n/3)*(e+f*x)^p=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(a + b*x)^(1/3)*(c + d*x)^(2/3)*(e + f*x)^2, x, 5, ((b*c - a*d)*(10*a^2*d^2*f^2 - 10*a*b*d*f*(3*d*e - c*f) + b^2*(27*d^2*e^2 - 24*c*d*e*f + 7*c^2*f^2))*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(81*b^3*d^3) + ((10*a^2*d^2*f^2 - 10*a*b*d*f*(3*d*e - c*f) + b^2*(27*d^2*e^2 - 24*c*d*e*f + 7*c^2*f^2))*(a + b*x)^(4/3)*(c + d*x)^(2/3))/(54*b^3*d^2) + (f*(15*b*d*e - 7*b*c*f - 8*a*d*f)*(a + b*x)^(4/3)*(c + d*x)^(5/3))/(36*b^2*d^2) + (f*(a + b*x)^(4/3)*(c + d*x)^(5/3)*(e + f*x))/(4*b*d) + ((b*c - a*d)^2*(10*a^2*d^2*f^2 - 10*a*b*d*f*(3*d*e - c*f) + b^2*(27*d^2*e^2 - 24*c*d*e*f + 7*c^2*f^2))*atan(1/sqrt(3) + (2*b^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*d^(1/3)*(a + b*x)^(1/3))))/(81*sqrt(3)*b^(11/3)*d^(10/3)) + ((b*c - a*d)^2*(10*a^2*d^2*f^2 - 10*a*b*d*f*(3*d*e - c*f) + b^2*(27*d^2*e^2 - 24*c*d*e*f + 7*c^2*f^2))*log(a + b*x))/(486*b^(11/3)*d^(10/3)) + ((b*c - a*d)^2*(10*a^2*d^2*f^2 - 10*a*b*d*f*(3*d*e - c*f) + b^2*(27*d^2*e^2 - 24*c*d*e*f + 7*c^2*f^2))*log(-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))))/(162*b^(11/3)*d^(10/3))]
    @test_int [(a + b*x)^(1/3)*(c + d*x)^(2/3)*(e + f*x)^1, x, 4, ((b*c - a*d)*(9*b*d*e - 4*b*c*f - 5*a*d*f)*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(27*b^2*d^2) + ((9*b*d*e - 4*b*c*f - 5*a*d*f)*(a + b*x)^(4/3)*(c + d*x)^(2/3))/(18*b^2*d) + (f*(a + b*x)^(4/3)*(c + d*x)^(5/3))/(3*b*d) + ((b*c - a*d)^2*(9*b*d*e - 4*b*c*f - 5*a*d*f)*atan(1/sqrt(3) + (2*b^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*d^(1/3)*(a + b*x)^(1/3))))/(27*sqrt(3)*b^(8/3)*d^(7/3)) + ((b*c - a*d)^2*(9*b*d*e - 4*b*c*f - 5*a*d*f)*log(a + b*x))/(162*b^(8/3)*d^(7/3)) + ((b*c - a*d)^2*(9*b*d*e - 4*b*c*f - 5*a*d*f)*log(-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))))/(54*b^(8/3)*d^(7/3))]
    @test_int [(a + b*x)^(1/3)*(c + d*x)^(2/3)*(e + f*x)^0, x, 3, ((b*c - a*d)*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(3*b*d) + ((a + b*x)^(4/3)*(c + d*x)^(2/3))/(2*b) + ((b*c - a*d)^2*atan(1/sqrt(3) + (2*b^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*d^(1/3)*(a + b*x)^(1/3))))/(3*sqrt(3)*b^(5/3)*d^(4/3)) + ((b*c - a*d)^2*log(a + b*x))/(18*b^(5/3)*d^(4/3)) + ((b*c - a*d)^2*log(-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))))/(6*b^(5/3)*d^(4/3))]
    @test_int [(a + b*x)^(1/3)*(c + d*x)^(2/3)/(e + f*x)^1, x, 4, ((a + b*x)^(1/3)*(c + d*x)^(2/3))/f + ((3*b*d*e - 2*b*c*f - a*d*f)*atan(1/sqrt(3) + (2*b^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*d^(1/3)*(a + b*x)^(1/3))))/(sqrt(3)*b^(2/3)*d^(1/3)*f^2) - (sqrt(3)*(b*e - a*f)^(1/3)*(d*e - c*f)^(2/3)*atan(1/sqrt(3) + (2*(b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*(d*e - c*f)^(1/3)*(a + b*x)^(1/3))))/f^2 + ((3*b*d*e - 2*b*c*f - a*d*f)*log(a + b*x))/(6*b^(2/3)*d^(1/3)*f^2) + ((b*e - a*f)^(1/3)*(d*e - c*f)^(2/3)*log(e + f*x))/(2*f^2) - (3*(b*e - a*f)^(1/3)*(d*e - c*f)^(2/3)*log(-(a + b*x)^(1/3) + ((b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(d*e - c*f)^(1/3)))/(2*f^2) + ((3*b*d*e - 2*b*c*f - a*d*f)*log(-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))))/(2*b^(2/3)*d^(1/3)*f^2)]
    @test_int [(a + b*x)^(1/3)*(c + d*x)^(2/3)/(e + f*x)^2, x, 4, -(((a + b*x)^(1/3)*(c + d*x)^(2/3))/(f*(e + f*x))) - (sqrt(3)*b^(1/3)*d^(2/3)*atan(1/sqrt(3) + (2*b^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*d^(1/3)*(a + b*x)^(1/3))))/f^2 + ((3*b*d*e - b*c*f - 2*a*d*f)*atan(1/sqrt(3) + (2*(b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*(d*e - c*f)^(1/3)*(a + b*x)^(1/3))))/(sqrt(3)*f^2*(b*e - a*f)^(2/3)*(d*e - c*f)^(1/3)) - (b^(1/3)*d^(2/3)*log(a + b*x))/(2*f^2) - ((3*b*d*e - b*c*f - 2*a*d*f)*log(e + f*x))/(6*f^2*(b*e - a*f)^(2/3)*(d*e - c*f)^(1/3)) + ((3*b*d*e - b*c*f - 2*a*d*f)*log(-(a + b*x)^(1/3) + ((b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(d*e - c*f)^(1/3)))/(2*f^2*(b*e - a*f)^(2/3)*(d*e - c*f)^(1/3)) - (3*b^(1/3)*d^(2/3)*log(-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))))/(2*f^2)]
    @test_int [(a + b*x)^(1/3)*(c + d*x)^(2/3)/(e + f*x)^3, x, 3, ((a + b*x)^(1/3)*(c + d*x)^(5/3))/(2*(d*e - c*f)*(e + f*x)^2) - ((b*c - a*d)*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(6*(b*e - a*f)*(d*e - c*f)*(e + f*x)) + ((b*c - a*d)^2*atan(1/sqrt(3) + (2*(b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*(d*e - c*f)^(1/3)*(a + b*x)^(1/3))))/(3*sqrt(3)*(b*e - a*f)^(5/3)*(d*e - c*f)^(4/3)) - ((b*c - a*d)^2*log(e + f*x))/(18*(b*e - a*f)^(5/3)*(d*e - c*f)^(4/3)) + ((b*c - a*d)^2*log(-(a + b*x)^(1/3) + ((b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(d*e - c*f)^(1/3)))/(6*(b*e - a*f)^(5/3)*(d*e - c*f)^(4/3))]
    @test_int [(a + b*x)^(1/3)*(c + d*x)^(2/3)/(e + f*x)^4, x, 4, -((f*(a + b*x)^(4/3)*(c + d*x)^(5/3))/(3*(b*e - a*f)*(d*e - c*f)*(e + f*x)^3)) + ((9*b*d*e - 5*b*c*f - 4*a*d*f)*(a + b*x)^(1/3)*(c + d*x)^(5/3))/(18*(b*e - a*f)*(d*e - c*f)^2*(e + f*x)^2) - ((b*c - a*d)*(9*b*d*e - 5*b*c*f - 4*a*d*f)*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(54*(b*e - a*f)^2*(d*e - c*f)^2*(e + f*x)) + ((b*c - a*d)^2*(9*b*d*e - 5*b*c*f - 4*a*d*f)*atan(1/sqrt(3) + (2*(b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*(d*e - c*f)^(1/3)*(a + b*x)^(1/3))))/(27*sqrt(3)*(b*e - a*f)^(8/3)*(d*e - c*f)^(7/3)) - ((b*c - a*d)^2*(9*b*d*e - 5*b*c*f - 4*a*d*f)*log(e + f*x))/(162*(b*e - a*f)^(8/3)*(d*e - c*f)^(7/3)) + ((b*c - a*d)^2*(9*b*d*e - 5*b*c*f - 4*a*d*f)*log(-(a + b*x)^(1/3) + ((b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(d*e - c*f)^(1/3)))/(54*(b*e - a*f)^(8/3)*(d*e - c*f)^(7/3))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(a + b*x)^(1/3)/(c + d*x)^(1/3)*(e + f*x)^2, x, 4, ((5*a^2*d^2*f^2 - 2*a*b*d*f*(9*d*e - 4*c*f) + b^2*(27*d^2*e^2 - 36*c*d*e*f + 14*c^2*f^2))*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(27*b^2*d^3) + (f*(12*b*d*e - 7*b*c*f - 5*a*d*f)*(a + b*x)^(4/3)*(c + d*x)^(2/3))/(18*b^2*d^2) + (f*(a + b*x)^(4/3)*(c + d*x)^(2/3)*(e + f*x))/(3*b*d) + ((b*c - a*d)*(5*a^2*d^2*f^2 - 2*a*b*d*f*(9*d*e - 4*c*f) + b^2*(27*d^2*e^2 - 36*c*d*e*f + 14*c^2*f^2))*atan(1/sqrt(3) + (2*b^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*d^(1/3)*(a + b*x)^(1/3))))/(27*sqrt(3)*b^(8/3)*d^(10/3)) + ((b*c - a*d)*(5*a^2*d^2*f^2 - 2*a*b*d*f*(9*d*e - 4*c*f) + b^2*(27*d^2*e^2 - 36*c*d*e*f + 14*c^2*f^2))*log(a + b*x))/(162*b^(8/3)*d^(10/3)) + ((b*c - a*d)*(5*a^2*d^2*f^2 - 2*a*b*d*f*(9*d*e - 4*c*f) + b^2*(27*d^2*e^2 - 36*c*d*e*f + 14*c^2*f^2))*log(-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))))/(54*b^(8/3)*d^(10/3))]
    @test_int [(a + b*x)^(1/3)/(c + d*x)^(1/3)*(e + f*x)^1, x, 3, ((3*b*d*e - 2*b*c*f - a*d*f)*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(3*b*d^2) + (f*(a + b*x)^(4/3)*(c + d*x)^(2/3))/(2*b*d) + ((b*c - a*d)*(3*b*d*e - 2*b*c*f - a*d*f)*atan(1/sqrt(3) + (2*b^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*d^(1/3)*(a + b*x)^(1/3))))/(3*sqrt(3)*b^(5/3)*d^(7/3)) + ((b*c - a*d)*(3*b*d*e - 2*b*c*f - a*d*f)*log(a + b*x))/(18*b^(5/3)*d^(7/3)) + ((b*c - a*d)*(3*b*d*e - 2*b*c*f - a*d*f)*log(-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))))/(6*b^(5/3)*d^(7/3))]
    @test_int [(a + b*x)^(1/3)/(c + d*x)^(1/3)*(e + f*x)^0, x, 2, ((a + b*x)^(1/3)*(c + d*x)^(2/3))/d + ((b*c - a*d)*atan(1/sqrt(3) + (2*b^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*d^(1/3)*(a + b*x)^(1/3))))/(sqrt(3)*b^(2/3)*d^(4/3)) + ((b*c - a*d)*log(a + b*x))/(6*b^(2/3)*d^(4/3)) + ((b*c - a*d)*log(-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))))/(2*b^(2/3)*d^(4/3))]
    @test_int [(a + b*x)^(1/3)/(c + d*x)^(1/3)/(e + f*x)^1, x, 4, -((sqrt(3)*b^(1/3)*atan(1/sqrt(3) + (2*b^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*d^(1/3)*(a + b*x)^(1/3))))/(d^(1/3)*f)) + (sqrt(3)*(b*e - a*f)^(1/3)*atan(1/sqrt(3) + (2*(b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*(d*e - c*f)^(1/3)*(a + b*x)^(1/3))))/(f*(d*e - c*f)^(1/3)) - (b^(1/3)*log(a + b*x))/(2*d^(1/3)*f) - ((b*e - a*f)^(1/3)*log(e + f*x))/(2*f*(d*e - c*f)^(1/3)) + (3*(b*e - a*f)^(1/3)*log(-(a + b*x)^(1/3) + ((b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(d*e - c*f)^(1/3)))/(2*f*(d*e - c*f)^(1/3)) - (3*b^(1/3)*log(-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))))/(2*d^(1/3)*f)]
    @test_int [(a + b*x)^(1/3)/(c + d*x)^(1/3)/(e + f*x)^2, x, 2, ((a + b*x)^(1/3)*(c + d*x)^(2/3))/((d*e - c*f)*(e + f*x)) + ((b*c - a*d)*atan(1/sqrt(3) + (2*(b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*(d*e - c*f)^(1/3)*(a + b*x)^(1/3))))/(sqrt(3)*(b*e - a*f)^(2/3)*(d*e - c*f)^(4/3)) - ((b*c - a*d)*log(e + f*x))/(6*(b*e - a*f)^(2/3)*(d*e - c*f)^(4/3)) + ((b*c - a*d)*log(-(a + b*x)^(1/3) + ((b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(d*e - c*f)^(1/3)))/(2*(b*e - a*f)^(2/3)*(d*e - c*f)^(4/3))]
    @test_int [(a + b*x)^(1/3)/(c + d*x)^(1/3)/(e + f*x)^3, x, 3, -((f*(a + b*x)^(4/3)*(c + d*x)^(2/3))/(2*(b*e - a*f)*(d*e - c*f)*(e + f*x)^2)) + ((3*b*d*e - b*c*f - 2*a*d*f)*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(3*(b*e - a*f)*(d*e - c*f)^2*(e + f*x)) + ((b*c - a*d)*(3*b*d*e - b*c*f - 2*a*d*f)*atan(1/sqrt(3) + (2*(b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*(d*e - c*f)^(1/3)*(a + b*x)^(1/3))))/(3*sqrt(3)*(b*e - a*f)^(5/3)*(d*e - c*f)^(7/3)) - ((b*c - a*d)*(3*b*d*e - b*c*f - 2*a*d*f)*log(e + f*x))/(18*(b*e - a*f)^(5/3)*(d*e - c*f)^(7/3)) + ((b*c - a*d)*(3*b*d*e - b*c*f - 2*a*d*f)*log(-(a + b*x)^(1/3) + ((b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(d*e - c*f)^(1/3)))/(6*(b*e - a*f)^(5/3)*(d*e - c*f)^(7/3))]
    @test_int [(a + b*x)^(1/3)/(c + d*x)^(1/3)/(e + f*x)^4, x, 5, ((a + b*x)^(1/3)*(c + d*x)^(2/3))/(3*(d*e - c*f)*(e + f*x)^3) + ((6*b*d*e + b*c*f - 7*a*d*f)*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(18*(b*e - a*f)*(d*e - c*f)^2*(e + f*x)^2) + ((28*a^2*d^2*f^2 - a*b*d*f*(51*d*e + 5*c*f) + b^2*(18*d^2*e^2 + 15*c*d*e*f - 5*c^2*f^2))*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(54*(b*e - a*f)^2*(d*e - c*f)^3*(e + f*x)) + ((b*c - a*d)*(14*a^2*d^2*f^2 - 4*a*b*d*f*(9*d*e - 2*c*f) + b^2*(27*d^2*e^2 - 18*c*d*e*f + 5*c^2*f^2))*atan(1/sqrt(3) + (2*(b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*(d*e - c*f)^(1/3)*(a + b*x)^(1/3))))/(27*sqrt(3)*(b*e - a*f)^(8/3)*(d*e - c*f)^(10/3)) - ((b*c - a*d)*(14*a^2*d^2*f^2 - 4*a*b*d*f*(9*d*e - 2*c*f) + b^2*(27*d^2*e^2 - 18*c*d*e*f + 5*c^2*f^2))*log(e + f*x))/(162*(b*e - a*f)^(8/3)*(d*e - c*f)^(10/3)) + ((b*c - a*d)*(14*a^2*d^2*f^2 - 4*a*b*d*f*(9*d*e - 2*c*f) + b^2*(27*d^2*e^2 - 18*c*d*e*f + 5*c^2*f^2))*log(-(a + b*x)^(1/3) + ((b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(d*e - c*f)^(1/3)))/(54*(b*e - a*f)^(8/3)*(d*e - c*f)^(10/3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*1 / (a+b*x)^(1/3)*(c+d*x)^(n/3)*(e+f*x)^p=#

    #= ::Subsubsection:: =#
    #=n>0=#

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [1/((a + b*x)^(1/3)*(c + d*x)^(2/3))*(e + f*x)^3, x, 3, (f*(a + b*x)^(2/3)*(c + d*x)^(1/3)*(e + f*x)^2)/(3*b*d) + (f*(a + b*x)^(2/3)*(c + d*x)^(1/3)*(28*a^2*d^2*f^2 - a*b*d*f*(108*d*e - 31*c*f) + b^2*(144*d^2*e^2 - 135*c*d*e*f + 40*c^2*f^2) + 3*b*d*f*(15*b*d*e - 8*b*c*f - 7*a*d*f)*x))/(54*b^3*d^3) + ((14*a^3*d^3*f^3 - 6*a^2*b*d^2*f^2*(9*d*e - 2*c*f) + 3*a*b^2*d*f*(27*d^2*e^2 - 18*c*d*e*f + 5*c^2*f^2) - b^3*(81*d^3*e^3 - 162*c*d^2*e^2*f + 135*c^2*d*e*f^2 - 40*c^3*f^3))*atan(1/sqrt(3) + (2*d^(1/3)*(a + b*x)^(1/3))/(sqrt(3)*b^(1/3)*(c + d*x)^(1/3))))/(27*sqrt(3)*b^(10/3)*d^(11/3)) + ((14*a^3*d^3*f^3 - 6*a^2*b*d^2*f^2*(9*d*e - 2*c*f) + 3*a*b^2*d*f*(27*d^2*e^2 - 18*c*d*e*f + 5*c^2*f^2) - b^3*(81*d^3*e^3 - 162*c*d^2*e^2*f + 135*c^2*d*e*f^2 - 40*c^3*f^3))*log(c + d*x))/(162*b^(10/3)*d^(11/3)) + ((14*a^3*d^3*f^3 - 6*a^2*b*d^2*f^2*(9*d*e - 2*c*f) + 3*a*b^2*d*f*(27*d^2*e^2 - 18*c*d*e*f + 5*c^2*f^2) - b^3*(81*d^3*e^3 - 162*c*d^2*e^2*f + 135*c^2*d*e*f^2 - 40*c^3*f^3))*log(-1 + (d^(1/3)*(a + b*x)^(1/3))/(b^(1/3)*(c + d*x)^(1/3))))/(54*b^(10/3)*d^(11/3))]
    @test_int [1/((a + b*x)^(1/3)*(c + d*x)^(2/3))*(e + f*x)^2, x, 3, (f*(9*b*d*e - 5*b*c*f - 4*a*d*f)*(a + b*x)^(2/3)*(c + d*x)^(1/3))/(6*b^2*d^2) + (f*(a + b*x)^(2/3)*(c + d*x)^(1/3)*(e + f*x))/(2*b*d) - ((2*a^2*d^2*f^2 - 2*a*b*d*f*(3*d*e - c*f) + b^2*(9*d^2*e^2 - 12*c*d*e*f + 5*c^2*f^2))*atan(1/sqrt(3) + (2*d^(1/3)*(a + b*x)^(1/3))/(sqrt(3)*b^(1/3)*(c + d*x)^(1/3))))/(3*sqrt(3)*b^(7/3)*d^(8/3)) - ((2*a^2*d^2*f^2 - 2*a*b*d*f*(3*d*e - c*f) + b^2*(9*d^2*e^2 - 12*c*d*e*f + 5*c^2*f^2))*log(c + d*x))/(18*b^(7/3)*d^(8/3)) - ((2*a^2*d^2*f^2 - 2*a*b*d*f*(3*d*e - c*f) + b^2*(9*d^2*e^2 - 12*c*d*e*f + 5*c^2*f^2))*log(-1 + (d^(1/3)*(a + b*x)^(1/3))/(b^(1/3)*(c + d*x)^(1/3))))/(6*b^(7/3)*d^(8/3))]
    @test_int [1/((a + b*x)^(1/3)*(c + d*x)^(2/3))*(e + f*x)^1, x, 2, (f*(a + b*x)^(2/3)*(c + d*x)^(1/3))/(b*d) - ((3*b*d*e - 2*b*c*f - a*d*f)*atan(1/sqrt(3) + (2*d^(1/3)*(a + b*x)^(1/3))/(sqrt(3)*b^(1/3)*(c + d*x)^(1/3))))/(sqrt(3)*b^(4/3)*d^(5/3)) - ((3*b*d*e - 2*b*c*f - a*d*f)*log(c + d*x))/(6*b^(4/3)*d^(5/3)) - ((3*b*d*e - 2*b*c*f - a*d*f)*log(-1 + (d^(1/3)*(a + b*x)^(1/3))/(b^(1/3)*(c + d*x)^(1/3))))/(2*b^(4/3)*d^(5/3))]
    @test_int [1/((a + b*x)^(1/3)*(c + d*x)^(2/3))*(e + f*x)^0, x, 1, -((sqrt(3)*atan(1/sqrt(3) + (2*d^(1/3)*(a + b*x)^(1/3))/(sqrt(3)*b^(1/3)*(c + d*x)^(1/3))))/(b^(1/3)*d^(2/3))) - log(c + d*x)/(2*b^(1/3)*d^(2/3)) - (3*log(-1 + (d^(1/3)*(a + b*x)^(1/3))/(b^(1/3)*(c + d*x)^(1/3))))/(2*b^(1/3)*d^(2/3))]
    @test_int [1/((a + b*x)^(1/3)*(c + d*x)^(2/3))/(e + f*x)^1, x, 1, -((sqrt(3)*atan(1/sqrt(3) + (2*(d*e - c*f)^(1/3)*(a + b*x)^(1/3))/(sqrt(3)*(b*e - a*f)^(1/3)*(c + d*x)^(1/3))))/((b*e - a*f)^(1/3)*(d*e - c*f)^(2/3))) + log(e + f*x)/(2*(b*e - a*f)^(1/3)*(d*e - c*f)^(2/3)) - (3*log(((d*e - c*f)^(1/3)*(a + b*x)^(1/3))/(b*e - a*f)^(1/3) - (c + d*x)^(1/3)))/(2*(b*e - a*f)^(1/3)*(d*e - c*f)^(2/3))]
    @test_int [1/((a + b*x)^(1/3)*(c + d*x)^(2/3))/(e + f*x)^2, x, 2, -((f*(a + b*x)^(2/3)*(c + d*x)^(1/3))/((b*e - a*f)*(d*e - c*f)*(e + f*x))) - ((3*b*d*e - b*c*f - 2*a*d*f)*atan(1/sqrt(3) + (2*(d*e - c*f)^(1/3)*(a + b*x)^(1/3))/(sqrt(3)*(b*e - a*f)^(1/3)*(c + d*x)^(1/3))))/(sqrt(3)*(b*e - a*f)^(4/3)*(d*e - c*f)^(5/3)) + ((3*b*d*e - b*c*f - 2*a*d*f)*log(e + f*x))/(6*(b*e - a*f)^(4/3)*(d*e - c*f)^(5/3)) - ((3*b*d*e - b*c*f - 2*a*d*f)*log(((d*e - c*f)^(1/3)*(a + b*x)^(1/3))/(b*e - a*f)^(1/3) - (c + d*x)^(1/3)))/(2*(b*e - a*f)^(4/3)*(d*e - c*f)^(5/3))]
    @test_int [1/((a + b*x)^(1/3)*(c + d*x)^(2/3))/(e + f*x)^3, x, 4, -((f*(a + b*x)^(2/3)*(c + d*x)^(1/3))/(2*(b*e - a*f)*(d*e - c*f)*(e + f*x)^2)) - (f*(9*b*d*e - 4*b*c*f - 5*a*d*f)*(a + b*x)^(2/3)*(c + d*x)^(1/3))/(6*(b*e - a*f)^2*(d*e - c*f)^2*(e + f*x)) - ((5*a^2*d^2*f^2 - 2*a*b*d*f*(6*d*e - c*f) + b^2*(9*d^2*e^2 - 6*c*d*e*f + 2*c^2*f^2))*atan(1/sqrt(3) + (2*(d*e - c*f)^(1/3)*(a + b*x)^(1/3))/(sqrt(3)*(b*e - a*f)^(1/3)*(c + d*x)^(1/3))))/(3*sqrt(3)*(b*e - a*f)^(7/3)*(d*e - c*f)^(8/3)) + ((5*a^2*d^2*f^2 - 2*a*b*d*f*(6*d*e - c*f) + b^2*(9*d^2*e^2 - 6*c*d*e*f + 2*c^2*f^2))*log(e + f*x))/(18*(b*e - a*f)^(7/3)*(d*e - c*f)^(8/3)) - ((5*a^2*d^2*f^2 - 2*a*b*d*f*(6*d*e - c*f) + b^2*(9*d^2*e^2 - 6*c*d*e*f + 2*c^2*f^2))*log(((d*e - c*f)^(1/3)*(a + b*x)^(1/3))/(b*e - a*f)^(1/3) - (c + d*x)^(1/3)))/(6*(b*e - a*f)^(7/3)*(d*e - c*f)^(8/3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m / ((c+d*x)^(1/3)*(e+f*x)^(n/3))*with*2*b*d*e-b*c*f-a*d*f=0=#

    #= ::Subsubsection:: =#
    #=n>0=#

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(a + b*x)^3/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)), x, 7, (3*(a + b*x)^2*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)^(2/3))/(20*d^2) + (9*(b*c - a*d)*(c + d*x)^(2/3)*(23*b*c - 39*a*d - 16*b*d*x)*(b*c + a*d + 2*b*d*x)^(2/3))/(560*d^4) - (81*(b*c - a*d)^3*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2))/(112*b^(2/3)*d^6*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))) + (81*3^(1/4)*sqrt(2 - sqrt(3))*(b*c - a*d)^(11/3)*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.E(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(224*b^(2/3)*d^4*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)) - (27*3^(3/4)*(b*c - a*d)^(11/3)*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(56*sqrt(2)*b^(2/3)*d^4*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2))]
    @test_int [(a + b*x)^2/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)), x, 7, -((45*(b*c - a*d)*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)^(2/3))/(112*d^3)) + (3*(a + b*x)*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)^(2/3))/(14*d^2) + (99*(b*c - a*d)^2*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2))/(112*b^(2/3)*d^5*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))) - (99*3^(1/4)*sqrt(2 - sqrt(3))*(b*c - a*d)^(8/3)*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.E(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(224*b^(2/3)*d^3*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)) + (33*3^(3/4)*(b*c - a*d)^(8/3)*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(56*sqrt(2)*b^(2/3)*d^3*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2))]
    @test_int [(a + b*x)^1/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)), x, 6, (3*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)^(2/3))/(8*d^2) - (9*(b*c - a*d)*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2))/(8*b^(2/3)*d^4*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))) + (9*3^(1/4)*sqrt(2 - sqrt(3))*(b*c - a*d)^(5/3)*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.E(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(16*b^(2/3)*d^2*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)) - (3*3^(3/4)*(b*c - a*d)^(5/3)*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(4*sqrt(2)*b^(2/3)*d^2*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2))]
    @test_int [(a + b*x)^0/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)), x, 5, (3*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2))/(2*b^(2/3)*d^3*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))) - (3*3^(1/4)*sqrt(2 - sqrt(3))*(b*c - a*d)^(2/3)*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.E(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(4*b^(2/3)*d*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)) + (3^(3/4)*(b*c - a*d)^(2/3)*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(sqrt(2)*b^(2/3)*d*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2))]
    @test_int [1/((a + b*x)^1*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)), x, 1, -((sqrt(3)*atan(1/sqrt(3) + (2*b^(2/3)*(c + d*x)^(2/3))/(sqrt(3)*(b*c - a*d)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3))))/(2*b^(2/3)*(b*c - a*d)^(2/3))) - log(a + b*x)/(2*b^(2/3)*(b*c - a*d)^(2/3)) + (3*log((b^(2/3)*(c + d*x)^(2/3))/(b*c - a*d)^(1/3) - (b*c + a*d + 2*b*d*x)^(1/3)))/(4*b^(2/3)*(b*c - a*d)^(2/3))]
    @test_int [1/((a + b*x)^2*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)), x, 8, -(((c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)^(2/3))/((b*c - a*d)^2*(a + b*x))) + (((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2))/(b^(2/3)*d*(b*c - a*d)^2*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))) + (sqrt(3)*d*atan(1/sqrt(3) + (2*b^(2/3)*(c + d*x)^(2/3))/(sqrt(3)*(b*c - a*d)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3))))/(2*b^(2/3)*(b*c - a*d)^(5/3)) - (3^(1/4)*sqrt(2 - sqrt(3))*d*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.E(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(2*b^(2/3)*(b*c - a*d)^(4/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)) + (sqrt(2)*d*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(3^(1/4)*b^(2/3)*(b*c - a*d)^(4/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)) + (d*log(a + b*x))/(2*b^(2/3)*(b*c - a*d)^(5/3)) - (3*d*log((b^(2/3)*(c + d*x)^(2/3))/(b*c - a*d)^(1/3) - (b*c + a*d + 2*b*d*x)^(1/3)))/(4*b^(2/3)*(b*c - a*d)^(5/3))]
    @test_int [1/((a + b*x)^3*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)), x, 9, -(((c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)^(2/3))/(2*(b*c - a*d)^2*(a + b*x)^2)) + (2*d*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)^(2/3))/((b*c - a*d)^3*(a + b*x)) - (2*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2))/(b^(2/3)*(b*c - a*d)^3*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))) - (2*d^2*atan(1/sqrt(3) + (2*b^(2/3)*(c + d*x)^(2/3))/(sqrt(3)*(b*c - a*d)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3))))/(sqrt(3)*b^(2/3)*(b*c - a*d)^(8/3)) + (3^(1/4)*sqrt(2 - sqrt(3))*d^2*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.E(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(b^(2/3)*(b*c - a*d)^(7/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)) - (2*sqrt(2)*d^2*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(3^(1/4)*b^(2/3)*(b*c - a*d)^(7/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)) - (2*d^2*log(a + b*x))/(3*b^(2/3)*(b*c - a*d)^(8/3)) + (d^2*log((b^(2/3)*(c + d*x)^(2/3))/(b*c - a*d)^(1/3) - (b*c + a*d + 2*b*d*x)^(1/3)))/(b^(2/3)*(b*c - a*d)^(8/3))]

    @test_int [(a + b*x)^3/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)), x, 7, (3*(a + b*x)^2*(c + d*x)^(2/3))/(14*d^2*(b*c + a*d + 2*b*d*x)^(1/3)) + (9*(b*c - a*d)*(c + d*x)^(2/3)*(b*c - 7*a*d - 6*b*d*x))/(112*d^4*(b*c + a*d + 2*b*d*x)^(1/3)) + (81*(b*c - a*d)^2*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2))/(112*b^(2/3)*d^6*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))) - (81*3^(1/4)*sqrt(2 - sqrt(3))*(b*c - a*d)^(8/3)*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.E(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(224*b^(2/3)*d^4*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)) + (27*3^(3/4)*(b*c - a*d)^(8/3)*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(56*sqrt(2)*b^(2/3)*d^4*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2))]
    @test_int [(a + b*x)^2/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)), x, 7, -((3*(b*c - a*d)*(c + d*x)^(2/3))/(4*d^3*(b*c + a*d + 2*b*d*x)^(1/3))) + (3*(c + d*x)^(2/3)*(b*c + a*d + 2*b*d*x)^(2/3))/(16*d^3) - (9*(b*c - a*d)*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2))/(16*b^(2/3)*d^5*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))) + (9*3^(1/4)*sqrt(2 - sqrt(3))*(b*c - a*d)^(5/3)*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.E(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(32*b^(2/3)*d^3*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)) - (3*3^(3/4)*(b*c - a*d)^(5/3)*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(8*sqrt(2)*b^(2/3)*d^3*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2))]
    @test_int [(a + b*x)^1/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)), x, 1, (3*(c + d*x)^(2/3))/(2*d^2*(b*c + a*d + 2*b*d*x)^(1/3))]
    @test_int [(a + b*x)^0/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)), x, 6, -((3*(c + d*x)^(2/3))/(d*(b*c - a*d)*(b*c + a*d + 2*b*d*x)^(1/3))) + (3*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2))/(2*b^(2/3)*d^3*(b*c - a*d)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))) - (3*3^(1/4)*sqrt(2 - sqrt(3))*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.E(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(4*b^(2/3)*d*(b*c - a*d)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)) + (3^(3/4)*((c + d*x)*(b*c + a*d + 2*b*d*x))^(1/3)*sqrt((d*(3*b*c + a*d) + 4*b*d^2*x)^2)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))*sqrt(((b*c - a*d)^(4/3) - 2*b^(1/3)*(b*c - a*d)^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3) + 4*b^(2/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(2/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))), -7 - 4*sqrt(3)))/(sqrt(2)*b^(2/3)*d*(b*c - a*d)^(1/3)*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(1/3)*(3*b*c + a*d + 4*b*d*x)*sqrt(d^2*(3*b*c + a*d + 4*b*d*x)^2)*sqrt(((b*c - a*d)^(2/3)*((b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3)))/((1 + sqrt(3))*(b*c - a*d)^(2/3) + 2*b^(1/3)*((c + d*x)*(a*d + b*(c + 2*d*x)))^(1/3))^2))]
    @test_int [1/((a + b*x)^1*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)), x, 2, (3*(c + d*x)^(2/3)*(-((b*c + a*d + 2*b*d*x)/(b*c - a*d)))^(1/3)*AppellF1(2/3, 4/3, 1, 5/3, (2*b*(c + d*x))/(b*c - a*d), (b*(c + d*x))/(b*c - a*d)))/(2*(b*c - a*d)^2*(b*c + a*d + 2*b*d*x)^(1/3))]
    @test_int [1/((a + b*x)^2*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)), x, 2, -((3*d*(c + d*x)^(2/3)*(-((b*c + a*d + 2*b*d*x)/(b*c - a*d)))^(1/3)*AppellF1(2/3, 4/3, 2, 5/3, (2*b*(c + d*x))/(b*c - a*d), (b*(c + d*x))/(b*c - a*d)))/(2*(b*c - a*d)^3*(b*c + a*d + 2*b*d*x)^(1/3)))]
    @test_int [1/((a + b*x)^3*(c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)), x, 2, (3*d^2*(c + d*x)^(2/3)*(-((b*c + a*d + 2*b*d*x)/(b*c - a*d)))^(1/3)*AppellF1(2/3, 4/3, 3, 5/3, (2*b*(c + d*x))/(b*c - a*d), (b*(c + d*x))/(b*c - a*d)))/(2*(b*c - a*d)^4*(b*c + a*d + 2*b*d*x)^(1/3))]

    @test_int [1/((d + e*x)*(d - 3*e*x)^(1/3)*(d + 3*e*x)^(1/3)), x, 1, (sqrt(3)*atan(1/sqrt(3) - (d - 3*e*x)^(2/3)/(sqrt(3)*d^(1/3)*(d + 3*e*x)^(1/3))))/(4*d^(2/3)*e) + log(d + e*x)/(4*d^(2/3)*e) - (3*log(-((d - 3*e*x)^(2/3)/(2*d^(1/3))) - (d + 3*e*x)^(1/3)))/(8*d^(2/3)*e)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^(4/3)*(c+d*x)^(n/3)*(e+f*x)^p=#

    #= ::Subsubsection:: =#
    #=n>0=#

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(a + b*x)^(4/3)/(c + d*x)^(4/3)*(e + f*x)^2, x, 5, (3*(d*e - c*f)^2*(a + b*x)^(7/3))/(d^2*(b*c - a*d)*(c + d*x)^(1/3)) - (4*(a^2*d^2*f^2 - a*b*d*f*(9*d*e - 7*c*f) - b^2*(27*d^2*e^2 - 63*c*d*e*f + 35*c^2*f^2))*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(27*b*d^4) + ((a^2*d^2*f^2 - a*b*d*f*(9*d*e - 7*c*f) - b^2*(27*d^2*e^2 - 63*c*d*e*f + 35*c^2*f^2))*(a + b*x)^(4/3)*(c + d*x)^(2/3))/(9*b*d^3*(b*c - a*d)) + (f^2*(a + b*x)^(7/3)*(c + d*x)^(2/3))/(3*b*d^2) - (4*(b*c - a*d)*(a^2*d^2*f^2 - a*b*d*f*(9*d*e - 7*c*f) - b^2*(27*d^2*e^2 - 63*c*d*e*f + 35*c^2*f^2))*atan(1/sqrt(3) + (2*b^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*d^(1/3)*(a + b*x)^(1/3))))/(27*sqrt(3)*b^(5/3)*d^(13/3)) - (2*(b*c - a*d)*(a^2*d^2*f^2 - a*b*d*f*(9*d*e - 7*c*f) - b^2*(27*d^2*e^2 - 63*c*d*e*f + 35*c^2*f^2))*log(a + b*x))/(81*b^(5/3)*d^(13/3)) - (2*(b*c - a*d)*(a^2*d^2*f^2 - a*b*d*f*(9*d*e - 7*c*f) - b^2*(27*d^2*e^2 - 63*c*d*e*f + 35*c^2*f^2))*log(-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))))/(27*b^(5/3)*d^(13/3))]
    @test_int [(a + b*x)^(4/3)/(c + d*x)^(4/3)*(e + f*x)^1, x, 4, (3*(d*e - c*f)*(a + b*x)^(7/3))/(d*(b*c - a*d)*(c + d*x)^(1/3)) + (2*(6*b*d*e - 7*b*c*f + a*d*f)*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(3*d^3) - ((6*b*d*e - 7*b*c*f + a*d*f)*(a + b*x)^(4/3)*(c + d*x)^(2/3))/(2*d^2*(b*c - a*d)) + (2*(b*c - a*d)*(6*b*d*e - 7*b*c*f + a*d*f)*atan(1/sqrt(3) + (2*b^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*d^(1/3)*(a + b*x)^(1/3))))/(3*sqrt(3)*b^(2/3)*d^(10/3)) + ((b*c - a*d)*(6*b*d*e - 7*b*c*f + a*d*f)*log(a + b*x))/(9*b^(2/3)*d^(10/3)) + ((b*c - a*d)*(6*b*d*e - 7*b*c*f + a*d*f)*log(-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))))/(3*b^(2/3)*d^(10/3))]
    @test_int [(a + b*x)^(4/3)/(c + d*x)^(4/3)*(e + f*x)^0, x, 3, -((3*(a + b*x)^(4/3))/(d*(c + d*x)^(1/3))) + (4*b*(a + b*x)^(1/3)*(c + d*x)^(2/3))/d^2 + (4*b^(1/3)*(b*c - a*d)*atan(1/sqrt(3) + (2*b^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*d^(1/3)*(a + b*x)^(1/3))))/(sqrt(3)*d^(7/3)) + (2*b^(1/3)*(b*c - a*d)*log(a + b*x))/(3*d^(7/3)) + (2*b^(1/3)*(b*c - a*d)*log(-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))))/d^(7/3)]
    @test_int [(a + b*x)^(4/3)/(c + d*x)^(4/3)/(e + f*x)^1, x, 4, (3*(b*c - a*d)*(a + b*x)^(1/3))/(d*(d*e - c*f)*(c + d*x)^(1/3)) - (sqrt(3)*b^(4/3)*atan(1/sqrt(3) + (2*b^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*d^(1/3)*(a + b*x)^(1/3))))/(d^(4/3)*f) + (sqrt(3)*(b*e - a*f)^(4/3)*atan(1/sqrt(3) + (2*(b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*(d*e - c*f)^(1/3)*(a + b*x)^(1/3))))/(f*(d*e - c*f)^(4/3)) - (b^(4/3)*log(a + b*x))/(2*d^(4/3)*f) - ((b*e - a*f)^(4/3)*log(e + f*x))/(2*f*(d*e - c*f)^(4/3)) + (3*(b*e - a*f)^(4/3)*log(-(a + b*x)^(1/3) + ((b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(d*e - c*f)^(1/3)))/(2*f*(d*e - c*f)^(4/3)) - (3*b^(4/3)*log(-1 + (b^(1/3)*(c + d*x)^(1/3))/(d^(1/3)*(a + b*x)^(1/3))))/(2*d^(4/3)*f)]
    @test_int [(a + b*x)^(4/3)/(c + d*x)^(4/3)/(e + f*x)^2, x, 3, -((3*(a + b*x)^(4/3))/((d*e - c*f)*(c + d*x)^(1/3)*(e + f*x))) + (4*(b*e - a*f)*(a + b*x)^(1/3)*(c + d*x)^(2/3))/((d*e - c*f)^2*(e + f*x)) + (4*(b*c - a*d)*(b*e - a*f)^(1/3)*atan(1/sqrt(3) + (2*(b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*(d*e - c*f)^(1/3)*(a + b*x)^(1/3))))/(sqrt(3)*(d*e - c*f)^(7/3)) - (2*(b*c - a*d)*(b*e - a*f)^(1/3)*log(e + f*x))/(3*(d*e - c*f)^(7/3)) + (2*(b*c - a*d)*(b*e - a*f)^(1/3)*log(-(a + b*x)^(1/3) + ((b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(d*e - c*f)^(1/3)))/(d*e - c*f)^(7/3)]
    @test_int [(a + b*x)^(4/3)/(c + d*x)^(4/3)/(e + f*x)^3, x, 4, (3*d*(a + b*x)^(7/3))/((b*c - a*d)*(d*e - c*f)*(c + d*x)^(1/3)*(e + f*x)^2) - ((6*b*d*e + b*c*f - 7*a*d*f)*(a + b*x)^(4/3)*(c + d*x)^(2/3))/(2*(b*c - a*d)*(d*e - c*f)^2*(e + f*x)^2) + (2*(6*b*d*e + b*c*f - 7*a*d*f)*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(3*(d*e - c*f)^3*(e + f*x)) + (2*(b*c - a*d)*(6*b*d*e + b*c*f - 7*a*d*f)*atan(1/sqrt(3) + (2*(b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*(d*e - c*f)^(1/3)*(a + b*x)^(1/3))))/(3*sqrt(3)*(b*e - a*f)^(2/3)*(d*e - c*f)^(10/3)) - ((b*c - a*d)*(6*b*d*e + b*c*f - 7*a*d*f)*log(e + f*x))/(9*(b*e - a*f)^(2/3)*(d*e - c*f)^(10/3)) + ((b*c - a*d)*(6*b*d*e + b*c*f - 7*a*d*f)*log(-(a + b*x)^(1/3) + ((b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(d*e - c*f)^(1/3)))/(3*(b*e - a*f)^(2/3)*(d*e - c*f)^(10/3))]
    @test_int [(a + b*x)^(4/3)/(c + d*x)^(4/3)/(e + f*x)^4, x, 6, (3*(b*c - a*d)*(a + b*x)^(1/3))/(d*(d*e - c*f)*(c + d*x)^(1/3)*(e + f*x)^3) + ((b*d*e + 9*b*c*f - 10*a*d*f)*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(3*d*(d*e - c*f)^2*(e + f*x)^3) + ((3*b*d*e + 32*b*c*f - 35*a*d*f)*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(9*(d*e - c*f)^3*(e + f*x)^2) + ((140*a^2*d^2*f^2 - 7*a*b*d*f*(21*d*e + 19*c*f) + b^2*(9*d^2*e^2 + 129*c*d*e*f + 2*c^2*f^2))*(a + b*x)^(1/3)*(c + d*x)^(2/3))/(27*(b*e - a*f)*(d*e - c*f)^4*(e + f*x)) + (4*(b*c - a*d)*(35*a^2*d^2*f^2 - 7*a*b*d*f*(9*d*e + c*f) + b^2*(27*d^2*e^2 + 9*c*d*e*f - c^2*f^2))*atan(1/sqrt(3) + (2*(b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(sqrt(3)*(d*e - c*f)^(1/3)*(a + b*x)^(1/3))))/(27*sqrt(3)*(b*e - a*f)^(5/3)*(d*e - c*f)^(13/3)) - (2*(b*c - a*d)*(35*a^2*d^2*f^2 - 7*a*b*d*f*(9*d*e + c*f) + b^2*(27*d^2*e^2 + 9*c*d*e*f - c^2*f^2))*log(e + f*x))/(81*(b*e - a*f)^(5/3)*(d*e - c*f)^(13/3)) + (2*(b*c - a*d)*(35*a^2*d^2*f^2 - 7*a*b*d*f*(9*d*e + c*f) + b^2*(27*d^2*e^2 + 9*c*d*e*f - c^2*f^2))*log(-(a + b*x)^(1/3) + ((b*e - a*f)^(1/3)*(c + d*x)^(1/3))/(d*e - c*f)^(1/3)))/(27*(b*e - a*f)^(5/3)*(d*e - c*f)^(13/3))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^(n/2)*(e+f*x)^(p/4)=#

    @test_int [1/((a + b*x)*sqrt(c + d*x)*(e + f*x)^(1/4)), x, 5, (2*(d*e - c*f)^(1/4)*sqrt(-((f*(c + d*x))/(d*e - c*f)))*Elliptic.Pi(-((sqrt(b)*sqrt(d*e - c*f))/(sqrt(d)*sqrt(b*e - a*f))), asin((d^(1/4)*(e + f*x)^(1/4))/(d*e - c*f)^(1/4)), -1))/(sqrt(b)*d^(1/4)*sqrt(b*e - a*f)*sqrt(c + d*x)) - (2*(d*e - c*f)^(1/4)*sqrt(-((f*(c + d*x))/(d*e - c*f)))*Elliptic.Pi((sqrt(b)*sqrt(d*e - c*f))/(sqrt(d)*sqrt(b*e - a*f)), asin((d^(1/4)*(e + f*x)^(1/4))/(d*e - c*f)^(1/4)), -1))/(sqrt(b)*d^(1/4)*sqrt(b*e - a*f)*sqrt(c + d*x))]

    @test_int [1/((a + b*x)*sqrt(c + d*x)*(e + f*x)^(3/4)), x, 5, -((2*(d*e - c*f)^(1/4)*sqrt(-((f*(c + d*x))/(d*e - c*f)))*Elliptic.Pi(-((sqrt(b)*sqrt(d*e - c*f))/(sqrt(d)*sqrt(b*e - a*f))), asin((d^(1/4)*(e + f*x)^(1/4))/(d*e - c*f)^(1/4)), -1))/(d^(1/4)*(b*e - a*f)*sqrt(c + d*x))) - (2*(d*e - c*f)^(1/4)*sqrt(-((f*(c + d*x))/(d*e - c*f)))*Elliptic.Pi((sqrt(b)*sqrt(d*e - c*f))/(sqrt(d)*sqrt(b*e - a*f)), asin((d^(1/4)*(e + f*x)^(1/4))/(d*e - c*f)^(1/4)), -1))/(d^(1/4)*(b*e - a*f)*sqrt(c + d*x))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^n*(e+f*x)^p*with*m, n*and/or*p*symbolic=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(A+B*x)*(d+e*x)^p=#

    @test_int [(a + b*x)^p*(A + B*x)*(d + e*x)^(-2 - p), x, 3, -(((B*d - A*e)*(a + b*x)^(1 + p)*(d + e*x)^(-1 - p))/(e*(b*d - a*e)*(1 + p))) - (B*(a + b*x)^p*HypergeometricFunctions._₂F₁(-p, -p, 1 - p, (b*(d + e*x))/(b*d - a*e)))/((-((e*(a + b*x))/(b*d - a*e)))^p*(d + e*x)^p*(e^2*p))]

    @test_int [(a + b*x)*(c + d*x)^(n - 0)/(e + f*x)^n, x, 3, (b*(c + d*x)^(1 + n)*(e + f*x)^(1 - n))/(2*d*f) + ((2*a*d*f - b*(c*f*(1 - n) + d*e*(1 + n)))*(c + d*x)^(1 + n)*((d*(e + f*x))/(d*e - c*f))^n*HypergeometricFunctions._₂F₁(n, 1 + n, 2 + n, -((f*(c + d*x))/(d*e - c*f))))/((e + f*x)^n*(2*d^2*f*(1 + n)))]
    @test_int [(a + b*x)*(c + d*x)^(n - 1)/(e + f*x)^n, x, 3, -(((b*c - a*d)*(c + d*x)^n*(e + f*x)^(1 - n))/(d*(d*e - c*f)*n)) - ((a*d*f - b*(c*f*(1 - n) + d*e*n))*(c + d*x)^(1 + n)*((d*(e + f*x))/(d*e - c*f))^n*HypergeometricFunctions._₂F₁(n, 1 + n, 2 + n, -((f*(c + d*x))/(d*e - c*f))))/((e + f*x)^n*(d^2*(d*e - c*f)*n*(1 + n)))]
    @test_int [(a + b*x)*(c + d*x)^(n - 2)/(e + f*x)^n, x, 3, ((b*c - a*d)*(c + d*x)^(-1 + n)*(e + f*x)^(1 - n))/(d*(d*e - c*f)*(1 - n)) + (b*(c + d*x)^n*((d*(e + f*x))/(d*e - c*f))^n*HypergeometricFunctions._₂F₁(n, n, 1 + n, -((f*(c + d*x))/(d*e - c*f))))/((e + f*x)^n*(d^2*n))]
    @test_int [(a + b*x)*(c + d*x)^(n - 3)/(e + f*x)^n, x, 2, ((b*c - a*d)*(c + d*x)^(-2 + n)*(e + f*x)^(1 - n))/(d*(d*e - c*f)*(2 - n)) + ((a*d*f + b*(c*f*(1 - n) - d*e*(2 - n)))*(c + d*x)^(-1 + n)*(e + f*x)^(1 - n))/(d*(d*e - c*f)^2*(1 - n)*(2 - n))]
    @test_int [(a + b*x)*(c + d*x)^(n - 4)/(e + f*x)^n, x, 3, ((b*c - a*d)*(c + d*x)^(-3 + n)*(e + f*x)^(1 - n))/(d*(d*e - c*f)*(3 - n)) + ((2*a*d*f + b*(c*f*(1 - n) - d*e*(3 - n)))*(c + d*x)^(-2 + n)*(e + f*x)^(1 - n))/(d*(d*e - c*f)^2*(2 - n)*(3 - n)) - (f*(2*a*d*f + b*(c*f*(1 - n) - d*e*(3 - n)))*(c + d*x)^(-1 + n)*(e + f*x)^(1 - n))/(d*(d*e - c*f)^3*(1 - n)*(2 - n)*(3 - n))]
    @test_int [(a + b*x)*(c + d*x)^(n - 5)/(e + f*x)^n, x, 4, ((b*c - a*d)*(c + d*x)^(-4 + n)*(e + f*x)^(1 - n))/(d*(d*e - c*f)*(4 - n)) + ((3*a*d*f + b*(c*f*(1 - n) - d*e*(4 - n)))*(c + d*x)^(-3 + n)*(e + f*x)^(1 - n))/(d*(d*e - c*f)^2*(3 - n)*(4 - n)) - (2*f*(3*a*d*f + b*(c*f*(1 - n) - d*e*(4 - n)))*(c + d*x)^(-2 + n)*(e + f*x)^(1 - n))/(d*(d*e - c*f)^3*(2 - n)*(3 - n)*(4 - n)) + (2*f^2*(3*a*d*f + b*(c*f*(1 - n) - d*e*(4 - n)))*(c + d*x)^(-1 + n)*(e + f*x)^(1 - n))/(d*(d*e - c*f)^4*(1 - n)*(2 - n)*(3 - n)*(4 - n))]

    @test_int [(c + d*x)*(e + f*x)^(n - 0)/(a + b*x)^n, x, 3, (d*(a + b*x)^(1 - n)*(e + f*x)^(1 + n))/(2*b*f) + ((b*(2*c*f - d*e*(1 - n)) - a*d*f*(1 + n))*(-((f*(a + b*x))/(b*e - a*f)))^n*(e + f*x)^(1 + n)*HypergeometricFunctions._₂F₁(n, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)))/((a + b*x)^n*(2*b*f^2*(1 + n)))]
    @test_int [(c + d*x)*(e + f*x)^(n - 1)/(a + b*x)^n, x, 3, ((d*e - c*f)*(a + b*x)^(1 - n)*(e + f*x)^n)/(f*(b*e - a*f)*n) + ((b*(c*f - d*e*(1 - n)) - a*d*f*n)*(-((f*(a + b*x))/(b*e - a*f)))^n*(e + f*x)^(1 + n)*HypergeometricFunctions._₂F₁(n, 1 + n, 2 + n, (b*(e + f*x))/(b*e - a*f)))/(a + b*x)^n/(f^2*(b*e - a*f)*n*(1 + n))]
    @test_int [(c + d*x)*(e + f*x)^(n - 2)/(a + b*x)^n, x, 3, -(((d*e - c*f)*(a + b*x)^(1 - n)*(e + f*x)^(-1 + n))/(f*(b*e - a*f)*(1 - n))) + (d*(-((f*(a + b*x))/(b*e - a*f)))^n*(e + f*x)^n*HypergeometricFunctions._₂F₁(n, n, 1 + n, (b*(e + f*x))/(b*e - a*f)))/((a + b*x)^n*(f^2*n))]
    @test_int [(c + d*x)*(e + f*x)^(n - 3)/(a + b*x)^n, x, 2, -(((d*e - c*f)*(a + b*x)^(1 - n)*(e + f*x)^(-2 + n))/(f*(b*e - a*f)*(2 - n))) - ((a*d*f*(2 - n) - b*(c*f + d*(e - e*n)))*(a + b*x)^(1 - n)*(e + f*x)^(-1 + n))/(f*(b*e - a*f)^2*(1 - n)*(2 - n))]
    @test_int [(c + d*x)*(e + f*x)^(n - 4)/(a + b*x)^n, x, 3, -(((d*e - c*f)*(a + b*x)^(1 - n)*(e + f*x)^(-3 + n))/(f*(b*e - a*f)*(3 - n))) + ((b*(2*c*f + d*e*(1 - n)) - a*d*f*(3 - n))*(a + b*x)^(1 - n)*(e + f*x)^(-2 + n))/(f*(b*e - a*f)^2*(2 - n)*(3 - n)) + (b*(b*(2*c*f + d*e*(1 - n)) - a*d*f*(3 - n))*(a + b*x)^(1 - n)*(e + f*x)^(-1 + n))/(f*(b*e - a*f)^3*(1 - n)*(2 - n)*(3 - n))]
    @test_int [(c + d*x)*(e + f*x)^(n - 5)/(a + b*x)^n, x, 4, -(((d*e - c*f)*(a + b*x)^(1 - n)*(e + f*x)^(-4 + n))/(f*(b*e - a*f)*(4 - n))) + ((b*(3*c*f + d*e*(1 - n)) - a*d*f*(4 - n))*(a + b*x)^(1 - n)*(e + f*x)^(-3 + n))/(f*(b*e - a*f)^2*(3 - n)*(4 - n)) + (2*b*(b*(3*c*f + d*e*(1 - n)) - a*d*f*(4 - n))*(a + b*x)^(1 - n)*(e + f*x)^(-2 + n))/(f*(b*e - a*f)^3*(2 - n)*(3 - n)*(4 - n)) + (2*b^2*(b*(3*c*f + d*e*(1 - n)) - a*d*f*(4 - n))*(a + b*x)^(1 - n)*(e + f*x)^(-1 + n))/(f*(b*e - a*f)^4*(1 - n)*(2 - n)*(3 - n)*(4 - n))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m / (c+d*x)^(m+n)*(e+f*x)^(n+p)=#

    #= ::Subsubsection::Closed:: =#
    #=n=0=#

    @test_int [(a + b*x)^m/(c + d*x)^m*(e + f*x)^p, x, 3, ((a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*(e + f*x)^p*AppellF1(1 + m, m, -p, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/((c + d*x)^m*((b*(e + f*x))/(b*e - a*f))^p*(b*(1 + m)))]

    @test_int [(2 + 3*x)^m/(1 + 2*x)^m*(5 - 4*x)^4, x, 4, (-(1/45))*(88 - m)*(5 - 4*x)^2*(1 + 2*x)^(1 - m)*(2 + 3*x)^(1 + m) - (2/15)*(5 - 4*x)^3*(1 + 2*x)^(1 - m)*(2 + 3*x)^(1 + m) - ((1 + 2*x)^(1 - m)*(2 + 3*x)^(1 + m)*(386850 - 25441*m + 426*m^2 - 2*m^3 - 24*(4359 - 154*m + m^2)*x))/1215 + (2^(-1 - m)*(3528363 - 639760*m + 29050*m^2 - 440*m^3 + 2*m^4)*(1 + 2*x)^(1 - m)*HypergeometricFunctions._₂F₁(1 - m, -m, 2 - m, -3*(1 + 2*x)))/(1215*(1 - m))]
    @test_int [(a + b*x)^m/(c + d*x)^m*(e + f*x)^3, x, 4, (f*(a + b*x)^(1 + m)*(c + d*x)^(1 - m)*(e + f*x)^2)/(4*b*d) + (f*(a + b*x)^(1 + m)*(c + d*x)^(1 - m)*(a^2*d^2*f^2*(6 - 5*m + m^2) - 2*a*b*d*f*(6*d*e*(2 - m) - c*f*(3 - m^2)) + b^2*(30*d^2*e^2 - 12*c*d*e*f*(2 + m) + c^2*f^2*(6 + 5*m + m^2)) - 2*b*d*f*(a*d*f*(3 - m) - b*(6*d*e - c*f*(3 + m)))*x))/(24*b^3*d^3) - (1/(24*b^4*d^3*(1 + m)))*(((a^3*d^3*f^3*(6 - 11*m + 6*m^2 - m^3) - 3*a^2*b*d^2*f^2*(2 - 3*m + m^2)*(4*d*e - c*f*(1 + m)) + 3*a*b^2*d*f*(1 - m)*(12*d^2*e^2 - 8*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)) - b^3*(24*d^3*e^3 - 36*c*d^2*e^2*f*(1 + m) + 12*c^2*d*e*f^2*(2 + 3*m + m^2) - c^3*f^3*(6 + 11*m + 6*m^2 + m^3)))*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/(c + d*x)^m)]
    @test_int [(a + b*x)^m/(c + d*x)^m*(e + f*x)^2, x, 4, -((f*(a*d*f*(2 - m) - b*(4*d*e - c*f*(2 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(1 - m))/(6*b^2*d^2)) + (f*(a + b*x)^(1 + m)*(c + d*x)^(1 - m)*(e + f*x))/(3*b*d) + ((a^2*d^2*f^2*(2 - 3*m + m^2) - 2*a*b*d*f*(1 - m)*(3*d*e - c*f*(1 + m)) + b^2*(6*d^2*e^2 - 6*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)))*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(6*b^3*d^2*(1 + m)))]
    @test_int [(a + b*x)^m/(c + d*x)^m*(e + f*x)^1, x, 3, (f*(a + b*x)^(1 + m)*(c + d*x)^(1 - m))/(2*b*d) - ((a*d*f*(1 - m) - b*(2*d*e - c*f*(1 + m)))*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(2*b^2*d*(1 + m)))]
    @test_int [(a + b*x)^m/(c + d*x)^m*(e + f*x)^0, x, 2, ((a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(b*(1 + m)))]
    @test_int [(a + b*x)^m/(c + d*x)^m/(e + f*x)^1, x, 5, -(((a + b*x)^m*HypergeometricFunctions._₂F₁(1, m, 1 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))))/((c + d*x)^m*(f*m))) + ((a + b*x)^m*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(m, m, 1 + m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(f*m))]
    @test_int [(a + b*x)^m/(c + d*x)^m/(e + f*x)^2, x, 1, ((b*c - a*d)*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*HypergeometricFunctions._₂F₁(2, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))))/((b*e - a*f)^2*(1 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^m/(e + f*x)^3, x, 2, -((f*(a + b*x)^(1 + m)*(c + d*x)^(1 - m))/(2*(b*e - a*f)*(d*e - c*f)*(e + f*x)^2)) + ((b*c - a*d)*(b*(2*d*e - c*f*(1 - m)) - a*d*f*(1 + m))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*HypergeometricFunctions._₂F₁(2, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))))/(2*(b*e - a*f)^3*(d*e - c*f)*(1 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^m/(e + f*x)^4, x, 4, -((f*(a + b*x)^(1 + m)*(c + d*x)^(1 - m))/(3*(b*e - a*f)*(d*e - c*f)*(e + f*x)^3)) - (f*(b*(4*d*e - c*f*(2 - m)) - a*d*f*(2 + m))*(a + b*x)^(1 + m)*(c + d*x)^(1 - m))/(6*(b*e - a*f)^2*(d*e - c*f)^2*(e + f*x)^2) - ((b*c - a*d)*(2*a*b*d*f*(3*d*e - c*f*(1 - m))*(1 + m) - a^2*d^2*f^2*(2 + 3*m + m^2) - b^2*(6*d^2*e^2 - 6*c*d*e*f*(1 - m) + c^2*f^2*(2 - 3*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*HypergeometricFunctions._₂F₁(2, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))))/(6*(b*e - a*f)^4*(d*e - c*f)^2*(1 + m))]
    @test_int [(2 + 3*x)^m/(1 + 2*x)^m/(5 - 4*x)^5, x, 5, ((1 + 2*x)^(1 - m)*(2 + 3*x)^(1 + m))/(322*(5 - 4*x)^4) + ((66 + m)*(1 + 2*x)^(1 - m)*(2 + 3*x)^(1 + m))/(77763*(5 - 4*x)^3) + ((4359 + 220*m + 2*m^2)*(1 + 2*x)^(1 - m)*(2 + 3*x)^(1 + m))/(25039686*(5 - 4*x)^2) + ((32010 + 4358*m + 132*m^2 + m^3)*(1 + 2*x)^(1 - m)*(2 + 3*x)^(-1 + m)*HypergeometricFunctions._₂F₁(2, 1 - m, 2 - m, (23*(1 + 2*x))/(14*(2 + 3*x))))/(2453889228*(1 - m))]

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(a + b*x)^m/(c + d*x)^(m + 1)*(e + f*x)^p, x, 3, ((a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*(e + f*x)^p*AppellF1(1 + m, 1 + m, -p, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/((c + d*x)^m*((b*(e + f*x))/(b*e - a*f))^p*((b*c - a*d)*(1 + m)))]

    @test_int [(2 + 3*x)^m/(1 + 2*x)^(m + 1)*(5 - 4*x)^3, x, 3, ((-(2/9))*(5 - 4*x)^2*(2 + 3*x)^(1 + m))/(1 + 2*x)^m - ((2 + 3*x)^(1 + m)*(9261 - 512*m + 4*m^2 - 4*(109 - 2*m)*m*x))/((1 + 2*x)^m*(27*m)) + (2^(-1 - m)*(27783 - 8324*m + 390*m^2 - 4*m^3)*(1 + 2*x)^(1 - m)*HypergeometricFunctions._₂F₁(1 - m, -m, 2 - m, -3*(1 + 2*x)))/(27*(1 - m)*m)]
    @test_int [(2 + 3*x)^m/(1 + 2*x)^(m + 1)*(5 - 4*x)^2, x, 3, -((7*(21 - m)*(2 + 3*x)^(1 + m))/((1 + 2*x)^m*(3*m))) - ((1/3)*(5 - 4*x)*(2 + 3*x)^(1 + m))/(1 + 2*x)^m + (2^(-1 - m)*(441 - 86*m + 2*m^2)*(1 + 2*x)^(1 - m)*HypergeometricFunctions._₂F₁(1 - m, -m, 2 - m, -3*(1 + 2*x)))/(3*(1 - m)*m)]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 1)*(e + f*x)^1, x, 3, ((d*e - c*f)*(a + b*x)^(1 + m))/((c + d*x)^m*(d*(b*c - a*d)*m)) - ((a*d*f*m + b*(d*e - c*f*(1 + m)))*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(b*d*(b*c - a*d)*m*(1 + m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 1)*(e + f*x)^0, x, 2, -(((a + b*x)^m*HypergeometricFunctions._₂F₁(-m, -m, 1 - m, (b*(c + d*x))/(b*c - a*d)))/((-((d*(a + b*x))/(b*c - a*d)))^m*(c + d*x)^m*(d*m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 1)/(e + f*x)^1, x, 1, -(((a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))))/((c + d*x)^m*((d*e - c*f)*m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 1)/(e + f*x)^2, x, 2, (d*(a + b*x)^(1 + m))/((c + d*x)^m*((b*c - a*d)*(d*e - c*f)*m*(e + f*x))) + ((a*d*f*(1 + m) - b*(d*e + c*f*m))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*HypergeometricFunctions._₂F₁(2, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))))/((b*e - a*f)^2*(d*e - c*f)*m*(1 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 1)/(e + f*x)^3, x, 4, -((f*(a + b*x)^(1 + m))/((c + d*x)^m*(2*(b*e - a*f)*(d*e - c*f)*(e + f*x)^2))) - (f*(b*(3*d*e - c*f*(1 - m)) - a*d*f*(2 + m))*(a + b*x)^(1 + m))/((c + d*x)^m*(2*(b*e - a*f)^2*(d*e - c*f)^2*(e + f*x))) + ((2*a*b*d*f*(1 + m)*(2*d*e + c*f*m) - b^2*(2*d^2*e^2 + 4*c*d*e*f*m - c^2*f^2*(1 - m)*m) - a^2*d^2*f^2*(2 + 3*m + m^2))*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))))/((c + d*x)^m*(2*(b*e - a*f)^2*(d*e - c*f)^3*m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 1)/(e + f*x)^4, x, 5, -((f*(a + b*x)^(1 + m))/((c + d*x)^m*(3*(b*e - a*f)*(d*e - c*f)*(e + f*x)^3))) - (f*(b*(5*d*e - c*f*(2 - m)) - a*d*f*(3 + m))*(a + b*x)^(1 + m))/((c + d*x)^m*(6*(b*e - a*f)^2*(d*e - c*f)^2*(e + f*x)^2)) - (f*(a^2*d^2*f^2*(6 + 5*m + m^2) - a*b*d*f*(d*e*(15 + 8*m) - c*f*(3 - 2*m - 2*m^2)) + b^2*(11*d^2*e^2 - c*d*e*f*(7 - 8*m) + c^2*f^2*(2 - 3*m + m^2)))*(a + b*x)^(1 + m))/((c + d*x)^m*(6*(b*e - a*f)^3*(d*e - c*f)^3*(e + f*x))) + (1/(6*(b*e - a*f)^3*(d*e - c*f)^4*m))*(((3*a*b^2*d*f*(1 + m)*(6*d^2*e^2 + 6*c*d*e*f*m - c^2*f^2*(1 - m)*m) - 3*a^2*b*d^2*f^2*(3*d*e + c*f*m)*(2 + 3*m + m^2) + a^3*d^3*f^3*(6 + 11*m + 6*m^2 + m^3) - b^3*(6*d^3*e^3 + 18*c*d^2*e^2*f*m - 9*c^2*d*e*f^2*(1 - m)*m + c^3*f^3*m*(2 - 3*m + m^2)))*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))))/(c + d*x)^m)]

    @test_int [(a + b*x)^m/(c + d*x)^(m + 2)*(e + f*x)^p, x, 3, (b*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*(e + f*x)^p*AppellF1(1 + m, 2 + m, -p, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/((c + d*x)^m*((b*(e + f*x))/(b*e - a*f))^p*((b*c - a*d)^2*(1 + m)))]

    @test_int [(2 + 3*x)^m/(1 + 2*x)^(m + 2)*(5 - 4*x)^3, x, 3, (-(1/3))*(5 - 4*x)^2*(1 + 2*x)^(-1 - m)*(2 + 3*x)^(1 + m) - ((1 + 2*x)^(-1 - m)*(2 + 3*x)^(1 + m)*(2768 - 315*m + 4*m^2 - 8*(43 - m)*(1 + m)*x))/(9*(1 + m)) + ((1323 - 128*m + 2*m^2)*HypergeometricFunctions._₂F₁(-m, -m, 1 - m, -3*(1 + 2*x)))/(2^m*(1 + 2*x)^m*(9*m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 2)*(e + f*x)^2, x, 4, ((d*e - c*f)*(a*d*f*(1 + m) + b*(d*e - c*f*(2 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(b*d^2*(b*c - a*d)*(1 + m)) + (f*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*(e + f*x))/(b*d) - (f*(a*d*f*m + b*(2*d*e - c*f*(2 + m)))*(a + b*x)^m*HypergeometricFunctions._₂F₁(-m, -m, 1 - m, (b*(c + d*x))/(b*c - a*d)))/((-((d*(a + b*x))/(b*c - a*d)))^m*(c + d*x)^m*(b*d^3*m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 2)*(e + f*x)^1, x, 3, ((d*e - c*f)*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(d*(b*c - a*d)*(1 + m)) - (f*(a + b*x)^m*HypergeometricFunctions._₂F₁(-m, -m, 1 - m, (b*(c + d*x))/(b*c - a*d)))/((-((d*(a + b*x))/(b*c - a*d)))^m*(c + d*x)^m*(d^2*m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 2)*(e + f*x)^0, x, 1, ((a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/((b*c - a*d)*(1 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 2)/(e + f*x)^1, x, 2, (d*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/((b*c - a*d)*(d*e - c*f)*(1 + m)) + (f*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))))/((c + d*x)^m*((d*e - c*f)^2*m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 2)/(e + f*x)^2, x, 4, -((d*(a*d*f*(2 + m) - b*(d*e + c*f*(1 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/((b*c - a*d)*(b*e - a*f)*(d*e - c*f)^2*(1 + m))) - (f*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/((b*e - a*f)*(d*e - c*f)*(e + f*x)) - (f*(a*d*f*(2 + m) - b*(2*d*e + c*f*m))*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))))/((c + d*x)^m*((b*e - a*f)*(d*e - c*f)^3*m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 2)/(e + f*x)^3, x, 5, (d*(a^2*d^2*f^2*(6 + 5*m + m^2) + b^2*(2*d^2*e^2 + 5*c*d*e*f*(1 + m) - c^2*f^2*(1 - m^2)) - a*b*d*f*(d*e*(9 + 5*m) + c*f*(3 + 5*m + 2*m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(2*(b*c - a*d)*(b*e - a*f)^2*(d*e - c*f)^3*(1 + m)) - (f*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(2*(b*e - a*f)*(d*e - c*f)*(e + f*x)^2) - (f*(b*(4*d*e - c*f*(1 - m)) - a*d*f*(3 + m))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(2*(b*e - a*f)^2*(d*e - c*f)^2*(e + f*x)) - (f*(2*a*b*d*f*(2 + m)*(3*d*e + c*f*m) - b^2*(6*d^2*e^2 + 6*c*d*e*f*m - c^2*f^2*(1 - m)*m) - a^2*d^2*f^2*(6 + 5*m + m^2))*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))))/((c + d*x)^m*(2*(b*e - a*f)^2*(d*e - c*f)^4*m))]

    @test_int [(a + b*x)^m/(c + d*x)^(m + 3)*(e + f*x)^p, x, 3, (b^2*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*(e + f*x)^p*AppellF1(1 + m, 3 + m, -p, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/((c + d*x)^m*((b*(e + f*x))/(b*e - a*f))^p*((b*c - a*d)^3*(1 + m)))]

    @test_int [(2 + 3*x)^m/(1 + 2*x)^(m + 3)*(5 - 4*x)^4, x, 4, If(13>=8, (-(1/9))*(107 - 2*m)*(5 - 4*x)^2*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m) - (1/3)*(5 - 4*x)^3*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m) + (7*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m)*(3*(4638 + 485*m + 108*m^2 - 2*m^3) + 2*(15209 + 1882*m - 530*m^2 + 8*m^3)*x))/(9*(2 + 3*m + m^2)) - (2^(2 - m)*(1323 - 85*m + m^2)*HypergeometricFunctions._₂F₁(-m, -m, 1 - m, -3*(1 + 2*x)))/((1 + 2*x)^m*(9*m)), (-(1/9))*(107 - 2*m)*(5 - 4*x)^2*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m) - (1/3)*(5 - 4*x)^3*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m) + (7*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m)*(3*(4638 + 485*m + 108*m^2 - 2*m^3) + 2*(15209 + 1882*m - 530*m^2 + 8*m^3)*x))/(9*(2 + 3*m + m^2)) - (2^(2 - m)*(1323 - 85*m + m^2)*HypergeometricFunctions._₂F₁(-m, -m, 1 - m, -3*(1 + 2*x)))/((1 + 2*x)^m*(9*m)))]
    @test_int [(2 + 3*x)^m/(1 + 2*x)^(m + 3)*(5 - 4*x)^3, x, 3, If(13>=8, (-(2/3))*(5 - 4*x)^2*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m) + (7*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m)*(3*(186 - m + 2*m^2) + 2*(677 + 102*m - 8*m^2)*x))/(3*(2 + 3*m + m^2)) - (2^(1 - m)*(63 - 2*m)*HypergeometricFunctions._₂F₁(-m, -m, 1 - m, -3*(1 + 2*x)))/((1 + 2*x)^m*(3*m)), (-(2/3))*(5 - 4*x)^2*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m) + (7*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m)*(3*(186 - m + 2*m^2) + 2*(677 + 102*m - 8*m^2)*x))/(3*(2 + 3*m + m^2)) - (2^(1 - m)*(63 - 2*m)*HypergeometricFunctions._₂F₁(-m, -m, 1 - m, -3*(1 + 2*x)))/((1 + 2*x)^m*(3*m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 3)*(e + f*x)^2, x, 4, ((d*e - c*f)^2*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/(d^2*(b*c - a*d)*(2 + m)) - ((d*e - c*f)*(2*a*d*f*(2 + m) - b*(d*e + c*f*(3 + 2*m)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(d^2*(b*c - a*d)^2*(1 + m)*(2 + m)) - (f^2*(a + b*x)^m*HypergeometricFunctions._₂F₁(-m, -m, 1 - m, (b*(c + d*x))/(b*c - a*d)))/((-((d*(a + b*x))/(b*c - a*d)))^m*(c + d*x)^m*(d^3*m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 3)*(e + f*x)^1, x, 2, ((d*e - c*f)*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/(d*(b*c - a*d)*(2 + m)) - ((a*d*f*(2 + m) - b*(d*e + c*f*(1 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(d*(b*c - a*d)^2*(1 + m)*(2 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 3)*(e + f*x)^0, x, 2, ((a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/((b*c - a*d)*(2 + m)) + (b*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/((b*c - a*d)^2*(1 + m)*(2 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 3)/(e + f*x)^1, x, 4, (d*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/((b*c - a*d)*(d*e - c*f)*(2 + m)) + (d*(a*d*f*(2 + m) + b*(d*e - c*f*(3 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/((b*c - a*d)^2*(d*e - c*f)^2*(1 + m)*(2 + m)) - (f^2*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))))/((c + d*x)^m*((d*e - c*f)^3*m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 3)/(e + f*x)^2, x, 5, -((d*(a*d*f*(3 + m) - b*(d*e + c*f*(2 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/((b*c - a*d)*(b*e - a*f)*(d*e - c*f)^2*(2 + m))) - (d*(a^2*d^2*f^2*(6 + 5*m + m^2) - b^2*(d^2*e^2 - c*d*e*f*(5 + 2*m) - c^2*f^2*(2 + 3*m + m^2)) - a*b*d*f*(d*e*(3 + 2*m) + c*f*(9 + 8*m + 2*m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/((b*c - a*d)^2*(b*e - a*f)*(d*e - c*f)^3*(1 + m)*(2 + m)) - (f*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/((b*e - a*f)*(d*e - c*f)*(e + f*x)) + (f^2*(a*d*f*(3 + m) - b*(3*d*e + c*f*m))*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))))/((c + d*x)^m*((b*e - a*f)*(d*e - c*f)^4*m))]

    @test_int [(a + b*x)^m/(c + d*x)^(m + 4)*(e + f*x)^p, x, 3, (b^3*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*(e + f*x)^p*AppellF1(1 + m, 4 + m, -p, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/((c + d*x)^m*((b*(e + f*x))/(b*e - a*f))^p*((b*c - a*d)^4*(1 + m)))]

    @test_int [(2 + 3*x)^m/(1 + 2*x)^(m + 4)*(5 - 4*x)^4, x, 9, If(13>=8, -((49*(15 - 2*m)*(27 + 2*m)*(1 + 2*x)^(-3 - m)*(2 + 3*x)^(1 + m))/(9*(3 + m))) + (14/9)*(15 - 2*m)*(5 - 4*x)*(1 + 2*x)^(-3 - m)*(2 + 3*x)^(1 + m) - (2/3)*(5 - 4*x)^3*(1 + 2*x)^(-3 - m)*(2 + 3*x)^(1 + m) + (196*(42 - m)*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m))/(3*(2 + m)) + (14*(15 - 2*m)*(579 + 52*m + 2*m^2)*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m))/(9*(2 + m)*(3 + m)) - (28*(42 - m)*(29 + 4*m)*(1 + 2*x)^(-1 - m)*(2 + 3*x)^(1 + m))/(3*(1 + m)*(2 + m)) - (14*(15 - 2*m)*(579 + 52*m + 2*m^2)*(1 + 2*x)^(-1 - m)*(2 + 3*x)^(1 + m))/(3*(3 + m)*(2 + 3*m + m^2)) + (2^(3 - m)*(42 - m)*HypergeometricFunctions._₂F₁(-m, -m, 1 - m, -3*(1 + 2*x)))/((1 + 2*x)^m*(3*m)), -((49*(15 - 2*m)*(27 + 2*m)*(1 + 2*x)^(-3 - m)*(2 + 3*x)^(1 + m))/(9*(3 + m))) + (14/9)*(15 - 2*m)*(5 - 4*x)*(1 + 2*x)^(-3 - m)*(2 + 3*x)^(1 + m) - (2/3)*(5 - 4*x)^3*(1 + 2*x)^(-3 - m)*(2 + 3*x)^(1 + m) + (196*(42 - m)*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m))/(3*(2 + m)) + (14*(15 - 2*m)*(579 + 52*m + 2*m^2)*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m))/(9*(6 + 5*m + m^2)) - (28*(42 - m)*(29 + 4*m)*(1 + 2*x)^(-1 - m)*(2 + 3*x)^(1 + m))/(3*(2 + 3*m + m^2)) - (14*(15 - 2*m)*(579 + 52*m + 2*m^2)*(1 + 2*x)^(-1 - m)*(2 + 3*x)^(1 + m))/(3*(6 + 11*m + 6*m^2 + m^3)) + (2^(3 - m)*(42 - m)*HypergeometricFunctions._₂F₁(-m, -m, 1 - m, -3*(1 + 2*x)))/((1 + 2*x)^m*(3*m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 4)*(e + f*x)^3, x, 10, ((d*e - c*f)^3*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m))/(d^3*(b*c - a*d)*(3 + m)) + (3*f*(d*e - c*f)^2*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/(d^3*(b*c - a*d)*(2 + m)) + (2*b*(d*e - c*f)^3*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/(d^3*(b*c - a*d)^2*(2 + m)*(3 + m)) + (3*f^2*(d*e - c*f)*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(d^3*(b*c - a*d)*(1 + m)) + (3*b*f*(d*e - c*f)^2*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(d^3*(b*c - a*d)^2*(1 + m)*(2 + m)) + (2*b^2*(d*e - c*f)^3*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(d^3*(b*c - a*d)^3*(1 + m)*(2 + m)*(3 + m)) - (f^3*(a + b*x)^m*HypergeometricFunctions._₂F₁(-m, -m, 1 - m, (b*(c + d*x))/(b*c - a*d)))/((-((d*(a + b*x))/(b*c - a*d)))^m*(c + d*x)^m*(d^4*m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 4)*(e + f*x)^2, x, 4, -(((d*e - c*f)*(a*d*f*(3 + m) - b*(d*e + c*f*(2 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m))/(b*d^2*(b*c - a*d)*(3 + m))) + ((a^2*d^2*f^2*(6 + 5*m + m^2) - 2*a*b*d*f*(3 + m)*(d*e + c*f*(1 + m)) + b^2*(2*d^2*e^2 + 2*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/(b*d^2*(b*c - a*d)^2*(2 + m)*(3 + m)) + ((a^2*d^2*f^2*(6 + 5*m + m^2) - 2*a*b*d*f*(3 + m)*(d*e + c*f*(1 + m)) + b^2*(2*d^2*e^2 + 2*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(d^2*(b*c - a*d)^3*(1 + m)*(2 + m)*(3 + m)) - (f*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m)*(e + f*x))/(b*d)]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 4)*(e + f*x)^1, x, 3, ((d*e - c*f)*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m))/(d*(b*c - a*d)*(3 + m)) - ((a*d*f*(3 + m) - b*(2*d*e + c*f*(1 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/(d*(b*c - a*d)^2*(2 + m)*(3 + m)) - (b*(a*d*f*(3 + m) - b*(2*d*e + c*f*(1 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(d*(b*c - a*d)^3*(1 + m)*(2 + m)*(3 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 4)*(e + f*x)^0, x, 3, ((a + b*x)^(1 + m)*(c + d*x)^(-3 - m))/((b*c - a*d)*(3 + m)) + (2*b*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/((b*c - a*d)^2*(2 + m)*(3 + m)) + (2*b^2*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/((b*c - a*d)^3*(1 + m)*(2 + m)*(3 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 4)/(e + f*x)^1, x, 5, (d*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m))/((b*c - a*d)*(d*e - c*f)*(3 + m)) + (d*(a*d*f*(3 + m) + b*(2*d*e - c*f*(5 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/((b*c - a*d)^2*(d*e - c*f)^2*(2 + m)*(3 + m)) + (d*(a^2*d^2*f^2*(6 + 5*m + m^2) + a*b*d*f*(3 + m)*(d*e - c*f*(5 + 2*m)) + b^2*(2*d^2*e^2 - c*d*e*f*(7 + m) + c^2*f^2*(11 + 6*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/((b*c - a*d)^3*(d*e - c*f)^3*(1 + m)*(2 + m)*(3 + m)) + (f^3*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))))/((c + d*x)^m*((d*e - c*f)^4*m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 4)/(e + f*x)^2, x, 6, -((d*(a*d*f*(4 + m) - b*(d*e + c*f*(3 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m))/((b*c - a*d)*(b*e - a*f)*(d*e - c*f)^2*(3 + m))) - (d*(a^2*d^2*f^2*(12 + 7*m + m^2) - b^2*(2*d^2*e^2 - 2*c*d*e*f*(4 + m) - c^2*f^2*(6 + 5*m + m^2)) - 2*a*b*d*f*(d*e*(2 + m) + c*f*(10 + 6*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/((b*c - a*d)^2*(b*e - a*f)*(d*e - c*f)^3*(2 + m)*(3 + m)) - (1/((b*c - a*d)^3*(b*e - a*f)*(d*e - c*f)^4*(1 + m)*(2 + m)*(3 + m)))*(d*(a^3*d^3*f^3*(24 + 26*m + 9*m^2 + m^3) - a^2*b*d^2*f^2*(3 + m)*(d*e*(4 + 3*m) + c*f*(20 + 15*m + 3*m^2)) - b^3*(2*d^3*e^3 - 2*c*d^2*e^2*f*(5 + m) + c^2*d*e*f^2*(26 + 17*m + 3*m^2) + c^3*f^3*(6 + 11*m + 6*m^2 + m^3)) - a*b^2*d*f*(2*d^2*e^2*(2 + m) - 2*c*d*e*f*(16 + 15*m + 3*m^2) - c^2*f^2*(44 + 50*m + 21*m^2 + 3*m^3)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)) - (f*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m))/((b*e - a*f)*(d*e - c*f)*(e + f*x)) - (f^3*(a*d*f*(4 + m) - b*(4*d*e + c*f*m))*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))))/((c + d*x)^m*((b*e - a*f)*(d*e - c*f)^5*m))]

    @test_int [(a + b*x)^m/(c + d*x)^(m + 5)*(e + f*x)^p, x, 3, (b^4*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*(e + f*x)^p*AppellF1(1 + m, 5 + m, -p, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/((c + d*x)^m*((b*(e + f*x))/(b*e - a*f))^p*((b*c - a*d)^5*(1 + m)))]

    @test_int [(2 + 3*x)^m/(1 + 2*x)^(m + 5)*(5 - 4*x)^5, x, 16, If(13>=8, -((7*(13 - 2*m)*(5 - 4*x)^3*(1 + 2*x)^(-4 - m)*(2 + 3*x)^(1 + m))/(3*(4 + m))) - (2/3)*(5 - 4*x)^4*(1 + 2*x)^(-4 - m)*(2 + 3*x)^(1 + m) + (24334*(105 - 2*m)*(1 + 2*x)^(-3 - m)*(2 + 3*x)^(1 + m))/(81*(3 + m)) + (1127*(13 - 2*m)*(27 + 2*m)*(1 + 2*x)^(-3 - m)*(2 + 3*x)^(1 + m))/(3*(3 + m)*(4 + m)) - (322*(13 - 2*m)*(5 - 4*x)*(1 + 2*x)^(-3 - m)*(2 + 3*x)^(1 + m))/(3*(4 + m)) - (48668*(105 - 2*m)*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m))/(27*(6 + 5*m + m^2)) - (322*(13 - 2*m)*(579 + 52*m + 2*m^2)*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m))/(3*(2 + m)*(3 + m)*(4 + m)) + (322*(13 - 2*m)*(579 + 52*m + 2*m^2)*(1 + 2*x)^(-1 - m)*(2 + 3*x)^(1 + m))/((3 + m)*(4 + m)*(2 + 3*m + m^2)) + (48668*(105 - 2*m)*(1 + 2*x)^(-1 - m)*(2 + 3*x)^(1 + m))/(9*(6 + 11*m + 6*m^2 + m^3)) - (4232*(105 - 2*m)*(1 + 2*x)^(-3 - m)*(2 + 3*x)^(2 + m))/(27*(3 + m)) + (4232*(105 - 2*m)*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(2 + m))/(9*(6 + 5*m + m^2)) + (736*(105 - 2*m)*(1 + 2*x)^(-3 - m)*(2 + 3*x)^(3 + m))/(27*(3 + m)) - (2^(3 - m)*(105 - 2*m)*(1 + 2*x)^(-3 - m)*HypergeometricFunctions._₂F₁(-3 - m, -3 - m, -2 - m, -3*(1 + 2*x)))/(81*(3 + m)), -((7*(13 - 2*m)*(5 - 4*x)^3*(1 + 2*x)^(-4 - m)*(2 + 3*x)^(1 + m))/(3*(4 + m))) - (2/3)*(5 - 4*x)^4*(1 + 2*x)^(-4 - m)*(2 + 3*x)^(1 + m) + (24334*(105 - 2*m)*(1 + 2*x)^(-3 - m)*(2 + 3*x)^(1 + m))/(81*(3 + m)) + (1127*(13 - 2*m)*(27 + 2*m)*(1 + 2*x)^(-3 - m)*(2 + 3*x)^(1 + m))/(3*(12 + 7*m + m^2)) - (322*(13 - 2*m)*(5 - 4*x)*(1 + 2*x)^(-3 - m)*(2 + 3*x)^(1 + m))/(3*(4 + m)) - (48668*(105 - 2*m)*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m))/(27*(6 + 5*m + m^2)) - (322*(13 - 2*m)*(579 + 52*m + 2*m^2)*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(1 + m))/(3*(24 + 26*m + 9*m^2 + m^3)) + (48668*(105 - 2*m)*(1 + 2*x)^(-1 - m)*(2 + 3*x)^(1 + m))/(9*(6 + 11*m + 6*m^2 + m^3)) + (322*(13 - 2*m)*(579 + 52*m + 2*m^2)*(1 + 2*x)^(-1 - m)*(2 + 3*x)^(1 + m))/(24 + 50*m + 35*m^2 + 10*m^3 + m^4) - (4232*(105 - 2*m)*(1 + 2*x)^(-3 - m)*(2 + 3*x)^(2 + m))/(27*(3 + m)) + (4232*(105 - 2*m)*(1 + 2*x)^(-2 - m)*(2 + 3*x)^(2 + m))/(9*(6 + 5*m + m^2)) + (736*(105 - 2*m)*(1 + 2*x)^(-3 - m)*(2 + 3*x)^(3 + m))/(27*(3 + m)) - (2^(3 - m)*(105 - 2*m)*(1 + 2*x)^(-3 - m)*HypergeometricFunctions._₂F₁(-3 - m, -3 - m, -2 - m, -3*(1 + 2*x)))/(81*(3 + m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 5)*(e + f*x)^4, x, 14, ((d*e - c*f)^4*(a + b*x)^(1 + m)*(c + d*x)^(-4 - m))/(d^4*(b*c - a*d)*(4 + m)) + (4*f*(d*e - c*f)^3*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m))/(d^4*(b*c - a*d)*(3 + m)) + (3*b*(d*e - c*f)^4*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m))/(d^4*(b*c - a*d)^2*(3 + m)*(4 + m)) + (6*f^2*(d*e - c*f)^2*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/(d^4*(b*c - a*d)*(2 + m)) + (8*b*f*(d*e - c*f)^3*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/(d^4*(b*c - a*d)^2*(2 + m)*(3 + m)) + (6*b^2*(d*e - c*f)^4*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/(d^4*(b*c - a*d)^3*(2 + m)*(3 + m)*(4 + m)) + (4*f^3*(d*e - c*f)*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(d^4*(b*c - a*d)*(1 + m)) + (6*b*f^2*(d*e - c*f)^2*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(d^4*(b*c - a*d)^2*(1 + m)*(2 + m)) + (8*b^2*f*(d*e - c*f)^3*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(d^4*(b*c - a*d)^3*(1 + m)*(2 + m)*(3 + m)) + (6*b^3*(d*e - c*f)^4*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(d^4*(b*c - a*d)^4*(1 + m)*(2 + m)*(3 + m)*(4 + m)) - (f^4*(a + b*x)^m*HypergeometricFunctions._₂F₁(-m, -m, 1 - m, (b*(c + d*x))/(b*c - a*d)))/((-((d*(a + b*x))/(b*c - a*d)))^m*(c + d*x)^m*(d^5*m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 5)*(e + f*x)^3, x, 5, -((3*(b*e - a*f)*(d*e - c*f)*(a*d*f*(3 + m) - b*(d*e + c*f*(2 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m))/(b*d^2*(b*c - a*d)^2*(3 + m)*(4 + m))) + (3*(b*e - a*f)*(a^2*d^2*f^2*(6 + 5*m + m^2) - 2*a*b*d*f*(3 + m)*(d*e + c*f*(1 + m)) + b^2*(2*d^2*e^2 + 2*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/(b*d^2*(b*c - a*d)^3*(2 + m)*(3 + m)*(4 + m)) + (3*(b*e - a*f)*(a^2*d^2*f^2*(6 + 5*m + m^2) - 2*a*b*d*f*(3 + m)*(d*e + c*f*(1 + m)) + b^2*(2*d^2*e^2 + 2*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(d^2*(b*c - a*d)^4*(1 + m)*(2 + m)*(3 + m)*(4 + m)) - (3*f*(b*e - a*f)*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m)*(e + f*x))/(b*d*(b*c - a*d)*(4 + m)) + ((a + b*x)^(1 + m)*(c + d*x)^(-4 - m)*(e + f*x)^3)/((b*c - a*d)*(4 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 5)*(e + f*x)^2, x, 5, -(((d*e - c*f)*(a*d*f*(4 + m) - b*(2*d*e + c*f*(2 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-4 - m))/(2*b*d^2*(b*c - a*d)*(4 + m))) + ((a^2*d^2*f^2*(12 + 7*m + m^2) - 2*a*b*d*f*(4 + m)*(2*d*e + c*f*(1 + m)) + b^2*(6*d^2*e^2 + 4*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m))/(2*b*d^2*(b*c - a*d)^2*(3 + m)*(4 + m)) + ((a^2*d^2*f^2*(12 + 7*m + m^2) - 2*a*b*d*f*(4 + m)*(2*d*e + c*f*(1 + m)) + b^2*(6*d^2*e^2 + 4*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/(d^2*(b*c - a*d)^3*(2 + m)*(3 + m)*(4 + m)) + (b*(a^2*d^2*f^2*(12 + 7*m + m^2) - 2*a*b*d*f*(4 + m)*(2*d*e + c*f*(1 + m)) + b^2*(6*d^2*e^2 + 4*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(d^2*(b*c - a*d)^4*(1 + m)*(2 + m)*(3 + m)*(4 + m)) - (f*(a + b*x)^(1 + m)*(c + d*x)^(-4 - m)*(e + f*x))/(2*b*d)]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 5)*(e + f*x)^1, x, 4, ((d*e - c*f)*(a + b*x)^(1 + m)*(c + d*x)^(-4 - m))/(d*(b*c - a*d)*(4 + m)) - ((a*d*f*(4 + m) - b*(3*d*e + c*f*(1 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m))/(d*(b*c - a*d)^2*(3 + m)*(4 + m)) - (2*b*(a*d*f*(4 + m) - b*(3*d*e + c*f*(1 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/(d*(b*c - a*d)^3*(2 + m)*(3 + m)*(4 + m)) - (2*b^2*(a*d*f*(4 + m) - b*(3*d*e + c*f*(1 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/(d*(b*c - a*d)^4*(1 + m)*(2 + m)*(3 + m)*(4 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 5)*(e + f*x)^0, x, 4, ((a + b*x)^(1 + m)*(c + d*x)^(-4 - m))/((b*c - a*d)*(4 + m)) + (3*b*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m))/((b*c - a*d)^2*(3 + m)*(4 + m)) + (6*b^2*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/((b*c - a*d)^3*(2 + m)*(3 + m)*(4 + m)) + (6*b^3*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/((b*c - a*d)^4*(1 + m)*(2 + m)*(3 + m)*(4 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + 5)/(e + f*x)^1, x, 6, (d*(a + b*x)^(1 + m)*(c + d*x)^(-4 - m))/((b*c - a*d)*(d*e - c*f)*(4 + m)) + (d*(a*d*f*(4 + m) + b*(3*d*e - c*f*(7 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m))/((b*c - a*d)^2*(d*e - c*f)^2*(3 + m)*(4 + m)) + (d*(a^2*d^2*f^2*(12 + 7*m + m^2) + 2*a*b*d*f*(4 + m)*(d*e - c*f*(4 + m)) + b^2*(6*d^2*e^2 - 2*c*d*e*f*(10 + m) + c^2*f^2*(26 + 9*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/((b*c - a*d)^3*(d*e - c*f)^3*(2 + m)*(3 + m)*(4 + m)) + (1/((b*c - a*d)^4*(d*e - c*f)^4*(1 + m)*(2 + m)*(3 + m)*(4 + m)))*(d*(a^3*d^3*f^3*(24 + 26*m + 9*m^2 + m^3) + a^2*b*d^2*f^2*(12 + 7*m + m^2)*(d*e - c*f*(7 + 3*m)) + a*b^2*d*f*(4 + m)*(2*d^2*e^2 - 2*c*d*e*f*(5 + m) + c^2*f^2*(26 + 17*m + 3*m^2)) + b^3*(6*d^3*e^3 - 2*c*d^2*e^2*f*(13 + m) + c^2*d*e*f^2*(46 + 11*m + m^2) - c^3*f^3*(50 + 35*m + 10*m^2 + m^3)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)) - (f^4*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))))/((c + d*x)^m*((d*e - c*f)^5*m))]
    #= [(a + b*x)^m/(c + d*x)^(m + 5)/(e + f*x)^2, x, 7, -((d*(a*d*f*(5 + m) - b*(d*e + c*f*(4 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-4 - m))/((b*c - a*d)*(b*e - a*f)*(d*e - c*f)^2*(4 + m))) - (d*(a^2*d^2*f^2*(20 + 9*m + m^2) - b^2*(3*d^2*e^2 - c*d*e*f*(11 + 2*m) - c^2*f^2*(12 + 7*m + m^2)) - a*b*d*f*(d*e*(5 + 2*m) + c*f*(35 + 16*m + 2*m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m))/((b*c - a*d)^2*(b*e - a*f)*(d*e - c*f)^3*(3 + m)*(4 + m)) - (d*(a^3*d^3*f^3*(60 + 47*m + 12*m^2 + m^3) - a^2*b*d^2*f^2*(4 + m)*(d*e*(5 + 3*m) + c*f*(40 + 21*m + 3*m^2)) - b^3*(6*d^3*e^3 - 4*c*d^2*e^2*f*(7 + m) + c^2*d*e*f^2*(58 + 25*m + 3*m^2) + c^3*f^3*(24 + 26*m + 9*m^2 + m^3)) - a*b^2*d*f*(2*d^2*e^2*(5 + 2*m) - 6*c*d*e*f*(10 + 7*m + m^2) - c^2*f^2*(130 + 103*m + 30*m^2 + 3*m^3)))*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/((b*c - a*d)^3*(b*e - a*f)*(d*e - c*f)^4*(2 + m)*(3 + m)*(4 + m)) - (d*(a^4*d^4*f^4*(120 + 154*m + 71*m^2 + 14*m^3 + m^4) - a^3*b*d^3*f^3*(12 + 7*m + m^2)*(d*e*(5 + 4*m) + c*f*(35 + 24*m + 4*m^2)) - a^2*b^2*d^2*f^2*(4 + m)*(d^2*e^2*(5 + 3*m) - c*d*e*f*(55 + 57*m + 12*m^2) - 2*c^2*f^2*(65 + 66*m + 24*m^2 + 3*m^3)) - b^4*(6*d^4*e^4 - 2*c*d^3*e^3*f*(17 + 2*m) + c^2*d^2*e^2*f^2*(86 + 29*m + 3*m^2) - c^3*d*e*f^3*(154 + 129*m + 39*m^2 + 4*m^3) - c^4*f^4*(24 + 50*m + 35*m^2 + 10*m^3 + m^4)) - a*b^3*d*f*(2*d^3*e^3*(5 + 2*m) - 2*c*d^2*e^2*f*(35 + 23*m + 3*m^2) + c^2*d*e*f^2*(290 + 329*m + 111*m^2 + 12*m^3) + c^3*f^3*(250 + 329*m + 179*m^2 + 44*m^3 + 4*m^4)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/((b*c - a*d)^4*(b*e - a*f)*(d*e - c*f)^5*(1 + m)*(2 + m)*(3 + m)*(4 + m)) - (f*(a + b*x)^(1 + m)*(c + d*x)^(-4 - m))/((b*e - a*f)*(d*e - c*f)*(e + f*x)) + (f^4*(a*d*f*(5 + m) - b*(5*d*e + c*f*m))*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))))/((c + d*x)^m*((b*e - a*f)*(d*e - c*f)^6*m))] =#

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(a + b*x)^m/(c + d*x)^(m - 1)*(e + f*x)^p, x, 3, ((b*c - a*d)*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*(e + f*x)^p*AppellF1(1 + m, -1 + m, -p, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/((c + d*x)^m*((b*(e + f*x))/(b*e - a*f))^p*(b^2*(1 + m)))]

    @test_int [(a + b*x)^m/(c + d*x)^(m - 1)*(e + f*x)^3, x, 4, (f*(a + b*x)^(1 + m)*(c + d*x)^(2 - m)*(e + f*x)^2)/(5*b*d) + (f*(a + b*x)^(1 + m)*(c + d*x)^(2 - m)*(a^2*d^2*f^2*(12 - 7*m + m^2) - a*b*d*f*(15*d*e*(3 - m) - c*f*(9 + 2*m - 2*m^2)) + b^2*(48*d^2*e^2 - 15*c*d*e*f*(2 + m) + c^2*f^2*(6 + 5*m + m^2)) - 3*b*d*f*(a*d*f*(4 - m) - b*(7*d*e - c*f*(3 + m)))*x))/(60*b^3*d^3) - (1/(60*b^5*d^3*(1 + m)))*(((b*c - a*d)*(a^3*d^3*f^3*(24 - 26*m + 9*m^2 - m^3) - 3*a^2*b*d^2*f^2*(6 - 5*m + m^2)*(5*d*e - c*f*(1 + m)) + 3*a*b^2*d*f*(2 - m)*(20*d^2*e^2 - 10*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)) - b^3*(60*d^3*e^3 - 60*c*d^2*e^2*f*(1 + m) + 15*c^2*d*e*f^2*(2 + 3*m + m^2) - c^3*f^3*(6 + 11*m + 6*m^2 + m^3)))*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(-1 + m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/(c + d*x)^m)]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 1)*(e + f*x)^2, x, 4, -((f*(a*d*f*(3 - m) - b*(5*d*e - c*f*(2 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(2 - m))/(12*b^2*d^2)) + (f*(a + b*x)^(1 + m)*(c + d*x)^(2 - m)*(e + f*x))/(4*b*d) + (1/(12*b^4*d^2*(1 + m)))*(((b*c - a*d)*(a^2*d^2*f^2*(6 - 5*m + m^2) - 2*a*b*d*f*(2 - m)*(4*d*e - c*f*(1 + m)) + b^2*(12*d^2*e^2 - 8*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)))*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(-1 + m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/(c + d*x)^m)]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 1)*(e + f*x)^1, x, 3, (f*(a + b*x)^(1 + m)*(c + d*x)^(2 - m))/(3*b*d) - ((b*c - a*d)*(a*d*f*(2 - m) - b*(3*d*e - c*f*(1 + m)))*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(-1 + m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(3*b^3*d*(1 + m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 1)*(e + f*x)^0, x, 2, ((b*c - a*d)*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(-1 + m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(b^2*(1 + m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 1)/(e + f*x)^1, x, 6, -((d*(d*e - c*f)*(a + b*x)^(1 + m))/((c + d*x)^m*((b*c - a*d)*f^2*m))) - ((d*e - c*f)*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))))/((c + d*x)^m*(f^2*m)) + (d*(b*(d*e - c*f*(1 - m)) - a*d*f*m)*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(b*(b*c - a*d)*f^2*m*(1 + m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 1)/(e + f*x)^2, x, 6, -(((a + b*x)^m*(c + d*x)^(1 - m))/(f*(e + f*x))) + ((a*d*f*(1 - m) - b*(d*e - c*f*m))*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, m, 1 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))))/((c + d*x)^m*(f^2*(b*e - a*f)*m)) + (d*(a + b*x)^m*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(m, m, 1 + m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(f^2*m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 1)/(e + f*x)^3, x, 1, ((b*c - a*d)^2*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*HypergeometricFunctions._₂F₁(3, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))))/((b*e - a*f)^3*(1 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 1)/(e + f*x)^4, x, 2, -((f*(a + b*x)^(1 + m)*(c + d*x)^(2 - m))/(3*(b*e - a*f)*(d*e - c*f)*(e + f*x)^3)) + ((b*c - a*d)^2*(b*(3*d*e - c*f*(2 - m)) - a*d*f*(1 + m))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*HypergeometricFunctions._₂F₁(3, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))))/(3*(b*e - a*f)^4*(d*e - c*f)*(1 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 1)/(e + f*x)^5, x, 4, -((f*(a + b*x)^(1 + m)*(c + d*x)^(2 - m))/(4*(b*e - a*f)*(d*e - c*f)*(e + f*x)^4)) - (f*(b*(5*d*e - c*f*(3 - m)) - a*d*f*(2 + m))*(a + b*x)^(1 + m)*(c + d*x)^(2 - m))/(12*(b*e - a*f)^2*(d*e - c*f)^2*(e + f*x)^3) - ((b*c - a*d)^2*(2*a*b*d*f*(4*d*e - c*f*(2 - m))*(1 + m) - a^2*d^2*f^2*(2 + 3*m + m^2) - b^2*(12*d^2*e^2 - 8*c*d*e*f*(2 - m) + c^2*f^2*(6 - 5*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*HypergeometricFunctions._₂F₁(3, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))))/(12*(b*e - a*f)^5*(d*e - c*f)^2*(1 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 1)/(e + f*x)^6, x, 5, -((f*(a + b*x)^(1 + m)*(c + d*x)^(2 - m))/(5*(b*e - a*f)*(d*e - c*f)*(e + f*x)^5)) - (f*(b*(7*d*e - c*f*(4 - m)) - a*d*f*(3 + m))*(a + b*x)^(1 + m)*(c + d*x)^(2 - m))/(20*(b*e - a*f)^2*(d*e - c*f)^2*(e + f*x)^4) - (f*(a^2*d^2*f^2*(6 + 5*m + m^2) - a*b*d*f*(3*d*e*(7 + 4*m) - c*f*(9 + 2*m - 2*m^2)) + b^2*(27*d^2*e^2 - 3*c*d*e*f*(11 - 4*m) + c^2*f^2*(12 - 7*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(2 - m))/(60*(b*e - a*f)^3*(d*e - c*f)^3*(e + f*x)^3) + (1/(60*(b*e - a*f)^6*(d*e - c*f)^3*(1 + m)))*((b*c - a*d)^2*(3*a^2*b*d^2*f^2*(5*d*e - c*f*(2 - m))*(2 + 3*m + m^2) - a^3*d^3*f^3*(6 + 11*m + 6*m^2 + m^3) - 3*a*b^2*d*f*(1 + m)*(20*d^2*e^2 - 10*c*d*e*f*(2 - m) + c^2*f^2*(6 - 5*m + m^2)) + b^3*(60*d^3*e^3 - 60*c*d^2*e^2*f*(2 - m) + 15*c^2*d*e*f^2*(6 - 5*m + m^2) - c^3*f^3*(24 - 26*m + 9*m^2 - m^3)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*HypergeometricFunctions._₂F₁(3, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))))]

    @test_int [(a + b*x)^m/(c + d*x)^(m - 2)*(e + f*x)^p, x, 3, ((b*c - a*d)^2*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*(e + f*x)^p*AppellF1(1 + m, -2 + m, -p, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/((c + d*x)^m*((b*(e + f*x))/(b*e - a*f))^p*(b^3*(1 + m)))]

    @test_int [(a + b*x)^m/(c + d*x)^(m - 2)*(e + f*x)^3, x, 4, (f*(a + b*x)^(1 + m)*(c + d*x)^(3 - m)*(e + f*x)^2)/(6*b*d) + (f*(a + b*x)^(1 + m)*(c + d*x)^(3 - m)*(a^2*d^2*f^2*(20 - 9*m + m^2) - 2*a*b*d*f*(9*d*e*(4 - m) - c*f*(6 + 2*m - m^2)) + b^2*(70*d^2*e^2 - 18*c*d*e*f*(2 + m) + c^2*f^2*(6 + 5*m + m^2)) - 4*b*d*f*(a*d*f*(5 - m) - b*(8*d*e - c*f*(3 + m)))*x))/(120*b^3*d^3) - (1/(120*b^6*d^3*(1 + m)))*(((b*c - a*d)^2*(a^3*d^3*f^3*(60 - 47*m + 12*m^2 - m^3) - 3*a^2*b*d^2*f^2*(12 - 7*m + m^2)*(6*d*e - c*f*(1 + m)) + 3*a*b^2*d*f*(3 - m)*(30*d^2*e^2 - 12*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)) - b^3*(120*d^3*e^3 - 90*c*d^2*e^2*f*(1 + m) + 18*c^2*d*e*f^2*(2 + 3*m + m^2) - c^3*f^3*(6 + 11*m + 6*m^2 + m^3)))*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(-2 + m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/(c + d*x)^m)]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 2)*(e + f*x)^2, x, 4, -((f*(a*d*f*(4 - m) - b*(6*d*e - c*f*(2 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(3 - m))/(20*b^2*d^2)) + (f*(a + b*x)^(1 + m)*(c + d*x)^(3 - m)*(e + f*x))/(5*b*d) + (1/(20*b^5*d^2*(1 + m)))*(((b*c - a*d)^2*(a^2*d^2*f^2*(12 - 7*m + m^2) - 2*a*b*d*f*(3 - m)*(5*d*e - c*f*(1 + m)) + b^2*(20*d^2*e^2 - 10*c*d*e*f*(1 + m) + c^2*f^2*(2 + 3*m + m^2)))*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(-2 + m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/(c + d*x)^m)]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 2)*(e + f*x)^1, x, 3, (f*(a + b*x)^(1 + m)*(c + d*x)^(3 - m))/(4*b*d) - ((b*c - a*d)^2*(a*d*f*(3 - m) - b*(4*d*e - c*f*(1 + m)))*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(-2 + m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(4*b^4*d*(1 + m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 2)*(e + f*x)^0, x, 2, ((b*c - a*d)^2*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(-2 + m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(b^3*(1 + m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 2)/(e + f*x)^1, x, 6, -((d*(2*a*b*c*d*f^2*m - a^2*d^2*f^2*m - b^2*(2*d^2*e^2 - 4*c*d*e*f + c^2*f^2*(2 + m)))*(a + b*x)^(1 + m))/((c + d*x)^m*(2*b^2*(b*c - a*d)*f^3*m))) + (d^2*(a + b*x)^(2 + m))/((c + d*x)^m*(2*b^2*f)) + ((d*e - c*f)^2*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))))/((c + d*x)^m*(f^3*m)) + (d*(2*a*b*d*f*(d*e - c*f*(2 - m))*m + a^2*d^2*f^2*(1 - m)*m - b^2*(2*d^2*e^2 - 2*c*d*e*f*(2 - m) + c^2*f^2*(2 - 3*m + m^2)))*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(2*b^2*(b*c - a*d)*f^3*m*(1 + m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 2)/(e + f*x)^2, x, 7, -((2*d^2*(d*e - c*f)*(a + b*x)^(1 + m))/((c + d*x)^m*((b*c - a*d)*f^3*m))) + ((d*e - c*f)^2*(a + b*x)^(1 + m))/((c + d*x)^m*(f^2*(b*e - a*f)*(e + f*x))) + ((d*e - c*f)*(a*d*f*(2 - m) - b*(2*d*e - c*f*m))*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))))/((c + d*x)^m*(f^3*(b*e - a*f)*m)) + (d^2*(b*(2*d*e - c*f*(2 - m)) - a*d*f*m)*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(b*(b*c - a*d)*f^3*m*(1 + m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 2)/(e + f*x)^3, x, 7, ((b*e - a*f)*(a + b*x)^(-1 + m)*(c + d*x)^(2 - m))/(2*f^2*(e + f*x)^2) + ((a*d*f*(2 - m) - b*(3*d*e - c*f*(1 + m)))*(a + b*x)^(-1 + m)*(c + d*x)^(2 - m))/(2*f^2*(d*e - c*f)*(e + f*x)) - ((2*a*b*d*f*(2 - m)*(d*e - c*f*m) - b^2*(2*d^2*e^2 - 2*c*d*e*f*m - c^2*f^2*(1 - m)*m) - a^2*d^2*f^2*(2 - 3*m + m^2))*(a + b*x)^(-1 + m)*(c + d*x)^(1 - m)*HypergeometricFunctions._₂F₁(1, -1 + m, m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))))/(2*f^3*(b*e - a*f)*(d*e - c*f)*(1 - m)) - (d*(b*c - a*d)*(a + b*x)^(-1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(-1 + m, -1 + m, m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(f^3*(1 - m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 2)/(e + f*x)^4, x, 1, ((b*c - a*d)^3*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*HypergeometricFunctions._₂F₁(4, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))))/((b*e - a*f)^4*(1 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 2)/(e + f*x)^5, x, 2, -((f*(a + b*x)^(1 + m)*(c + d*x)^(3 - m))/(4*(b*e - a*f)*(d*e - c*f)*(e + f*x)^4)) + ((b*c - a*d)^3*(b*(4*d*e - c*f*(3 - m)) - a*d*f*(1 + m))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*HypergeometricFunctions._₂F₁(4, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))))/(4*(b*e - a*f)^5*(d*e - c*f)*(1 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 2)/(e + f*x)^6, x, 4, -((f*(a + b*x)^(1 + m)*(c + d*x)^(3 - m))/(5*(b*e - a*f)*(d*e - c*f)*(e + f*x)^5)) - (f*(b*(6*d*e - c*f*(4 - m)) - a*d*f*(2 + m))*(a + b*x)^(1 + m)*(c + d*x)^(3 - m))/(20*(b*e - a*f)^2*(d*e - c*f)^2*(e + f*x)^4) - ((b*c - a*d)^3*(2*a*b*d*f*(5*d*e - c*f*(3 - m))*(1 + m) - a^2*d^2*f^2*(2 + 3*m + m^2) - b^2*(20*d^2*e^2 - 10*c*d*e*f*(3 - m) + c^2*f^2*(12 - 7*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*HypergeometricFunctions._₂F₁(4, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))))/(20*(b*e - a*f)^6*(d*e - c*f)^2*(1 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 2)/(e + f*x)^7, x, 5, -((f*(a + b*x)^(1 + m)*(c + d*x)^(3 - m))/(6*(b*e - a*f)*(d*e - c*f)*(e + f*x)^6)) - (f*(b*(8*d*e - c*f*(5 - m)) - a*d*f*(3 + m))*(a + b*x)^(1 + m)*(c + d*x)^(3 - m))/(30*(b*e - a*f)^2*(d*e - c*f)^2*(e + f*x)^5) - (f*(a^2*d^2*f^2*(6 + 5*m + m^2) - 2*a*b*d*f*(d*e*(12 + 7*m) - c*f*(6 + 2*m - m^2)) + b^2*(38*d^2*e^2 - 2*c*d*e*f*(26 - 7*m) + c^2*f^2*(20 - 9*m + m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(3 - m))/(120*(b*e - a*f)^3*(d*e - c*f)^3*(e + f*x)^4) + (1/(120*(b*e - a*f)^7*(d*e - c*f)^3*(1 + m)))*(b*c - a*d)^3*(3*a^2*b*d^2*f^2*(6*d*e - c*f*(3 - m))*(2 + 3*m + m^2) - a^3*d^3*f^3*(6 + 11*m + 6*m^2 + m^3) - 3*a*b^2*d*f*(1 + m)*(30*d^2*e^2 - 12*c*d*e*f*(3 - m) + c^2*f^2*(12 - 7*m + m^2)) + b^3*(120*d^3*e^3 - 90*c*d^2*e^2*f*(3 - m) + 18*c^2*d*e*f^2*(12 - 7*m + m^2) - c^3*f^3*(60 - 47*m + 12*m^2 - m^3)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*HypergeometricFunctions._₂F₁(4, 1 + m, 2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x)))]

    @test_int [(a + b*x)^m/(c + d*x)^(m - 3)/(e + f*x)^1, x, 7, (b*(b*e - a*f)^3*(a + b*x)^(-3 + m)*(c + d*x)^(4 - m))/((b*c - a*d)*f^4*(3 - m)) - (b*(b*(3*d*e - c*f*(1 - m)) - a*d*f*(2 + m))*(a + b*x)^(-2 + m)*(c + d*x)^(4 - m))/(6*d^2*f^2) + (b*(a + b*x)^(-1 + m)*(c + d*x)^(4 - m))/(3*d*f) - ((b*e - a*f)^3*(a + b*x)^(-3 + m)*(c + d*x)^(3 - m)*HypergeometricFunctions._₂F₁(1, -3 + m, -2 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))))/(f^4*(3 - m)) - (1/((6*b^3*d^2*f^4*(2 - m)*(3 - m))*(c + d*x)^m))*((b*c - a*d)^2*(3*a^2*b*d^2*f^2*(d*e - c*f*(3 - m))*(1 - m)*m + a^3*d^3*f^3*m*(2 - 3*m + m^2) + 3*a*b^2*d*f*m*(2*d^2*e^2 - 2*c*d*e*f*(3 - m) + c^2*f^2*(6 - 5*m + m^2)) - b^3*(6*d^3*e^3 - 6*c*d^2*e^2*f*(3 - m) + 3*c^2*d*e*f^2*(6 - 5*m + m^2) - c^3*f^3*(6 - 11*m + 6*m^2 - m^3)))*(a + b*x)^(-2 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(-3 + m, -2 + m, -1 + m, -((d*(a + b*x))/(b*c - a*d)))), -((d*(3*a^2*b*d^2*f^2*(d*e - c*f*(5 - m))*m - 3*a*b^2*c*d*f^2*(2*d*e - c*f*(6 - m))*m + a^3*d^3*f^3*(4 - m)*m + b^3*(6*d^3*e^3 - 18*c*d^2*e^2*f + 3*c^2*d*e*f^2*(6 + m) - c^3*f^3*(6 + 7*m - m^2)))*(a + b*x)^(1 + m))/((c + d*x)^m*(6*b^3*(b*c - a*d)*f^4*m))) - (d^2*(b*(3*d*e - c*f*(9 - m)) + a*d*f*(6 - m))*(a + b*x)^(2 + m))/((c + d*x)^m*(6*b^3*f^2)) + (d^3*(a + b*x)^(3 + m))/((c + d*x)^m*(3*b^3*f)) - ((d*e - c*f)^3*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))))/((c + d*x)^m*(f^4*m)) - (1/((6*b^3*(b*c - a*d)*f^4*m*(1 + m))*(c + d*x)^m))*(d*(3*a^2*b*d^2*f^2*(d*e - c*f*(3 - m))*(1 - m)*m + a^3*d^3*f^3*m*(2 - 3*m + m^2) + 3*a*b^2*d*f*m*(2*d^2*e^2 - 2*c*d*e*f*(3 - m) + c^2*f^2*(6 - 5*m + m^2)) - b^3*(6*d^3*e^3 - 6*c*d^2*e^2*f*(3 - m) + 3*c^2*d*e*f^2*(6 - 5*m + m^2) - c^3*f^3*(6 - 11*m + 6*m^2 - m^3)))*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 3)/(e + f*x)^2, x, 2, (3*b*d*(d*e - c*f)^2*(a + b*x)^m*(c + d*x)^(1 - m))/((b*c - a*d)*f^4*m) + (d^2*(a + b*x)^(1 + m)*(c + d*x)^(1 - m))/(2*b*f^2) - ((d*e - c*f)^2*(a + b*x)^m*(c + d*x)^(1 - m))/(f^3*(e + f*x)) + ((d*e - c*f)^2*(a*d*f*(3 - m) - b*(3*d*e - c*f*m))*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, m, 1 + m, ((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x))))/((c + d*x)^m*(f^4*(b*e - a*f)*m)) + (d^2*(2*a*b*d*f*(2*d*e - c*f*(3 - m))*m + a^2*d^2*f^2*(1 - m)*m - b^2*(6*d^2*e^2 - 4*c*d*e*f*(3 - m) + c^2*f^2*(6 - 5*m + m^2)))*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(2*b^2*(b*c - a*d)*f^4*m*(1 + m))), ((b*c - a*d)^3*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*AppellF1(1 + m, -3 + m, 2, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/((c + d*x)^m*(b^2*(b*e - a*f)^2*(1 + m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m - 3)/(e + f*x)^3, x, 8, -((3*d^3*(d*e - c*f)*(a + b*x)^(1 + m))/((c + d*x)^m*((b*c - a*d)*f^4*m))) - ((d*e - c*f)^3*(a + b*x)^(1 + m))/((c + d*x)^m*(2*f^3*(b*e - a*f)*(e + f*x)^2)) + ((d*e - c*f)^2*(b*(5*d*e + c*f*(1 - m)) - a*d*f*(6 - m))*(a + b*x)^(1 + m))/((c + d*x)^m*(2*f^3*(b*e - a*f)^2*(e + f*x))) + ((d*e - c*f)*(2*a*b*d*f*(3 - m)*(2*d*e - c*f*m) - b^2*(6*d^2*e^2 - 4*c*d*e*f*m - c^2*f^2*(1 - m)*m) - a^2*d^2*f^2*(6 - 5*m + m^2))*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))))/((c + d*x)^m*(2*f^4*(b*e - a*f)^2*m)) + (d^3*(b*(3*d*e - c*f*(3 - m)) - a*d*f*m)*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(b*(b*c - a*d)*f^4*m*(1 + m)))]

    @test_int [(a + b*x)^(1 - n)*(c + d*x)^(1 + n)/(b*c + a*d + 2*b*d*x)^1, x, 6, ((b*c - a*d)*(3 - 2*n)*(a + b*x)^(2 - n)*(c + d*x)^(-1 + n))/(8*b^3*(1 - n)) + (d*(a + b*x)^(3 - n)*(c + d*x)^(-1 + n))/(4*b^3) + ((b*c - a*d)^2*(a + b*x)^(1 - n)*(c + d*x)^(-1 + n)*HypergeometricFunctions._₂F₁(1, -1 + n, n, -((b*(c + d*x))/(d*(a + b*x)))))/(8*b^3*d*(1 - n)) - ((b*c - a*d)^2*(1 - 2*n^2)*(-((d*(a + b*x))/(b*c - a*d)))^n*(c + d*x)^n*HypergeometricFunctions._₂F₁(-1 + n, n, 1 + n, (b*(c + d*x))/(b*c - a*d)))/((a + b*x)^n*(8*b^2*d^2*(1 - n)*n))]
    @test_int [(a + b*x)^(1 - n)*(c + d*x)^(1 + n)/(b*c + a*d + 2*b*d*x)^2, x, 4, -(((b*c - a*d)*(a + b*x)^(1 - n)*(c + d*x)^(-1 + n)*HypergeometricFunctions._₂F₁(2, 1 - n, 2 - n, -((d*(a + b*x))/(b*(c + d*x)))))/(4*b^3*d*(1 - n))) + ((-((d*(a + b*x))/(b*c - a*d)))^n*(c + d*x)^(1 + n)*HypergeometricFunctions._₂F₁(n, 1 + n, 2 + n, (b*(c + d*x))/(b*c - a*d)))/((a + b*x)^n*(4*b*d^2*(1 + n)))]
    @test_int [(a + b*x)^(1 - n)*(c + d*x)^(1 + n)/(b*c + a*d + 2*b*d*x)^3, x, 7, -(((b*c - a*d)*(a + b*x)^(1 - n)*(c + d*x)^n)/(8*b^2*d*(b*c + a*d + 2*b*d*x)^2)) - ((1 + 2*n)*(a + b*x)^(1 - n)*(c + d*x)^n)/(8*b^2*d*(b*c + a*d + 2*b*d*x)) - ((1 - 2*n^2)*(c + d*x)^n*HypergeometricFunctions._₂F₁(1, n, 1 + n, -((b*(c + d*x))/(d*(a + b*x)))))/((a + b*x)^n*(8*b^2*d^2*n)) + ((-((d*(a + b*x))/(b*c - a*d)))^n*(c + d*x)^n*HypergeometricFunctions._₂F₁(n, n, 1 + n, (b*(c + d*x))/(b*c - a*d)))/((a + b*x)^n*(8*b^2*d^2*n))]
    @test_int [(a + b*x)^(1 - n)*(c + d*x)^(1 + n)/(b*c + a*d + 2*b*d*x)^4, x, 1, ((a + b*x)^(2 - n)*(c + d*x)^(-2 + n)*HypergeometricFunctions._₂F₁(4, 2 - n, 3 - n, -((d*(a + b*x))/(b*(c + d*x)))))/(b^4*(b*c - a*d)*(2 - n))]

    @test_int [(a + b*x)^m*(c + d*x)^(2 - m)/(b*c + a*d + 2*b*d*x)^1, x, 6, ((b*c - a*d)*(1 + 2*m)*(a + b*x)^(1 + m))/((c + d*x)^m*(8*b^3*m)) + (d*(a + b*x)^(2 + m))/((c + d*x)^m*(4*b^3)) + ((b*c - a*d)^2*(a + b*x)^m*HypergeometricFunctions._₂F₁(1, -m, 1 - m, -((b*(c + d*x))/(d*(a + b*x)))))/((c + d*x)^m*(8*b^3*d*m)) - ((b*c - a*d)*(1 - 4*m + 2*m^2)*(a + b*x)^(1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(m, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(8*b^3*m*(1 + m)))]
    @test_int [(a + b*x)^m*(c + d*x)^(2 - m)/(b*c + a*d + 2*b*d*x)^2, x, 4, -(((b*c - a*d)*(a + b*x)^m*HypergeometricFunctions._₂F₁(2, m, 1 + m, -((d*(a + b*x))/(b*(c + d*x)))))/((c + d*x)^m*(4*b^3*d*m))) + ((b*c - a*d)*(a + b*x)^m*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(-1 + m, m, 1 + m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(4*b^3*d*m))]
    @test_int [(a + b*x)^m*(c + d*x)^(2 - m)/(b*c + a*d + 2*b*d*x)^3, x, 7, ((b*c - a*d)*(a + b*x)^(-1 + m)*(c + d*x)^(2 - m))/(8*b*d^2*(b*c + a*d + 2*b*d*x)^2) + ((1 - 2*m)*(a + b*x)^(-1 + m)*(c + d*x)^(2 - m))/(8*b*d^2*(b*c + a*d + 2*b*d*x)) - ((1 - 4*m + 2*m^2)*(a + b*x)^(-1 + m)*(c + d*x)^(1 - m)*HypergeometricFunctions._₂F₁(1, -1 + m, m, -((d*(a + b*x))/(b*(c + d*x)))))/(8*b^2*d^2*(1 - m)) - ((b*c - a*d)*(a + b*x)^(-1 + m)*((b*(c + d*x))/(b*c - a*d))^m*HypergeometricFunctions._₂F₁(-1 + m, -1 + m, m, -((d*(a + b*x))/(b*c - a*d))))/((c + d*x)^m*(8*b^3*d^2*(1 - m)))]
    @test_int [(a + b*x)^m*(c + d*x)^(2 - m)/(b*c + a*d + 2*b*d*x)^4, x, 1, ((a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*HypergeometricFunctions._₂F₁(4, 1 + m, 2 + m, -((d*(a + b*x))/(b*(c + d*x)))))/(b^4*(b*c - a*d)*(1 + m))]

    #= ::Subsubsection::Closed:: =#
    #=n*symbolic=#

    @test_int [(a + b*x)^m/(c + d*x)^(m + n)*(e + f*x)^(n + p), x, 3, ((a + b*x)^(1 + m)*(c + d*x)^(-m - n)*((b*(c + d*x))/(b*c - a*d))^(m + n)*(e + f*x)^(n + p)*((b*(e + f*x))/(b*e - a*f))^(-n - p)*AppellF1(1 + m, m + n, -n - p, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(b*(1 + m))]

    @test_int [(a + b*x)^m/(c + d*x)^(m + n)*(e + f*x)^(n + 1), x, 3, ((b*e - a*f)*(a + b*x)^(1 + m)*(c + d*x)^(-m - n)*((b*(c + d*x))/(b*c - a*d))^(m + n)*(e + f*x)^n*AppellF1(1 + m, m + n, -1 - n, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(((b*(e + f*x))/(b*e - a*f))^n*(b^2*(1 + m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + n)*(e + f*x)^(n + 0), x, 3, ((a + b*x)^(1 + m)*(c + d*x)^(-m - n)*((b*(c + d*x))/(b*c - a*d))^(m + n)*(e + f*x)^n*AppellF1(1 + m, m + n, -n, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(((b*(e + f*x))/(b*e - a*f))^n*(b*(1 + m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + n)*(e + f*x)^(n - 1), x, 3, ((a + b*x)^(1 + m)*(c + d*x)^(-m - n)*((b*(c + d*x))/(b*c - a*d))^(m + n)*(e + f*x)^n*AppellF1(1 + m, m + n, 1 - n, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(((b*(e + f*x))/(b*e - a*f))^n*((b*e - a*f)*(1 + m)))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + n)*(e + f*x)^(n - 2), x, 1, ((a + b*x)^(1 + m)*(c + d*x)^(-m - n)*(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^(m + n)*(e + f*x)^(-1 + n)*HypergeometricFunctions._₂F₁(1 + m, m + n, 2 + m, -(((d*e - c*f)*(a + b*x))/((b*c - a*d)*(e + f*x)))))/((b*e - a*f)*(1 + m))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + n)*(e + f*x)^(n - 3), x, 2, -((f*(a + b*x)^(1 + m)*(c + d*x)^(1 - m - n)*(e + f*x)^(-2 + n))/((b*e - a*f)*(d*e - c*f)*(2 - n))) - ((a*d*f*(1 + m) - b*(d*e*(2 - n) - c*f*(1 - m - n)))*(a + b*x)^(1 + m)*(c + d*x)^(-m - n)*(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^(m + n)*(e + f*x)^(-1 + n)*HypergeometricFunctions._₂F₁(1 + m, m + n, 2 + m, -(((d*e - c*f)*(a + b*x))/((b*c - a*d)*(e + f*x)))))/((b*e - a*f)^2*(d*e - c*f)*(1 + m)*(2 - n))]
    @test_int [(a + b*x)^m/(c + d*x)^(m + n)*(e + f*x)^(n - 4), x, 4, -((f*(a + b*x)^(1 + m)*(c + d*x)^(1 - m - n)*(e + f*x)^(-3 + n))/((b*e - a*f)*(d*e - c*f)*(3 - n))) + (f*(a*d*f*(2 + m) - b*(d*e*(4 - n) - c*f*(2 - m - n)))*(a + b*x)^(1 + m)*(c + d*x)^(1 - m - n)*(e + f*x)^(-2 + n))/((b*e - a*f)^2*(d*e - c*f)^2*(2 - n)*(3 - n)) + (1/((b*e - a*f)^3*(d*e - c*f)^2*(1 + m)*(2 - n)*(3 - n)))*((a^2*d^2*f^2*(2 + 3*m + m^2) - 2*a*b*d*f*(1 + m)*(d*e*(3 - n) - c*f*(1 - m - n)) - b^2*(2*c*d*e*f*(3 - n)*(1 - m - n) - d^2*e^2*(6 - 5*n + n^2) - c^2*f^2*(2 + m^2 - m*(3 - 2*n) - 3*n + n^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-m - n)*(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^(m + n)*(e + f*x)^(-1 + n)*HypergeometricFunctions._₂F₁(1 + m, m + n, 2 + m, -(((d*e - c*f)*(a + b*x))/((b*c - a*d)*(e + f*x)))))]
    #= [(a + b*x)^m/(c + d*x)^(m + n)*(e + f*x)^(n - 5), x, 5, -((f*(a + b*x)^(1 + m)*(c + d*x)^(1 - m - n)*(e + f*x)^(-4 + n))/((b*e - a*f)*(d*e - c*f)*(4 - n))) + (f*(a*d*f*(3 + m) - b*(d*e*(6 - n) - c*f*(3 - m - n)))*(a + b*x)^(1 + m)*(c + d*x)^(1 - m - n)*(e + f*x)^(-3 + n))/((b*e - a*f)^2*(d*e - c*f)^2*(3 - n)*(4 - n)) - (1/((b*e - a*f)^3*(d*e - c*f)^3*(2 - n)*(3 - n)*(4 - n)))*(f*(a^2*d^2*f^2*(6 + 5*m + m^2) - a*b*d*f*(d*e*(2*m*(5 - n) + 3*(6 - n)) - c*f*(6 - 2*m^2 - 3*n - 2*m*n)) + b^2*(d^2*e^2*(18 - 8*n + n^2) + c^2*f^2*(6 + m^2 - m*(5 - 2*n) - 5*n + n^2) - c*d*e*f*(18 - 2*m*(5 - n) - 13*n + 2*n^2)))*(a + b*x)^(1 + m)*(c + d*x)^(1 - m - n)*(e + f*x)^(-2 + n)) - ((a^3*d^3*f^3*(6 + 11*m + 6*m^2 + m^3) - 3*a^2*b*d^2*f^2*(2 + 3*m + m^2)*(d*e*(4 - n) - c*f*(1 - m - n)) - 3*a*b^2*d*f*(1 + m)*(2*c*d*e*f*(4 - n)*(1 - m - n) - d^2*e^2*(12 - 7*n + n^2) - c^2*f^2*(2 + m^2 - m*(3 - 2*n) - 3*n + n^2)) + b^3*(3*c*d^2*e^2*f*(1 - m - n)*(12 - 7*n + n^2) - 3*c^2*d*e*f^2*(4 - n)*(2 + m^2 - m*(3 - 2*n) - 3*n + n^2) - d^3*e^3*(24 - 26*n + 9*n^2 - n^3) + c^3*f^3*(6 - m^3 + 3*m^2*(2 - n) - 11*n + 6*n^2 - n^3 - m*(11 - 12*n + 3*n^2))))*(a + b*x)^(1 + m)*(c + d*x)^(-m - n)*(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^(m + n)*(e + f*x)^(-1 + n)*HypergeometricFunctions._₂F₁(1 + m, m + n, 2 + m, -(((d*e - c*f)*(a + b*x))/((b*c - a*d)*(e + f*x)))))/((b*e - a*f)^4*(d*e - c*f)^3*(1 + m)*(2 - n)*(3 - n)*(4 - n))] =#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^n*(e+f*x)^p=#

    @test_int [(a + b*x)^m*(c + d*x)^n/((b*c*f + a*d*f + a*d*f*m + b*c*f*n)/(b*d*(m + n + 2)) + f*x)^(m + n + 3), x, 1, (b*d*(2 + m + n)*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*((f*(a*d*(1 + m) + b*c*(1 + n)))/(b*d*(2 + m + n)) + f*x)^(-2 - m - n))/((b*c - a*d)^2*f*(1 + m)*(1 + n))]
    @test_int [(a + b*x)^m*(c + d*x)^(-1 - (d*(b*e - a*f)*(1 + m))/(b*(d*e - c*f)))*(e + f*x)^(-1 + ((b*c - a*d)*f*(1 + m))/(b*(d*e - c*f))), x, 1, (b*(a + b*x)^(1 + m)*(e + f*x)^(((b*c - a*d)*f*(1 + m))/(b*(d*e - c*f))))/((c + d*x)^((d*(b*e - a*f)*(1 + m))/(b*(d*e - c*f)))*((b*c - a*d)*(b*e - a*f)*(1 + m)))]

    @test_int [(a + b*x)^m*(c + d*x)^n/(e + f*x)^(m + n + 0), x, 3, ((a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-m - n)*((b*(e + f*x))/(b*e - a*f))^(m + n)*AppellF1(1 + m, -n, m + n, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(((b*(c + d*x))/(b*c - a*d))^n*(b*(1 + m)))]
    @test_int [(a + b*x)^m*(c + d*x)^n/(e + f*x)^(m + n + 1), x, 3, ((a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-m - n)*((b*(e + f*x))/(b*e - a*f))^(m + n)*AppellF1(1 + m, -n, 1 + m + n, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(((b*(c + d*x))/(b*c - a*d))^n*((b*e - a*f)*(1 + m)))]
    @test_int [(a + b*x)^m*(c + d*x)^n/(e + f*x)^(m + n + 2), x, 1, ((a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-1 - m - n)*HypergeometricFunctions._₂F₁(1 + m, -n, 2 + m, -(((d*e - c*f)*(a + b*x))/((b*c - a*d)*(e + f*x)))))/((((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^n*((b*e - a*f)*(1 + m)))]
    @test_int [(a + b*x)^m*(c + d*x)^n/(e + f*x)^(m + n + 3), x, 2, -((f*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*(e + f*x)^(-2 - m - n))/((b*e - a*f)*(d*e - c*f)*(2 + m + n))) - ((a*d*f*(1 + m) + b*(c*f*(1 + n) - d*e*(2 + m + n)))*(a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-1 - m - n)*HypergeometricFunctions._₂F₁(1 + m, -n, 2 + m, -(((d*e - c*f)*(a + b*x))/((b*c - a*d)*(e + f*x)))))/((((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^n*((b*e - a*f)^2*(d*e - c*f)*(1 + m)*(2 + m + n)))]
    @test_int [(a + b*x)^m*(c + d*x)^n/(e + f*x)^(m + n + 4), x, 4, -((f*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*(e + f*x)^(-3 - m - n))/((b*e - a*f)*(d*e - c*f)*(3 + m + n))) + (f*(a*d*f*(2 + m) + b*(c*f*(2 + n) - d*e*(4 + m + n)))*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*(e + f*x)^(-2 - m - n))/((b*e - a*f)^2*(d*e - c*f)^2*(2 + m + n)*(3 + m + n)) + (1/((b*e - a*f)^3*(d*e - c*f)^2*(1 + m)*(2 + m + n)*(3 + m + n)))*(((a^2*d^2*f^2*(2 + 3*m + m^2) + 2*a*b*d*f*(1 + m)*(c*f*(1 + n) - d*e*(3 + m + n)) - b^2*(2*c*d*e*f*(1 + n)*(3 + m + n) - c^2*f^2*(2 + 3*n + n^2) - d^2*e^2*(6 + m^2 + 5*n + n^2 + m*(5 + 2*n))))*(a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-1 - m - n)*HypergeometricFunctions._₂F₁(1 + m, -n, 2 + m, -(((d*e - c*f)*(a + b*x))/((b*c - a*d)*(e + f*x)))))/(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^n)]
    #= [(a + b*x)^m*(c + d*x)^n/(e + f*x)^(m + n + 5), x, 5, -((f*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*(e + f*x)^(-4 - m - n))/((b*e - a*f)*(d*e - c*f)*(4 + m + n))) + (f*(a*d*f*(3 + m) + b*(c*f*(3 + n) - d*e*(6 + m + n)))*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*(e + f*x)^(-3 - m - n))/((b*e - a*f)^2*(d*e - c*f)^2*(3 + m + n)*(4 + m + n)) - (f*(a^2*d^2*f^2*(6 + 5*m + m^2) + b^2*(c^2*f^2*(6 + 5*n + n^2) + d^2*e^2*(18 + m^2 + 8*n + n^2 + 2*m*(4 + n)) - c*d*e*f*(18 + 13*n + 2*n^2 + m*(3 + 2*n))) + a*b*d*f*(c*f*(6 + 3*m + 3*n + 2*m*n) - d*e*(2*m^2 + 3*(6 + n) + m*(13 + 2*n))))*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*(e + f*x)^(-2 - m - n))/((b*e - a*f)^3*(d*e - c*f)^3*(2 + m + n)*(3 + m + n)*(4 + m + n)) + (1/((b*e - a*f)^4*(d*e - c*f)^3*(1 + m)*(2 + m + n)*(3 + m + n)*(4 + m + n)))*(((f*(b*c*(1 + m) + a*d*(1 + n))*(a^2*d^2*f^2*(6 + 5*m + m^2) + b^2*(c^2*f^2*(6 + 5*n + n^2) + d^2*e^2*(18 + m^2 + 8*n + n^2 + 2*m*(4 + n)) - c*d*e*f*(18 + 13*n + 2*n^2 + m*(3 + 2*n))) + a*b*d*f*(c*f*(6 + 3*m + 3*n + 2*m*n) - d*e*(2*m^2 + 3*(6 + n) + m*(13 + 2*n)))) + (2 + m + n)*(a*b*c*d*f^2*(a*d*f*(3 + m) + b*(c*f*(3 + n) - d*e*(6 + m + n))) - b*d*e*(f*(b*c*(1 + m) + a*d*(1 + n))*(a*d*f*(3 + m) + b*(c*f*(3 + n) - d*e*(6 + m + n))) + (3 + m + n)*(2*a*b*c*d*f^2 + b*d*e*(a*d*f*(3 + m) + b*(c*f*(3 + n) - d*e*(4 + m + n))) - (b*c + a*d)*f*(a*d*f*(3 + m) + b*(c*f*(3 + n) - d*e*(4 + m + n))))) + (b*c + a*d)*f*(f*(b*c*(1 + m) + a*d*(1 + n))*(a*d*f*(3 + m) + b*(c*f*(3 + n) - d*e*(6 + m + n))) + (3 + m + n)*(2*a*b*c*d*f^2 + b*d*e*(a*d*f*(3 + m) + b*(c*f*(3 + n) - d*e*(4 + m + n))) - (b*c + a*d)*f*(a*d*f*(3 + m) + b*(c*f*(3 + n) - d*e*(4 + m + n)))))))*(a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-1 - m - n)*HypergeometricFunctions._₂F₁(1 + m, -n, 2 + m, -(((d*e - c*f)*(a + b*x))/((b*c - a*d)*(e + f*x)))))/(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^n)] =#

    @test_int [(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x, 3, ((a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^p*AppellF1(1 + m, -n, -p, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(((b*(c + d*x))/(b*c - a*d))^n*((b*(e + f*x))/(b*e - a*f))^p*(b*(1 + m)))]

    @test_int [(a + b*x)^m*(c + d*x)^n*(e + f*x)^2, x, 4, (f*(b*d*e*(4 + m + n) - f*(b*c*(2 + m) + a*d*(2 + n)))*(a + b*x)^(1 + m)*(c + d*x)^(1 + n))/(b^2*d^2*(2 + m + n)*(3 + m + n)) + (f*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*(e + f*x))/(b*d*(3 + m + n)) + (1/(b^2*d^2*(b*c - a*d)*(1 + n)*(2 + m + n)*(3 + m + n)))*((f*(b*c*(1 + m) + a*d*(1 + n))*(b*d*e*(4 + m + n) - f*(b*c*(2 + m) + a*d*(2 + n))) + b*d*(2 + m + n)*(a*f*(c*f + d*e*(1 + n)) + b*e*(c*f*(1 + m) - d*e*(3 + m + n))))*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 2 + m + n, 2 + n, (b*(c + d*x))/(b*c - a*d))), (f*(b*d*e*(4 + m + n) - f*(b*c*(2 + m) + a*d*(2 + n)))*(a + b*x)^(1 + m)*(c + d*x)^(1 + n))/(b^2*d^2*(2 + m + n)*(3 + m + n)) + (f*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*(e + f*x))/(b*d*(3 + m + n)) - ((f*(b*c*(1 + m) + a*d*(1 + n))*(b*d*e*(4 + m + n) - f*(b*c*(2 + m) + a*d*(2 + n))) + b*d*(2 + m + n)*(a*f*(c*f + d*e*(1 + n)) + b*e*(c*f*(1 + m) - d*e*(3 + m + n))))*(a + b*x)^(1 + m)*(c + d*x)^n*HypergeometricFunctions._₂F₁(1 + m, -n, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/(((b*(c + d*x))/(b*c - a*d))^n*(b^3*d^2*(1 + m)*(2 + m + n)*(3 + m + n)))]
    @test_int [(a + b*x)^m*(c + d*x)^n*(e + f*x)^1, x, 3, (f*(a + b*x)^(1 + m)*(c + d*x)^(1 + n))/(b*d*(2 + m + n)) - ((b*d*e*(2 + m + n) - f*(b*c*(1 + m) + a*d*(1 + n)))*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 2 + m + n, 2 + n, (b*(c + d*x))/(b*c - a*d)))/(b*d*(b*c - a*d)*(1 + n)*(2 + m + n)), (f*(a + b*x)^(1 + m)*(c + d*x)^(1 + n))/(b*d*(2 + m + n)) + ((b*d*e*(2 + m + n) - f*(b*c*(1 + m) + a*d*(1 + n)))*(a + b*x)^(1 + m)*(c + d*x)^n*HypergeometricFunctions._₂F₁(1 + m, -n, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/(((b*(c + d*x))/(b*c - a*d))^n*(b^2*d*(1 + m)*(2 + m + n)))]
    @test_int [(a + b*x)^m*(c + d*x)^n*(e + f*x)^0, x, 2, -(((a + b*x)^(1 + m)*(c + d*x)^(1 + n)*HypergeometricFunctions._₂F₁(1, 2 + m + n, 2 + n, (b*(c + d*x))/(b*c - a*d)))/((b*c - a*d)*(1 + n))), ((a + b*x)^(1 + m)*(c + d*x)^n*HypergeometricFunctions._₂F₁(1 + m, -n, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/(((b*(c + d*x))/(b*c - a*d))^n*(b*(1 + m)))]
    @test_int [(a + b*x)^m*(c + d*x)^n/(e + f*x)^1, x, 2, ((a + b*x)^(1 + m)*(c + d*x)^n*AppellF1(1 + m, -n, 1, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(((b*(c + d*x))/(b*c - a*d))^n*((b*e - a*f)*(1 + m)))]
    @test_int [(a + b*x)^m*(c + d*x)^n/(e + f*x)^2, x, 2, (b*(a + b*x)^(1 + m)*(c + d*x)^n*AppellF1(1 + m, -n, 2, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(((b*(c + d*x))/(b*c - a*d))^n*((b*e - a*f)^2*(1 + m)))]
    @test_int [(a + b*x)^m*(c + d*x)^n/(e + f*x)^3, x, 2, (b^2*(a + b*x)^(1 + m)*(c + d*x)^n*AppellF1(1 + m, -n, 3, 2 + m, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(((b*(c + d*x))/(b*c - a*d))^n*((b*e - a*f)^3*(1 + m)))]

    @test_int [(3 + 4*x)^n/(sqrt(1 - x)*sqrt(1 + x)), x, 1, (-sqrt(2))*7^n*sqrt(1 - x)*AppellF1(1/2, 1/2, -n, 3/2, (1 - x)/2, (4*(1 - x))/7)]
    @test_int [(3 - 4*x)^n/(sqrt(1 - x)*sqrt(1 + x)), x, 1, sqrt(2)*7^n*sqrt(1 + x)*AppellF1(1/2, -n, 1/2, 3/2, (4*(1 + x))/7, (1 + x)/2)]

    @test_int [(-3 + 4*x)^n/(sqrt(1 - x)*sqrt(1 + x)), x, 1, (-sqrt(2))*sqrt(1 - x)*AppellF1(1/2, 1/2, -n, 3/2, (1 - x)/2, 4*(1 - x))]
    @test_int [(-3 - 4*x)^n/(sqrt(1 - x)*sqrt(1 + x)), x, 1, sqrt(2)*sqrt(1 + x)*AppellF1(1/2, -n, 1/2, 3/2, 4*(1 + x), (1 + x)/2)]

    @test_int [(a + b*x)^(4/3)/(sqrt(c + d*x)*(e + f*x)), x, 2, (3*(a + b*x)^(7/3)*sqrt((b*(c + d*x))/(b*c - a*d))*AppellF1(7/3, 1/2, 1, 10/3, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(7*(b*e - a*f)*sqrt(c + d*x))]

    @test_int [((c + d*x)^(2/5)*(e + f*x)^(3/5))/sqrt(a + b*x), x, 3, (2*sqrt(a + b*x)*(c + d*x)^(2/5)*(e + f*x)^(3/5)*AppellF1(1/2, -(2/5), -(3/5), 3/2, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(b*((b*(c + d*x))/(b*c - a*d))^(2/5)*((b*(e + f*x))/(b*e - a*f))^(3/5))]

    @test_int [sqrt(a + b*x)*(e + f*x)^n/sqrt(c + d*x), x, 3, (2*(a + b*x)^(3/2)*sqrt((b*(c + d*x))/(b*c - a*d))*(e + f*x)^n*AppellF1(3/2, 1/2, -n, 5/2, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(((b*(e + f*x))/(b*e - a*f))^n*(3*b*sqrt(c + d*x)))]
    @test_int [sqrt(c + d*x)*(e + f*x)^n/sqrt(a + b*x), x, 3, (2*sqrt(a + b*x)*sqrt(c + d*x)*(e + f*x)^n*AppellF1(1/2, -(1/2), -n, 3/2, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(((b*(e + f*x))/(b*e - a*f))^n*(b*sqrt((b*(c + d*x))/(b*c - a*d))))]

    @test_int [(e + f*x)^n/(sqrt(a + b*x)*(c + d*x)^(3/2)), x, 3, (2*sqrt(a + b*x)*sqrt((b*(c + d*x))/(b*c - a*d))*(e + f*x)^n*AppellF1(1/2, 3/2, -n, 3/2, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(((b*(e + f*x))/(b*e - a*f))^n*((b*c - a*d)*sqrt(c + d*x)))]
    @test_int [(e + f*x)^n/(sqrt(c + d*x)*(a + b*x)^(3/2)), x, 3, -((2*sqrt((b*(c + d*x))/(b*c - a*d))*(e + f*x)^n*AppellF1(-(1/2), 1/2, -n, 1/2, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(((b*(e + f*x))/(b*e - a*f))^n*(b*sqrt(a + b*x)*sqrt(c + d*x))))]

    @test_int [(a + b*x)^(1/2)*(c + d*x)^(1/3)/(e + f*x), x, 2, (2*(a + b*x)^(3/2)*(c + d*x)^(1/3)*AppellF1(3/2, -(1/3), 1, 5/2, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(3*(b*e - a*f)*((b*(c + d*x))/(b*c - a*d))^(1/3))]
    @test_int [(a + b*x)^(1/3)*(c + d*x)^(1/2)/(e + f*x), x, 2, (3*(a + b*x)^(4/3)*sqrt(c + d*x)*AppellF1(4/3, -(1/2), 1, 7/3, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(4*(b*e - a*f)*sqrt((b*(c + d*x))/(b*c - a*d)))]

    @test_int [(a + b*x)^(1/2)*(c + d*x)^(1/3)*(e + f*x)^(1/4), x, 3, (2*(a + b*x)^(3/2)*(c + d*x)^(1/3)*(e + f*x)^(1/4)*AppellF1(3/2, -(1/3), -(1/4), 5/2, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(3*b*((b*(c + d*x))/(b*c - a*d))^(1/3)*((b*(e + f*x))/(b*e - a*f))^(1/4))]
    @test_int [(a + b*x)^(1/3)*(c + d*x)^(1/2)*(e + f*x)^(1/4), x, 3, (3*(a + b*x)^(4/3)*sqrt(c + d*x)*(e + f*x)^(1/4)*AppellF1(4/3, -(1/2), -(1/4), 7/3, -((d*(a + b*x))/(b*c - a*d)), -((f*(a + b*x))/(b*e - a*f))))/(4*b*sqrt((b*(c + d*x))/(b*c - a*d))*((b*(e + f*x))/(b*e - a*f))^(1/4))]

    @test_int [(a + b*x)^4*(A + B*x)*(d + e*x)^m, x, 2, -(((b*d - a*e)^4*(B*d - A*e)*(d + e*x)^(1 + m))/(e^6*(1 + m))) + ((b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x)^(2 + m))/(e^6*(2 + m)) - (2*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^(3 + m))/(e^6*(3 + m)) + (2*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^(4 + m))/(e^6*(4 + m)) - (b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^(5 + m))/(e^6*(5 + m)) + (b^4*B*(d + e*x)^(6 + m))/(e^6*(6 + m))]
    @test_int [(a + b*x)^3*(A + B*x)*(d + e*x)^m, x, 2, ((b*d - a*e)^3*(B*d - A*e)*(d + e*x)^(1 + m))/(e^5*(1 + m)) - ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)^(2 + m))/(e^5*(2 + m)) + (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(3 + m))/(e^5*(3 + m)) - (b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^(4 + m))/(e^5*(4 + m)) + (b^3*B*(d + e*x)^(5 + m))/(e^5*(5 + m))]
    @test_int [(a + b*x)^2*(A + B*x)*(d + e*x)^m, x, 2, -(((b*d - a*e)^2*(B*d - A*e)*(d + e*x)^(1 + m))/(e^4*(1 + m))) + ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(2 + m))/(e^4*(2 + m)) - (b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(3 + m))/(e^4*(3 + m)) + (b^2*B*(d + e*x)^(4 + m))/(e^4*(4 + m))]
    @test_int [(a + b*x)^1*(A + B*x)*(d + e*x)^m, x, 2, ((b*d - a*e)*(B*d - A*e)*(d + e*x)^(1 + m))/(e^3*(1 + m)) - ((2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(2 + m))/(e^3*(2 + m)) + (b*B*(d + e*x)^(3 + m))/(e^3*(3 + m))]
    @test_int [(a + b*x)^0*(A + B*x)*(d + e*x)^m, x, 2, -(((B*d - A*e)*(d + e*x)^(1 + m))/(e^2*(1 + m))) + (B*(d + e*x)^(2 + m))/(e^2*(2 + m))]
    @test_int [(A + B*x)*(d + e*x)^m/(a + b*x)^1, x, 2, (B*(d + e*x)^(1 + m))/(b*e*(1 + m)) - ((A*b - a*B)*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)))/(b*(b*d - a*e)*(1 + m))]
    @test_int [(A + B*x)*(d + e*x)^m/(a + b*x)^2, x, 2, -(((A*b - a*B)*(d + e*x)^(1 + m))/(b*(b*d - a*e)*(a + b*x))) + ((a*B*e*(1 + m) - b*(B*d + A*e*m))*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)))/(b*(b*d - a*e)^2*(1 + m))]

    @test_int [(1 - 2*x)*(2 + 3*x)^m*(3 + 5*x)^3, x, 2, -((7*(2 + 3*x)^(1 + m))/(243*(1 + m))) + (107*(2 + 3*x)^(2 + m))/(243*(2 + m)) - (185*(2 + 3*x)^(3 + m))/(81*(3 + m)) + (1025*(2 + 3*x)^(4 + m))/(243*(4 + m)) - (250*(2 + 3*x)^(5 + m))/(243*(5 + m))]
    @test_int [(1 - 2*x)*(2 + 3*x)^m*(3 + 5*x)^2, x, 2, (7*(2 + 3*x)^(1 + m))/(81*(1 + m)) - (8*(2 + 3*x)^(2 + m))/(9*(2 + m)) + (65*(2 + 3*x)^(3 + m))/(27*(3 + m)) - (50*(2 + 3*x)^(4 + m))/(81*(4 + m))]
    @test_int [(1 - 2*x)*(2 + 3*x)^m*(3 + 5*x)^1, x, 2, -((7*(2 + 3*x)^(1 + m))/(27*(1 + m))) + (37*(2 + 3*x)^(2 + m))/(27*(2 + m)) - (10*(2 + 3*x)^(3 + m))/(27*(3 + m))]
    @test_int [(1 - 2*x)*(2 + 3*x)^m/(3 + 5*x)^1, x, 2, -((2*(2 + 3*x)^(1 + m))/(15*(1 + m))) - (11*(2 + 3*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, 5*(2 + 3*x)))/(5*(1 + m))]
    @test_int [(1 - 2*x)*(2 + 3*x)^m/(3 + 5*x)^2, x, 2, -((11*(2 + 3*x)^(1 + m))/(5*(3 + 5*x))) + ((2 - 33*m)*(2 + 3*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, 5*(2 + 3*x)))/(5*(1 + m))]
    @test_int [(1 - 2*x)*(2 + 3*x)^m/(3 + 5*x)^3, x, 2, -((11*(2 + 3*x)^(1 + m))/(10*(3 + 5*x)^2)) - (3*(37 - 33*m)*(2 + 3*x)^(1 + m)*HypergeometricFunctions._₂F₁(2, 1 + m, 2 + m, 5*(2 + 3*x)))/(10*(1 + m))]

    @test_int [((2 + 3*x)^m*(3 + 5*x)^3)/(1 - 2*x), x, 3, -((5135*(2 + 3*x)^(1 + m))/(216*(1 + m))) - (725*(2 + 3*x)^(2 + m))/(108*(2 + m)) - (125*(2 + 3*x)^(3 + m))/(54*(3 + m)) + (1331*(2 + 3*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (2/7)*(2 + 3*x)))/(56*(1 + m))]
    @test_int [((2 + 3*x)^m*(3 + 5*x)^2)/(1 - 2*x), x, 3, -((155*(2 + 3*x)^(1 + m))/(36*(1 + m))) - (25*(2 + 3*x)^(2 + m))/(18*(2 + m)) + (121*(2 + 3*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (2/7)*(2 + 3*x)))/(28*(1 + m))]
    @test_int [((2 + 3*x)^m*(3 + 5*x))/(1 - 2*x), x, 2, -((5*(2 + 3*x)^(1 + m))/(6*(1 + m))) + (11*(2 + 3*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (2/7)*(2 + 3*x)))/(14*(1 + m))]
    @test_int [(2 + 3*x)^m/((1 - 2*x)*(3 + 5*x)), x, 3, (2*(2 + 3*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (2/7)*(2 + 3*x)))/(77*(1 + m)) - (5*(2 + 3*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, 5*(2 + 3*x)))/(11*(1 + m))]
    @test_int [(2 + 3*x)^m/((1 - 2*x)*(3 + 5*x)^2), x, 4, -((5*(2 + 3*x)^(1 + m))/(11*(3 + 5*x))) + (4*(2 + 3*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (2/7)*(2 + 3*x)))/(847*(1 + m)) - (5*(2 + 33*m)*(2 + 3*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, 5*(2 + 3*x)))/(121*(1 + m))]
    @test_int [(2 + 3*x)^m/((1 - 2*x)*(3 + 5*x)^3), x, 5, -((5*(2 + 3*x)^(1 + m))/(22*(3 + 5*x)^2)) + (5*(29 - 33*m)*(2 + 3*x)^(1 + m))/(242*(3 + 5*x)) + (8*(2 + 3*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (2/7)*(2 + 3*x)))/(9317*(1 + m)) - (5*(8 - 957*m + 1089*m^2)*(2 + 3*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, 5*(2 + 3*x)))/(2662*(1 + m))]

    #= Mathematica*8*cannot*get*these. =#
    @test_int [(a + b*x)^m/((c + d*x)^0*(e + f*x)^2), x, 1, (b*(a + b*x)^(1 + m)*HypergeometricFunctions._₂F₁(2, 1 + m, 2 + m, -((f*(a + b*x))/(b*e - a*f))))/((b*e - a*f)^2*(1 + m))]
    @test_int [(a + b*x)^m/((c + d*x)^1*(e + f*x)^2), x, 4, -((f*(a + b*x)^(1 + m))/((b*e - a*f)*(d*e - c*f)*(e + f*x))) + (d^2*(a + b*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/((b*c - a*d)*(d*e - c*f)^2*(1 + m)) + (f*(a*d*f - b*(d*e*(1 - m) + c*f*m))*(a + b*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((f*(a + b*x))/(b*e - a*f))))/((b*e - a*f)^2*(d*e - c*f)^2*(1 + m))]
    @test_int [(a + b*x)^m/((c + d*x)^2*(e + f*x)^2), x, 5, (f*(b*d*e + b*c*f - 2*a*d*f)*(a + b*x)^(1 + m))/((b*c - a*d)*(b*e - a*f)*(d*e - c*f)^2*(e + f*x)) + (d*(a + b*x)^(1 + m))/((b*c - a*d)*(d*e - c*f)*(c + d*x)*(e + f*x)) + (d^2*(2*a*d*f - b*(c*f*(2 - m) + d*e*m))*(a + b*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((d*(a + b*x))/(b*c - a*d))))/((b*c - a*d)^2*(d*e - c*f)^3*(1 + m)) - (f^2*(2*a*d*f - b*(d*e*(2 - m) + c*f*m))*(a + b*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, -((f*(a + b*x))/(b*e - a*f))))/((b*e - a*f)^2*(d*e - c*f)^3*(1 + m))]
    end

max_stars_repo_path: test/1 Algebraic functions/1.1 Binomial products/1.1.1 Linear/1.1.1.3 (a+b x)^m (c+d x)^n (e+f x)^p.jl