text:
@testset "1.2.1.2 (d+e x)^m (a+b x+c x^2)^p" begin
    (a, b, c, d, e, k, m, n, p, x, ) = @variables a b c d e k m n p x

    #= ::Package:: =#

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

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

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

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

    @test_int [x^3*(b*x + c*x^2)^(1/2), x, 6, -((7*b^3*(b + 2*c*x)*sqrt(b*x + c*x^2))/(128*c^4)) + (7*b^2*(b*x + c*x^2)^(3/2))/(48*c^3) - (7*b*x*(b*x + c*x^2)^(3/2))/(40*c^2) + (x^2*(b*x + c*x^2)^(3/2))/(5*c) + (7*b^5*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(128*c^(9/2))]
    @test_int [x^2*(b*x + c*x^2)^(1/2), x, 5, (5*b^2*(b + 2*c*x)*sqrt(b*x + c*x^2))/(64*c^3) - (5*b*(b*x + c*x^2)^(3/2))/(24*c^2) + (x*(b*x + c*x^2)^(3/2))/(4*c) - (5*b^4*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(64*c^(7/2))]
    @test_int [x^1*(b*x + c*x^2)^(1/2), x, 4, -((b*(b + 2*c*x)*sqrt(b*x + c*x^2))/(8*c^2)) + (b*x + c*x^2)^(3/2)/(3*c) + (b^3*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(8*c^(5/2))]
    @test_int [x^0*(b*x + c*x^2)^(1/2), x, 3, ((b + 2*c*x)*sqrt(b*x + c*x^2))/(4*c) - (b^2*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(4*c^(3/2))]
    @test_int [(b*x + c*x^2)^(1/2)/x^1, x, 3, sqrt(b*x + c*x^2) + (b*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/sqrt(c)]
    @test_int [(b*x + c*x^2)^(1/2)/x^2, x, 3, -((2*sqrt(b*x + c*x^2))/x) + 2*sqrt(c)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2))]
    @test_int [(b*x + c*x^2)^(1/2)/x^3, x, 1, -((2*(b*x + c*x^2)^(3/2))/(3*b*x^3))]
    @test_int [(b*x + c*x^2)^(1/2)/x^4, x, 2, -((2*(b*x + c*x^2)^(3/2))/(5*b*x^4)) + (4*c*(b*x + c*x^2)^(3/2))/(15*b^2*x^3)]
    @test_int [(b*x + c*x^2)^(1/2)/x^5, x, 3, -((2*(b*x + c*x^2)^(3/2))/(7*b*x^5)) + (8*c*(b*x + c*x^2)^(3/2))/(35*b^2*x^4) - (16*c^2*(b*x + c*x^2)^(3/2))/(105*b^3*x^3)]
    @test_int [(b*x + c*x^2)^(1/2)/x^6, x, 4, -((2*(b*x + c*x^2)^(3/2))/(9*b*x^6)) + (4*c*(b*x + c*x^2)^(3/2))/(21*b^2*x^5) - (16*c^2*(b*x + c*x^2)^(3/2))/(105*b^3*x^4) + (32*c^3*(b*x + c*x^2)^(3/2))/(315*b^4*x^3)]
    @test_int [(b*x + c*x^2)^(1/2)/x^7, x, 5, -((2*(b*x + c*x^2)^(3/2))/(11*b*x^7)) + (16*c*(b*x + c*x^2)^(3/2))/(99*b^2*x^6) - (32*c^2*(b*x + c*x^2)^(3/2))/(231*b^3*x^5) + (128*c^3*(b*x + c*x^2)^(3/2))/(1155*b^4*x^4) - (256*c^4*(b*x + c*x^2)^(3/2))/(3465*b^5*x^3)]

    @test_int [x^2*(b*x + c*x^2)^(3/2), x, 6, -((7*b^4*(b + 2*c*x)*sqrt(b*x + c*x^2))/(512*c^4)) + (7*b^2*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(192*c^3) - (7*b*(b*x + c*x^2)^(5/2))/(60*c^2) + (x*(b*x + c*x^2)^(5/2))/(6*c) + (7*b^6*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(512*c^(9/2))]
    @test_int [x^1*(b*x + c*x^2)^(3/2), x, 5, (3*b^3*(b + 2*c*x)*sqrt(b*x + c*x^2))/(128*c^3) - (b*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(16*c^2) + (b*x + c*x^2)^(5/2)/(5*c) - (3*b^5*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(128*c^(7/2))]
    @test_int [x^0*(b*x + c*x^2)^(3/2), x, 4, -((3*b^2*(b + 2*c*x)*sqrt(b*x + c*x^2))/(64*c^2)) + ((b + 2*c*x)*(b*x + c*x^2)^(3/2))/(8*c) + (3*b^4*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(64*c^(5/2))]
    @test_int [(b*x + c*x^2)^(3/2)/x^1, x, 4, (b*(b + 2*c*x)*sqrt(b*x + c*x^2))/(8*c) + (1/3)*(b*x + c*x^2)^(3/2) - (b^3*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(8*c^(3/2))]
    @test_int [(b*x + c*x^2)^(3/2)/x^2, x, 4, (3/4)*b*sqrt(b*x + c*x^2) + (b*x + c*x^2)^(3/2)/(2*x) + (3*b^2*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(4*sqrt(c))]
    @test_int [(b*x + c*x^2)^(3/2)/x^3, x, 4, 3*c*sqrt(b*x + c*x^2) - (2*(b*x + c*x^2)^(3/2))/x^2 + 3*b*sqrt(c)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2))]
    @test_int [(b*x + c*x^2)^(3/2)/x^4, x, 4, -((2*c*sqrt(b*x + c*x^2))/x) - (2*(b*x + c*x^2)^(3/2))/(3*x^3) + 2*c^(3/2)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2))]
    @test_int [(b*x + c*x^2)^(3/2)/x^5, x, 1, -((2*(b*x + c*x^2)^(5/2))/(5*b*x^5))]
    @test_int [(b*x + c*x^2)^(3/2)/x^6, x, 2, -((2*(b*x + c*x^2)^(5/2))/(7*b*x^6)) + (4*c*(b*x + c*x^2)^(5/2))/(35*b^2*x^5)]
    @test_int [(b*x + c*x^2)^(3/2)/x^7, x, 3, -((2*(b*x + c*x^2)^(5/2))/(9*b*x^7)) + (8*c*(b*x + c*x^2)^(5/2))/(63*b^2*x^6) - (16*c^2*(b*x + c*x^2)^(5/2))/(315*b^3*x^5)]
    @test_int [(b*x + c*x^2)^(3/2)/x^8, x, 4, -((2*(b*x + c*x^2)^(5/2))/(11*b*x^8)) + (4*c*(b*x + c*x^2)^(5/2))/(33*b^2*x^7) - (16*c^2*(b*x + c*x^2)^(5/2))/(231*b^3*x^6) + (32*c^3*(b*x + c*x^2)^(5/2))/(1155*b^4*x^5)]
    @test_int [(b*x + c*x^2)^(3/2)/x^9, x, 5, -((2*(b*x + c*x^2)^(5/2))/(13*b*x^9)) + (16*c*(b*x + c*x^2)^(5/2))/(143*b^2*x^8) - (32*c^2*(b*x + c*x^2)^(5/2))/(429*b^3*x^7) + (128*c^3*(b*x + c*x^2)^(5/2))/(3003*b^4*x^6) - (256*c^4*(b*x + c*x^2)^(5/2))/(15015*b^5*x^5)]

    @test_int [x^2*(a*x + b*x^2)^(5/2), x, 7, (45*a^6*(a + 2*b*x)*sqrt(a*x + b*x^2))/(16384*b^5) - (15*a^4*(a + 2*b*x)*(a*x + b*x^2)^(3/2))/(2048*b^4) + (3*a^2*(a + 2*b*x)*(a*x + b*x^2)^(5/2))/(128*b^3) - (9*a*(a*x + b*x^2)^(7/2))/(112*b^2) + (x*(a*x + b*x^2)^(7/2))/(8*b) - (45*a^8*atanh((sqrt(b)*x)/sqrt(a*x + b*x^2)))/(16384*b^(11/2))]
    @test_int [x^1*(a*x + b*x^2)^(5/2), x, 6, -((5*a^5*(a + 2*b*x)*sqrt(a*x + b*x^2))/(1024*b^4)) + (5*a^3*(a + 2*b*x)*(a*x + b*x^2)^(3/2))/(384*b^3) - (a*(a + 2*b*x)*(a*x + b*x^2)^(5/2))/(24*b^2) + (a*x + b*x^2)^(7/2)/(7*b) + (5*a^7*atanh((sqrt(b)*x)/sqrt(a*x + b*x^2)))/(1024*b^(9/2))]
    @test_int [x^0*(a*x + b*x^2)^(5/2), x, 5, (5*a^4*(a + 2*b*x)*sqrt(a*x + b*x^2))/(512*b^3) - (5*a^2*(a + 2*b*x)*(a*x + b*x^2)^(3/2))/(192*b^2) + ((a + 2*b*x)*(a*x + b*x^2)^(5/2))/(12*b) - (5*a^6*atanh((sqrt(b)*x)/sqrt(a*x + b*x^2)))/(512*b^(7/2))]
    @test_int [(a*x + b*x^2)^(5/2)/x^1, x, 5, -((3*a^3*(a + 2*b*x)*sqrt(a*x + b*x^2))/(128*b^2)) + (a*(a + 2*b*x)*(a*x + b*x^2)^(3/2))/(16*b) + (1/5)*(a*x + b*x^2)^(5/2) + (3*a^5*atanh((sqrt(b)*x)/sqrt(a*x + b*x^2)))/(128*b^(5/2))]
    @test_int [(a*x + b*x^2)^(5/2)/x^2, x, 5, (5*a^2*(a + 2*b*x)*sqrt(a*x + b*x^2))/(64*b) + (5/24)*a*(a*x + b*x^2)^(3/2) + (a*x + b*x^2)^(5/2)/(4*x) - (5*a^4*atanh((sqrt(b)*x)/sqrt(a*x + b*x^2)))/(64*b^(3/2))]
    @test_int [(a*x + b*x^2)^(5/2)/x^3, x, 5, (-(5/8))*a*(a + 2*b*x)*sqrt(a*x + b*x^2) - (5/3)*b*(a*x + b*x^2)^(3/2) + (2*(a*x + b*x^2)^(5/2))/x^2 + (5*a^3*atanh((sqrt(b)*x)/sqrt(a*x + b*x^2)))/(8*sqrt(b))]
    @test_int [(a*x + b*x^2)^(5/2)/x^4, x, 5, (15/4)*a*b*sqrt(a*x + b*x^2) + (5*b*(a*x + b*x^2)^(3/2))/(2*x) - (2*(a*x + b*x^2)^(5/2))/x^3 + (15/4)*a^2*sqrt(b)*atanh((sqrt(b)*x)/sqrt(a*x + b*x^2))]
    @test_int [(a*x + b*x^2)^(5/2)/x^5, x, 5, 5*b^2*sqrt(a*x + b*x^2) - (10*b*(a*x + b*x^2)^(3/2))/(3*x^2) - (2*(a*x + b*x^2)^(5/2))/(3*x^4) + 5*a*b^(3/2)*atanh((sqrt(b)*x)/sqrt(a*x + b*x^2))]
    @test_int [(a*x + b*x^2)^(5/2)/x^6, x, 5, -((2*b^2*sqrt(a*x + b*x^2))/x) - (2*b*(a*x + b*x^2)^(3/2))/(3*x^3) - (2*(a*x + b*x^2)^(5/2))/(5*x^5) + 2*b^(5/2)*atanh((sqrt(b)*x)/sqrt(a*x + b*x^2))]
    @test_int [(a*x + b*x^2)^(5/2)/x^7, x, 1, -((2*(a*x + b*x^2)^(7/2))/(7*a*x^7))]
    @test_int [(a*x + b*x^2)^(5/2)/x^8, x, 2, -((2*(a*x + b*x^2)^(7/2))/(9*a*x^8)) + (4*b*(a*x + b*x^2)^(7/2))/(63*a^2*x^7)]
    @test_int [(a*x + b*x^2)^(5/2)/x^9, x, 3, -((2*(a*x + b*x^2)^(7/2))/(11*a*x^9)) + (8*b*(a*x + b*x^2)^(7/2))/(99*a^2*x^8) - (16*b^2*(a*x + b*x^2)^(7/2))/(693*a^3*x^7)]
    @test_int [(a*x + b*x^2)^(5/2)/x^10, x, 4, -((2*(a*x + b*x^2)^(7/2))/(13*a*x^10)) + (12*b*(a*x + b*x^2)^(7/2))/(143*a^2*x^9) - (16*b^2*(a*x + b*x^2)^(7/2))/(429*a^3*x^8) + (32*b^3*(a*x + b*x^2)^(7/2))/(3003*a^4*x^7)]
    @test_int [(a*x + b*x^2)^(5/2)/x^11, x, 5, -((2*(a*x + b*x^2)^(7/2))/(15*a*x^11)) + (16*b*(a*x + b*x^2)^(7/2))/(195*a^2*x^10) - (32*b^2*(a*x + b*x^2)^(7/2))/(715*a^3*x^9) + (128*b^3*(a*x + b*x^2)^(7/2))/(6435*a^4*x^8) - (256*b^4*(a*x + b*x^2)^(7/2))/(45045*a^5*x^7)]
    @test_int [(a*x + b*x^2)^(5/2)/x^12, x, 6, -((2*(a*x + b*x^2)^(7/2))/(17*a*x^12)) + (4*b*(a*x + b*x^2)^(7/2))/(51*a^2*x^11) - (32*b^2*(a*x + b*x^2)^(7/2))/(663*a^3*x^10) + (64*b^3*(a*x + b*x^2)^(7/2))/(2431*a^4*x^9) - (256*b^4*(a*x + b*x^2)^(7/2))/(21879*a^5*x^8) + (512*b^5*(a*x + b*x^2)^(7/2))/(153153*a^6*x^7)]

    @test_int [x*sqrt(2*x - x^2), x, 4, (-(1/2))*(1 - x)*sqrt(2*x - x^2) - (1/3)*(2*x - x^2)^(3/2) - (1/2)*asin(1 - x)]
    @test_int [x*sqrt(3*x - 4*x^2), x, 4, (-(3/128))*(3 - 8*x)*sqrt(3*x - 4*x^2) - (1/12)*(3*x - 4*x^2)^(3/2) - (27/512)*asin(1 - (8*x)/3)]
    @test_int [x*sqrt(x + x^2), x, 4, (-(1/8))*(1 + 2*x)*sqrt(x + x^2) + (1/3)*(x + x^2)^(3/2) + (1/8)*atanh(x/sqrt(x + x^2))]

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

    @test_int [x^4/(b*x + c*x^2)^(1/2), x, 6, -((35*b^3*sqrt(b*x + c*x^2))/(64*c^4)) + (35*b^2*x*sqrt(b*x + c*x^2))/(96*c^3) - (7*b*x^2*sqrt(b*x + c*x^2))/(24*c^2) + (x^3*sqrt(b*x + c*x^2))/(4*c) + (35*b^4*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(64*c^(9/2))]
    @test_int [x^3/(b*x + c*x^2)^(1/2), x, 5, (5*b^2*sqrt(b*x + c*x^2))/(8*c^3) - (5*b*x*sqrt(b*x + c*x^2))/(12*c^2) + (x^2*sqrt(b*x + c*x^2))/(3*c) - (5*b^3*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(8*c^(7/2))]
    @test_int [x^2/(b*x + c*x^2)^(1/2), x, 4, -((3*b*sqrt(b*x + c*x^2))/(4*c^2)) + (x*sqrt(b*x + c*x^2))/(2*c) + (3*b^2*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(4*c^(5/2))]
    @test_int [x^1/(b*x + c*x^2)^(1/2), x, 3, sqrt(b*x + c*x^2)/c - (b*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/c^(3/2)]
    @test_int [x^0/(b*x + c*x^2)^(1/2), x, 2, (2*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/sqrt(c)]
    @test_int [1/(x^1*(b*x + c*x^2)^(1/2)), x, 1, -((2*sqrt(b*x + c*x^2))/(b*x))]
    @test_int [1/(x^2*(b*x + c*x^2)^(1/2)), x, 2, -((2*sqrt(b*x + c*x^2))/(3*b*x^2)) + (4*c*sqrt(b*x + c*x^2))/(3*b^2*x)]
    @test_int [1/(x^3*(b*x + c*x^2)^(1/2)), x, 3, -((2*sqrt(b*x + c*x^2))/(5*b*x^3)) + (8*c*sqrt(b*x + c*x^2))/(15*b^2*x^2) - (16*c^2*sqrt(b*x + c*x^2))/(15*b^3*x)]
    @test_int [1/(x^4*(b*x + c*x^2)^(1/2)), x, 4, -((2*sqrt(b*x + c*x^2))/(7*b*x^4)) + (12*c*sqrt(b*x + c*x^2))/(35*b^2*x^3) - (16*c^2*sqrt(b*x + c*x^2))/(35*b^3*x^2) + (32*c^3*sqrt(b*x + c*x^2))/(35*b^4*x)]
    @test_int [1/(x^5*(b*x + c*x^2)^(1/2)), x, 5, -((2*sqrt(b*x + c*x^2))/(9*b*x^5)) + (16*c*sqrt(b*x + c*x^2))/(63*b^2*x^4) - (32*c^2*sqrt(b*x + c*x^2))/(105*b^3*x^3) + (128*c^3*sqrt(b*x + c*x^2))/(315*b^4*x^2) - (256*c^4*sqrt(b*x + c*x^2))/(315*b^5*x)]

    @test_int [x^4/(b*x + c*x^2)^(3/2), x, 5, -((2*x^3)/(c*sqrt(b*x + c*x^2))) - (15*b*sqrt(b*x + c*x^2))/(4*c^3) + (5*x*sqrt(b*x + c*x^2))/(2*c^2) + (15*b^2*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(4*c^(7/2))]
    @test_int [x^3/(b*x + c*x^2)^(3/2), x, 4, -((2*x^2)/(c*sqrt(b*x + c*x^2))) + (3*sqrt(b*x + c*x^2))/c^2 - (3*b*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/c^(5/2)]
    @test_int [x^2/(b*x + c*x^2)^(3/2), x, 3, -((2*x)/(c*sqrt(b*x + c*x^2))) + (2*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/c^(3/2)]
    @test_int [x^1/(b*x + c*x^2)^(3/2), x, 1, (2*x)/(b*sqrt(b*x + c*x^2))]
    @test_int [x^0/(b*x + c*x^2)^(3/2), x, 1, -((2*(b + 2*c*x))/(b^2*sqrt(b*x + c*x^2)))]
    @test_int [1/(x^1*(b*x + c*x^2)^(3/2)), x, 2, -(2/(3*b*x*sqrt(b*x + c*x^2))) + (8*c*(b + 2*c*x))/(3*b^3*sqrt(b*x + c*x^2))]
    @test_int [1/(x^2*(b*x + c*x^2)^(3/2)), x, 3, -(2/(5*b*x^2*sqrt(b*x + c*x^2))) + (4*c)/(5*b^2*x*sqrt(b*x + c*x^2)) - (16*c^2*(b + 2*c*x))/(5*b^4*sqrt(b*x + c*x^2))]
    @test_int [1/(x^3*(b*x + c*x^2)^(3/2)), x, 4, -(2/(7*b*x^3*sqrt(b*x + c*x^2))) + (16*c)/(35*b^2*x^2*sqrt(b*x + c*x^2)) - (32*c^2)/(35*b^3*x*sqrt(b*x + c*x^2)) + (128*c^3*(b + 2*c*x))/(35*b^5*sqrt(b*x + c*x^2))]

    @test_int [x^6/(a*x + b*x^2)^(5/2), x, 6, -((2*x^5)/(3*b*(a*x + b*x^2)^(3/2))) - (14*x^3)/(3*b^2*sqrt(a*x + b*x^2)) - (35*a*sqrt(a*x + b*x^2))/(4*b^4) + (35*x*sqrt(a*x + b*x^2))/(6*b^3) + (35*a^2*atanh((sqrt(b)*x)/sqrt(a*x + b*x^2)))/(4*b^(9/2))]
    @test_int [x^5/(a*x + b*x^2)^(5/2), x, 5, -((2*x^4)/(3*b*(a*x + b*x^2)^(3/2))) - (10*x^2)/(3*b^2*sqrt(a*x + b*x^2)) + (5*sqrt(a*x + b*x^2))/b^3 - (5*a*atanh((sqrt(b)*x)/sqrt(a*x + b*x^2)))/b^(7/2)]
    @test_int [x^4/(a*x + b*x^2)^(5/2), x, 4, -((2*x^3)/(3*b*(a*x + b*x^2)^(3/2))) - (2*x)/(b^2*sqrt(a*x + b*x^2)) + (2*atanh((sqrt(b)*x)/sqrt(a*x + b*x^2)))/b^(5/2)]
    @test_int [x^3/(a*x + b*x^2)^(5/2), x, 1, (2*x^3)/(3*a*(a*x + b*x^2)^(3/2))]
    @test_int [x^2/(a*x + b*x^2)^(5/2), x, 2, -((2*x)/(3*b*(a*x + b*x^2)^(3/2))) + (2*(a + 2*b*x))/(3*a^2*b*sqrt(a*x + b*x^2))]
    @test_int [x^1/(a*x + b*x^2)^(5/2), x, 2, (2*x)/(3*a*(a*x + b*x^2)^(3/2)) - (8*(a + 2*b*x))/(3*a^3*sqrt(a*x + b*x^2))]
    @test_int [x^0/(a*x + b*x^2)^(5/2), x, 2, -((2*(a + 2*b*x))/(3*a^2*(a*x + b*x^2)^(3/2))) + (16*b*(a + 2*b*x))/(3*a^4*sqrt(a*x + b*x^2))]
    @test_int [1/(x^1*(a*x + b*x^2)^(5/2)), x, 3, -(2/(5*a*x*(a*x + b*x^2)^(3/2))) + (16*b*(a + 2*b*x))/(15*a^3*(a*x + b*x^2)^(3/2)) - (128*b^2*(a + 2*b*x))/(15*a^5*sqrt(a*x + b*x^2))]
    @test_int [1/(x^2*(a*x + b*x^2)^(5/2)), x, 4, -(2/(7*a*x^2*(a*x + b*x^2)^(3/2))) + (4*b)/(7*a^2*x*(a*x + b*x^2)^(3/2)) - (32*b^2*(a + 2*b*x))/(21*a^4*(a*x + b*x^2)^(3/2)) + (256*b^3*(a + 2*b*x))/(21*a^6*sqrt(a*x + b*x^2))]

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

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

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

    @test_int [x^(7/2)*(b*x + c*x^2)^(1/2), x, 5, (256*b^4*(b*x + c*x^2)^(3/2))/(3465*c^5*x^(3/2)) - (128*b^3*(b*x + c*x^2)^(3/2))/(1155*c^4*sqrt(x)) + (32*b^2*sqrt(x)*(b*x + c*x^2)^(3/2))/(231*c^3) - (16*b*x^(3/2)*(b*x + c*x^2)^(3/2))/(99*c^2) + (2*x^(5/2)*(b*x + c*x^2)^(3/2))/(11*c)]
    @test_int [x^(5/2)*(b*x + c*x^2)^(1/2), x, 4, -((32*b^3*(b*x + c*x^2)^(3/2))/(315*c^4*x^(3/2))) + (16*b^2*(b*x + c*x^2)^(3/2))/(105*c^3*sqrt(x)) - (4*b*sqrt(x)*(b*x + c*x^2)^(3/2))/(21*c^2) + (2*x^(3/2)*(b*x + c*x^2)^(3/2))/(9*c)]
    @test_int [x^(3/2)*(b*x + c*x^2)^(1/2), x, 3, (16*b^2*(b*x + c*x^2)^(3/2))/(105*c^3*x^(3/2)) - (8*b*(b*x + c*x^2)^(3/2))/(35*c^2*sqrt(x)) + (2*sqrt(x)*(b*x + c*x^2)^(3/2))/(7*c)]
    @test_int [x^(1/2)*(b*x + c*x^2)^(1/2), x, 2, -((4*b*(b*x + c*x^2)^(3/2))/(15*c^2*x^(3/2))) + (2*(b*x + c*x^2)^(3/2))/(5*c*sqrt(x))]
    @test_int [(b*x + c*x^2)^(1/2)/x^(1/2), x, 1, (2*(b*x + c*x^2)^(3/2))/(3*c*x^(3/2))]
    @test_int [(b*x + c*x^2)^(1/2)/x^(3/2), x, 3, (2*sqrt(b*x + c*x^2))/sqrt(x) - 2*sqrt(b)*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x)))]
    @test_int [(b*x + c*x^2)^(1/2)/x^(5/2), x, 3, -(sqrt(b*x + c*x^2)/x^(3/2)) - (c*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x))))/sqrt(b)]
    @test_int [(b*x + c*x^2)^(1/2)/x^(7/2), x, 4, -(sqrt(b*x + c*x^2)/(2*x^(5/2))) - (c*sqrt(b*x + c*x^2))/(4*b*x^(3/2)) + (c^2*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x))))/(4*b^(3/2))]
    @test_int [(b*x + c*x^2)^(1/2)/x^(9/2), x, 5, -(sqrt(b*x + c*x^2)/(3*x^(7/2))) - (c*sqrt(b*x + c*x^2))/(12*b*x^(5/2)) + (c^2*sqrt(b*x + c*x^2))/(8*b^2*x^(3/2)) - (c^3*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x))))/(8*b^(5/2))]
    @test_int [(b*x + c*x^2)^(1/2)/x^(11/2), x, 6, -(sqrt(b*x + c*x^2)/(4*x^(9/2))) - (c*sqrt(b*x + c*x^2))/(24*b*x^(7/2)) + (5*c^2*sqrt(b*x + c*x^2))/(96*b^2*x^(5/2)) - (5*c^3*sqrt(b*x + c*x^2))/(64*b^3*x^(3/2)) + (5*c^4*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x))))/(64*b^(7/2))]

    @test_int [x^(7/2)*(b*x + c*x^2)^(3/2), x, 6, -((512*b^5*(b*x + c*x^2)^(5/2))/(45045*c^6*x^(5/2))) + (256*b^4*(b*x + c*x^2)^(5/2))/(9009*c^5*x^(3/2)) - (64*b^3*(b*x + c*x^2)^(5/2))/(1287*c^4*sqrt(x)) + (32*b^2*sqrt(x)*(b*x + c*x^2)^(5/2))/(429*c^3) - (4*b*x^(3/2)*(b*x + c*x^2)^(5/2))/(39*c^2) + (2*x^(5/2)*(b*x + c*x^2)^(5/2))/(15*c)]
    @test_int [x^(5/2)*(b*x + c*x^2)^(3/2), x, 5, (256*b^4*(b*x + c*x^2)^(5/2))/(15015*c^5*x^(5/2)) - (128*b^3*(b*x + c*x^2)^(5/2))/(3003*c^4*x^(3/2)) + (32*b^2*(b*x + c*x^2)^(5/2))/(429*c^3*sqrt(x)) - (16*b*sqrt(x)*(b*x + c*x^2)^(5/2))/(143*c^2) + (2*x^(3/2)*(b*x + c*x^2)^(5/2))/(13*c)]
    @test_int [x^(3/2)*(b*x + c*x^2)^(3/2), x, 4, -((32*b^3*(b*x + c*x^2)^(5/2))/(1155*c^4*x^(5/2))) + (16*b^2*(b*x + c*x^2)^(5/2))/(231*c^3*x^(3/2)) - (4*b*(b*x + c*x^2)^(5/2))/(33*c^2*sqrt(x)) + (2*sqrt(x)*(b*x + c*x^2)^(5/2))/(11*c)]
    @test_int [x^(1/2)*(b*x + c*x^2)^(3/2), x, 3, (16*b^2*(b*x + c*x^2)^(5/2))/(315*c^3*x^(5/2)) - (8*b*(b*x + c*x^2)^(5/2))/(63*c^2*x^(3/2)) + (2*(b*x + c*x^2)^(5/2))/(9*c*sqrt(x))]
    @test_int [(b*x + c*x^2)^(3/2)/x^(1/2), x, 2, -((4*b*(b*x + c*x^2)^(5/2))/(35*c^2*x^(5/2))) + (2*(b*x + c*x^2)^(5/2))/(7*c*x^(3/2))]
    @test_int [(b*x + c*x^2)^(3/2)/x^(3/2), x, 1, (2*(b*x + c*x^2)^(5/2))/(5*c*x^(5/2))]
    @test_int [(b*x + c*x^2)^(3/2)/x^(5/2), x, 4, (2*b*sqrt(b*x + c*x^2))/sqrt(x) + (2*(b*x + c*x^2)^(3/2))/(3*x^(3/2)) - 2*b^(3/2)*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x)))]
    @test_int [(b*x + c*x^2)^(3/2)/x^(7/2), x, 4, (3*c*sqrt(b*x + c*x^2))/sqrt(x) - (b*x + c*x^2)^(3/2)/x^(5/2) - 3*sqrt(b)*c*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x)))]
    @test_int [(b*x + c*x^2)^(3/2)/x^(9/2), x, 4, -((3*c*sqrt(b*x + c*x^2))/(4*x^(3/2))) - (b*x + c*x^2)^(3/2)/(2*x^(7/2)) - (3*c^2*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x))))/(4*sqrt(b))]
    @test_int [(b*x + c*x^2)^(3/2)/x^(11/2), x, 5, -((c*sqrt(b*x + c*x^2))/(4*x^(5/2))) - (c^2*sqrt(b*x + c*x^2))/(8*b*x^(3/2)) - (b*x + c*x^2)^(3/2)/(3*x^(9/2)) + (c^3*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x))))/(8*b^(3/2))]
    @test_int [(b*x + c*x^2)^(3/2)/x^(13/2), x, 6, -((c*sqrt(b*x + c*x^2))/(8*x^(7/2))) - (c^2*sqrt(b*x + c*x^2))/(32*b*x^(5/2)) + (3*c^3*sqrt(b*x + c*x^2))/(64*b^2*x^(3/2)) - (b*x + c*x^2)^(3/2)/(4*x^(11/2)) - (3*c^4*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x))))/(64*b^(5/2))]
    @test_int [(b*x + c*x^2)^(3/2)/x^(15/2), x, 7, -((3*c*sqrt(b*x + c*x^2))/(40*x^(9/2))) - (c^2*sqrt(b*x + c*x^2))/(80*b*x^(7/2)) + (c^3*sqrt(b*x + c*x^2))/(64*b^2*x^(5/2)) - (3*c^4*sqrt(b*x + c*x^2))/(128*b^3*x^(3/2)) - (b*x + c*x^2)^(3/2)/(5*x^(13/2)) + (3*c^5*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x))))/(128*b^(7/2))]

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

    @test_int [x^(7/2)/(b*x + c*x^2)^(1/2), x, 4, -((32*b^3*sqrt(b*x + c*x^2))/(35*c^4*sqrt(x))) + (16*b^2*sqrt(x)*sqrt(b*x + c*x^2))/(35*c^3) - (12*b*x^(3/2)*sqrt(b*x + c*x^2))/(35*c^2) + (2*x^(5/2)*sqrt(b*x + c*x^2))/(7*c)]
    @test_int [x^(5/2)/(b*x + c*x^2)^(1/2), x, 3, (16*b^2*sqrt(b*x + c*x^2))/(15*c^3*sqrt(x)) - (8*b*sqrt(x)*sqrt(b*x + c*x^2))/(15*c^2) + (2*x^(3/2)*sqrt(b*x + c*x^2))/(5*c)]
    @test_int [x^(3/2)/(b*x + c*x^2)^(1/2), x, 2, -((4*b*sqrt(b*x + c*x^2))/(3*c^2*sqrt(x))) + (2*sqrt(x)*sqrt(b*x + c*x^2))/(3*c)]
    @test_int [x^(1/2)/(b*x + c*x^2)^(1/2), x, 1, (2*sqrt(b*x + c*x^2))/(c*sqrt(x))]
    @test_int [1/(x^(1/2)*(b*x + c*x^2)^(1/2)), x, 2, -((2*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x))))/sqrt(b))]
    @test_int [1/(x^(3/2)*(b*x + c*x^2)^(1/2)), x, 3, -(sqrt(b*x + c*x^2)/(b*x^(3/2))) + (c*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x))))/b^(3/2)]
    @test_int [1/(x^(5/2)*(b*x + c*x^2)^(1/2)), x, 4, -(sqrt(b*x + c*x^2)/(2*b*x^(5/2))) + (3*c*sqrt(b*x + c*x^2))/(4*b^2*x^(3/2)) - (3*c^2*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x))))/(4*b^(5/2))]
    @test_int [1/(x^(7/2)*(b*x + c*x^2)^(1/2)), x, 5, -(sqrt(b*x + c*x^2)/(3*b*x^(7/2))) + (5*c*sqrt(b*x + c*x^2))/(12*b^2*x^(5/2)) - (5*c^2*sqrt(b*x + c*x^2))/(8*b^3*x^(3/2)) + (5*c^3*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x))))/(8*b^(7/2))]

    @test_int [x^(13/2)/(b*x + c*x^2)^(3/2), x, 6, (512*b^5*sqrt(x))/(63*c^6*sqrt(b*x + c*x^2)) + (256*b^4*x^(3/2))/(63*c^5*sqrt(b*x + c*x^2)) - (64*b^3*x^(5/2))/(63*c^4*sqrt(b*x + c*x^2)) + (32*b^2*x^(7/2))/(63*c^3*sqrt(b*x + c*x^2)) - (20*b*x^(9/2))/(63*c^2*sqrt(b*x + c*x^2)) + (2*x^(11/2))/(9*c*sqrt(b*x + c*x^2))]
    @test_int [x^(11/2)/(b*x + c*x^2)^(3/2), x, 5, -((256*b^4*sqrt(x))/(35*c^5*sqrt(b*x + c*x^2))) - (128*b^3*x^(3/2))/(35*c^4*sqrt(b*x + c*x^2)) + (32*b^2*x^(5/2))/(35*c^3*sqrt(b*x + c*x^2)) - (16*b*x^(7/2))/(35*c^2*sqrt(b*x + c*x^2)) + (2*x^(9/2))/(7*c*sqrt(b*x + c*x^2))]
    @test_int [x^(9/2)/(b*x + c*x^2)^(3/2), x, 4, (32*b^3*sqrt(x))/(5*c^4*sqrt(b*x + c*x^2)) + (16*b^2*x^(3/2))/(5*c^3*sqrt(b*x + c*x^2)) - (4*b*x^(5/2))/(5*c^2*sqrt(b*x + c*x^2)) + (2*x^(7/2))/(5*c*sqrt(b*x + c*x^2))]
    @test_int [x^(7/2)/(b*x + c*x^2)^(3/2), x, 3, -((16*b^2*sqrt(x))/(3*c^3*sqrt(b*x + c*x^2))) - (8*b*x^(3/2))/(3*c^2*sqrt(b*x + c*x^2)) + (2*x^(5/2))/(3*c*sqrt(b*x + c*x^2))]
    @test_int [x^(5/2)/(b*x + c*x^2)^(3/2), x, 2, (4*b*sqrt(x))/(c^2*sqrt(b*x + c*x^2)) + (2*x^(3/2))/(c*sqrt(b*x + c*x^2))]
    @test_int [x^(3/2)/(b*x + c*x^2)^(3/2), x, 1, -((2*sqrt(x))/(c*sqrt(b*x + c*x^2)))]
    @test_int [x^(1/2)/(b*x + c*x^2)^(3/2), x, 3, (2*sqrt(x))/(b*sqrt(b*x + c*x^2)) - (2*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x))))/b^(3/2)]
    @test_int [1/(x^(1/2)*(b*x + c*x^2)^(3/2)), x, 4, -(1/(b*sqrt(x)*sqrt(b*x + c*x^2))) - (3*c*sqrt(x))/(b^2*sqrt(b*x + c*x^2)) + (3*c*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x))))/b^(5/2)]
    @test_int [1/(x^(3/2)*(b*x + c*x^2)^(3/2)), x, 5, -(1/(2*b*x^(3/2)*sqrt(b*x + c*x^2))) + (5*c)/(4*b^2*sqrt(x)*sqrt(b*x + c*x^2)) + (15*c^2*sqrt(x))/(4*b^3*sqrt(b*x + c*x^2)) - (15*c^2*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x))))/(4*b^(7/2))]
    @test_int [1/(x^(5/2)*(b*x + c*x^2)^(3/2)), x, 6, -(1/(3*b*x^(5/2)*sqrt(b*x + c*x^2))) + (7*c)/(12*b^2*x^(3/2)*sqrt(b*x + c*x^2)) - (35*c^2)/(24*b^3*sqrt(x)*sqrt(b*x + c*x^2)) - (35*c^3*sqrt(x))/(8*b^4*sqrt(b*x + c*x^2)) + (35*c^3*atanh(sqrt(b*x + c*x^2)/(sqrt(b)*sqrt(x))))/(8*b^(9/2))]

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

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

    @test_int [(d*x)^m*(b*x + c*x^2)^(5/2), x, 3, (2*b^2*(-((c*x)/b))^(-(1/2) - m)*(d*x)^m*(b + c*x)*(b*x + c*x^2)^(5/2)*HypergeometricFunctions._₂F₁(7/2, -(5/2) - m, 9/2, 1 + (c*x)/b))/(7*c^3*x^2)]
    @test_int [(d*x)^m*(b*x + c*x^2)^(3/2), x, 3, -((2*b*(-((c*x)/b))^(-(1/2) - m)*(d*x)^m*(b + c*x)*(b*x + c*x^2)^(3/2)*HypergeometricFunctions._₂F₁(5/2, -(3/2) - m, 7/2, 1 + (c*x)/b))/(5*c^2*x))]
    @test_int [(d*x)^m*(b*x + c*x^2)^(1/2), x, 3, (2*(-((c*x)/b))^(-(1/2) - m)*(d*x)^m*(b + c*x)*sqrt(b*x + c*x^2)*HypergeometricFunctions._₂F₁(3/2, -(1/2) - m, 5/2, 1 + (c*x)/b))/(3*c)]
    @test_int [(d*x)^m/(b*x + c*x^2)^(1/2), x, 3, (2*(-((c*x)/b))^(1/2 - m)*(d*x)^m*(b + c*x)*HypergeometricFunctions._₂F₁(1/2, 1/2 - m, 3/2, 1 + (c*x)/b))/(c*sqrt(b*x + c*x^2))]
    @test_int [(d*x)^m/(b*x + c*x^2)^(3/2), x, 3, (2*x*(-((c*x)/b))^(1/2 - m)*(d*x)^m*(b + c*x)*HypergeometricFunctions._₂F₁(-(1/2), 3/2 - m, 1/2, 1 + (c*x)/b))/(b*(b*x + c*x^2)^(3/2))]
    @test_int [(d*x)^m/(b*x + c*x^2)^(5/2), x, 3, -((2*c*x^2*(-((c*x)/b))^(1/2 - m)*(d*x)^m*(b + c*x)*HypergeometricFunctions._₂F₁(-(3/2), 5/2 - m, -(1/2), 1 + (c*x)/b))/(3*b^2*(b*x + c*x^2)^(5/2)))]

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

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

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

    @test_int [(d*x)^(5/2)*(b*x + c*x^2)^p, x, 3, (2*x*(d*x)^(5/2)*(b*x + c*x^2)^p*HypergeometricFunctions._₂F₁(-p, 7/2 + p, 9/2 + p, -((c*x)/b)))/((1 + (c*x)/b)^p*(7 + 2*p))]
    @test_int [(d*x)^(3/2)*(b*x + c*x^2)^p, x, 3, (2*x*(d*x)^(3/2)*(b*x + c*x^2)^p*HypergeometricFunctions._₂F₁(-p, 5/2 + p, 7/2 + p, -((c*x)/b)))/((1 + (c*x)/b)^p*(5 + 2*p))]
    @test_int [(d*x)^(1/2)*(b*x + c*x^2)^p, x, 3, (2*x*sqrt(d*x)*(b*x + c*x^2)^p*HypergeometricFunctions._₂F₁(-p, 3/2 + p, 5/2 + p, -((c*x)/b)))/((1 + (c*x)/b)^p*(3 + 2*p))]
    @test_int [(b*x + c*x^2)^p/(d*x)^(1/2), x, 3, (2*x*(b*x + c*x^2)^p*HypergeometricFunctions._₂F₁(-p, 1/2 + p, 3/2 + p, -((c*x)/b)))/((1 + (c*x)/b)^p*((1 + 2*p)*sqrt(d*x)))]
    @test_int [(b*x + c*x^2)^p/(d*x)^(3/2), x, 3, -((2*x*(b*x + c*x^2)^p*HypergeometricFunctions._₂F₁(-(1/2) + p, -p, 1/2 + p, -((c*x)/b)))/((1 + (c*x)/b)^p*((1 - 2*p)*(d*x)^(3/2))))]
    @test_int [(b*x + c*x^2)^p/(d*x)^(5/2), x, 3, -((2*x*(b*x + c*x^2)^p*HypergeometricFunctions._₂F₁(-(3/2) + p, -p, -(1/2) + p, -((c*x)/b)))/((1 + (c*x)/b)^p*((3 - 2*p)*(d*x)^(5/2))))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(d*x)^m*(a+b*x+c*x^2)^p*when*b^2-4*a*c=0=#

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

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

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

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

    @test_int [x^5*(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 3, (a^3*x^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*(a + b*x)) + (3*a^2*b*x^7*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*(a + b*x)) + (3*a*b^2*x^8*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(8*(a + b*x)) + (b^3*x^9*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*(a + b*x))]
    @test_int [x^4*(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 3, (a^3*x^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*(a + b*x)) + (a^2*b*x^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*(a + b*x)) + (3*a*b^2*x^7*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*(a + b*x)) + (b^3*x^8*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(8*(a + b*x))]
    @test_int [x^3*(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 3, (a^3*x^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*(a + b*x)) + (3*a^2*b*x^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*(a + b*x)) + (a*b^2*x^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*(a + b*x)) + (b^3*x^7*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*(a + b*x))]
    @test_int [x^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 2, (a^2*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(4*b^3) - (2*a*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(5*b^3) + ((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(6*b^3), (a^2*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*b^3) - (2*a*(a + b*x)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*b^3) + ((a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*b^3)]
    @test_int [x^1*(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 2, -(a*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(4*b^2) + (a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(5*b^2)]
    @test_int [x^0*(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 1, ((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(4*b)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x^1, x, 3, (3*a^2*b*x*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(a + b*x) + (3*a*b^2*x^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*(a + b*x)) + (b^3*x^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*(a + b*x)) + (a^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(x))/(a + b*x)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x^2, x, 3, -((a^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(x*(a + b*x))) + (3*a*b^2*x*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(a + b*x) + (b^3*x^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*(a + b*x)) + (3*a^2*b*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(x))/(a + b*x)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x^3, x, 3, -(a^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*x^2*(a + b*x)) - (3*a^2*b*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(x*(a + b*x)) + (b^3*x*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(a + b*x) + (3*a*b^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(x))/(a + b*x)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x^4, x, 3, -(a^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*x^3*(a + b*x)) - (3*a^2*b*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*x^2*(a + b*x)) - (3*a*b^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(x*(a + b*x)) + (b^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(x))/(a + b*x)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x^5, x, 2, -((a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*a*x^4)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x^6, x, 3, -((a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*a*x^5) + (b*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(20*a^2*x^4)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x^7, x, 3, -((a^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*x^6*(a + b*x))) - (3*a^2*b*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*x^5*(a + b*x)) - (3*a*b^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*x^4*(a + b*x)) - (b^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*x^3*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x^8, x, 3, -(a^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*x^7*(a + b*x)) - (a^2*b*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*x^6*(a + b*x)) - (3*a*b^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*x^5*(a + b*x)) - (b^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*x^4*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/x^9, x, 3, -(a^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(8*x^8*(a + b*x)) - (3*a^2*b*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*x^7*(a + b*x)) - (a*b^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*x^6*(a + b*x)) - (b^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*x^5*(a + b*x))]

    @test_int [x^5*(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, (a^5*x^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*(a + b*x)) + (5*a^4*b*x^7*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*(a + b*x)) + (5*a^3*b^2*x^8*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*(a + b*x)) + (10*a^2*b^3*x^9*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*(a + b*x)) + (a*b^4*x^10*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*(a + b*x)) + (b^5*x^11*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(11*(a + b*x))]
    @test_int [x^4*(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 2, (a^4*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*b^5) - (4*a^3*(a + b*x)^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*b^5) + (3*a^2*(a + b*x)^7*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*b^5) - (4*a*(a + b*x)^8*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*b^5) + ((a + b*x)^9*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(10*b^5)]
    @test_int [x^3*(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, -(a^3*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*b^4) + (3*a^2*(a + b*x)^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*b^4) - (3*a*(a + b*x)^7*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(8*b^4) + ((a + b*x)^8*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*b^4)]
    @test_int [x^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, (a^2*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*b^3) - (2*a*(a + b*x)^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*b^3) + ((a + b*x)^7*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(8*b^3)]
    @test_int [x^1*(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 2, -(a*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(6*b^2) + (a^2 + 2*a*b*x + b^2*x^2)^(7/2)/(7*b^2)]
    @test_int [x^0*(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 1, ((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(6*b)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^1, x, 3, (5*a^4*b*x*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(a + b*x) + (5*a^3*b^2*x^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(a + b*x) + (10*a^2*b^3*x^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*(a + b*x)) + (5*a*b^4*x^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*(a + b*x)) + (b^5*x^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*(a + b*x)) + (a^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(x))/(a + b*x)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^2, x, 3, -((a^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(x*(a + b*x))) + (10*a^3*b^2*x*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(a + b*x) + (5*a^2*b^3*x^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(a + b*x) + (5*a*b^4*x^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*(a + b*x)) + (b^5*x^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*(a + b*x)) + (5*a^4*b*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(x))/(a + b*x)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^3, x, 3, -(a^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*x^2*(a + b*x)) - (5*a^4*b*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(x*(a + b*x)) + (10*a^2*b^3*x*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(a + b*x) + (5*a*b^4*x^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*(a + b*x)) + (b^5*x^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*(a + b*x)) + (10*a^3*b^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(x))/(a + b*x)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^4, x, 3, -(a^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*x^3*(a + b*x)) - (5*a^4*b*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*x^2*(a + b*x)) - (10*a^3*b^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(x*(a + b*x)) + (5*a*b^4*x*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(a + b*x) + (b^5*x^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*(a + b*x)) + (10*a^2*b^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(x))/(a + b*x)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^5, x, 3, -(a^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*x^4*(a + b*x)) - (5*a^4*b*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*x^3*(a + b*x)) - (5*a^3*b^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(x^2*(a + b*x)) - (10*a^2*b^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(x*(a + b*x)) + (b^5*x*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(a + b*x) + (5*a*b^4*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(x))/(a + b*x)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^6, x, 3, -(a^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*x^5*(a + b*x)) - (5*a^4*b*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*x^4*(a + b*x)) - (10*a^3*b^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*x^3*(a + b*x)) - (5*a^2*b^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(x^2*(a + b*x)) - (5*a*b^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(x*(a + b*x)) + (b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(x))/(a + b*x)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^7, x, 2, -((a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*a*x^6)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^8, x, 3, -((a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*a*x^7) + (b*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(42*a^2*x^6)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^9, x, 4, -((a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(8*a*x^8) + (b*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(28*a^2*x^7) - (b^2*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(168*a^3*x^6)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^10, x, 3, -(a^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*x^9*(a + b*x)) - (5*a^4*b*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(8*x^8*(a + b*x)) - (10*a^3*b^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*x^7*(a + b*x)) - (5*a^2*b^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*x^6*(a + b*x)) - (a*b^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(x^5*(a + b*x)) - (b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*x^4*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^11, x, 3, -(a^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(10*x^10*(a + b*x)) - (5*a^4*b*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*x^9*(a + b*x)) - (5*a^3*b^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*x^8*(a + b*x)) - (10*a^2*b^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*x^7*(a + b*x)) - (5*a*b^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*x^6*(a + b*x)) - (b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*x^5*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/x^12, x, 3, -(a^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(11*x^11*(a + b*x)) - (a^4*b*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*x^10*(a + b*x)) - (10*a^3*b^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*x^9*(a + b*x)) - (5*a^2*b^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*x^8*(a + b*x)) - (5*a*b^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*x^7*(a + b*x)) - (b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*x^6*(a + b*x))]

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

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

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

    @test_int [x^6/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, (20*a^3)/(b^7*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - a^6/(4*b^7*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (2*a^5)/(b^7*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (15*a^4)/(2*b^7*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (5*a*x*(a + b*x))/(b^6*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (x^2*(a + b*x))/(2*b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (15*a^2*(a + b*x)*log(a + b*x))/(b^7*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [x^5/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, (-10*a^2)/(b^6*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + a^5/(4*b^6*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (5*a^4)/(3*b^6*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (5*a^3)/(b^6*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (x*(a + b*x))/(b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (5*a*(a + b*x)*log(a + b*x))/(b^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [x^4/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, (4*a)/(b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - a^4/(4*b^5*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (4*a^3)/(3*b^5*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (3*a^2)/(b^5*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + ((a + b*x)*log(a + b*x))/(b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [x^3/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 2, x^4/(4*a*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [x^2/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, -a^2/(4*b^3*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (2*a)/(3*b^3*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - 1/(2*b^3*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [x^1/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 2, -1/(3*b^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)) + a/(4*b^2*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))]
    @test_int [x^0/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 1, -1/(4*b*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))]
    @test_int [1/(x^1*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)), x, 3, 1/(a^4*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + 1/(4*a*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + 1/(3*a^2*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + 1/(2*a^3*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + ((a + b*x)*log(x))/(a^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - ((a + b*x)*log(a + b*x))/(a^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [1/(x^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)), x, 3, (-4*b)/(a^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - b/(4*a^2*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (2*b)/(3*a^3*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (3*b)/(2*a^4*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (a + b*x)/(a^5*x*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (5*b*(a + b*x)*log(x))/(a^6*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (5*b*(a + b*x)*log(a + b*x))/(a^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [1/(x^3*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)), x, 3, (10*b^2)/(a^6*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + b^2/(4*a^3*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + b^2/(a^4*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (3*b^2)/(a^5*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (a + b*x)/(2*a^5*x^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (5*b*(a + b*x))/(a^6*x*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (15*b^2*(a + b*x)*log(x))/(a^7*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (15*b^2*(a + b*x)*log(a + b*x))/(a^7*sqrt(a^2 + 2*a*b*x + b^2*x^2))]

    @test_int [x*(9 + 12*x + 4*x^2)^(5/2), x, 2, -((3 + 2*x)*(9 + 12*x + 4*x^2)^(5/2))/8 + (9 + 12*x + 4*x^2)^(7/2)/28]
    @test_int [x*(9 + 12*x + 4*x^2)^(3/2), x, 2, (-3*(3 + 2*x)*(9 + 12*x + 4*x^2)^(3/2))/16 + (9 + 12*x + 4*x^2)^(5/2)/20]
    @test_int [x*(9 + 12*x + 4*x^2)^(1/2), x, 2, (-3*(3 + 2*x)*sqrt(9 + 12*x + 4*x^2))/8 + (9 + 12*x + 4*x^2)^(3/2)/12]
    @test_int [x/(9 + 12*x + 4*x^2)^(1/2), x, 3, sqrt(9 + 12*x + 4*x^2)/4 - (3*(3 + 2*x)*log(3 + 2*x))/(4*sqrt(9 + 12*x + 4*x^2))]
    @test_int [x/(9 + 12*x + 4*x^2)^(3/2), x, 2, -1/(4*sqrt(9 + 12*x + 4*x^2)) + 3/(8*(3 + 2*x)*sqrt(9 + 12*x + 4*x^2))]
    @test_int [x/(9 + 12*x + 4*x^2)^(5/2), x, 2, -1/(12*(9 + 12*x + 4*x^2)^(3/2)) + 3/(16*(3 + 2*x)*(9 + 12*x + 4*x^2)^(3/2))]
    @test_int [x/(9 + 12*x + 4*x^2)^(7/2), x, 2, -1/(20*(9 + 12*x + 4*x^2)^(5/2)) + 1/(8*(3 + 2*x)*(9 + 12*x + 4*x^2)^(5/2))]

    @test_int [x/sqrt(4 + 12*x + 9*x^2), x, 3, (1/9)*sqrt(4 + 12*x + 9*x^2) - (2*(2 + 3*x)*log(2 + 3*x))/(9*sqrt(4 + 12*x + 9*x^2))]
    @test_int [x/sqrt(4 - 12*x + 9*x^2), x, 3, (1/9)*sqrt(4 - 12*x + 9*x^2) - (2*(2 - 3*x)*log(2 - 3*x))/(9*sqrt(4 - 12*x + 9*x^2))]
    @test_int [x/sqrt(-4 + 12*x - 9*x^2), x, 3, (-(1/9))*sqrt(-4 + 12*x - 9*x^2) - (2*(2 - 3*x)*log(2 - 3*x))/(9*sqrt(-4 + 12*x - 9*x^2))]
    @test_int [x/sqrt(-4 - 12*x - 9*x^2), x, 3, (-(1/9))*sqrt(-4 - 12*x - 9*x^2) - (2*(2 + 3*x)*log(2 + 3*x))/(9*sqrt(-4 - 12*x - 9*x^2))]

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

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

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

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

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

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

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

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

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

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

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

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

    @test_int [(d + e*x)^4*(b*x + c*x^2)^2, x, 2, (d^2*(c*d - b*e)^2*(d + e*x)^5)/(5*e^5) - (d*(c*d - b*e)*(2*c*d - b*e)*(d + e*x)^6)/(3*e^5) + ((6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^7)/(7*e^5) - (c*(2*c*d - b*e)*(d + e*x)^8)/(4*e^5) + (c^2*(d + e*x)^9)/(9*e^5)]
    @test_int [(d + e*x)^3*(b*x + c*x^2)^2, x, 2, (1/3)*b^2*d^3*x^3 + (1/4)*b*d^2*(2*c*d + 3*b*e)*x^4 + (1/5)*d*(c^2*d^2 + 6*b*c*d*e + 3*b^2*e^2)*x^5 + (1/6)*e*(3*c^2*d^2 + 6*b*c*d*e + b^2*e^2)*x^6 + (1/7)*c*e^2*(3*c*d + 2*b*e)*x^7 + (1/8)*c^2*e^3*x^8]
    @test_int [(d + e*x)^2*(b*x + c*x^2)^2, x, 2, (b^2*d^2*x^3)/3 + (b*d*(c*d + b*e)*x^4)/2 + ((c^2*d^2 + 4*b*c*d*e + b^2*e^2)*x^5)/5 + (c*e*(c*d + b*e)*x^6)/3 + (c^2*e^2*x^7)/7]
    @test_int [(d + e*x)^1*(b*x + c*x^2)^2, x, 2, (b^2*d*x^3)/3 + (b*(2*c*d + b*e)*x^4)/4 + (c*(c*d + 2*b*e)*x^5)/5 + (c^2*e*x^6)/6]
    @test_int [(d + e*x)^0*(b*x + c*x^2)^2, x, 2, (b^2*x^3)/3 + (b*c*x^4)/2 + (c^2*x^5)/5]

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

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

    @test_int [(d + e*x)^4*(b*x + c*x^2)^3, x, 2, (1/4)*b^3*d^4*x^4 + (1/5)*b^2*d^3*(3*c*d + 4*b*e)*x^5 + (1/2)*b*d^2*(c^2*d^2 + 4*b*c*d*e + 2*b^2*e^2)*x^6 + (1/7)*d*(c^3*d^3 + 12*b*c^2*d^2*e + 18*b^2*c*d*e^2 + 4*b^3*e^3)*x^7 + (1/8)*e*(4*c^3*d^3 + 18*b*c^2*d^2*e + 12*b^2*c*d*e^2 + b^3*e^3)*x^8 + (1/3)*c*e^2*(2*c^2*d^2 + 4*b*c*d*e + b^2*e^2)*x^9 + (1/10)*c^2*e^3*(4*c*d + 3*b*e)*x^10 + (1/11)*c^3*e^4*x^11]
    @test_int [(d + e*x)^3*(b*x + c*x^2)^3, x, 2, (1/4)*b^3*d^3*x^4 + (3/5)*b^2*d^2*(c*d + b*e)*x^5 + (1/2)*b*d*(c^2*d^2 + 3*b*c*d*e + b^2*e^2)*x^6 + (1/7)*(c*d + b*e)*(c^2*d^2 + 8*b*c*d*e + b^2*e^2)*x^7 + (3/8)*c*e*(c^2*d^2 + 3*b*c*d*e + b^2*e^2)*x^8 + (1/3)*c^2*e^2*(c*d + b*e)*x^9 + (1/10)*c^3*e^3*x^10]
    @test_int [(d + e*x)^2*(b*x + c*x^2)^3, x, 2, (b^3*d^2*x^4)/4 + (b^2*d*(3*c*d + 2*b*e)*x^5)/5 + (b*(3*c^2*d^2 + 6*b*c*d*e + b^2*e^2)*x^6)/6 + (c*(c^2*d^2 + 6*b*c*d*e + 3*b^2*e^2)*x^7)/7 + (c^2*e*(2*c*d + 3*b*e)*x^8)/8 + (c^3*e^2*x^9)/9]
    @test_int [(d + e*x)^1*(b*x + c*x^2)^3, x, 2, (b^3*d*x^4)/4 + (b^2*(3*c*d + b*e)*x^5)/5 + (b*c*(c*d + b*e)*x^6)/2 + (c^2*(c*d + 3*b*e)*x^7)/7 + (c^3*e*x^8)/8]
    @test_int [(d + e*x)^0*(b*x + c*x^2)^3, x, 2, (b^3*x^4)/4 + (3*b^2*c*x^5)/5 + (b*c^2*x^6)/2 + (c^3*x^7)/7]

    @test_int [(b*x + c*x^2)^3/(d + e*x)^1, x, 2, -((d^2*(c*d - b*e)^3*x)/e^6) + (d*(c*d - b*e)^3*x^2)/(2*e^5) - ((c*d - b*e)^3*x^3)/(3*e^4) + (c*(c^2*d^2 - 3*b*c*d*e + 3*b^2*e^2)*x^4)/(4*e^3) - (c^2*(c*d - 3*b*e)*x^5)/(5*e^2) + (c^3*x^6)/(6*e) + (d^3*(c*d - b*e)^3*log(d + e*x))/e^7]
    @test_int [(b*x + c*x^2)^3/(d + e*x)^2, x, 2, (d*(5*c*d - 2*b*e)*(c*d - b*e)^2*x)/e^6 - ((c*d - b*e)^2*(4*c*d - b*e)*x^2)/(2*e^5) + (c*(c*d - b*e)^2*x^3)/e^4 - (c^2*(2*c*d - 3*b*e)*x^4)/(4*e^3) + (c^3*x^5)/(5*e^2) - (d^3*(c*d - b*e)^3)/(e^7*(d + e*x)) - (3*d^2*(c*d - b*e)^2*(2*c*d - b*e)*log(d + e*x))/e^7]
    @test_int [(b*x + c*x^2)^3/(d + e*x)^3, x, 2, -(((c*d - b*e)*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2)*x)/e^6) + (3*c*(c*d - b*e)*(2*c*d - b*e)*x^2)/(2*e^5) - (c^2*(c*d - b*e)*x^3)/e^4 + (c^3*x^4)/(4*e^3) - (d^3*(c*d - b*e)^3)/(2*e^7*(d + e*x)^2) + (3*d^2*(c*d - b*e)^2*(2*c*d - b*e))/(e^7*(d + e*x)) + (3*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*log(d + e*x))/e^7]
    @test_int [(b*x + c*x^2)^3/(d + e*x)^4, x, 2, (c*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2)*x)/e^6 - (c^2*(4*c*d - 3*b*e)*x^2)/(2*e^5) + (c^3*x^3)/(3*e^4) - (d^3*(c*d - b*e)^3)/(3*e^7*(d + e*x)^3) + (3*d^2*(c*d - b*e)^2*(2*c*d - b*e))/(2*e^7*(d + e*x)^2) - (3*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(e^7*(d + e*x)) - ((2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*log(d + e*x))/e^7]
    @test_int [(b*x + c*x^2)^3/(d + e*x)^5, x, 2, -((c^2*(5*c*d - 3*b*e)*x)/e^6) + (c^3*x^2)/(2*e^5) - (d^3*(c*d - b*e)^3)/(4*e^7*(d + e*x)^4) + (d^2*(c*d - b*e)^2*(2*c*d - b*e))/(e^7*(d + e*x)^3) - (3*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(2*e^7*(d + e*x)^2) + ((2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2))/(e^7*(d + e*x)) + (3*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*log(d + e*x))/e^7]
    @test_int [(b*x + c*x^2)^3/(d + e*x)^6, x, 2, (c^3*x)/e^6 - (d^3*(c*d - b*e)^3)/(5*e^7*(d + e*x)^5) + (3*d^2*(c*d - b*e)^2*(2*c*d - b*e))/(4*e^7*(d + e*x)^4) - (d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(e^7*(d + e*x)^3) + ((2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2))/(2*e^7*(d + e*x)^2) - (3*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(e^7*(d + e*x)) - (3*c^2*(2*c*d - b*e)*log(d + e*x))/e^7]
    @test_int [(b*x + c*x^2)^3/(d + e*x)^7, x, 2, -((d^3*(c*d - b*e)^3)/(6*e^7*(d + e*x)^6)) + (3*d^2*(c*d - b*e)^2*(2*c*d - b*e))/(5*e^7*(d + e*x)^5) - (3*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(4*e^7*(d + e*x)^4) + ((2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2))/(3*e^7*(d + e*x)^3) - (3*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(2*e^7*(d + e*x)^2) + (3*c^2*(2*c*d - b*e))/(e^7*(d + e*x)) + (c^3*log(d + e*x))/e^7]

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

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

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

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

    @test_int [(d + e*x)^7/(b*x + c*x^2)^3, x, 2, -(d^7/(2*b^3*x^2)) + (d^6*(3*c*d - 7*b*e))/(b^4*x) + (e^6*(7*c*d - 3*b*e)*x)/c^4 + (e^7*x^2)/(2*c^3) + (c*d - b*e)^7/(2*b^3*c^5*(b + c*x)^2) + ((c*d - b*e)^6*(3*c*d + 4*b*e))/(b^4*c^5*(b + c*x)) + (3*d^5*(2*c^2*d^2 - 7*b*c*d*e + 7*b^2*e^2)*log(x))/b^5 - (3*(c*d - b*e)^5*(2*c^2*d^2 + 3*b*c*d*e + 2*b^2*e^2)*log(b + c*x))/(b^5*c^5)]
    @test_int [(d + e*x)^6/(b*x + c*x^2)^3, x, 2, -(d^6/(2*b^3*x^2)) + (3*d^5*(c*d - 2*b*e))/(b^4*x) + (e^6*x)/c^3 + (c*d - b*e)^6/(2*b^3*c^4*(b + c*x)^2) + (3*(c*d - b*e)^5*(c*d + b*e))/(b^4*c^4*(b + c*x)) + (3*d^4*(2*c^2*d^2 - 6*b*c*d*e + 5*b^2*e^2)*log(x))/b^5 - (3*(c*d - b*e)^4*(2*c^2*d^2 + 2*b*c*d*e + b^2*e^2)*log(b + c*x))/(b^5*c^4)]
    @test_int [(d + e*x)^5/(b*x + c*x^2)^3, x, 2, -(d^5/(2*b^3*x^2)) + (d^4*(3*c*d - 5*b*e))/(b^4*x) + (c*d - b*e)^5/(2*b^3*c^3*(b + c*x)^2) + ((c*d - b*e)^4*(3*c*d + 2*b*e))/(b^4*c^3*(b + c*x)) + (d^3*(6*c^2*d^2 - 15*b*c*d*e + 10*b^2*e^2)*log(x))/b^5 - ((c*d - b*e)^3*(6*c^2*d^2 + 3*b*c*d*e + b^2*e^2)*log(b + c*x))/(b^5*c^3)]
    @test_int [(d + e*x)^4/(b*x + c*x^2)^3, x, 2, -(d^4/(2*b^3*x^2)) + (d^3*(3*c*d - 4*b*e))/(b^4*x) + (c*d - b*e)^4/(2*b^3*c^2*(b + c*x)^2) + ((c*d - b*e)^3*(3*c*d + b*e))/(b^4*c^2*(b + c*x)) + (6*d^2*(c*d - b*e)^2*log(x))/b^5 - (6*d^2*(c*d - b*e)^2*log(b + c*x))/b^5]
    @test_int [(d + e*x)^3/(b*x + c*x^2)^3, x, 2, -(d^3/(2*b^3*x^2)) + (3*d^2*(c*d - b*e))/(b^4*x) + (c*d - b*e)^3/(2*b^3*c*(b + c*x)^2) + (3*d*(c*d - b*e)^2)/(b^4*(b + c*x)) + (3*d*(c*d - b*e)*(2*c*d - b*e)*log(x))/b^5 - (3*d*(c*d - b*e)*(2*c*d - b*e)*log(b + c*x))/b^5]
    @test_int [(d + e*x)^2/(b*x + c*x^2)^3, x, 2, -(d^2/(2*b^3*x^2)) + (d*(3*c*d - 2*b*e))/(b^4*x) + (c*d - b*e)^2/(2*b^3*(b + c*x)^2) + ((c*d - b*e)*(3*c*d - b*e))/(b^4*(b + c*x)) + ((6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*log(x))/b^5 - ((6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*log(b + c*x))/b^5]
    @test_int [(d + e*x)^1/(b*x + c*x^2)^3, x, 2, -(d/(2*b^3*x^2)) + (3*c*d - b*e)/(b^4*x) + (c*(c*d - b*e))/(2*b^3*(b + c*x)^2) + (c*(3*c*d - 2*b*e))/(b^4*(b + c*x)) + (3*c*(2*c*d - b*e)*log(x))/b^5 - (3*c*(2*c*d - b*e)*log(b + c*x))/b^5]
    @test_int [(d + e*x)^0/(b*x + c*x^2)^3, x, 3, -((b + 2*c*x)/(2*b^2*(b*x + c*x^2)^2)) + (3*c*(b + 2*c*x))/(b^4*(b*x + c*x^2)) + (6*c^2*log(x))/b^5 - (6*c^2*log(b + c*x))/b^5]
    @test_int [1/((d + e*x)^1*(b*x + c*x^2)^3), x, 2, -(1/(2*b^3*d*x^2)) + (3*c*d + b*e)/(b^4*d^2*x) + c^3/(2*b^3*(c*d - b*e)*(b + c*x)^2) + (c^3*(3*c*d - 4*b*e))/(b^4*(c*d - b*e)^2*(b + c*x)) + ((6*c^2*d^2 + 3*b*c*d*e + b^2*e^2)*log(x))/(b^5*d^3) - (c^3*(6*c^2*d^2 - 15*b*c*d*e + 10*b^2*e^2)*log(b + c*x))/(b^5*(c*d - b*e)^3) + (e^5*log(d + e*x))/(d^3*(c*d - b*e)^3)]
    @test_int [1/((d + e*x)^2*(b*x + c*x^2)^3), x, 2, -(1/(2*b^3*d^2*x^2)) + (3*c*d + 2*b*e)/(b^4*d^3*x) + c^4/(2*b^3*(c*d - b*e)^2*(b + c*x)^2) + (c^4*(3*c*d - 5*b*e))/(b^4*(c*d - b*e)^3*(b + c*x)) - e^5/(d^3*(c*d - b*e)^3*(d + e*x)) + (3*(2*c^2*d^2 + 2*b*c*d*e + b^2*e^2)*log(x))/(b^5*d^4) - (3*c^4*(2*c^2*d^2 - 6*b*c*d*e + 5*b^2*e^2)*log(b + c*x))/(b^5*(c*d - b*e)^4) + (3*e^5*(2*c*d - b*e)*log(d + e*x))/(d^4*(c*d - b*e)^4)]

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

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

    @test_int [(d + e*x)^3*(b*x + c*x^2)^(1/2), x, 5, ((2*c*d - b*e)*(16*c^2*d^2 - 16*b*c*d*e + 7*b^2*e^2)*(b + 2*c*x)*sqrt(b*x + c*x^2))/(128*c^4) + (e*(d + e*x)^2*(b*x + c*x^2)^(3/2))/(5*c) + (e*(192*c^2*d^2 - 150*b*c*d*e + 35*b^2*e^2 + 42*c*e*(2*c*d - b*e)*x)*(b*x + c*x^2)^(3/2))/(240*c^3) - (b^2*(2*c*d - b*e)*(16*c^2*d^2 - 16*b*c*d*e + 7*b^2*e^2)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(128*c^(9/2))]
    @test_int [(d + e*x)^2*(b*x + c*x^2)^(1/2), x, 5, ((16*c^2*d^2 - 16*b*c*d*e + 5*b^2*e^2)*(b + 2*c*x)*sqrt(b*x + c*x^2))/(64*c^3) + (5*e*(2*c*d - b*e)*(b*x + c*x^2)^(3/2))/(24*c^2) + (e*(d + e*x)*(b*x + c*x^2)^(3/2))/(4*c) - (b^2*(16*c^2*d^2 - 16*b*c*d*e + 5*b^2*e^2)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(64*c^(7/2))]
    @test_int [(d + e*x)^1*(b*x + c*x^2)^(1/2), x, 4, ((2*c*d - b*e)*(b + 2*c*x)*sqrt(b*x + c*x^2))/(8*c^2) + (e*(b*x + c*x^2)^(3/2))/(3*c) - (b^2*(2*c*d - b*e)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(8*c^(5/2))]
    @test_int [(d + e*x)^0*(b*x + c*x^2)^(1/2), x, 3, ((b + 2*c*x)*sqrt(b*x + c*x^2))/(4*c) - (b^2*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(4*c^(3/2))]
    @test_int [(b*x + c*x^2)^(1/2)/(d + e*x)^1, x, 6, sqrt(b*x + c*x^2)/e - ((2*c*d - b*e)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(sqrt(c)*e^2) + (sqrt(d)*sqrt(c*d - b*e)*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/e^2]
    @test_int [(b*x + c*x^2)^(1/2)/(d + e*x)^2, x, 6, -(sqrt(b*x + c*x^2)/(e*(d + e*x))) + (2*sqrt(c)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/e^2 - ((2*c*d - b*e)*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/(2*sqrt(d)*e^2*sqrt(c*d - b*e))]
    @test_int [(b*x + c*x^2)^(1/2)/(d + e*x)^3, x, 3, ((b*d + (2*c*d - b*e)*x)*sqrt(b*x + c*x^2))/(4*d*(c*d - b*e)*(d + e*x)^2) - (b^2*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/(8*d^(3/2)*(c*d - b*e)^(3/2))]
    @test_int [(b*x + c*x^2)^(1/2)/(d + e*x)^4, x, 4, ((2*c*d - b*e)*(b*d + (2*c*d - b*e)*x)*sqrt(b*x + c*x^2))/(8*d^2*(c*d - b*e)^2*(d + e*x)^2) - (e*(b*x + c*x^2)^(3/2))/(3*d*(c*d - b*e)*(d + e*x)^3) - (b^2*(2*c*d - b*e)*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/(16*d^(5/2)*(c*d - b*e)^(5/2))]
    @test_int [(b*x + c*x^2)^(1/2)/(d + e*x)^5, x, 5, ((16*c^2*d^2 - 16*b*c*d*e + 5*b^2*e^2)*(b*d + (2*c*d - b*e)*x)*sqrt(b*x + c*x^2))/(64*d^3*(c*d - b*e)^3*(d + e*x)^2) - (e*(b*x + c*x^2)^(3/2))/(4*d*(c*d - b*e)*(d + e*x)^4) - (5*e*(2*c*d - b*e)*(b*x + c*x^2)^(3/2))/(24*d^2*(c*d - b*e)^2*(d + e*x)^3) - (b^2*(16*c^2*d^2 - 16*b*c*d*e + 5*b^2*e^2)*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/(128*d^(7/2)*(c*d - b*e)^(7/2))]
    @test_int [(b*x + c*x^2)^(1/2)/(d + e*x)^6, x, 6, ((2*c*d - b*e)*(16*c^2*d^2 - 16*b*c*d*e + 7*b^2*e^2)*(b*d + (2*c*d - b*e)*x)*sqrt(b*x + c*x^2))/(128*d^4*(c*d - b*e)^4*(d + e*x)^2) - (e*(b*x + c*x^2)^(3/2))/(5*d*(c*d - b*e)*(d + e*x)^5) - (7*e*(2*c*d - b*e)*(b*x + c*x^2)^(3/2))/(40*d^2*(c*d - b*e)^2*(d + e*x)^4) - (e*(108*c^2*d^2 - 108*b*c*d*e + 35*b^2*e^2)*(b*x + c*x^2)^(3/2))/(240*d^3*(c*d - b*e)^3*(d + e*x)^3) - (b^2*(2*c*d - b*e)*(16*c^2*d^2 - 16*b*c*d*e + 7*b^2*e^2)*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/(256*d^(9/2)*(c*d - b*e)^(9/2))]

    @test_int [(d + e*x)^3*(b*x + c*x^2)^(3/2), x, 6, -((3*b^2*(2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2)*(b + 2*c*x)*sqrt(b*x + c*x^2))/(1024*c^5)) + ((2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(128*c^4) + (e*(d + e*x)^2*(b*x + c*x^2)^(5/2))/(7*c) + (e*(128*c^2*d^2 - 98*b*c*d*e + 21*b^2*e^2 + 30*c*e*(2*c*d - b*e)*x)*(b*x + c*x^2)^(5/2))/(280*c^3) + (3*b^4*(2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(1024*c^(11/2))]
    @test_int [(d + e*x)^2*(b*x + c*x^2)^(3/2), x, 6, -((b^2*(24*c^2*d^2 - 24*b*c*d*e + 7*b^2*e^2)*(b + 2*c*x)*sqrt(b*x + c*x^2))/(512*c^4)) + ((24*c^2*d^2 - 24*b*c*d*e + 7*b^2*e^2)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(192*c^3) + (7*e*(2*c*d - b*e)*(b*x + c*x^2)^(5/2))/(60*c^2) + (e*(d + e*x)*(b*x + c*x^2)^(5/2))/(6*c) + (b^4*(24*c^2*d^2 - 24*b*c*d*e + 7*b^2*e^2)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(512*c^(9/2))]
    @test_int [(d + e*x)^1*(b*x + c*x^2)^(3/2), x, 5, -((3*b^2*(2*c*d - b*e)*(b + 2*c*x)*sqrt(b*x + c*x^2))/(128*c^3)) + ((2*c*d - b*e)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(16*c^2) + (e*(b*x + c*x^2)^(5/2))/(5*c) + (3*b^4*(2*c*d - b*e)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(128*c^(7/2))]
    @test_int [(d + e*x)^0*(b*x + c*x^2)^(3/2), x, 4, -((3*b^2*(b + 2*c*x)*sqrt(b*x + c*x^2))/(64*c^2)) + ((b + 2*c*x)*(b*x + c*x^2)^(3/2))/(8*c) + (3*b^4*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(64*c^(5/2))]
    @test_int [(b*x + c*x^2)^(3/2)/(d + e*x)^1, x, 7, ((8*c^2*d^2 - 10*b*c*d*e + b^2*e^2 - 2*c*e*(2*c*d - b*e)*x)*sqrt(b*x + c*x^2))/(8*c*e^3) + (b*x + c*x^2)^(3/2)/(3*e) - ((2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e - b^2*e^2)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(8*c^(3/2)*e^4) + (d^(3/2)*(c*d - b*e)^(3/2)*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/e^4]
    @test_int [(b*x + c*x^2)^(3/2)/(d + e*x)^2, x, 7, -((3*(4*c*d - 3*b*e - 2*c*e*x)*sqrt(b*x + c*x^2))/(4*e^3)) - (b*x + c*x^2)^(3/2)/(e*(d + e*x)) + (3*(8*c^2*d^2 - 8*b*c*d*e + b^2*e^2)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(4*sqrt(c)*e^4) - (3*sqrt(d)*sqrt(c*d - b*e)*(2*c*d - b*e)*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/(2*e^4)]
    @test_int [(b*x + c*x^2)^(3/2)/(d + e*x)^3, x, 7, (3*(4*c*d - b*e + 2*c*e*x)*sqrt(b*x + c*x^2))/(4*e^3*(d + e*x)) - (b*x + c*x^2)^(3/2)/(2*e*(d + e*x)^2) - (3*sqrt(c)*(2*c*d - b*e)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/e^4 + (3*(8*c^2*d^2 - 8*b*c*d*e + b^2*e^2)*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/(8*sqrt(d)*e^4*sqrt(c*d - b*e))]

    @test_int [(d + e*x)^3*(b*x + c*x^2)^(5/2), x, 7, (5*b^4*(2*c*d - b*e)*(32*c^2*d^2 - 32*b*c*d*e + 11*b^2*e^2)*(b + 2*c*x)*sqrt(b*x + c*x^2))/(32768*c^6) - (5*b^2*(2*c*d - b*e)*(32*c^2*d^2 - 32*b*c*d*e + 11*b^2*e^2)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(12288*c^5) + ((2*c*d - b*e)*(32*c^2*d^2 - 32*b*c*d*e + 11*b^2*e^2)*(b + 2*c*x)*(b*x + c*x^2)^(5/2))/(768*c^4) + (e*(d + e*x)^2*(b*x + c*x^2)^(7/2))/(9*c) + (e*(640*c^2*d^2 - 486*b*c*d*e + 99*b^2*e^2 + 154*c*e*(2*c*d - b*e)*x)*(b*x + c*x^2)^(7/2))/(2016*c^3) - (5*b^6*(2*c*d - b*e)*(32*c^2*d^2 - 32*b*c*d*e + 11*b^2*e^2)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(32768*c^(13/2))]
    @test_int [(d + e*x)^2*(b*x + c*x^2)^(5/2), x, 7, (5*b^4*(32*c^2*d^2 - 32*b*c*d*e + 9*b^2*e^2)*(b + 2*c*x)*sqrt(b*x + c*x^2))/(16384*c^5) - (5*b^2*(32*c^2*d^2 - 32*b*c*d*e + 9*b^2*e^2)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(6144*c^4) + ((32*c^2*d^2 - 32*b*c*d*e + 9*b^2*e^2)*(b + 2*c*x)*(b*x + c*x^2)^(5/2))/(384*c^3) + (9*e*(2*c*d - b*e)*(b*x + c*x^2)^(7/2))/(112*c^2) + (e*(d + e*x)*(b*x + c*x^2)^(7/2))/(8*c) - (5*b^6*(32*c^2*d^2 - 32*b*c*d*e + 9*b^2*e^2)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(16384*c^(11/2))]
    @test_int [(d + e*x)^1*(b*x + c*x^2)^(5/2), x, 6, (5*b^4*(2*c*d - b*e)*(b + 2*c*x)*sqrt(b*x + c*x^2))/(1024*c^4) - (5*b^2*(2*c*d - b*e)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(384*c^3) + ((2*c*d - b*e)*(b + 2*c*x)*(b*x + c*x^2)^(5/2))/(24*c^2) + (e*(b*x + c*x^2)^(7/2))/(7*c) - (5*b^6*(2*c*d - b*e)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(1024*c^(9/2))]
    @test_int [(d + e*x)^0*(b*x + c*x^2)^(5/2), x, 5, (5*b^4*(b + 2*c*x)*sqrt(b*x + c*x^2))/(512*c^3) - (5*b^2*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(192*c^2) + ((b + 2*c*x)*(b*x + c*x^2)^(5/2))/(12*c) - (5*b^6*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(512*c^(7/2))]
    @test_int [(b*x + c*x^2)^(5/2)/(d + e*x)^1, x, 8, ((128*c^4*d^4 - 288*b*c^3*d^3*e + 176*b^2*c^2*d^2*e^2 - 10*b^3*c*d*e^3 - 3*b^4*e^4 - 2*c*e*(2*c*d - b*e)*(16*c^2*d^2 - 16*b*c*d*e - 3*b^2*e^2)*x)*sqrt(b*x + c*x^2))/(128*c^2*e^5) + ((16*c^2*d^2 - 22*b*c*d*e + 3*b^2*e^2 - 6*c*e*(2*c*d - b*e)*x)*(b*x + c*x^2)^(3/2))/(48*c*e^3) + (b*x + c*x^2)^(5/2)/(5*e) - ((2*c*d - b*e)*(128*c^4*d^4 - 256*b*c^3*d^3*e + 112*b^2*c^2*d^2*e^2 + 16*b^3*c*d*e^3 + 3*b^4*e^4)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(128*c^(5/2)*e^6) + (d^(5/2)*(c*d - b*e)^(5/2)*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/e^6]
    @test_int [(b*x + c*x^2)^(5/2)/(d + e*x)^2, x, 8, (-5*(64*c^3*d^3 - 112*b*c^2*d^2*e + 48*b^2*c*d*e^2 - b^3*e^3 - 2*c*e*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2)*x)*sqrt(b*x + c*x^2))/(64*c*e^5) - (5*(8*c*d - 7*b*e - 6*c*e*x)*(b*x + c*x^2)^(3/2))/(24*e^3) - (b*x + c*x^2)^(5/2)/(e*(d + e*x)) + (5*(128*c^4*d^4 - 256*b*c^3*d^3*e + 144*b^2*c^2*d^2*e^2 - 16*b^3*c*d*e^3 - b^4*e^4)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(64*c^(3/2)*e^6) - (5*d^(3/2)*(c*d - b*e)^(3/2)*(2*c*d - b*e)*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/(2*e^6)]
    @test_int [(b*x + c*x^2)^(5/2)/(d + e*x)^3, x, 8, (5*(16*c^2*d^2 - 20*b*c*d*e + 5*b^2*e^2 - 4*c*e*(2*c*d - b*e)*x)*sqrt(b*x + c*x^2))/(8*e^5) + (5*(8*c*d - 3*b*e + 2*c*e*x)*(b*x + c*x^2)^(3/2))/(12*e^3*(d + e*x)) - (b*x + c*x^2)^(5/2)/(2*e*(d + e*x)^2) - (5*(2*c*d - b*e)*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(8*sqrt(c)*e^6) + (5*sqrt(d)*(4*c*d - 3*b*e)*sqrt(c*d - b*e)*(4*c*d - b*e)*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/(8*e^6)]

    #= Integrands*of*the*form*(d+e*x)^m*(b*x+c*x^2)^p*where*2*c*d-b*e=0 =#
    @test_int [sqrt(2*x + x^2)/(1 + x), x, 3, sqrt(2*x + x^2) - atan(sqrt(2*x + x^2))]

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

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

    @test_int [(d + e*x)^3/(b*x + c*x^2)^(1/2), x, 4, (e*(d + e*x)^2*sqrt(b*x + c*x^2))/(3*c) + (e*(64*c^2*d^2 - 54*b*c*d*e + 15*b^2*e^2 + 10*c*e*(2*c*d - b*e)*x)*sqrt(b*x + c*x^2))/(24*c^3) + ((2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e + 5*b^2*e^2)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(8*c^(7/2))]
    @test_int [(d + e*x)^2/(b*x + c*x^2)^(1/2), x, 4, (3*e*(2*c*d - b*e)*sqrt(b*x + c*x^2))/(4*c^2) + (e*(d + e*x)*sqrt(b*x + c*x^2))/(2*c) + ((8*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/(4*c^(5/2))]
    @test_int [(d + e*x)^1/(b*x + c*x^2)^(1/2), x, 3, (e*sqrt(b*x + c*x^2))/c + ((2*c*d - b*e)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/c^(3/2)]
    @test_int [(d + e*x)^0/(b*x + c*x^2)^(1/2), x, 2, (2*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/sqrt(c)]
    @test_int [1/((d + e*x)^1*(b*x + c*x^2)^(1/2)), x, 2, atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2)))/(sqrt(d)*sqrt(c*d - b*e))]
    @test_int [1/((d + e*x)^2*(b*x + c*x^2)^(1/2)), x, 3, -((e*sqrt(b*x + c*x^2))/(d*(c*d - b*e)*(d + e*x))) + ((2*c*d - b*e)*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/(2*d^(3/2)*(c*d - b*e)^(3/2))]
    @test_int [1/((d + e*x)^3*(b*x + c*x^2)^(1/2)), x, 4, -((e*sqrt(b*x + c*x^2))/(2*d*(c*d - b*e)*(d + e*x)^2)) - (3*e*(2*c*d - b*e)*sqrt(b*x + c*x^2))/(4*d^2*(c*d - b*e)^2*(d + e*x)) + ((8*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2)*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/(8*d^(5/2)*(c*d - b*e)^(5/2))]

    @test_int [(d + e*x)^3/(b*x + c*x^2)^(3/2), x, 4, -((2*(d + e*x)^2*(b*d + (2*c*d - b*e)*x))/(b^2*sqrt(b*x + c*x^2))) + (e*(8*c^2*d^2 - 6*b*c*d*e + 3*b^2*e^2 + 2*c*e*(2*c*d - b*e)*x)*sqrt(b*x + c*x^2))/(b^2*c^2) + (3*e^2*(2*c*d - b*e)*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/c^(5/2)]
    @test_int [(d + e*x)^2/(b*x + c*x^2)^(3/2), x, 4, -((2*(d + e*x)*(b*d + (2*c*d - b*e)*x))/(b^2*sqrt(b*x + c*x^2))) + (2*e*(2*c*d - b*e)*sqrt(b*x + c*x^2))/(b^2*c) + (2*e^2*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/c^(3/2)]
    @test_int [(d + e*x)^1/(b*x + c*x^2)^(3/2), x, 1, -((2*(b*d + (2*c*d - b*e)*x))/(b^2*sqrt(b*x + c*x^2)))]
    @test_int [(d + e*x)^0/(b*x + c*x^2)^(3/2), x, 1, -((2*(b + 2*c*x))/(b^2*sqrt(b*x + c*x^2)))]
    @test_int [1/((d + e*x)^1*(b*x + c*x^2)^(3/2)), x, 4, -((2*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(b^2*d*(c*d - b*e)*sqrt(b*x + c*x^2))) + (e^2*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/(d^(3/2)*(c*d - b*e)^(3/2))]
    @test_int [1/((d + e*x)^2*(b*x + c*x^2)^(3/2)), x, 4, -((2*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(b^2*d*(c*d - b*e)*(d + e*x)*sqrt(b*x + c*x^2))) - (e*(4*c^2*d^2 - 4*b*c*d*e + 3*b^2*e^2)*sqrt(b*x + c*x^2))/(b^2*d^2*(c*d - b*e)^2*(d + e*x)) + (3*e^2*(2*c*d - b*e)*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/(2*d^(5/2)*(c*d - b*e)^(5/2))]
    @test_int [1/((d + e*x)^3*(b*x + c*x^2)^(3/2)), x, 5, -((2*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(b^2*d*(c*d - b*e)*(d + e*x)^2*sqrt(b*x + c*x^2))) - (e*(8*c^2*d^2 - 8*b*c*d*e + 5*b^2*e^2)*sqrt(b*x + c*x^2))/(2*b^2*d^2*(c*d - b*e)^2*(d + e*x)^2) - (e*(2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e + 15*b^2*e^2)*sqrt(b*x + c*x^2))/(4*b^2*d^3*(c*d - b*e)^3*(d + e*x)) + (3*e^2*(16*c^2*d^2 - 16*b*c*d*e + 5*b^2*e^2)*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/(8*d^(7/2)*(c*d - b*e)^(7/2))]

    @test_int [(d + e*x)^4/(b*x + c*x^2)^(5/2), x, 5, -((2*(d + e*x)^3*(b*d + (2*c*d - b*e)*x))/(3*b^2*(b*x + c*x^2)^(3/2))) + (4*(d + e*x)*(b*c*d^2*(4*c*d - 5*b*e) + (2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*x))/(3*b^4*c*sqrt(b*x + c*x^2)) - (2*e*(2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e - 3*b^2*e^2)*sqrt(b*x + c*x^2))/(3*b^4*c^2) + (2*e^4*atanh((sqrt(c)*x)/sqrt(b*x + c*x^2)))/c^(5/2)]
    @test_int [(d + e*x)^3/(b*x + c*x^2)^(5/2), x, 2, -((2*(d + e*x)^2*(b*d + (2*c*d - b*e)*x))/(3*b^2*(b*x + c*x^2)^(3/2))) + (16*d*(c*d - b*e)*(b*d + (2*c*d - b*e)*x))/(3*b^4*sqrt(b*x + c*x^2))]
    @test_int [(d + e*x)^2/(b*x + c*x^2)^(5/2), x, 2, -((2*(b + 2*c*x)*(d + e*x)^2)/(3*b^2*(b*x + c*x^2)^(3/2))) + (8*(2*c*d - b*e)*(b*d + (2*c*d - b*e)*x))/(3*b^4*sqrt(b*x + c*x^2))]
    @test_int [(d + e*x)^1/(b*x + c*x^2)^(5/2), x, 2, -((2*(b*d + (2*c*d - b*e)*x))/(3*b^2*(b*x + c*x^2)^(3/2))) + (8*(2*c*d - b*e)*(b + 2*c*x))/(3*b^4*sqrt(b*x + c*x^2))]
    @test_int [(d + e*x)^0/(b*x + c*x^2)^(5/2), x, 2, -((2*(b + 2*c*x))/(3*b^2*(b*x + c*x^2)^(3/2))) + (16*c*(b + 2*c*x))/(3*b^4*sqrt(b*x + c*x^2))]
    @test_int [1/((d + e*x)^1*(b*x + c*x^2)^(5/2)), x, 5, -((2*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(3*b^2*d*(c*d - b*e)*(b*x + c*x^2)^(3/2))) + (2*(b*(c*d - b*e)*(8*c^2*d^2 - 4*b*c*d*e - 3*b^2*e^2) + c*(2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e - 3*b^2*e^2)*x))/(3*b^4*d^2*(c*d - b*e)^2*sqrt(b*x + c*x^2)) + (e^4*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/(d^(5/2)*(c*d - b*e)^(5/2))]
    @test_int [1/((d + e*x)^2*(b*x + c*x^2)^(5/2)), x, 5, -((2*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(3*b^2*d*(c*d - b*e)*(d + e*x)*(b*x + c*x^2)^(3/2))) + (2*(b*(c*d - b*e)*(8*c^2*d^2 - 2*b*c*d*e - 5*b^2*e^2) + c*(2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e - 5*b^2*e^2)*x))/(3*b^4*d^2*(c*d - b*e)^2*(d + e*x)*sqrt(b*x + c*x^2)) + (e*(32*c^4*d^4 - 64*b*c^3*d^3*e + 12*b^2*c^2*d^2*e^2 + 20*b^3*c*d*e^3 - 15*b^4*e^4)*sqrt(b*x + c*x^2))/(3*b^4*d^3*(c*d - b*e)^3*(d + e*x)) + (5*e^4*(2*c*d - b*e)*atanh((b*d + (2*c*d - b*e)*x)/(2*sqrt(d)*sqrt(c*d - b*e)*sqrt(b*x + c*x^2))))/(2*d^(7/2)*(c*d - b*e)^(7/2))]

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

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

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

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

    @test_int [(d + e*x)^(7/2)*(b*x + c*x^2)^2, x, 2, (2*d^2*(c*d - b*e)^2*(d + e*x)^(9/2))/(9*e^5) - (4*d*(c*d - b*e)*(2*c*d - b*e)*(d + e*x)^(11/2))/(11*e^5) + (2*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^(13/2))/(13*e^5) - (4*c*(2*c*d - b*e)*(d + e*x)^(15/2))/(15*e^5) + (2*c^2*(d + e*x)^(17/2))/(17*e^5)]
    @test_int [(d + e*x)^(5/2)*(b*x + c*x^2)^2, x, 2, (2*d^2*(c*d - b*e)^2*(d + e*x)^(7/2))/(7*e^5) - (4*d*(c*d - b*e)*(2*c*d - b*e)*(d + e*x)^(9/2))/(9*e^5) + (2*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^(11/2))/(11*e^5) - (4*c*(2*c*d - b*e)*(d + e*x)^(13/2))/(13*e^5) + (2*c^2*(d + e*x)^(15/2))/(15*e^5)]
    @test_int [(d + e*x)^(3/2)*(b*x + c*x^2)^2, x, 2, (2*d^2*(c*d - b*e)^2*(d + e*x)^(5/2))/(5*e^5) - (4*d*(c*d - b*e)*(2*c*d - b*e)*(d + e*x)^(7/2))/(7*e^5) + (2*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^(9/2))/(9*e^5) - (4*c*(2*c*d - b*e)*(d + e*x)^(11/2))/(11*e^5) + (2*c^2*(d + e*x)^(13/2))/(13*e^5)]
    @test_int [(d + e*x)^(1/2)*(b*x + c*x^2)^2, x, 2, (2*d^2*(c*d - b*e)^2*(d + e*x)^(3/2))/(3*e^5) - (4*d*(c*d - b*e)*(2*c*d - b*e)*(d + e*x)^(5/2))/(5*e^5) + (2*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^(7/2))/(7*e^5) - (4*c*(2*c*d - b*e)*(d + e*x)^(9/2))/(9*e^5) + (2*c^2*(d + e*x)^(11/2))/(11*e^5)]
    @test_int [(b*x + c*x^2)^2/(d + e*x)^(1/2), x, 2, (2*d^2*(c*d - b*e)^2*sqrt(d + e*x))/e^5 - (4*d*(c*d - b*e)*(2*c*d - b*e)*(d + e*x)^(3/2))/(3*e^5) + (2*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^(5/2))/(5*e^5) - (4*c*(2*c*d - b*e)*(d + e*x)^(7/2))/(7*e^5) + (2*c^2*(d + e*x)^(9/2))/(9*e^5)]
    @test_int [(b*x + c*x^2)^2/(d + e*x)^(3/2), x, 2, -((2*d^2*(c*d - b*e)^2)/(e^5*sqrt(d + e*x))) - (4*d*(c*d - b*e)*(2*c*d - b*e)*sqrt(d + e*x))/e^5 + (2*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^(3/2))/(3*e^5) - (4*c*(2*c*d - b*e)*(d + e*x)^(5/2))/(5*e^5) + (2*c^2*(d + e*x)^(7/2))/(7*e^5)]
    @test_int [(b*x + c*x^2)^2/(d + e*x)^(5/2), x, 2, -((2*d^2*(c*d - b*e)^2)/(3*e^5*(d + e*x)^(3/2))) + (4*d*(c*d - b*e)*(2*c*d - b*e))/(e^5*sqrt(d + e*x)) + (2*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*sqrt(d + e*x))/e^5 - (4*c*(2*c*d - b*e)*(d + e*x)^(3/2))/(3*e^5) + (2*c^2*(d + e*x)^(5/2))/(5*e^5)]
    @test_int [(b*x + c*x^2)^2/(d + e*x)^(7/2), x, 2, -((2*d^2*(c*d - b*e)^2)/(5*e^5*(d + e*x)^(5/2))) + (4*d*(c*d - b*e)*(2*c*d - b*e))/(3*e^5*(d + e*x)^(3/2)) - (2*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2))/(e^5*sqrt(d + e*x)) - (4*c*(2*c*d - b*e)*sqrt(d + e*x))/e^5 + (2*c^2*(d + e*x)^(3/2))/(3*e^5)]

    @test_int [(d + e*x)^(7/2)*(b*x + c*x^2)^3, x, 2, (2*d^3*(c*d - b*e)^3*(d + e*x)^(9/2))/(9*e^7) - (6*d^2*(c*d - b*e)^2*(2*c*d - b*e)*(d + e*x)^(11/2))/(11*e^7) + (6*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(13/2))/(13*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*(d + e*x)^(15/2))/(15*e^7) + (6*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(17/2))/(17*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(19/2))/(19*e^7) + (2*c^3*(d + e*x)^(21/2))/(21*e^7)]
    @test_int [(d + e*x)^(5/2)*(b*x + c*x^2)^3, x, 2, (2*d^3*(c*d - b*e)^3*(d + e*x)^(7/2))/(7*e^7) - (2*d^2*(c*d - b*e)^2*(2*c*d - b*e)*(d + e*x)^(9/2))/(3*e^7) + (6*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(11/2))/(11*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*(d + e*x)^(13/2))/(13*e^7) + (2*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(15/2))/(5*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(17/2))/(17*e^7) + (2*c^3*(d + e*x)^(19/2))/(19*e^7)]
    @test_int [(d + e*x)^(3/2)*(b*x + c*x^2)^3, x, 2, (2*d^3*(c*d - b*e)^3*(d + e*x)^(5/2))/(5*e^7) - (6*d^2*(c*d - b*e)^2*(2*c*d - b*e)*(d + e*x)^(7/2))/(7*e^7) + (2*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(9/2))/(3*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*(d + e*x)^(11/2))/(11*e^7) + (6*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(13/2))/(13*e^7) - (2*c^2*(2*c*d - b*e)*(d + e*x)^(15/2))/(5*e^7) + (2*c^3*(d + e*x)^(17/2))/(17*e^7)]
    @test_int [(d + e*x)^(1/2)*(b*x + c*x^2)^3, x, 2, (2*d^3*(c*d - b*e)^3*(d + e*x)^(3/2))/(3*e^7) - (6*d^2*(c*d - b*e)^2*(2*c*d - b*e)*(d + e*x)^(5/2))/(5*e^7) + (6*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(7/2))/(7*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*(d + e*x)^(9/2))/(9*e^7) + (6*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(11/2))/(11*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(13/2))/(13*e^7) + (2*c^3*(d + e*x)^(15/2))/(15*e^7)]
    @test_int [(b*x + c*x^2)^3/(d + e*x)^(1/2), x, 2, (2*d^3*(c*d - b*e)^3*sqrt(d + e*x))/e^7 - (2*d^2*(c*d - b*e)^2*(2*c*d - b*e)*(d + e*x)^(3/2))/e^7 + (6*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(5/2))/(5*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*(d + e*x)^(7/2))/(7*e^7) + (2*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(9/2))/(3*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(11/2))/(11*e^7) + (2*c^3*(d + e*x)^(13/2))/(13*e^7)]
    @test_int [(b*x + c*x^2)^3/(d + e*x)^(3/2), x, 2, -((2*d^3*(c*d - b*e)^3)/(e^7*sqrt(d + e*x))) - (6*d^2*(c*d - b*e)^2*(2*c*d - b*e)*sqrt(d + e*x))/e^7 + (2*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(3/2))/e^7 - (2*(2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*(d + e*x)^(5/2))/(5*e^7) + (6*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(7/2))/(7*e^7) - (2*c^2*(2*c*d - b*e)*(d + e*x)^(9/2))/(3*e^7) + (2*c^3*(d + e*x)^(11/2))/(11*e^7)]
    @test_int [(b*x + c*x^2)^3/(d + e*x)^(5/2), x, 2, -((2*d^3*(c*d - b*e)^3)/(3*e^7*(d + e*x)^(3/2))) + (6*d^2*(c*d - b*e)^2*(2*c*d - b*e))/(e^7*sqrt(d + e*x)) + (6*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*sqrt(d + e*x))/e^7 - (2*(2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*(d + e*x)^(3/2))/(3*e^7) + (6*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(5/2))/(5*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(7/2))/(7*e^7) + (2*c^3*(d + e*x)^(9/2))/(9*e^7)]
    @test_int [(b*x + c*x^2)^3/(d + e*x)^(7/2), x, 2, -((2*d^3*(c*d - b*e)^3)/(5*e^7*(d + e*x)^(5/2))) + (2*d^2*(c*d - b*e)^2*(2*c*d - b*e))/(e^7*(d + e*x)^(3/2)) - (6*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))/(e^7*sqrt(d + e*x)) - (2*(2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*sqrt(d + e*x))/e^7 + (2*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(3/2))/e^7 - (6*c^2*(2*c*d - b*e)*(d + e*x)^(5/2))/(5*e^7) + (2*c^3*(d + e*x)^(7/2))/(7*e^7)]

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

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

    @test_int [(d + e*x)^(9/2)/(b*x + c*x^2)^2, x, 8, (e*(2*c*d - b*e)*(c^2*d^2 - b*c*d*e + 5*b^2*e^2)*sqrt(d + e*x))/(b^2*c^3) + (e*(6*c^2*d^2 - 6*b*c*d*e + 5*b^2*e^2)*(d + e*x)^(3/2))/(3*b^2*c^2) + (e*(2*c*d - b*e)*(d + e*x)^(5/2))/(b^2*c) - ((d + e*x)^(7/2)*(b*d + (2*c*d - b*e)*x))/(b^2*(b*x + c*x^2)) + (d^(7/2)*(4*c*d - 9*b*e)*atanh(sqrt(d + e*x)/sqrt(d)))/b^3 - ((c*d - b*e)^(7/2)*(4*c*d + 5*b*e)*atanh((sqrt(c)*sqrt(d + e*x))/sqrt(c*d - b*e)))/(b^3*c^(7/2))]
    @test_int [(d + e*x)^(7/2)/(b*x + c*x^2)^2, x, 7, (e*(2*c^2*d^2 - 2*b*c*d*e + 3*b^2*e^2)*sqrt(d + e*x))/(b^2*c^2) + (e*(2*c*d - b*e)*(d + e*x)^(3/2))/(b^2*c) - ((d + e*x)^(5/2)*(b*d + (2*c*d - b*e)*x))/(b^2*(b*x + c*x^2)) + (d^(5/2)*(4*c*d - 7*b*e)*atanh(sqrt(d + e*x)/sqrt(d)))/b^3 - ((c*d - b*e)^(5/2)*(4*c*d + 3*b*e)*atanh((sqrt(c)*sqrt(d + e*x))/sqrt(c*d - b*e)))/(b^3*c^(5/2))]
    @test_int [(d + e*x)^(5/2)/(b*x + c*x^2)^2, x, 6, (e*(2*c*d - b*e)*sqrt(d + e*x))/(b^2*c) - ((d + e*x)^(3/2)*(b*d + (2*c*d - b*e)*x))/(b^2*(b*x + c*x^2)) + (d^(3/2)*(4*c*d - 5*b*e)*atanh(sqrt(d + e*x)/sqrt(d)))/b^3 - ((c*d - b*e)^(3/2)*(4*c*d + b*e)*atanh((sqrt(c)*sqrt(d + e*x))/sqrt(c*d - b*e)))/(b^3*c^(3/2))]
    @test_int [(d + e*x)^(3/2)/(b*x + c*x^2)^2, x, 5, -((sqrt(d + e*x)*(b*d + (2*c*d - b*e)*x))/(b^2*(b*x + c*x^2))) + (sqrt(d)*(4*c*d - 3*b*e)*atanh(sqrt(d + e*x)/sqrt(d)))/b^3 - (sqrt(c*d - b*e)*(4*c*d - b*e)*atanh((sqrt(c)*sqrt(d + e*x))/sqrt(c*d - b*e)))/(b^3*sqrt(c))]
    @test_int [(d + e*x)^(1/2)/(b*x + c*x^2)^2, x, 5, -(((b + 2*c*x)*sqrt(d + e*x))/(b^2*(b*x + c*x^2))) + ((4*c*d - b*e)*atanh(sqrt(d + e*x)/sqrt(d)))/(b^3*sqrt(d)) - (sqrt(c)*(4*c*d - 3*b*e)*atanh((sqrt(c)*sqrt(d + e*x))/sqrt(c*d - b*e)))/(b^3*sqrt(c*d - b*e))]
    @test_int [1/((d + e*x)^(1/2)*(b*x + c*x^2)^2), x, 5, -((sqrt(d + e*x)*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(b^2*d*(c*d - b*e)*(b*x + c*x^2))) + ((4*c*d + b*e)*atanh(sqrt(d + e*x)/sqrt(d)))/(b^3*d^(3/2)) - (c^(3/2)*(4*c*d - 5*b*e)*atanh((sqrt(c)*sqrt(d + e*x))/sqrt(c*d - b*e)))/(b^3*(c*d - b*e)^(3/2))]
    @test_int [1/((d + e*x)^(3/2)*(b*x + c*x^2)^2), x, 6, -((e*(2*c^2*d^2 - 2*b*c*d*e + 3*b^2*e^2))/(b^2*d^2*(c*d - b*e)^2*sqrt(d + e*x))) - (b*(c*d - b*e) + c*(2*c*d - b*e)*x)/(b^2*d*(c*d - b*e)*sqrt(d + e*x)*(b*x + c*x^2)) + ((4*c*d + 3*b*e)*atanh(sqrt(d + e*x)/sqrt(d)))/(b^3*d^(5/2)) - (c^(5/2)*(4*c*d - 7*b*e)*atanh((sqrt(c)*sqrt(d + e*x))/sqrt(c*d - b*e)))/(b^3*(c*d - b*e)^(5/2))]
    @test_int [1/((d + e*x)^(5/2)*(b*x + c*x^2)^2), x, 7, -((e*(6*c^2*d^2 - 6*b*c*d*e + 5*b^2*e^2))/(3*b^2*d^2*(c*d - b*e)^2*(d + e*x)^(3/2))) - (e*(2*c*d - b*e)*(c^2*d^2 - b*c*d*e + 5*b^2*e^2))/(b^2*d^3*(c*d - b*e)^3*sqrt(d + e*x)) - (b*(c*d - b*e) + c*(2*c*d - b*e)*x)/(b^2*d*(c*d - b*e)*(d + e*x)^(3/2)*(b*x + c*x^2)) + ((4*c*d + 5*b*e)*atanh(sqrt(d + e*x)/sqrt(d)))/(b^3*d^(7/2)) - (c^(7/2)*(4*c*d - 9*b*e)*atanh((sqrt(c)*sqrt(d + e*x))/sqrt(c*d - b*e)))/(b^3*(c*d - b*e)^(7/2))]
    @test_int [1/((d + e*x)^(7/2)*(b*x + c*x^2)^2), x, 8, -((e*(10*c^2*d^2 - 10*b*c*d*e + 7*b^2*e^2))/(5*b^2*d^2*(c*d - b*e)^2*(d + e*x)^(5/2))) - (e*(2*c*d - b*e)*(3*c^2*d^2 - 3*b*c*d*e + 7*b^2*e^2))/(3*b^2*d^3*(c*d - b*e)^3*(d + e*x)^(3/2)) - (e*(2*c^4*d^4 - 4*b*c^3*d^3*e + 26*b^2*c^2*d^2*e^2 - 24*b^3*c*d*e^3 + 7*b^4*e^4))/(b^2*d^4*(c*d - b*e)^4*sqrt(d + e*x)) - (b*(c*d - b*e) + c*(2*c*d - b*e)*x)/(b^2*d*(c*d - b*e)*(d + e*x)^(5/2)*(b*x + c*x^2)) + ((4*c*d + 7*b*e)*atanh(sqrt(d + e*x)/sqrt(d)))/(b^3*d^(9/2)) - (c^(9/2)*(4*c*d - 11*b*e)*atanh((sqrt(c)*sqrt(d + e*x))/sqrt(c*d - b*e)))/(b^3*(c*d - b*e)^(9/2))]

    @test_int [(d + e*x)^(9/2)/(b*x + c*x^2)^3, x, 7, -((3*e*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*sqrt(d + e*x))/(4*b^4*c^2)) - ((d + e*x)^(7/2)*(b*d + (2*c*d - b*e)*x))/(2*b^2*(b*x + c*x^2)^2) + ((d + e*x)^(3/2)*(b*c*d^2*(12*c*d - 13*b*e) + (2*c*d - b*e)*(12*c^2*d^2 - 12*b*c*d*e - b^2*e^2)*x))/(4*b^4*c*(b*x + c*x^2)) - (3*d^(5/2)*(16*c^2*d^2 - 36*b*c*d*e + 21*b^2*e^2)*atanh(sqrt(d + e*x)/sqrt(d)))/(4*b^5) + (3*(c*d - b*e)^(5/2)*(16*c^2*d^2 + 4*b*c*d*e + b^2*e^2)*atanh((sqrt(c)*sqrt(d + e*x))/sqrt(c*d - b*e)))/(4*b^5*c^(5/2))]
    @test_int [(d + e*x)^(7/2)/(b*x + c*x^2)^3, x, 6, -(((d + e*x)^(5/2)*(b*d + (2*c*d - b*e)*x))/(2*b^2*(b*x + c*x^2)^2)) + (sqrt(d + e*x)*(b*c*d^2*(12*c*d - 11*b*e) + (2*c*d - b*e)*(12*c^2*d^2 - 12*b*c*d*e + b^2*e^2)*x))/(4*b^4*c*(b*x + c*x^2)) - (d^(3/2)*(48*c^2*d^2 - 84*b*c*d*e + 35*b^2*e^2)*atanh(sqrt(d + e*x)/sqrt(d)))/(4*b^5) + ((c*d - b*e)^(3/2)*(48*c^2*d^2 - 12*b*c*d*e - b^2*e^2)*atanh((sqrt(c)*sqrt(d + e*x))/sqrt(c*d - b*e)))/(4*b^5*c^(3/2))]
    @test_int [(d + e*x)^(5/2)/(b*x + c*x^2)^3, x, 6, -(((d + e*x)^(3/2)*(b*d + (2*c*d - b*e)*x))/(2*b^2*(b*x + c*x^2)^2)) + (3*sqrt(d + e*x)*(b*d*(4*c*d - 3*b*e) + (8*c^2*d^2 - 8*b*c*d*e + b^2*e^2)*x))/(4*b^4*(b*x + c*x^2)) - (3*sqrt(d)*(16*c^2*d^2 - 20*b*c*d*e + 5*b^2*e^2)*atanh(sqrt(d + e*x)/sqrt(d)))/(4*b^5) + (3*sqrt(c*d - b*e)*(16*c^2*d^2 - 12*b*c*d*e + b^2*e^2)*atanh((sqrt(c)*sqrt(d + e*x))/sqrt(c*d - b*e)))/(4*b^5*sqrt(c))]
    @test_int [(d + e*x)^(3/2)/(b*x + c*x^2)^3, x, 6, -((sqrt(d + e*x)*(b*d + (2*c*d - b*e)*x))/(2*b^2*(b*x + c*x^2)^2)) + (sqrt(d + e*x)*(b*(12*c*d - 7*b*e)*(c*d - b*e) + 12*c*(c*d - b*e)*(2*c*d - b*e)*x))/(4*b^4*(c*d - b*e)*(b*x + c*x^2)) - (3*(16*c^2*d^2 - 12*b*c*d*e + b^2*e^2)*atanh(sqrt(d + e*x)/sqrt(d)))/(4*b^5*sqrt(d)) + (3*sqrt(c)*(16*c^2*d^2 - 20*b*c*d*e + 5*b^2*e^2)*atanh((sqrt(c)*sqrt(d + e*x))/sqrt(c*d - b*e)))/(4*b^5*sqrt(c*d - b*e))]
    @test_int [(d + e*x)^(1/2)/(b*x + c*x^2)^3, x, 6, -(((b + 2*c*x)*sqrt(d + e*x))/(2*b^2*(b*x + c*x^2)^2)) + (sqrt(d + e*x)*(b*(c*d - b*e)*(12*c*d - b*e) + c*(24*c^2*d^2 - 24*b*c*d*e + b^2*e^2)*x))/(4*b^4*d*(c*d - b*e)*(b*x + c*x^2)) - ((48*c^2*d^2 - 12*b*c*d*e - b^2*e^2)*atanh(sqrt(d + e*x)/sqrt(d)))/(4*b^5*d^(3/2)) + (c^(3/2)*(48*c^2*d^2 - 84*b*c*d*e + 35*b^2*e^2)*atanh((sqrt(c)*sqrt(d + e*x))/sqrt(c*d - b*e)))/(4*b^5*(c*d - b*e)^(3/2))]
    @test_int [1/((d + e*x)^(1/2)*(b*x + c*x^2)^3), x, 6, -((sqrt(d + e*x)*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(2*b^2*d*(c*d - b*e)*(b*x + c*x^2)^2)) + (sqrt(d + e*x)*(b*(c*d - b*e)*(12*c^2*d^2 - 7*b*c*d*e - 3*b^2*e^2) + 3*c*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*x))/(4*b^4*d^2*(c*d - b*e)^2*(b*x + c*x^2)) - (3*(16*c^2*d^2 + 4*b*c*d*e + b^2*e^2)*atanh(sqrt(d + e*x)/sqrt(d)))/(4*b^5*d^(5/2)) + (3*c^(5/2)*(16*c^2*d^2 - 36*b*c*d*e + 21*b^2*e^2)*atanh((sqrt(c)*sqrt(d + e*x))/sqrt(c*d - b*e)))/(4*b^5*(c*d - b*e)^(5/2))]
    @test_int [1/((d + e*x)^(3/2)*(b*x + c*x^2)^3), x, 7, (3*e*(c^2*d^2 - b*c*d*e - b^2*e^2)*(8*c^2*d^2 - 8*b*c*d*e + 5*b^2*e^2))/(4*b^4*d^3*(c*d - b*e)^3*sqrt(d + e*x)) - (b*(c*d - b*e) + c*(2*c*d - b*e)*x)/(2*b^2*d*(c*d - b*e)*sqrt(d + e*x)*(b*x + c*x^2)^2) + (b*(12*c^3*d^3 - 17*b*c^2*d^2*e + 5*b^3*e^3) + c*(2*c*d - b*e)*(12*c^2*d^2 - 12*b*c*d*e - 5*b^2*e^2)*x)/(4*b^4*d^2*(c*d - b*e)^2*sqrt(d + e*x)*(b*x + c*x^2)) - (3*(16*c^2*d^2 + 12*b*c*d*e + 5*b^2*e^2)*atanh(sqrt(d + e*x)/sqrt(d)))/(4*b^5*d^(7/2)) + (3*c^(7/2)*(16*c^2*d^2 - 44*b*c*d*e + 33*b^2*e^2)*atanh((sqrt(c)*sqrt(d + e*x))/sqrt(c*d - b*e)))/(4*b^5*(c*d - b*e)^(7/2))]
    @test_int [1/((d + e*x)^(5/2)*(b*x + c*x^2)^3), x, 8, (e*(72*c^4*d^4 - 144*b*c^3*d^3*e + 27*b^2*c^2*d^2*e^2 + 45*b^3*c*d*e^3 - 35*b^4*e^4))/(12*b^4*d^3*(c*d - b*e)^3*(d + e*x)^(3/2)) + (e*(2*c*d - b*e)*(12*c^4*d^4 - 24*b*c^3*d^3*e + 2*b^2*c^2*d^2*e^2 + 10*b^3*c*d*e^3 - 35*b^4*e^4))/(4*b^4*d^4*(c*d - b*e)^4*sqrt(d + e*x)) - (b*(c*d - b*e) + c*(2*c*d - b*e)*x)/(2*b^2*d*(c*d - b*e)*(d + e*x)^(3/2)*(b*x + c*x^2)^2) + (b*(c*d - b*e)*(12*c^2*d^2 - 3*b*c*d*e - 7*b^2*e^2) + c*(2*c*d - b*e)*(12*c^2*d^2 - 12*b*c*d*e - 7*b^2*e^2)*x)/(4*b^4*d^2*(c*d - b*e)^2*(d + e*x)^(3/2)*(b*x + c*x^2)) - ((48*c^2*d^2 + 60*b*c*d*e + 35*b^2*e^2)*atanh(sqrt(d + e*x)/sqrt(d)))/(4*b^5*d^(9/2)) + (c^(9/2)*(48*c^2*d^2 - 156*b*c*d*e + 143*b^2*e^2)*atanh((sqrt(c)*sqrt(d + e*x))/sqrt(c*d - b*e)))/(4*b^5*(c*d - b*e)^(9/2))]

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

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

    @test_int [(d + e*x)^(3/2)*sqrt(b*x + c*x^2), x, 9, (2*sqrt(d + e*x)*(3*c^2*d^2 + 9*b*c*d*e - 4*b^2*e^2 + 12*c*e*(2*c*d - b*e)*x)*sqrt(b*x + c*x^2))/(105*c^2*e) + (2*e*sqrt(d + e*x)*(b*x + c*x^2)^(3/2))/(7*c) - (2*sqrt(-b)*(2*c*d - b*e)*(3*c^2*d^2 - 3*b*c*d*e + 8*b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(105*c^(5/2)*e^2*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (4*sqrt(-b)*d*(c*d - b*e)*(3*c^2*d^2 - 3*b*c*d*e + 2*b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(105*c^(5/2)*e^2*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [sqrt(d + e*x)*sqrt(b*x + c*x^2), x, 9, (-2*(2*c*d - b*e)*sqrt(d + e*x)*sqrt(b*x + c*x^2))/(15*c*e) + (2*(d + e*x)^(3/2)*sqrt(b*x + c*x^2))/(5*e) - (4*sqrt(-b)*(c^2*d^2 - b*c*d*e + b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(15*c^(3/2)*e^2*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (2*sqrt(-b)*d*(c*d - b*e)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(15*c^(3/2)*e^2*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [sqrt(b*x + c*x^2)/sqrt(d + e*x), x, 8, (2*sqrt(d + e*x)*sqrt(b*x + c*x^2))/(3*e) - (2*sqrt(-b)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*sqrt(c)*e^2*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (4*sqrt(-b)*d*(c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*sqrt(c)*e^2*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [sqrt(b*x + c*x^2)/(d + e*x)^(3/2), x, 8, (-2*sqrt(b*x + c*x^2))/(e*sqrt(d + e*x)) + (4*sqrt(-b)*sqrt(c)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(e^2*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (2*sqrt(-b)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(sqrt(c)*e^2*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [sqrt(b*x + c*x^2)/(d + e*x)^(5/2), x, 9, (-2*sqrt(b*x + c*x^2))/(3*e*(d + e*x)^(3/2)) + (2*(2*c*d - b*e)*sqrt(b*x + c*x^2))/(3*d*e*(c*d - b*e)*sqrt(d + e*x)) - (2*sqrt(-b)*sqrt(c)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*d*e^2*(c*d - b*e)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (4*sqrt(-b)*sqrt(c)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*e^2*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [sqrt(b*x + c*x^2)/(d + e*x)^(7/2), x, 10, (-2*sqrt(b*x + c*x^2))/(5*e*(d + e*x)^(5/2)) + (2*(2*c*d - b*e)*sqrt(b*x + c*x^2))/(15*d*e*(c*d - b*e)*(d + e*x)^(3/2)) + (4*(c^2*d^2 - b*c*d*e + b^2*e^2)*sqrt(b*x + c*x^2))/(15*d^2*e*(c*d - b*e)^2*sqrt(d + e*x)) - (4*sqrt(-b)*sqrt(c)*(c^2*d^2 - b*c*d*e + b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(15*d^2*e^2*(c*d - b*e)^2*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (2*sqrt(-b)*sqrt(c)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(15*d*e^2*(c*d - b*e)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]

    @test_int [(d + e*x)^(3/2)*(b*x + c*x^2)^(3/2), x, 10, (2*sqrt(d + e*x)*(8*c^4*d^4 - 19*b*c^3*d^3*e + 6*b^2*c^2*d^2*e^2 - 19*b^3*c*d*e^3 + 8*b^4*e^4 - 3*c*e*(2*c*d - b*e)*(c^2*d^2 - b*c*d*e + 8*b^2*e^2)*x)*sqrt(b*x + c*x^2))/(1155*c^3*e^3) + (2*sqrt(d + e*x)*(c^2*d^2 + 13*b*c*d*e - 6*b^2*e^2 + 14*c*e*(2*c*d - b*e)*x)*(b*x + c*x^2)^(3/2))/(231*c^2*e) + (2*e*sqrt(d + e*x)*(b*x + c*x^2)^(5/2))/(11*c) - (16*sqrt(-b)*(c*d - 2*b*e)*(2*c*d - b*e)*(c*d + b*e)*(c^2*d^2 - b*c*d*e + b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(1155*c^(7/2)*e^4*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (2*sqrt(-b)*d*(c*d - b*e)*(16*c^4*d^4 - 32*b*c^3*d^3*e + 3*b^2*c^2*d^2*e^2 + 13*b^3*c*d*e^3 - 8*b^4*e^4)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(1155*c^(7/2)*e^4*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [sqrt(d + e*x)*(b*x + c*x^2)^(3/2), x, 10, (2*sqrt(d + e*x)*(8*c^3*d^3 - 15*b*c^2*d^2*e + 3*b^2*c*d*e^2 - 4*b^3*e^3 - 6*c*e*(c^2*d^2 - b*c*d*e + 2*b^2*e^2)*x)*sqrt(b*x + c*x^2))/(315*c^2*e^3) - (2*(2*c*d - b*e)*sqrt(d + e*x)*(b*x + c*x^2)^(3/2))/(21*c*e) + (2*(d + e*x)^(3/2)*(b*x + c*x^2)^(3/2))/(9*e) - (2*sqrt(-b)*(16*c^4*d^4 - 32*b*c^3*d^3*e + 9*b^2*c^2*d^2*e^2 + 7*b^3*c*d*e^3 - 8*b^4*e^4)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(315*c^(5/2)*e^4*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (8*sqrt(-b)*d*(c*d - b*e)*(2*c*d - b*e)*(2*c^2*d^2 - 2*b*c*d*e - b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(315*c^(5/2)*e^4*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(b*x + c*x^2)^(3/2)/sqrt(d + e*x), x, 9, (2*sqrt(d + e*x)*(8*c^2*d^2 - 11*b*c*d*e + b^2*e^2 - 3*c*e*(2*c*d - b*e)*x)*sqrt(b*x + c*x^2))/(35*c*e^3) + (2*sqrt(d + e*x)*(b*x + c*x^2)^(3/2))/(7*e) - (4*sqrt(-b)*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(35*c^(3/2)*e^4*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (2*sqrt(-b)*d*(c*d - b*e)*(16*c^2*d^2 - 16*b*c*d*e - b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(35*c^(3/2)*e^4*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(b*x + c*x^2)^(3/2)/(d + e*x)^(3/2), x, 9, (-2*sqrt(d + e*x)*(8*c*d - 7*b*e - 6*c*e*x)*sqrt(b*x + c*x^2))/(5*e^3) - (2*(b*x + c*x^2)^(3/2))/(e*sqrt(d + e*x)) + (2*sqrt(-b)*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(5*sqrt(c)*e^4*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (16*sqrt(-b)*d*(c*d - b*e)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(5*sqrt(c)*e^4*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(b*x + c*x^2)^(3/2)/(d + e*x)^(5/2), x, 9, (2*(8*c*d - 3*b*e + 2*c*e*x)*sqrt(b*x + c*x^2))/(3*e^3*sqrt(d + e*x)) - (2*(b*x + c*x^2)^(3/2))/(3*e*(d + e*x)^(3/2)) - (16*sqrt(-b)*sqrt(c)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*e^4*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (2*sqrt(-b)*(4*c*d - 3*b*e)*(4*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*sqrt(c)*e^4*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(b*x + c*x^2)^(3/2)/(d + e*x)^(7/2), x, 9, -((2*(c*d^2*(8*c*d - 7*b*e) + e*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*x)*sqrt(b*x + c*x^2))/(5*d*e^3*(c*d - b*e)*(d + e*x)^(3/2))) - (2*(b*x + c*x^2)^(3/2))/(5*e*(d + e*x)^(5/2)) + (2*sqrt(-b)*sqrt(c)*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(5*d*e^4*(c*d - b*e)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (16*sqrt(-b)*sqrt(c)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(5*e^4*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(b*x + c*x^2)^(3/2)/(d + e*x)^(9/2), x, 10, (4*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*sqrt(b*x + c*x^2))/(35*d^2*e^3*(c*d - b*e)^2*sqrt(d + e*x)) - (2*(d*(8*c^2*d^2 - 5*b*c*d*e - 2*b^2*e^2) + e*(14*c^2*d^2 - 14*b*c*d*e + b^2*e^2)*x)*sqrt(b*x + c*x^2))/(35*d*e^3*(c*d - b*e)*(d + e*x)^(5/2)) - (2*(b*x + c*x^2)^(3/2))/(7*e*(d + e*x)^(7/2)) - (4*sqrt(-b)*sqrt(c)*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(35*d^2*e^4*(c*d - b*e)^2*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (2*sqrt(-b)*sqrt(c)*(16*c^2*d^2 - 16*b*c*d*e - b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(35*d*e^4*(c*d - b*e)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]

    @test_int [sqrt(d + e*x)*(b*x + c*x^2)^(5/2), x, 11, (2*sqrt(d + e*x)*(128*c^5*d^5 - 368*b*c^4*d^4*e + 303*b^2*c^3*d^3*e^2 - 22*b^3*c^2*d^2*e^3 - 17*b^4*c*d*e^4 + 24*b^5*e^5 - 3*c*e*(32*c^4*d^4 - 64*b*c^3*d^3*e + 21*b^2*c^2*d^2*e^2 + 11*b^3*c*d*e^3 - 24*b^4*e^4)*x)*sqrt(b*x + c*x^2))/(9009*c^3*e^5) + (10*sqrt(d + e*x)*(16*c^3*d^3 - 31*b*c^2*d^2*e + 9*b^2*c*d*e^2 - 18*b^3*e^3 - 14*c*e*(c^2*d^2 - b*c*d*e + 3*b^2*e^2)*x)*(b*x + c*x^2)^(3/2))/(9009*c^2*e^3) - (10*(2*c*d - b*e)*sqrt(d + e*x)*(b*x + c*x^2)^(5/2))/(143*c*e) + (2*(d + e*x)^(3/2)*(b*x + c*x^2)^(5/2))/(13*e) - (4*sqrt(-b)*(128*c^6*d^6 - 384*b*c^5*d^5*e + 343*b^2*c^4*d^4*e^2 - 46*b^3*c^3*d^3*e^3 - 21*b^4*c^2*d^2*e^4 - 20*b^5*c*d*e^5 + 24*b^6*e^6)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(9009*c^(7/2)*e^6*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (2*sqrt(-b)*d*(c*d - b*e)*(2*c*d - b*e)*(128*c^4*d^4 - 256*b*c^3*d^3*e + 79*b^2*c^2*d^2*e^2 + 49*b^3*c*d*e^3 + 24*b^4*e^4)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(9009*c^(7/2)*e^6*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(b*x + c*x^2)^(5/2)/sqrt(d + e*x), x, 10, (2*sqrt(d + e*x)*(128*c^4*d^4 - 304*b*c^3*d^3*e + 195*b^2*c^2*d^2*e^2 - 7*b^3*c*d*e^3 - 4*b^4*e^4 - 12*c*e*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*x)*sqrt(b*x + c*x^2))/(693*c^2*e^5) + (10*sqrt(d + e*x)*(16*c^2*d^2 - 23*b*c*d*e + 3*b^2*e^2 - 7*c*e*(2*c*d - b*e)*x)*(b*x + c*x^2)^(3/2))/(693*c*e^3) + (2*sqrt(d + e*x)*(b*x + c*x^2)^(5/2))/(11*e) - (2*sqrt(-b)*(2*c*d - b*e)*(128*c^4*d^4 - 256*b*c^3*d^3*e + 99*b^2*c^2*d^2*e^2 + 29*b^3*c*d*e^3 + 8*b^4*e^4)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(693*c^(5/2)*e^6*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (4*sqrt(-b)*d*(c*d - b*e)*(128*c^4*d^4 - 256*b*c^3*d^3*e + 123*b^2*c^2*d^2*e^2 + 5*b^3*c*d*e^3 + 2*b^4*e^4)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(693*c^(5/2)*e^6*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(b*x + c*x^2)^(5/2)/(d + e*x)^(3/2), x, 10, (-2*sqrt(d + e*x)*(128*c^3*d^3 - 240*b*c^2*d^2*e + 111*b^2*c*d*e^2 - b^3*e^3 - 3*c*e*(32*c^2*d^2 - 32*b*c*d*e + b^2*e^2)*x)*sqrt(b*x + c*x^2))/(63*c*e^5) - (10*sqrt(d + e*x)*(16*c*d - 15*b*e - 14*c*e*x)*(b*x + c*x^2)^(3/2))/(63*e^3) - (2*(b*x + c*x^2)^(5/2))/(e*sqrt(d + e*x)) + (4*sqrt(-b)*(128*c^4*d^4 - 256*b*c^3*d^3*e + 135*b^2*c^2*d^2*e^2 - 7*b^3*c*d*e^3 - b^4*e^4)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(63*c^(3/2)*e^6*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (2*sqrt(-b)*d*(c*d - b*e)*(2*c*d - b*e)*(128*c^2*d^2 - 128*b*c*d*e - b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(63*c^(3/2)*e^6*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(b*x + c*x^2)^(5/2)/(d + e*x)^(5/2), x, 10, (2*sqrt(d + e*x)*(128*c^2*d^2 - 176*b*c*d*e + 51*b^2*e^2 - 48*c*e*(2*c*d - b*e)*x)*sqrt(b*x + c*x^2))/(21*e^5) + (10*(16*c*d - 7*b*e + 2*c*e*x)*(b*x + c*x^2)^(3/2))/(21*e^3*sqrt(d + e*x)) - (2*(b*x + c*x^2)^(5/2))/(3*e*(d + e*x)^(3/2)) - (2*sqrt(-b)*(2*c*d - b*e)*(128*c^2*d^2 - 128*b*c*d*e + 3*b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(21*sqrt(c)*e^6*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (4*sqrt(-b)*d*(c*d - b*e)*(128*c^2*d^2 - 128*b*c*d*e + 27*b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(21*sqrt(c)*e^6*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(b*x + c*x^2)^(5/2)/(d + e*x)^(7/2), x, 10, (-2*(128*c^2*d^2 - 112*b*c*d*e + 15*b^2*e^2 + 16*c*e*(2*c*d - b*e)*x)*sqrt(b*x + c*x^2))/(15*e^5*sqrt(d + e*x)) + (2*(16*c*d - 5*b*e + 6*c*e*x)*(b*x + c*x^2)^(3/2))/(15*e^3*(d + e*x)^(3/2)) - (2*(b*x + c*x^2)^(5/2))/(5*e*(d + e*x)^(5/2)) + (4*sqrt(-b)*sqrt(c)*(128*c^2*d^2 - 128*b*c*d*e + 23*b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(15*e^6*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (2*sqrt(-b)*(2*c*d - b*e)*(128*c^2*d^2 - 128*b*c*d*e + 15*b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(15*sqrt(c)*e^6*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(b*x + c*x^2)^(5/2)/(d + e*x)^(9/2), x, 10, (2*c*(d*(128*c^2*d^2 - 176*b*c*d*e + 51*b^2*e^2) + e*(32*c^2*d^2 - 32*b*c*d*e + 3*b^2*e^2)*x)*sqrt(b*x + c*x^2))/(21*d*e^5*(c*d - b*e)*sqrt(d + e*x)) - (2*(c*d^2*(16*c*d - 13*b*e) + e*(22*c^2*d^2 - 22*b*c*d*e + 3*b^2*e^2)*x)*(b*x + c*x^2)^(3/2))/(21*d*e^3*(c*d - b*e)*(d + e*x)^(5/2)) - (2*(b*x + c*x^2)^(5/2))/(7*e*(d + e*x)^(7/2)) - (2*sqrt(-b)*sqrt(c)*(2*c*d - b*e)*(128*c^2*d^2 - 128*b*c*d*e + 3*b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(21*d*e^6*(c*d - b*e)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (4*sqrt(-b)*sqrt(c)*(128*c^2*d^2 - 128*b*c*d*e + 27*b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(21*e^6*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(b*x + c*x^2)^(5/2)/(d + e*x)^(11/2), x, 10, -((2*(c*d^2*(128*c^3*d^3 - 240*b*c^2*d^2*e + 111*b^2*c*d*e^2 - b^3*e^3) + e*(160*c^4*d^4 - 320*b*c^3*d^3*e + 171*b^2*c^2*d^2*e^2 - 11*b^3*c*d*e^3 - 2*b^4*e^4)*x)*sqrt(b*x + c*x^2))/(63*d^2*e^5*(c*d - b*e)^2*(d + e*x)^(3/2))) - (2*(d*(16*c^2*d^2 - 11*b*c*d*e - 2*b^2*e^2) + e*(26*c^2*d^2 - 26*b*c*d*e + 3*b^2*e^2)*x)*(b*x + c*x^2)^(3/2))/(63*d*e^3*(c*d - b*e)*(d + e*x)^(7/2)) - (2*(b*x + c*x^2)^(5/2))/(9*e*(d + e*x)^(9/2)) + (4*sqrt(-b)*sqrt(c)*(128*c^4*d^4 - 256*b*c^3*d^3*e + 135*b^2*c^2*d^2*e^2 - 7*b^3*c*d*e^3 - b^4*e^4)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(63*d^2*e^6*(c*d - b*e)^2*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (2*sqrt(-b)*sqrt(c)*(2*c*d - b*e)*(128*c^2*d^2 - 128*b*c*d*e - b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(63*d*e^6*(c*d - b*e)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]

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

    @test_int [(d + e*x)^(7/2)/sqrt(b*x + c*x^2), x, 10, (2*e*(71*c^2*d^2 - 71*b*c*d*e + 24*b^2*e^2)*sqrt(d + e*x)*sqrt(b*x + c*x^2))/(105*c^3) + (12*e*(2*c*d - b*e)*(d + e*x)^(3/2)*sqrt(b*x + c*x^2))/(35*c^2) + (2*e*(d + e*x)^(5/2)*sqrt(b*x + c*x^2))/(7*c) + (16*sqrt(-b)*(2*c*d - b*e)*(11*c^2*d^2 - 11*b*c*d*e + 6*b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(105*c^(7/2)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (2*sqrt(-b)*d*(c*d - b*e)*(71*c^2*d^2 - 71*b*c*d*e + 24*b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(105*c^(7/2)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(d + e*x)^(5/2)/sqrt(b*x + c*x^2), x, 9, (8*e*(2*c*d - b*e)*sqrt(d + e*x)*sqrt(b*x + c*x^2))/(15*c^2) + (2*e*(d + e*x)^(3/2)*sqrt(b*x + c*x^2))/(5*c) + (2*sqrt(-b)*(23*c^2*d^2 - 23*b*c*d*e + 8*b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(15*c^(5/2)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (8*sqrt(-b)*d*(c*d - b*e)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(15*c^(5/2)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(d + e*x)^(3/2)/sqrt(b*x + c*x^2), x, 8, (2*e*sqrt(d + e*x)*sqrt(b*x + c*x^2))/(3*c) + (4*sqrt(-b)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*c^(3/2)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (2*sqrt(-b)*d*(c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*c^(3/2)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [sqrt(d + e*x)/sqrt(b*x + c*x^2), x, 3, (2*sqrt(-b)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(sqrt(c)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2))]
    @test_int [1/(sqrt(d + e*x)*sqrt(b*x + c*x^2)), x, 3, (2*sqrt(-b)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(sqrt(c)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [1/((d + e*x)^(3/2)*sqrt(b*x + c*x^2)), x, 5, (-2*e*sqrt(b*x + c*x^2))/(d*(c*d - b*e)*sqrt(d + e*x)) + (2*sqrt(-b)*sqrt(c)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(d*(c*d - b*e)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2))]
    @test_int [1/((d + e*x)^(5/2)*sqrt(b*x + c*x^2)), x, 9, (-2*e*sqrt(b*x + c*x^2))/(3*d*(c*d - b*e)*(d + e*x)^(3/2)) - (4*e*(2*c*d - b*e)*sqrt(b*x + c*x^2))/(3*d^2*(c*d - b*e)^2*sqrt(d + e*x)) + (4*sqrt(-b)*sqrt(c)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*d^2*(c*d - b*e)^2*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (2*sqrt(-b)*sqrt(c)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*d*(c*d - b*e)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [1/((d + e*x)^(7/2)*sqrt(b*x + c*x^2)), x, 10, (-2*e*sqrt(b*x + c*x^2))/(5*d*(c*d - b*e)*(d + e*x)^(5/2)) - (8*e*(2*c*d - b*e)*sqrt(b*x + c*x^2))/(15*d^2*(c*d - b*e)^2*(d + e*x)^(3/2)) - (2*e*(23*c^2*d^2 - 23*b*c*d*e + 8*b^2*e^2)*sqrt(b*x + c*x^2))/(15*d^3*(c*d - b*e)^3*sqrt(d + e*x)) + (2*sqrt(-b)*sqrt(c)*(23*c^2*d^2 - 23*b*c*d*e + 8*b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(15*d^3*(c*d - b*e)^3*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (8*sqrt(-b)*sqrt(c)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(15*d^2*(c*d - b*e)^2*sqrt(d + e*x)*sqrt(b*x + c*x^2))]

    @test_int [(d + e*x)^(7/2)/(b*x + c*x^2)^(3/2), x, 10, (-2*(d + e*x)^(5/2)*(b*d + (2*c*d - b*e)*x))/(b^2*sqrt(b*x + c*x^2)) + (4*e*(3*c^2*d^2 - 3*b*c*d*e + 2*b^2*e^2)*sqrt(d + e*x)*sqrt(b*x + c*x^2))/(3*b^2*c^2) + (2*e*(2*c*d - b*e)*(d + e*x)^(3/2)*sqrt(b*x + c*x^2))/(b^2*c) + (2*(2*c*d - b*e)*(3*c^2*d^2 - 3*b*c*d*e + 8*b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(3/2)*c^(5/2)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (4*d*(c*d - b*e)*(3*c^2*d^2 - 3*b*c*d*e + 2*b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(3/2)*c^(5/2)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(d + e*x)^(5/2)/(b*x + c*x^2)^(3/2), x, 9, (-2*(d + e*x)^(3/2)*(b*d + (2*c*d - b*e)*x))/(b^2*sqrt(b*x + c*x^2)) + (2*e*(2*c*d - b*e)*sqrt(d + e*x)*sqrt(b*x + c*x^2))/(b^2*c) + (4*(c^2*d^2 - b*c*d*e + b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/((-b)^(3/2)*c^(3/2)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (2*d*(c*d - b*e)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/((-b)^(3/2)*c^(3/2)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(d + e*x)^(3/2)/(b*x + c*x^2)^(3/2), x, 8, (-2*sqrt(d + e*x)*(b*d + (2*c*d - b*e)*x))/(b^2*sqrt(b*x + c*x^2)) + (2*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/((-b)^(3/2)*sqrt(c)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (4*d*(c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/((-b)^(3/2)*sqrt(c)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [sqrt(d + e*x)/(b*x + c*x^2)^(3/2), x, 8, (-2*(b + 2*c*x)*sqrt(d + e*x))/(b^2*sqrt(b*x + c*x^2)) + (4*sqrt(c)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/((-b)^(3/2)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (2*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/((-b)^(3/2)*sqrt(c)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [1/(sqrt(d + e*x)*(b*x + c*x^2)^(3/2)), x, 8, (-2*sqrt(d + e*x)*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(b^2*d*(c*d - b*e)*sqrt(b*x + c*x^2)) + (2*sqrt(c)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/((-b)^(3/2)*d*(c*d - b*e)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (4*sqrt(c)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/((-b)^(3/2)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [1/((d + e*x)^(3/2)*(b*x + c*x^2)^(3/2)), x, 9, (-2*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(b^2*d*(c*d - b*e)*sqrt(d + e*x)*sqrt(b*x + c*x^2)) - (4*e*(c^2*d^2 - b*c*d*e + b^2*e^2)*sqrt(b*x + c*x^2))/(b^2*d^2*(c*d - b*e)^2*sqrt(d + e*x)) + (4*sqrt(c)*(c^2*d^2 - b*c*d*e + b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/((-b)^(3/2)*d^2*(c*d - b*e)^2*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (2*sqrt(c)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/((-b)^(3/2)*d*(c*d - b*e)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [1/((d + e*x)^(5/2)*(b*x + c*x^2)^(3/2)), x, 10, (-2*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(b^2*d*(c*d - b*e)*(d + e*x)^(3/2)*sqrt(b*x + c*x^2)) - (4*e*(3*c^2*d^2 - 3*b*c*d*e + 2*b^2*e^2)*sqrt(b*x + c*x^2))/(3*b^2*d^2*(c*d - b*e)^2*(d + e*x)^(3/2)) - (2*e*(2*c*d - b*e)*(3*c^2*d^2 - 3*b*c*d*e + 8*b^2*e^2)*sqrt(b*x + c*x^2))/(3*b^2*d^3*(c*d - b*e)^3*sqrt(d + e*x)) + (2*sqrt(c)*(2*c*d - b*e)*(3*c^2*d^2 - 3*b*c*d*e + 8*b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(3/2)*d^3*(c*d - b*e)^3*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) - (4*sqrt(c)*(3*c^2*d^2 - 3*b*c*d*e + 2*b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(3/2)*d^2*(c*d - b*e)^2*sqrt(d + e*x)*sqrt(b*x + c*x^2))]

    @test_int [(d + e*x)^(9/2)/(b*x + c*x^2)^(5/2), x, 10, -((2*(d + e*x)^(7/2)*(b*d + (2*c*d - b*e)*x))/(3*b^2*(b*x + c*x^2)^(3/2))) + (2*(d + e*x)^(3/2)*(b*c*d^2*(8*c*d - 11*b*e) + (2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e - 3*b^2*e^2)*x))/(3*b^4*c*sqrt(b*x + c*x^2)) - (8*e*(4*c^3*d^3 - 6*b*c^2*d^2*e + b^3*e^3)*sqrt(d + e*x)*sqrt(b*x + c*x^2))/(3*b^4*c^2) - (2*(16*c^4*d^4 - 32*b*c^3*d^3*e + 9*b^2*c^2*d^2*e^2 + 7*b^3*c*d*e^3 - 8*b^4*e^4)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(7/2)*c^(5/2)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (8*d*(c*d - b*e)*(2*c*d - b*e)*(2*c^2*d^2 - 2*b*c*d*e - b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(7/2)*c^(5/2)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(d + e*x)^(7/2)/(b*x + c*x^2)^(5/2), x, 9, -((2*(d + e*x)^(5/2)*(b*d + (2*c*d - b*e)*x))/(3*b^2*(b*x + c*x^2)^(3/2))) + (2*sqrt(d + e*x)*(b*c*d^2*(8*c*d - 9*b*e) + (2*c*d - b*e)*(8*c^2*d^2 - 8*b*c*d*e - b^2*e^2)*x))/(3*b^4*c*sqrt(b*x + c*x^2)) - (4*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(7/2)*c^(3/2)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (2*d*(c*d - b*e)*(16*c^2*d^2 - 16*b*c*d*e - b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(7/2)*c^(3/2)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(d + e*x)^(5/2)/(b*x + c*x^2)^(5/2), x, 9, (-2*(d + e*x)^(3/2)*(b*d + (2*c*d - b*e)*x))/(3*b^2*(b*x + c*x^2)^(3/2)) + (2*sqrt(d + e*x)*(b*d*(8*c*d - 7*b*e) + (16*c^2*d^2 - 16*b*c*d*e + b^2*e^2)*x))/(3*b^4*sqrt(b*x + c*x^2)) - (2*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(7/2)*sqrt(c)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (16*d*(c*d - b*e)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(7/2)*sqrt(c)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [(d + e*x)^(3/2)/(b*x + c*x^2)^(5/2), x, 9, (-2*sqrt(d + e*x)*(b*d + (2*c*d - b*e)*x))/(3*b^2*(b*x + c*x^2)^(3/2)) + (2*sqrt(d + e*x)*(b*(8*c*d - 5*b*e)*(c*d - b*e) + 8*c*(c*d - b*e)*(2*c*d - b*e)*x))/(3*b^4*(c*d - b*e)*sqrt(b*x + c*x^2)) - (16*sqrt(c)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(7/2)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (2*(4*c*d - 3*b*e)*(4*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(7/2)*sqrt(c)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [sqrt(d + e*x)/(b*x + c*x^2)^(5/2), x, 9, (-2*(b + 2*c*x)*sqrt(d + e*x))/(3*b^2*(b*x + c*x^2)^(3/2)) + (2*sqrt(d + e*x)*(b*(c*d - b*e)*(8*c*d - b*e) + c*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2)*x))/(3*b^4*d*(c*d - b*e)*sqrt(b*x + c*x^2)) - (2*sqrt(c)*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(7/2)*d*(c*d - b*e)*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (16*sqrt(c)*(2*c*d - b*e)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(7/2)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [1/(sqrt(d + e*x)*(b*x + c*x^2)^(5/2)), x, 9, (-2*sqrt(d + e*x)*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(3*b^2*d*(c*d - b*e)*(b*x + c*x^2)^(3/2)) + (2*sqrt(d + e*x)*(b*(c*d - b*e)*(8*c^2*d^2 - 5*b*c*d*e - 2*b^2*e^2) + 2*c*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*x))/(3*b^4*d^2*(c*d - b*e)^2*sqrt(b*x + c*x^2)) - (4*sqrt(c)*(2*c*d - b*e)*(4*c^2*d^2 - 4*b*c*d*e - b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(7/2)*d^2*(c*d - b*e)^2*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (2*sqrt(c)*(16*c^2*d^2 - 16*b*c*d*e - b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(7/2)*d*(c*d - b*e)*sqrt(d + e*x)*sqrt(b*x + c*x^2))]
    @test_int [1/((d + e*x)^(3/2)*(b*x + c*x^2)^(5/2)), x, 10, (-2*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(3*b^2*d*(c*d - b*e)*sqrt(d + e*x)*(b*x + c*x^2)^(3/2)) + (2*(b*(c*d - b*e)*(8*c^2*d^2 - 3*b*c*d*e - 4*b^2*e^2) + 4*c*(4*c^3*d^3 - 6*b*c^2*d^2*e + b^3*e^3)*x))/(3*b^4*d^2*(c*d - b*e)^2*sqrt(d + e*x)*sqrt(b*x + c*x^2)) + (2*e*(16*c^4*d^4 - 32*b*c^3*d^3*e + 9*b^2*c^2*d^2*e^2 + 7*b^3*c*d*e^3 - 8*b^4*e^4)*sqrt(b*x + c*x^2))/(3*b^4*d^3*(c*d - b*e)^3*sqrt(d + e*x)) - (2*sqrt(c)*(16*c^4*d^4 - 32*b*c^3*d^3*e + 9*b^2*c^2*d^2*e^2 + 7*b^3*c*d*e^3 - 8*b^4*e^4)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(d + e*x)*Elliptic.E(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(7/2)*d^3*(c*d - b*e)^3*sqrt(1 + (e*x)/d)*sqrt(b*x + c*x^2)) + (8*sqrt(c)*(2*c*d - b*e)*(2*c^2*d^2 - 2*b*c*d*e - b^2*e^2)*sqrt(x)*sqrt(1 + (c*x)/b)*sqrt(1 + (e*x)/d)*Elliptic.F(asin((sqrt(c)*sqrt(x))/sqrt(-b)), (b*e)/(c*d)))/(3*(-b)^(7/2)*d^2*(c*d - b*e)^2*sqrt(d + e*x)*sqrt(b*x + c*x^2))]

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

    #= Note: Integrands*are*equal. =#
    @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)]

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

    @test_int [(d + e*x)^m*(c*d*x + c*e*x^2)^3, x, 4, -((c^3*d^3*(d + e*x)^(4 + m))/(e^4*(4 + m))) + (3*c^3*d^2*(d + e*x)^(5 + m))/(e^4*(5 + m)) - (3*c^3*d*(d + e*x)^(6 + m))/(e^4*(6 + m)) + (c^3*(d + e*x)^(7 + m))/(e^4*(7 + m))]
    @test_int [(d + e*x)^m*(c*d*x + c*e*x^2)^2, x, 4, (c^2*d^2*(d + e*x)^(3 + m))/(e^3*(3 + m)) - (2*c^2*d*(d + e*x)^(4 + m))/(e^3*(4 + m)) + (c^2*(d + e*x)^(5 + m))/(e^3*(5 + m))]
    @test_int [(d + e*x)^m*(c*d*x + c*e*x^2)^1, x, 4, -((c*d*(d + e*x)^(2 + m))/(e^2*(2 + m))) + (c*(d + e*x)^(3 + m))/(e^2*(3 + m))]
    @test_int [(d + e*x)^m*(c*d*x + c*e*x^2)^0, x, 1, (d + e*x)^(1 + m)/(e*(1 + m))]
    @test_int [(d + e*x)^m/(c*d*x + c*e*x^2)^1, x, 3, -(((d + e*x)^m*HypergeometricFunctions._₂F₁(1, m, 1 + m, 1 + (e*x)/d))/(c*d*m))]
    @test_int [(d + e*x)^m/(c*d*x + c*e*x^2)^2, x, 3, -((e*(d + e*x)^(-1 + m)*HypergeometricFunctions._₂F₁(2, -1 + m, m, 1 + (e*x)/d))/(c^2*d^2*(1 - m)))]

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

    @test_int [(d + e*x)^m*(b*x + c*x^2)^3, x, 2, (d^3*(c*d - b*e)^3*(d + e*x)^(1 + m))/(e^7*(1 + m)) - (3*d^2*(c*d - b*e)^2*(2*c*d - b*e)*(d + e*x)^(2 + m))/(e^7*(2 + m)) + (3*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(3 + m))/(e^7*(3 + m)) - ((2*c*d - b*e)*(10*c^2*d^2 - 10*b*c*d*e + b^2*e^2)*(d + e*x)^(4 + m))/(e^7*(4 + m)) + (3*c*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*(d + e*x)^(5 + m))/(e^7*(5 + m)) - (3*c^2*(2*c*d - b*e)*(d + e*x)^(6 + m))/(e^7*(6 + m)) + (c^3*(d + e*x)^(7 + m))/(e^7*(7 + m))]
    @test_int [(d + e*x)^m*(b*x + c*x^2)^2, x, 2, (d^2*(c*d - b*e)^2*(d + e*x)^(1 + m))/(e^5*(1 + m)) - (2*d*(c*d - b*e)*(2*c*d - b*e)*(d + e*x)^(2 + m))/(e^5*(2 + m)) + ((6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*(d + e*x)^(3 + m))/(e^5*(3 + m)) - (2*c*(2*c*d - b*e)*(d + e*x)^(4 + m))/(e^5*(4 + m)) + (c^2*(d + e*x)^(5 + m))/(e^5*(5 + m))]
    @test_int [(d + e*x)^m*(b*x + c*x^2)^1, x, 2, (d*(c*d - b*e)*(d + e*x)^(1 + m))/(e^3*(1 + m)) - ((2*c*d - b*e)*(d + e*x)^(2 + m))/(e^3*(2 + m)) + (c*(d + e*x)^(3 + m))/(e^3*(3 + m))]
    @test_int [(d + e*x)^m/(b*x + c*x^2)^1, x, 4, (c*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (c*(d + e*x))/(c*d - b*e)))/(b*(c*d - b*e)*(1 + m)) - ((d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, 1 + (e*x)/d))/(b*d*(1 + m))]
    @test_int [(d + e*x)^m/(b*x + c*x^2)^2, x, 5, -(((d + e*x)^(1 + m)*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(b^2*d*(c*d - b*e)*(b*x + c*x^2))) - (c^2*(2*c*d - b*e*(2 - m))*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (c*(d + e*x))/(c*d - b*e)))/(b^3*(c*d - b*e)^2*(1 + m)) + ((2*c*d - b*e*m)*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, 1 + (e*x)/d))/(b^3*d^2*(1 + m))]
    @test_int [(d + e*x)^m/(b*x + c*x^2)^3, x, 6, -(((d + e*x)^(1 + m)*(b*(c*d - b*e) + c*(2*c*d - b*e)*x))/(2*b^2*d*(c*d - b*e)*(b*x + c*x^2)^2)) + ((d + e*x)^(1 + m)*(b*(c*d - b*e)*(6*c^2*d^2 - b^2*e^2*(1 - m) - b*c*d*e*(4 + m)) + c*(2*c*d - b*e)*(6*c^2*d^2 - 6*b*c*d*e - b^2*e^2*(1 - m))*x))/(2*b^4*d^2*(c*d - b*e)^2*(b*x + c*x^2)) + (c^3*(12*c^2*d^2 - 6*b*c*d*e*(4 - m) + b^2*e^2*(12 - 7*m + m^2))*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (c*(d + e*x))/(c*d - b*e)))/(2*b^5*(c*d - b*e)^3*(1 + m)) - ((12*c^2*d^2 - 6*b*c*d*e*m - b^2*e^2*(1 - m)*m)*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, 1 + (e*x)/d))/(2*b^5*d^3*(1 + m))]

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

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

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

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

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

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

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

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

    @test_int [(d + e*x)^6*(a + c*x^2)^3, x, 2, ((c*d^2 + a*e^2)^3*(d + e*x)^7)/(7*e^7) - (3*c*d*(c*d^2 + a*e^2)^2*(d + e*x)^8)/(4*e^7) + (c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*(d + e*x)^9)/(3*e^7) - (2*c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^10)/(5*e^7) + (3*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^11)/(11*e^7) - (c^3*d*(d + e*x)^12)/(2*e^7) + (c^3*(d + e*x)^13)/(13*e^7)]
    @test_int [(d + e*x)^5*(a + c*x^2)^3, x, 2, ((c*d^2 + a*e^2)^3*(d + e*x)^6)/(6*e^7) - (6*c*d*(c*d^2 + a*e^2)^2*(d + e*x)^7)/(7*e^7) + (3*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*(d + e*x)^8)/(8*e^7) - (4*c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^9)/(9*e^7) + (3*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^10)/(10*e^7) - (6*c^3*d*(d + e*x)^11)/(11*e^7) + (c^3*(d + e*x)^12)/(12*e^7)]
    @test_int [(d + e*x)^4*(a + c*x^2)^3, x, 2, ((c*d^2 + a*e^2)^3*(d + e*x)^5)/(5*e^7) - (c*d*(c*d^2 + a*e^2)^2*(d + e*x)^6)/e^7 + (3*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*(d + e*x)^7)/(7*e^7) - (c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^8)/(2*e^7) + (c^2*(5*c*d^2 + a*e^2)*(d + e*x)^9)/(3*e^7) - (3*c^3*d*(d + e*x)^10)/(5*e^7) + (c^3*(d + e*x)^11)/(11*e^7)]
    @test_int [(d + e*x)^3*(a + c*x^2)^3, x, 3, a^3*d^3*x + a^2*d*(c*d^2 + a*e^2)*x^3 + (1/4)*a^3*e^3*x^4 + (3/5)*a*c*d*(c*d^2 + 3*a*e^2)*x^5 + (1/2)*a^2*c*e^3*x^6 + (1/7)*c^2*d*(c*d^2 + 9*a*e^2)*x^7 + (3/8)*a*c^2*e^3*x^8 + (1/3)*c^3*d*e^2*x^9 + (1/10)*c^3*e^3*x^10 + (3*d^2*e*(a + c*x^2)^4)/(8*c)]
    @test_int [(d + e*x)^2*(a + c*x^2)^3, x, 3, a^3*d^2*x + (1/3)*a^2*(3*c*d^2 + a*e^2)*x^3 + (3/5)*a*c*(c*d^2 + a*e^2)*x^5 + (1/7)*c^2*(c*d^2 + 3*a*e^2)*x^7 + (1/9)*c^3*e^2*x^9 + (d*e*(a + c*x^2)^4)/(4*c)]
    @test_int [(d + e*x)^1*(a + c*x^2)^3, x, 3, a^3*d*x + a^2*c*d*x^3 + (3/5)*a*c^2*d*x^5 + (1/7)*c^3*d*x^7 + (e*(a + c*x^2)^4)/(8*c)]
    @test_int [(a + c*x^2)^3/(d + e*x)^1, x, 2, -((c*d*(c^2*d^4 + 3*a*c*d^2*e^2 + 3*a^2*e^4)*x)/e^6) + (c*(c^2*d^4 + 3*a*c*d^2*e^2 + 3*a^2*e^4)*x^2)/(2*e^5) - (c^2*d*(c*d^2 + 3*a*e^2)*x^3)/(3*e^4) + (c^2*(c*d^2 + 3*a*e^2)*x^4)/(4*e^3) - (c^3*d*x^5)/(5*e^2) + (c^3*x^6)/(6*e) + ((c*d^2 + a*e^2)^3*log(d + e*x))/e^7]
    @test_int [(a + c*x^2)^3/(d + e*x)^2, x, 2, (c*(5*c^2*d^4 + 9*a*c*d^2*e^2 + 3*a^2*e^4)*x)/e^6 - (c^2*d*(2*c*d^2 + 3*a*e^2)*x^2)/e^5 + (c^2*(c*d^2 + a*e^2)*x^3)/e^4 - (c^3*d*x^4)/(2*e^3) + (c^3*x^5)/(5*e^2) - (c*d^2 + a*e^2)^3/(e^7*(d + e*x)) - (6*c*d*(c*d^2 + a*e^2)^2*log(d + e*x))/e^7]
    @test_int [(a + c*x^2)^3/(d + e*x)^3, x, 2, -((c^2*d*(10*c*d^2 + 9*a*e^2)*x)/e^6) + (3*c^2*(2*c*d^2 + a*e^2)*x^2)/(2*e^5) - (c^3*d*x^3)/e^4 + (c^3*x^4)/(4*e^3) - (c*d^2 + a*e^2)^3/(2*e^7*(d + e*x)^2) + (6*c*d*(c*d^2 + a*e^2)^2)/(e^7*(d + e*x)) + (3*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*log(d + e*x))/e^7]
    @test_int [(a + c*x^2)^3/(d + e*x)^4, x, 2, (c^2*(10*c*d^2 + 3*a*e^2)*x)/e^6 - (2*c^3*d*x^2)/e^5 + (c^3*x^3)/(3*e^4) - (c*d^2 + a*e^2)^3/(3*e^7*(d + e*x)^3) + (3*c*d*(c*d^2 + a*e^2)^2)/(e^7*(d + e*x)^2) - (3*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2))/(e^7*(d + e*x)) - (4*c^2*d*(5*c*d^2 + 3*a*e^2)*log(d + e*x))/e^7]
    @test_int [(a + c*x^2)^3/(d + e*x)^5, x, 2, -((5*c^3*d*x)/e^6) + (c^3*x^2)/(2*e^5) - (c*d^2 + a*e^2)^3/(4*e^7*(d + e*x)^4) + (2*c*d*(c*d^2 + a*e^2)^2)/(e^7*(d + e*x)^3) - (3*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2))/(2*e^7*(d + e*x)^2) + (4*c^2*d*(5*c*d^2 + 3*a*e^2))/(e^7*(d + e*x)) + (3*c^2*(5*c*d^2 + a*e^2)*log(d + e*x))/e^7]
    @test_int [(a + c*x^2)^3/(d + e*x)^6, x, 2, (c^3*x)/e^6 - (c*d^2 + a*e^2)^3/(5*e^7*(d + e*x)^5) + (3*c*d*(c*d^2 + a*e^2)^2)/(2*e^7*(d + e*x)^4) - (c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2))/(e^7*(d + e*x)^3) + (2*c^2*d*(5*c*d^2 + 3*a*e^2))/(e^7*(d + e*x)^2) - (3*c^2*(5*c*d^2 + a*e^2))/(e^7*(d + e*x)) - (6*c^3*d*log(d + e*x))/e^7]
    @test_int [(a + c*x^2)^3/(d + e*x)^7, x, 2, -((c*d^2 + a*e^2)^3/(6*e^7*(d + e*x)^6)) + (6*c*d*(c*d^2 + a*e^2)^2)/(5*e^7*(d + e*x)^5) - (3*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2))/(4*e^7*(d + e*x)^4) + (4*c^2*d*(5*c*d^2 + 3*a*e^2))/(3*e^7*(d + e*x)^3) - (3*c^2*(5*c*d^2 + a*e^2))/(2*e^7*(d + e*x)^2) + (6*c^3*d)/(e^7*(d + e*x)) + (c^3*log(d + e*x))/e^7]
    @test_int [(a + c*x^2)^3/(d + e*x)^8, x, 2, -((c*d^2 + a*e^2)^3/(7*e^7*(d + e*x)^7)) + (c*d*(c*d^2 + a*e^2)^2)/(e^7*(d + e*x)^6) - (3*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2))/(5*e^7*(d + e*x)^5) + (c^2*d*(5*c*d^2 + 3*a*e^2))/(e^7*(d + e*x)^4) - (c^2*(5*c*d^2 + a*e^2))/(e^7*(d + e*x)^3) + (3*c^3*d)/(e^7*(d + e*x)^2) - c^3/(e^7*(d + e*x))]
    @test_int [(a + c*x^2)^3/(d + e*x)^9, x, 2, -((c*d^2 + a*e^2)^3/(8*e^7*(d + e*x)^8)) + (6*c*d*(c*d^2 + a*e^2)^2)/(7*e^7*(d + e*x)^7) - (c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2))/(2*e^7*(d + e*x)^6) + (4*c^2*d*(5*c*d^2 + 3*a*e^2))/(5*e^7*(d + e*x)^5) - (3*c^2*(5*c*d^2 + a*e^2))/(4*e^7*(d + e*x)^4) + (2*c^3*d)/(e^7*(d + e*x)^3) - c^3/(2*e^7*(d + e*x)^2)]
    @test_int [(a + c*x^2)^3/(d + e*x)^10, x, 2, -((c*d^2 + a*e^2)^3/(9*e^7*(d + e*x)^9)) + (3*c*d*(c*d^2 + a*e^2)^2)/(4*e^7*(d + e*x)^8) - (3*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2))/(7*e^7*(d + e*x)^7) + (2*c^2*d*(5*c*d^2 + 3*a*e^2))/(3*e^7*(d + e*x)^6) - (3*c^2*(5*c*d^2 + a*e^2))/(5*e^7*(d + e*x)^5) + (3*c^3*d)/(2*e^7*(d + e*x)^4) - c^3/(3*e^7*(d + e*x)^3)]

    @test_int [(d + e*x)^7*(a + c*x^2)^4, x, 2, ((c*d^2 + a*e^2)^4*(d + e*x)^8)/(8*e^9) - (8*c*d*(c*d^2 + a*e^2)^3*(d + e*x)^9)/(9*e^9) + (2*c*(c*d^2 + a*e^2)^2*(7*c*d^2 + a*e^2)*(d + e*x)^10)/(5*e^9) - (8*c^2*d*(c*d^2 + a*e^2)*(7*c*d^2 + 3*a*e^2)*(d + e*x)^11)/(11*e^9) + (c^2*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)*(d + e*x)^12)/(6*e^9) - (8*c^3*d*(7*c*d^2 + 3*a*e^2)*(d + e*x)^13)/(13*e^9) + (2*c^3*(7*c*d^2 + a*e^2)*(d + e*x)^14)/(7*e^9) - (8*c^4*d*(d + e*x)^15)/(15*e^9) + (c^4*(d + e*x)^16)/(16*e^9)]
    @test_int [(d + e*x)^6*(a + c*x^2)^4, x, 2, ((c*d^2 + a*e^2)^4*(d + e*x)^7)/(7*e^9) - (c*d*(c*d^2 + a*e^2)^3*(d + e*x)^8)/e^9 + (4*c*(c*d^2 + a*e^2)^2*(7*c*d^2 + a*e^2)*(d + e*x)^9)/(9*e^9) - (4*c^2*d*(c*d^2 + a*e^2)*(7*c*d^2 + 3*a*e^2)*(d + e*x)^10)/(5*e^9) + (2*c^2*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)*(d + e*x)^11)/(11*e^9) - (2*c^3*d*(7*c*d^2 + 3*a*e^2)*(d + e*x)^12)/(3*e^9) + (4*c^3*(7*c*d^2 + a*e^2)*(d + e*x)^13)/(13*e^9) - (4*c^4*d*(d + e*x)^14)/(7*e^9) + (c^4*(d + e*x)^15)/(15*e^9)]
    @test_int [(d + e*x)^5*(a + c*x^2)^4, x, 2, ((c*d^2 + a*e^2)^4*(d + e*x)^6)/(6*e^9) - (8*c*d*(c*d^2 + a*e^2)^3*(d + e*x)^7)/(7*e^9) + (c*(c*d^2 + a*e^2)^2*(7*c*d^2 + a*e^2)*(d + e*x)^8)/(2*e^9) - (8*c^2*d*(c*d^2 + a*e^2)*(7*c*d^2 + 3*a*e^2)*(d + e*x)^9)/(9*e^9) + (c^2*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)*(d + e*x)^10)/(5*e^9) - (8*c^3*d*(7*c*d^2 + 3*a*e^2)*(d + e*x)^11)/(11*e^9) + (c^3*(7*c*d^2 + a*e^2)*(d + e*x)^12)/(3*e^9) - (8*c^4*d*(d + e*x)^13)/(13*e^9) + (c^4*(d + e*x)^14)/(14*e^9)]
    @test_int [(d + e*x)^4*(a + c*x^2)^4, x, 3, a^4*d^4*x + (2/3)*a^3*d^2*(2*c*d^2 + 3*a*e^2)*x^3 + a^4*d*e^3*x^4 + (1/5)*a^2*(6*c^2*d^4 + 24*a*c*d^2*e^2 + a^2*e^4)*x^5 + (8/3)*a^3*c*d*e^3*x^6 + (4/7)*a*c*(c^2*d^4 + 9*a*c*d^2*e^2 + a^2*e^4)*x^7 + 3*a^2*c^2*d*e^3*x^8 + (1/9)*c^2*(c^2*d^4 + 24*a*c*d^2*e^2 + 6*a^2*e^4)*x^9 + (8/5)*a*c^3*d*e^3*x^10 + (2/11)*c^3*e^2*(3*c*d^2 + 2*a*e^2)*x^11 + (1/3)*c^4*d*e^3*x^12 + (1/13)*c^4*e^4*x^13 + (2*d^3*e*(a + c*x^2)^5)/(5*c)]
    @test_int [(d + e*x)^3*(a + c*x^2)^4, x, 3, a^4*d^3*x + (1/3)*a^3*d*(4*c*d^2 + 3*a*e^2)*x^3 + (1/4)*a^4*e^3*x^4 + (6/5)*a^2*c*d*(c*d^2 + 2*a*e^2)*x^5 + (2/3)*a^3*c*e^3*x^6 + (2/7)*a*c^2*d*(2*c*d^2 + 9*a*e^2)*x^7 + (3/4)*a^2*c^2*e^3*x^8 + (1/9)*c^3*d*(c*d^2 + 12*a*e^2)*x^9 + (2/5)*a*c^3*e^3*x^10 + (3/11)*c^4*d*e^2*x^11 + (1/12)*c^4*e^3*x^12 + (3*d^2*e*(a + c*x^2)^5)/(10*c)]
    @test_int [(d + e*x)^2*(a + c*x^2)^4, x, 3, a^4*d^2*x + (1/3)*a^3*(4*c*d^2 + a*e^2)*x^3 + (2/5)*a^2*c*(3*c*d^2 + 2*a*e^2)*x^5 + (2/7)*a*c^2*(2*c*d^2 + 3*a*e^2)*x^7 + (1/9)*c^3*(c*d^2 + 4*a*e^2)*x^9 + (1/11)*c^4*e^2*x^11 + (d*e*(a + c*x^2)^5)/(5*c)]
    @test_int [(d + e*x)^1*(a + c*x^2)^4, x, 3, a^4*d*x + (4/3)*a^3*c*d*x^3 + (6/5)*a^2*c^2*d*x^5 + (4/7)*a*c^3*d*x^7 + (1/9)*c^4*d*x^9 + (e*(a + c*x^2)^5)/(10*c)]
    @test_int [(a + c*x^2)^4/(d + e*x)^1, x, 2, -((8*c*d*(c*d^2 + a*e^2)^3*x)/e^8) + (2*c*(c*d^2 + a*e^2)^2*(7*c*d^2 + a*e^2)*(d + e*x)^2)/e^9 - (8*c^2*d*(c*d^2 + a*e^2)*(7*c*d^2 + 3*a*e^2)*(d + e*x)^3)/(3*e^9) + (c^2*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)*(d + e*x)^4)/(2*e^9) - (8*c^3*d*(7*c*d^2 + 3*a*e^2)*(d + e*x)^5)/(5*e^9) + (2*c^3*(7*c*d^2 + a*e^2)*(d + e*x)^6)/(3*e^9) - (8*c^4*d*(d + e*x)^7)/(7*e^9) + (c^4*(d + e*x)^8)/(8*e^9) + ((c*d^2 + a*e^2)^4*log(d + e*x))/e^9]
    @test_int [(a + c*x^2)^4/(d + e*x)^2, x, 2, (c*(7*c^3*d^6 + 20*a*c^2*d^4*e^2 + 18*a^2*c*d^2*e^4 + 4*a^3*e^6)*x)/e^8 - (c^2*d*(3*c^2*d^4 + 8*a*c*d^2*e^2 + 6*a^2*e^4)*x^2)/e^7 + (c^2*(5*c^2*d^4 + 12*a*c*d^2*e^2 + 6*a^2*e^4)*x^3)/(3*e^6) - (c^3*d*(c*d^2 + 2*a*e^2)*x^4)/e^5 + (c^3*(3*c*d^2 + 4*a*e^2)*x^5)/(5*e^4) - (c^4*d*x^6)/(3*e^3) + (c^4*x^7)/(7*e^2) - (c*d^2 + a*e^2)^4/(e^9*(d + e*x)) - (8*c*d*(c*d^2 + a*e^2)^3*log(d + e*x))/e^9]

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

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

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

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

    @test_int [(d + e*x)^5/(a + c*x^2)^3, x, 6, -((d*e^2*(3*c*d^2 + 7*a*e^2)*x)/(8*a^2*c^2)) - ((a*e - c*d*x)*(d + e*x)^4)/(4*a*c*(a + c*x^2)^2) - ((d + e*x)^2*(2*a*e*(c*d^2 + 2*a*e^2) - c*d*(3*c*d^2 + 5*a*e^2)*x))/(8*a^2*c^2*(a + c*x^2)) + (d*(3*c^2*d^4 + 10*a*c*d^2*e^2 + 15*a^2*e^4)*atan((sqrt(c)*x)/sqrt(a)))/(8*a^(5/2)*c^(5/2)) + (e^5*log(a + c*x^2))/(2*c^3)]
    @test_int [(d + e*x)^4/(a + c*x^2)^3, x, 3, -((a*e - c*d*x)*(d + e*x)^3)/(4*a*c*(a + c*x^2)^2) - (3*(c*d^2 + a*e^2)*(a*e - c*d*x)*(d + e*x))/(8*a^2*c^2*(a + c*x^2)) + (3*(c*d^2 + a*e^2)^2*atan((sqrt(c)*x)/sqrt(a)))/(8*a^(5/2)*c^(5/2))]
    @test_int [(d + e*x)^3/(a + c*x^2)^3, x, 3, (x*(d + e*x)^3)/(4*a*(a + c*x^2)^2) - (3*d*(a*e - c*d*x)*(d + e*x))/(8*a^2*c*(a + c*x^2)) + (3*d*(c*d^2 + a*e^2)*atan((sqrt(c)*x)/sqrt(a)))/(8*a^(5/2)*c^(3/2))]
    @test_int [(d + e*x)^2/(a + c*x^2)^3, x, 3, -(((a*e - c*d*x)*(d + e*x))/(4*a*c*(a + c*x^2)^2)) - (2*a*d*e - (3*c*d^2 + a*e^2)*x)/(8*a^2*c*(a + c*x^2)) + ((3*c*d^2 + a*e^2)*atan((sqrt(c)*x)/sqrt(a)))/(8*a^(5/2)*c^(3/2))]
    @test_int [(d + e*x)^1/(a + c*x^2)^3, x, 3, -(a*e - c*d*x)/(4*a*c*(a + c*x^2)^2) + (3*d*x)/(8*a^2*(a + c*x^2)) + (3*d*atan((sqrt(c)*x)/sqrt(a)))/(8*a^(5/2)*sqrt(c))]
    @test_int [1/((d + e*x)^1*(a + c*x^2)^3), x, 7, (a*e + c*d*x)/(4*a*(c*d^2 + a*e^2)*(a + c*x^2)^2) + (4*a^2*e^3 + c*d*(3*c*d^2 + 7*a*e^2)*x)/(8*a^2*(c*d^2 + a*e^2)^2*(a + c*x^2)) + (sqrt(c)*d*(3*c^2*d^4 + 10*a*c*d^2*e^2 + 15*a^2*e^4)*atan((sqrt(c)*x)/sqrt(a)))/(8*a^(5/2)*(c*d^2 + a*e^2)^3) + (e^5*log(d + e*x))/(c*d^2 + a*e^2)^3 - (e^5*log(a + c*x^2))/(2*(c*d^2 + a*e^2)^3)]
    @test_int [1/((d + e*x)^2*(a + c*x^2)^3), x, 7, (3*e*(c*d^2 - a*e^2)*(c*d^2 + 5*a*e^2))/(8*a^2*(c*d^2 + a*e^2)^3*(d + e*x)) + (a*e + c*d*x)/(4*a*(c*d^2 + a*e^2)*(d + e*x)*(a + c*x^2)^2) - (a*e*(c*d^2 - 5*a*e^2) - 3*c*d*(c*d^2 + 3*a*e^2)*x)/(8*a^2*(c*d^2 + a*e^2)^2*(d + e*x)*(a + c*x^2)) + (3*sqrt(c)*(c^3*d^6 + 5*a*c^2*d^4*e^2 + 15*a^2*c*d^2*e^4 - 5*a^3*e^6)*atan((sqrt(c)*x)/sqrt(a)))/(8*a^(5/2)*(c*d^2 + a*e^2)^4) + (6*c*d*e^5*log(d + e*x))/(c*d^2 + a*e^2)^4 - (3*c*d*e^5*log(a + c*x^2))/(c*d^2 + a*e^2)^4]

    @test_int [(d + e*x)^4/(a + c*x^2)^4, x, 4, (x*(d + e*x)^4)/(6*a*(a + c*x^2)^3) - ((a*e - 5*c*d*x)*(d + e*x)^3)/(24*a^2*c*(a + c*x^2)^2) - ((5*c*d^2 + a*e^2)*(a*e - c*d*x)*(d + e*x))/(16*a^3*c^2*(a + c*x^2)) + ((c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*atan((sqrt(c)*x)/sqrt(a)))/(16*a^(7/2)*c^(5/2))]
    @test_int [(d + e*x)^3/(a + c*x^2)^4, x, 4, (x*(d + e*x)^3)/(6*a*(a + c*x^2)^3) - ((2*a*e - 5*c*d*x)*(d + e*x)^2)/(24*a^2*c*(a + c*x^2)^2) - (4*a*e*(5*c*d^2 + a*e^2) - c*d*(15*c*d^2 - a*e^2)*x)/(48*a^3*c^2*(a + c*x^2)) + (d*(5*c*d^2 + 3*a*e^2)*atan((sqrt(c)*x)/sqrt(a)))/(16*a^(7/2)*c^(3/2))]
    @test_int [(d + e*x)^2/(a + c*x^2)^4, x, 4, -(((a*e - c*d*x)*(d + e*x))/(6*a*c*(a + c*x^2)^3)) - (4*a*d*e - (5*c*d^2 + a*e^2)*x)/(24*a^2*c*(a + c*x^2)^2) + ((5*c*d^2 + a*e^2)*x)/(16*a^3*c*(a + c*x^2)) + ((5*c*d^2 + a*e^2)*atan((sqrt(c)*x)/sqrt(a)))/(16*a^(7/2)*c^(3/2))]
    @test_int [(d + e*x)^1/(a + c*x^2)^4, x, 4, -(a*e - c*d*x)/(6*a*c*(a + c*x^2)^3) + (5*d*x)/(24*a^2*(a + c*x^2)^2) + (5*d*x)/(16*a^3*(a + c*x^2)) + (5*d*atan((sqrt(c)*x)/sqrt(a)))/(16*a^(7/2)*sqrt(c))]
    @test_int [1/((d + e*x)^1*(a + c*x^2)^4), x, 8, (a*e + c*d*x)/(6*a*(c*d^2 + a*e^2)*(a + c*x^2)^3) + (6*a^2*e^3 + c*d*(5*c*d^2 + 11*a*e^2)*x)/(24*a^2*(c*d^2 + a*e^2)^2*(a + c*x^2)^2) + (8*a^3*e^5 + c*d*(5*c^2*d^4 + 16*a*c*d^2*e^2 + 19*a^2*e^4)*x)/(16*a^3*(c*d^2 + a*e^2)^3*(a + c*x^2)) + (sqrt(c)*d*(5*c^3*d^6 + 21*a*c^2*d^4*e^2 + 35*a^2*c*d^2*e^4 + 35*a^3*e^6)*atan((sqrt(c)*x)/sqrt(a)))/(16*a^(7/2)*(c*d^2 + a*e^2)^4) + (e^7*log(d + e*x))/(c*d^2 + a*e^2)^4 - (e^7*log(a + c*x^2))/(2*(c*d^2 + a*e^2)^4)]
    @test_int [1/((d + e*x)^2*(a + c*x^2)^4), x, 8, (e*(5*c^3*d^6 + 23*a*c^2*d^4*e^2 + 47*a^2*c*d^2*e^4 - 35*a^3*e^6))/(16*a^3*(c*d^2 + a*e^2)^4*(d + e*x)) + (a*e + c*d*x)/(6*a*(c*d^2 + a*e^2)*(d + e*x)*(a + c*x^2)^3) - (a*e*(c*d^2 - 7*a*e^2) - c*d*(5*c*d^2 + 13*a*e^2)*x)/(24*a^2*(c*d^2 + a*e^2)^2*(d + e*x)*(a + c*x^2)^2) - (a*e*(5*c*d^2 - 7*a*e^2)*(c*d^2 + 5*a*e^2) - 3*c*d*(5*c^2*d^4 + 18*a*c*d^2*e^2 + 29*a^2*e^4)*x)/(48*a^3*(c*d^2 + a*e^2)^3*(d + e*x)*(a + c*x^2)) + (sqrt(c)*(5*c^4*d^8 + 28*a*c^3*d^6*e^2 + 70*a^2*c^2*d^4*e^4 + 140*a^3*c*d^2*e^6 - 35*a^4*e^8)*atan((sqrt(c)*x)/sqrt(a)))/(16*a^(7/2)*(c*d^2 + a*e^2)^5) + (8*c*d*e^7*log(d + e*x))/(c*d^2 + a*e^2)^5 - (4*c*d*e^7*log(a + c*x^2))/(c*d^2 + a*e^2)^5]

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

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

    @test_int [(d + e*x)^4*sqrt(a + c*x^2), x, 6, ((8*c^2*d^4 - 12*a*c*d^2*e^2 + a^2*e^4)*x*sqrt(a + c*x^2))/(16*c^2) + (3*d*e*(d + e*x)^2*(a + c*x^2)^(3/2))/(10*c) + (e*(d + e*x)^3*(a + c*x^2)^(3/2))/(6*c) + (e*(8*d*(13*c*d^2 - 8*a*e^2) + 3*e*(16*c*d^2 - 5*a*e^2)*x)*(a + c*x^2)^(3/2))/(120*c^2) + (a*(8*c^2*d^4 - 12*a*c*d^2*e^2 + a^2*e^4)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(16*c^(5/2))]
    @test_int [(d + e*x)^3*sqrt(a + c*x^2), x, 5, (d*(4*c*d^2 - 3*a*e^2)*x*sqrt(a + c*x^2))/(8*c) + (e*(d + e*x)^2*(a + c*x^2)^(3/2))/(5*c) + (e*(8*(6*c*d^2 - a*e^2) + 21*c*d*e*x)*(a + c*x^2)^(3/2))/(60*c^2) + (a*d*(4*c*d^2 - 3*a*e^2)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(8*c^(3/2))]
    @test_int [(d + e*x)^2*sqrt(a + c*x^2), x, 5, ((4*c*d^2 - a*e^2)*x*sqrt(a + c*x^2))/(8*c) + (5*d*e*(a + c*x^2)^(3/2))/(12*c) + (e*(d + e*x)*(a + c*x^2)^(3/2))/(4*c) + (a*(4*c*d^2 - a*e^2)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(8*c^(3/2))]
    @test_int [(d + e*x)^1*sqrt(a + c*x^2), x, 4, (d*x*sqrt(a + c*x^2))/2 + (e*(a + c*x^2)^(3/2))/(3*c) + (a*d*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(2*sqrt(c))]
    @test_int [sqrt(a + c*x^2)/(d + e*x)^1, x, 6, sqrt(a + c*x^2)/e - (sqrt(c)*d*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/e^2 - (sqrt(c*d^2 + a*e^2)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/e^2]
    @test_int [sqrt(a + c*x^2)/(d + e*x)^2, x, 6, -(sqrt(a + c*x^2)/(e*(d + e*x))) + (sqrt(c)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/e^2 + (c*d*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(e^2*sqrt(c*d^2 + a*e^2))]
    @test_int [sqrt(a + c*x^2)/(d + e*x)^3, x, 3, -((a*e - c*d*x)*sqrt(a + c*x^2))/(2*(c*d^2 + a*e^2)*(d + e*x)^2) - (a*c*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(2*(c*d^2 + a*e^2)^(3/2))]
    @test_int [sqrt(a + c*x^2)/(d + e*x)^4, x, 4, -(c*d*(a*e - c*d*x)*sqrt(a + c*x^2))/(2*(c*d^2 + a*e^2)^2*(d + e*x)^2) - (e*(a + c*x^2)^(3/2))/(3*(c*d^2 + a*e^2)*(d + e*x)^3) - (a*c^2*d*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(2*(c*d^2 + a*e^2)^(5/2))]
    @test_int [sqrt(a + c*x^2)/(d + e*x)^5, x, 5, -((c*(4*c*d^2 - a*e^2)*(a*e - c*d*x)*sqrt(a + c*x^2))/(8*(c*d^2 + a*e^2)^3*(d + e*x)^2)) - (e*(a + c*x^2)^(3/2))/(4*(c*d^2 + a*e^2)*(d + e*x)^4) - (5*c*d*e*(a + c*x^2)^(3/2))/(12*(c*d^2 + a*e^2)^2*(d + e*x)^3) - (a*c^2*(4*c*d^2 - a*e^2)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(8*(c*d^2 + a*e^2)^(7/2))]

    @test_int [(d + e*x)^4*(a + c*x^2)^(3/2), x, 7, (3*a*(16*c^2*d^4 - 16*a*c*d^2*e^2 + a^2*e^4)*x*sqrt(a + c*x^2))/(128*c^2) + ((16*c^2*d^4 - 16*a*c*d^2*e^2 + a^2*e^4)*x*(a + c*x^2)^(3/2))/(64*c^2) + (11*d*e*(d + e*x)^2*(a + c*x^2)^(5/2))/(56*c) + (e*(d + e*x)^3*(a + c*x^2)^(5/2))/(8*c) + (e*(4*d*(67*c*d^2 - 32*a*e^2) + 5*e*(26*c*d^2 - 7*a*e^2)*x)*(a + c*x^2)^(5/2))/(560*c^2) + (3*a^2*(16*c^2*d^4 - 16*a*c*d^2*e^2 + a^2*e^4)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(128*c^(5/2))]
    @test_int [(d + e*x)^3*(a + c*x^2)^(3/2), x, 6, (3*a*d*(2*c*d^2 - a*e^2)*x*sqrt(a + c*x^2))/(16*c) + (d*(2*c*d^2 - a*e^2)*x*(a + c*x^2)^(3/2))/(8*c) + (e*(d + e*x)^2*(a + c*x^2)^(5/2))/(7*c) + (e*(4*(8*c*d^2 - a*e^2) + 15*c*d*e*x)*(a + c*x^2)^(5/2))/(70*c^2) + (3*a^2*d*(2*c*d^2 - a*e^2)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(16*c^(3/2))]
    @test_int [(d + e*x)^2*(a + c*x^2)^(3/2), x, 6, (a*(6*c*d^2 - a*e^2)*x*sqrt(a + c*x^2))/(16*c) + ((6*c*d^2 - a*e^2)*x*(a + c*x^2)^(3/2))/(24*c) + (7*d*e*(a + c*x^2)^(5/2))/(30*c) + (e*(d + e*x)*(a + c*x^2)^(5/2))/(6*c) + (a^2*(6*c*d^2 - a*e^2)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(16*c^(3/2))]
    @test_int [(d + e*x)^1*(a + c*x^2)^(3/2), x, 5, (3*a*d*x*sqrt(a + c*x^2))/8 + (d*x*(a + c*x^2)^(3/2))/4 + (e*(a + c*x^2)^(5/2))/(5*c) + (3*a^2*d*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(8*sqrt(c))]
    @test_int [(a + c*x^2)^(3/2)/(d + e*x)^1, x, 7, ((2*(c*d^2 + a*e^2) - c*d*e*x)*sqrt(a + c*x^2))/(2*e^3) + (a + c*x^2)^(3/2)/(3*e) - (sqrt(c)*d*(2*c*d^2 + 3*a*e^2)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(2*e^4) - ((c*d^2 + a*e^2)^(3/2)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/e^4]
    @test_int [(a + c*x^2)^(3/2)/(d + e*x)^2, x, 7, (-3*c*(2*d - e*x)*sqrt(a + c*x^2))/(2*e^3) - (a + c*x^2)^(3/2)/(e*(d + e*x)) + (3*sqrt(c)*(2*c*d^2 + a*e^2)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(2*e^4) + (3*c*d*sqrt(c*d^2 + a*e^2)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/e^4]
    @test_int [(a + c*x^2)^(3/2)/(d + e*x)^3, x, 7, (3*c*(2*d + e*x)*sqrt(a + c*x^2))/(2*e^3*(d + e*x)) - (a + c*x^2)^(3/2)/(2*e*(d + e*x)^2) - (3*c^(3/2)*d*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/e^4 - (3*c*(2*c*d^2 + a*e^2)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(2*e^4*sqrt(c*d^2 + a*e^2))]
    @test_int [(a + c*x^2)^(3/2)/(d + e*x)^4, x, 7, -((c*(d*(2*c*d^2 + a*e^2) + e*(3*c*d^2 + 2*a*e^2)*x)*sqrt(a + c*x^2))/(2*e^3*(c*d^2 + a*e^2)*(d + e*x)^2)) - (a + c*x^2)^(3/2)/(3*e*(d + e*x)^3) + (c^(3/2)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/e^4 + (c^2*d*(2*c*d^2 + 3*a*e^2)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(2*e^4*(c*d^2 + a*e^2)^(3/2))]
    @test_int [(a + c*x^2)^(3/2)/(d + e*x)^5, x, 4, (-3*a*c*(a*e - c*d*x)*sqrt(a + c*x^2))/(8*(c*d^2 + a*e^2)^2*(d + e*x)^2) - ((a*e - c*d*x)*(a + c*x^2)^(3/2))/(4*(c*d^2 + a*e^2)*(d + e*x)^4) - (3*a^2*c^2*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(8*(c*d^2 + a*e^2)^(5/2))]
    @test_int [(a + c*x^2)^(3/2)/(d + e*x)^6, x, 5, -((3*a*c^2*d*(a*e - c*d*x)*sqrt(a + c*x^2))/(8*(c*d^2 + a*e^2)^3*(d + e*x)^2)) - (c*d*(a*e - c*d*x)*(a + c*x^2)^(3/2))/(4*(c*d^2 + a*e^2)^2*(d + e*x)^4) - (e*(a + c*x^2)^(5/2))/(5*(c*d^2 + a*e^2)*(d + e*x)^5) - (3*a^2*c^3*d*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(8*(c*d^2 + a*e^2)^(7/2))]
    @test_int [(a + c*x^2)^(3/2)/(d + e*x)^7, x, 6, -((a*c^2*(6*c*d^2 - a*e^2)*(a*e - c*d*x)*sqrt(a + c*x^2))/(16*(c*d^2 + a*e^2)^4*(d + e*x)^2)) - (c*(6*c*d^2 - a*e^2)*(a*e - c*d*x)*(a + c*x^2)^(3/2))/(24*(c*d^2 + a*e^2)^3*(d + e*x)^4) - (e*(a + c*x^2)^(5/2))/(6*(c*d^2 + a*e^2)*(d + e*x)^6) - (7*c*d*e*(a + c*x^2)^(5/2))/(30*(c*d^2 + a*e^2)^2*(d + e*x)^5) - (a^2*c^3*(6*c*d^2 - a*e^2)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(16*(c*d^2 + a*e^2)^(9/2))]

    @test_int [(d + e*x)^4*(a + c*x^2)^(5/2), x, 8, (a^2*(80*c^2*d^4 - 60*a*c*d^2*e^2 + 3*a^2*e^4)*x*sqrt(a + c*x^2))/(256*c^2) + (a*(80*c^2*d^4 - 60*a*c*d^2*e^2 + 3*a^2*e^4)*x*(a + c*x^2)^(3/2))/(384*c^2) + ((80*c^2*d^4 - 60*a*c*d^2*e^2 + 3*a^2*e^4)*x*(a + c*x^2)^(5/2))/(480*c^2) + (13*d*e*(d + e*x)^2*(a + c*x^2)^(7/2))/(90*c) + (e*(d + e*x)^3*(a + c*x^2)^(7/2))/(10*c) + (e*(16*d*(103*c*d^2 - 40*a*e^2) + 7*e*(116*c*d^2 - 27*a*e^2)*x)*(a + c*x^2)^(7/2))/(5040*c^2) + (a^3*(80*c^2*d^4 - 60*a*c*d^2*e^2 + 3*a^2*e^4)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(256*c^(5/2))]
    @test_int [(d + e*x)^3*(a + c*x^2)^(5/2), x, 7, (5*a^2*d*(8*c*d^2 - 3*a*e^2)*x*sqrt(a + c*x^2))/(128*c) + (5*a*d*(8*c*d^2 - 3*a*e^2)*x*(a + c*x^2)^(3/2))/(192*c) + (d*(8*c*d^2 - 3*a*e^2)*x*(a + c*x^2)^(5/2))/(48*c) + (e*(d + e*x)^2*(a + c*x^2)^(7/2))/(9*c) + (e*(16*(10*c*d^2 - a*e^2) + 77*c*d*e*x)*(a + c*x^2)^(7/2))/(504*c^2) + (5*a^3*d*(8*c*d^2 - 3*a*e^2)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(128*c^(3/2))]
    @test_int [(d + e*x)^2*(a + c*x^2)^(5/2), x, 7, (5*a^2*(8*c*d^2 - a*e^2)*x*sqrt(a + c*x^2))/(128*c) + (5*a*(8*c*d^2 - a*e^2)*x*(a + c*x^2)^(3/2))/(192*c) + ((8*c*d^2 - a*e^2)*x*(a + c*x^2)^(5/2))/(48*c) + (9*d*e*(a + c*x^2)^(7/2))/(56*c) + (e*(d + e*x)*(a + c*x^2)^(7/2))/(8*c) + (5*a^3*(8*c*d^2 - a*e^2)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(128*c^(3/2))]
    @test_int [(d + e*x)^1*(a + c*x^2)^(5/2), x, 6, (5*a^2*d*x*sqrt(a + c*x^2))/16 + (5*a*d*x*(a + c*x^2)^(3/2))/24 + (d*x*(a + c*x^2)^(5/2))/6 + (e*(a + c*x^2)^(7/2))/(7*c) + (5*a^3*d*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(16*sqrt(c))]
    @test_int [(a + c*x^2)^(5/2)/(d + e*x)^1, x, 8, ((8*(c*d^2 + a*e^2)^2 - c*d*e*(4*c*d^2 + 7*a*e^2)*x)*sqrt(a + c*x^2))/(8*e^5) + ((4*(c*d^2 + a*e^2) - 3*c*d*e*x)*(a + c*x^2)^(3/2))/(12*e^3) + (a + c*x^2)^(5/2)/(5*e) - (sqrt(c)*d*(8*c^2*d^4 + 20*a*c*d^2*e^2 + 15*a^2*e^4)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(8*e^6) - ((c*d^2 + a*e^2)^(5/2)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/e^6]
    @test_int [(a + c*x^2)^(5/2)/(d + e*x)^2, x, 8, (-5*c*(8*d*(c*d^2 + a*e^2) - e*(4*c*d^2 + 3*a*e^2)*x)*sqrt(a + c*x^2))/(8*e^5) - (5*c*(4*d - 3*e*x)*(a + c*x^2)^(3/2))/(12*e^3) - (a + c*x^2)^(5/2)/(e*(d + e*x)) + (5*sqrt(c)*(8*c^2*d^4 + 12*a*c*d^2*e^2 + 3*a^2*e^4)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(8*e^6) + (5*c*d*(c*d^2 + a*e^2)^(3/2)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/e^6]
    @test_int [(a + c*x^2)^(5/2)/(d + e*x)^3, x, 8, (5*c*(4*c*d^2 + a*e^2 - 2*c*d*e*x)*sqrt(a + c*x^2))/(2*e^5) + (5*c*(4*d + e*x)*(a + c*x^2)^(3/2))/(6*e^3*(d + e*x)) - (a + c*x^2)^(5/2)/(2*e*(d + e*x)^2) - (5*c^(3/2)*d*(4*c*d^2 + 3*a*e^2)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(2*e^6) - (5*c*sqrt(c*d^2 + a*e^2)*(4*c*d^2 + a*e^2)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(2*e^6)]
    @test_int [(a + c*x^2)^(5/2)/(d + e*x)^4, x, 8, (-5*c*(4*c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a + c*x^2))/(2*e^5*(d + e*x)) + (5*c*(2*d + e*x)*(a + c*x^2)^(3/2))/(6*e^3*(d + e*x)^2) - (a + c*x^2)^(5/2)/(3*e*(d + e*x)^3) + (5*c^(3/2)*(4*c*d^2 + a*e^2)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(2*e^6) + (5*c^2*d*(4*c*d^2 + 3*a*e^2)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(2*e^6*sqrt(c*d^2 + a*e^2))]
    @test_int [(a + c*x^2)^(5/2)/(d + e*x)^5, x, 8, (5*c^2*(8*d*(c*d^2 + a*e^2) + e*(4*c*d^2 + 3*a*e^2)*x)*sqrt(a + c*x^2))/(8*e^5*(c*d^2 + a*e^2)*(d + e*x)) - (5*c*(d*(4*c*d^2 + a*e^2) + 3*e*(2*c*d^2 + a*e^2)*x)*(a + c*x^2)^(3/2))/(24*e^3*(c*d^2 + a*e^2)*(d + e*x)^3) - (a + c*x^2)^(5/2)/(4*e*(d + e*x)^4) - (5*c^(5/2)*d*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/e^6 - (5*c^2*(8*c^2*d^4 + 12*a*c*d^2*e^2 + 3*a^2*e^4)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(8*e^6*(c*d^2 + a*e^2)^(3/2))]
    @test_int [(a + c*x^2)^(5/2)/(d + e*x)^6, x, 8, -((c^2*(d*(8*c^2*d^4 + 12*a*c*d^2*e^2 + a^2*e^4) + e*(12*c^2*d^4 + 23*a*c*d^2*e^2 + 8*a^2*e^4)*x)*sqrt(a + c*x^2))/(8*e^5*(c*d^2 + a*e^2)^2*(d + e*x)^2)) - (c*(d*(4*c*d^2 + a*e^2) + e*(7*c*d^2 + 4*a*e^2)*x)*(a + c*x^2)^(3/2))/(12*e^3*(c*d^2 + a*e^2)*(d + e*x)^4) - (a + c*x^2)^(5/2)/(5*e*(d + e*x)^5) + (c^(5/2)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/e^6 + (c^3*d*(8*c^2*d^4 + 20*a*c*d^2*e^2 + 15*a^2*e^4)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(8*e^6*(c*d^2 + a*e^2)^(5/2))]
    @test_int [(a + c*x^2)^(5/2)/(d + e*x)^7, x, 5, -((5*a^2*c^2*(a*e - c*d*x)*sqrt(a + c*x^2))/(16*(c*d^2 + a*e^2)^3*(d + e*x)^2)) - (5*a*c*(a*e - c*d*x)*(a + c*x^2)^(3/2))/(24*(c*d^2 + a*e^2)^2*(d + e*x)^4) - ((a*e - c*d*x)*(a + c*x^2)^(5/2))/(6*(c*d^2 + a*e^2)*(d + e*x)^6) - (5*a^3*c^3*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(16*(c*d^2 + a*e^2)^(7/2))]
    @test_int [(a + c*x^2)^(5/2)/(d + e*x)^8, x, 6, -((5*a^2*c^3*d*(a*e - c*d*x)*sqrt(a + c*x^2))/(16*(c*d^2 + a*e^2)^4*(d + e*x)^2)) - (5*a*c^2*d*(a*e - c*d*x)*(a + c*x^2)^(3/2))/(24*(c*d^2 + a*e^2)^3*(d + e*x)^4) - (c*d*(a*e - c*d*x)*(a + c*x^2)^(5/2))/(6*(c*d^2 + a*e^2)^2*(d + e*x)^6) - (e*(a + c*x^2)^(7/2))/(7*(c*d^2 + a*e^2)*(d + e*x)^7) - (5*a^3*c^4*d*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(16*(c*d^2 + a*e^2)^(9/2))]
    @test_int [(a + c*x^2)^(5/2)/(d + e*x)^9, x, 7, -((5*a^2*c^3*(8*c*d^2 - a*e^2)*(a*e - c*d*x)*sqrt(a + c*x^2))/(128*(c*d^2 + a*e^2)^5*(d + e*x)^2)) - (5*a*c^2*(8*c*d^2 - a*e^2)*(a*e - c*d*x)*(a + c*x^2)^(3/2))/(192*(c*d^2 + a*e^2)^4*(d + e*x)^4) - (c*(8*c*d^2 - a*e^2)*(a*e - c*d*x)*(a + c*x^2)^(5/2))/(48*(c*d^2 + a*e^2)^3*(d + e*x)^6) - (e*(a + c*x^2)^(7/2))/(8*(c*d^2 + a*e^2)*(d + e*x)^8) - (9*c*d*e*(a + c*x^2)^(7/2))/(56*(c*d^2 + a*e^2)^2*(d + e*x)^7) - (5*a^3*c^4*(8*c*d^2 - a*e^2)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(128*(c*d^2 + a*e^2)^(11/2))]

    @test_int [sqrt(2 + x^2)/(1 + 4*x), x, 5, sqrt(2 + x^2)/4 - (1/16)*asinh(x/sqrt(2)) - (1/16)*sqrt(33)*atanh((8 - x)/(sqrt(33)*sqrt(2 + x^2)))]
    @test_int [sqrt(2 + 4*x^2)/(5 + 4*x), x, 5, sqrt(1 + 2*x^2)/(2*sqrt(2)) - (5/8)*asinh(sqrt(2)*x) - (1/8)*sqrt(33)*atanh((sqrt(2/33)*(2 - 5*x))/sqrt(1 + 2*x^2))]

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

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

    @test_int [(d + e*x)^4/sqrt(a + c*x^2), x, 5, (7*d*e*(d + e*x)^2*sqrt(a + c*x^2))/(12*c) + (e*(d + e*x)^3*sqrt(a + c*x^2))/(4*c) + (e*(4*d*(19*c*d^2 - 16*a*e^2) + e*(26*c*d^2 - 9*a*e^2)*x)*sqrt(a + c*x^2))/(24*c^2) + ((8*c^2*d^4 - 24*a*c*d^2*e^2 + 3*a^2*e^4)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(8*c^(5/2))]
    @test_int [(d + e*x)^3/sqrt(a + c*x^2), x, 4, (e*(d + e*x)^2*sqrt(a + c*x^2))/(3*c) + (e*(4*(4*c*d^2 - a*e^2) + 5*c*d*e*x)*sqrt(a + c*x^2))/(6*c^2) + (d*(2*c*d^2 - 3*a*e^2)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(2*c^(3/2))]
    @test_int [(d + e*x)^2/sqrt(a + c*x^2), x, 4, (3*d*e*sqrt(a + c*x^2))/(2*c) + (e*(d + e*x)*sqrt(a + c*x^2))/(2*c) + ((2*c*d^2 - a*e^2)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(2*c^(3/2))]
    @test_int [(d + e*x)^1/sqrt(a + c*x^2), x, 3, (e*sqrt(a + c*x^2))/c + (d*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/sqrt(c)]
    @test_int [1/((d + e*x)^1*sqrt(a + c*x^2)), x, 2, -(atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2)))/sqrt(c*d^2 + a*e^2))]
    @test_int [1/((d + e*x)^2*sqrt(a + c*x^2)), x, 3, -((e*sqrt(a + c*x^2))/((c*d^2 + a*e^2)*(d + e*x))) - (c*d*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(c*d^2 + a*e^2)^(3/2)]
    @test_int [1/((d + e*x)^3*sqrt(a + c*x^2)), x, 4, -(e*sqrt(a + c*x^2))/(2*(c*d^2 + a*e^2)*(d + e*x)^2) - (3*c*d*e*sqrt(a + c*x^2))/(2*(c*d^2 + a*e^2)^2*(d + e*x)) - (c*(2*c*d^2 - a*e^2)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(2*(c*d^2 + a*e^2)^(5/2))]
    @test_int [1/((d + e*x)^4*sqrt(a + c*x^2)), x, 5, -(e*sqrt(a + c*x^2))/(3*(c*d^2 + a*e^2)*(d + e*x)^3) - (5*c*d*e*sqrt(a + c*x^2))/(6*(c*d^2 + a*e^2)^2*(d + e*x)^2) - (c*e*(11*c*d^2 - 4*a*e^2)*sqrt(a + c*x^2))/(6*(c*d^2 + a*e^2)^3*(d + e*x)) - (c^2*d*(2*c*d^2 - 3*a*e^2)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(2*(c*d^2 + a*e^2)^(7/2))]

    @test_int [(d + e*x)^4/(a + c*x^2)^(3/2), x, 5, -(((a*e - c*d*x)*(d + e*x)^3)/(a*c*sqrt(a + c*x^2))) - (d*e*(d + e*x)^2*sqrt(a + c*x^2))/(a*c) - (e*(4*d*(c*d^2 - 4*a*e^2) + e*(2*c*d^2 - 3*a*e^2)*x)*sqrt(a + c*x^2))/(2*a*c^2) + (3*e^2*(4*c*d^2 - a*e^2)*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/(2*c^(5/2))]
    @test_int [(d + e*x)^3/(a + c*x^2)^(3/2), x, 4, -(((a*e - c*d*x)*(d + e*x)^2)/(a*c*sqrt(a + c*x^2))) - (e*(2*(c*d^2 - a*e^2) + c*d*e*x)*sqrt(a + c*x^2))/(a*c^2) + (3*d*e^2*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/c^(3/2)]
    @test_int [(d + e*x)^2/(a + c*x^2)^(3/2), x, 4, -(((a*e - c*d*x)*(d + e*x))/(a*c*sqrt(a + c*x^2))) - (d*e*sqrt(a + c*x^2))/(a*c) + (e^2*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/c^(3/2)]
    @test_int [(d + e*x)^1/(a + c*x^2)^(3/2), x, 1, -((a*e - c*d*x)/(a*c*sqrt(a + c*x^2)))]
    @test_int [1/((d + e*x)^1*(a + c*x^2)^(3/2)), x, 4, (a*e + c*d*x)/(a*(c*d^2 + a*e^2)*sqrt(a + c*x^2)) - (e^2*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(c*d^2 + a*e^2)^(3/2)]
    @test_int [1/((d + e*x)^2*(a + c*x^2)^(3/2)), x, 4, (a*e + c*d*x)/(a*(c*d^2 + a*e^2)*(d + e*x)*sqrt(a + c*x^2)) + (e*(c*d^2 - 2*a*e^2)*sqrt(a + c*x^2))/(a*(c*d^2 + a*e^2)^2*(d + e*x)) - (3*c*d*e^2*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(c*d^2 + a*e^2)^(5/2)]
    @test_int [1/((d + e*x)^3*(a + c*x^2)^(3/2)), x, 5, (a*e + c*d*x)/(a*(c*d^2 + a*e^2)*(d + e*x)^2*sqrt(a + c*x^2)) + (e*(2*c*d^2 - 3*a*e^2)*sqrt(a + c*x^2))/(2*a*(c*d^2 + a*e^2)^2*(d + e*x)^2) + (c*d*e*(2*c*d^2 - 13*a*e^2)*sqrt(a + c*x^2))/(2*a*(c*d^2 + a*e^2)^3*(d + e*x)) - (3*c*e^2*(4*c*d^2 - a*e^2)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(2*(c*d^2 + a*e^2)^(7/2))]
    @test_int [1/((d + e*x)^4*(a + c*x^2)^(3/2)), x, 6, (a*e + c*d*x)/(a*(c*d^2 + a*e^2)*(d + e*x)^3*sqrt(a + c*x^2)) + (e*(3*c*d^2 - 4*a*e^2)*sqrt(a + c*x^2))/(3*a*(c*d^2 + a*e^2)^2*(d + e*x)^3) + (c*d*e*(6*c*d^2 - 29*a*e^2)*sqrt(a + c*x^2))/(6*a*(c*d^2 + a*e^2)^3*(d + e*x)^2) + (c*e*(6*c^2*d^4 - 83*a*c*d^2*e^2 + 16*a^2*e^4)*sqrt(a + c*x^2))/(6*a*(c*d^2 + a*e^2)^4*(d + e*x)) - (5*c^2*d*e^2*(4*c*d^2 - 3*a*e^2)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(2*(c*d^2 + a*e^2)^(9/2))]

    @test_int [(d + e*x)^5/(a + c*x^2)^(5/2), x, 5, -(((a*e - c*d*x)*(d + e*x)^4)/(3*a*c*(a + c*x^2)^(3/2))) - (2*(d + e*x)^2*(2*a^2*e^3 - c*d*(c*d^2 + 3*a*e^2)*x))/(3*a^2*c^2*sqrt(a + c*x^2)) - (e*(4*(c^2*d^4 + 4*a*c*d^2*e^2 - 2*a^2*e^4) + c*d*e*(2*c*d^2 + 7*a*e^2)*x)*sqrt(a + c*x^2))/(3*a^2*c^3) + (5*d*e^4*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/c^(5/2)]
    @test_int [(d + e*x)^4/(a + c*x^2)^(5/2), x, 5, -(((a*e - c*d*x)*(d + e*x)^3)/(3*a*c*(a + c*x^2)^(3/2))) - ((d + e*x)*(a*e*(c*d^2 + 3*a*e^2) - 2*c*d*(c*d^2 + 2*a*e^2)*x))/(3*a^2*c^2*sqrt(a + c*x^2)) - (d*e*(2*c*d^2 + 5*a*e^2)*sqrt(a + c*x^2))/(3*a^2*c^2) + (e^4*atanh((sqrt(c)*x)/sqrt(a + c*x^2)))/c^(5/2)]
    @test_int [(d + e*x)^3/(a + c*x^2)^(5/2), x, 2, -((a*e - c*d*x)*(d + e*x)^2)/(3*a*c*(a + c*x^2)^(3/2)) - (2*(c*d^2 + a*e^2)*(a*e - c*d*x))/(3*a^2*c^2*sqrt(a + c*x^2))]
    @test_int [(d + e*x)^2/(a + c*x^2)^(5/2), x, 2, (x*(d + e*x)^2)/(3*a*(a + c*x^2)^(3/2)) - (2*d*(a*e - c*d*x))/(3*a^2*c*sqrt(a + c*x^2))]
    @test_int [(d + e*x)^1/(a + c*x^2)^(5/2), x, 2, -(a*e - c*d*x)/(3*a*c*(a + c*x^2)^(3/2)) + (2*d*x)/(3*a^2*sqrt(a + c*x^2))]
    @test_int [1/((d + e*x)^1*(a + c*x^2)^(5/2)), x, 5, (a*e + c*d*x)/(3*a*(c*d^2 + a*e^2)*(a + c*x^2)^(3/2)) + (3*a^2*e^3 + c*d*(2*c*d^2 + 5*a*e^2)*x)/(3*a^2*(c*d^2 + a*e^2)^2*sqrt(a + c*x^2)) - (e^4*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(c*d^2 + a*e^2)^(5/2)]
    @test_int [1/((d + e*x)^2*(a + c*x^2)^(5/2)), x, 5, (a*e + c*d*x)/(3*a*(c*d^2 + a*e^2)*(d + e*x)*(a + c*x^2)^(3/2)) - (a*e*(c*d^2 - 4*a*e^2) - c*d*(2*c*d^2 + 7*a*e^2)*x)/(3*a^2*(c*d^2 + a*e^2)^2*(d + e*x)*sqrt(a + c*x^2)) + (e*(2*c^2*d^4 + 9*a*c*d^2*e^2 - 8*a^2*e^4)*sqrt(a + c*x^2))/(3*a^2*(c*d^2 + a*e^2)^3*(d + e*x)) - (5*c*d*e^4*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(c*d^2 + a*e^2)^(7/2)]
    @test_int [1/((d + e*x)^3*(a + c*x^2)^(5/2)), x, 6, (a*e + c*d*x)/(3*a*(c*d^2 + a*e^2)*(d + e*x)^2*(a + c*x^2)^(3/2)) - (a*e*(2*c*d^2 - 5*a*e^2) - c*d*(2*c*d^2 + 9*a*e^2)*x)/(3*a^2*(c*d^2 + a*e^2)^2*(d + e*x)^2*sqrt(a + c*x^2)) + (e*(4*c^2*d^4 + 24*a*c*d^2*e^2 - 15*a^2*e^4)*sqrt(a + c*x^2))/(6*a^2*(c*d^2 + a*e^2)^3*(d + e*x)^2) + (c*d*e*(4*c^2*d^4 + 28*a*c*d^2*e^2 - 81*a^2*e^4)*sqrt(a + c*x^2))/(6*a^2*(c*d^2 + a*e^2)^4*(d + e*x)) - (5*c*e^4*(6*c*d^2 - a*e^2)*atanh((a*e - c*d*x)/(sqrt(c*d^2 + a*e^2)*sqrt(a + c*x^2))))/(2*(c*d^2 + a*e^2)^(9/2))]

    @test_int [(3 + x)/sqrt(1 - x^2), x, 2, -sqrt(1 - x^2) + 3*asin(x)]
    @test_int [(1 + x)/sqrt(4 - x^2), x, 2, -sqrt(4 - x^2) + asin(x/2)]
    @test_int [(2 + x)/sqrt(9 + x^2), x, 2, sqrt(9 + x^2) + 2*asinh(x/3)]

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

    @test_int [(2 + 3*x)/(4 + x^2)^(3/2), x, 1, -((6 - x)/(2*sqrt(4 + x^2)))]

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

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

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

    @test_int [(d + e*x)^(5/2)*(a + c*x^2)^2, x, 2, (2*(c*d^2 + a*e^2)^2*(d + e*x)^(7/2))/(7*e^5) - (8*c*d*(c*d^2 + a*e^2)*(d + e*x)^(9/2))/(9*e^5) + (4*c*(3*c*d^2 + a*e^2)*(d + e*x)^(11/2))/(11*e^5) - (8*c^2*d*(d + e*x)^(13/2))/(13*e^5) + (2*c^2*(d + e*x)^(15/2))/(15*e^5)]
    @test_int [(d + e*x)^(3/2)*(a + c*x^2)^2, x, 2, (2*(c*d^2 + a*e^2)^2*(d + e*x)^(5/2))/(5*e^5) - (8*c*d*(c*d^2 + a*e^2)*(d + e*x)^(7/2))/(7*e^5) + (4*c*(3*c*d^2 + a*e^2)*(d + e*x)^(9/2))/(9*e^5) - (8*c^2*d*(d + e*x)^(11/2))/(11*e^5) + (2*c^2*(d + e*x)^(13/2))/(13*e^5)]
    @test_int [sqrt(d + e*x)*(a + c*x^2)^2, x, 2, (2*(c*d^2 + a*e^2)^2*(d + e*x)^(3/2))/(3*e^5) - (8*c*d*(c*d^2 + a*e^2)*(d + e*x)^(5/2))/(5*e^5) + (4*c*(3*c*d^2 + a*e^2)*(d + e*x)^(7/2))/(7*e^5) - (8*c^2*d*(d + e*x)^(9/2))/(9*e^5) + (2*c^2*(d + e*x)^(11/2))/(11*e^5)]
    @test_int [(a + c*x^2)^2/sqrt(d + e*x), x, 2, (2*(c*d^2 + a*e^2)^2*sqrt(d + e*x))/e^5 - (8*c*d*(c*d^2 + a*e^2)*(d + e*x)^(3/2))/(3*e^5) + (4*c*(3*c*d^2 + a*e^2)*(d + e*x)^(5/2))/(5*e^5) - (8*c^2*d*(d + e*x)^(7/2))/(7*e^5) + (2*c^2*(d + e*x)^(9/2))/(9*e^5)]
    @test_int [(a + c*x^2)^2/(d + e*x)^(3/2), x, 2, (-2*(c*d^2 + a*e^2)^2)/(e^5*sqrt(d + e*x)) - (8*c*d*(c*d^2 + a*e^2)*sqrt(d + e*x))/e^5 + (4*c*(3*c*d^2 + a*e^2)*(d + e*x)^(3/2))/(3*e^5) - (8*c^2*d*(d + e*x)^(5/2))/(5*e^5) + (2*c^2*(d + e*x)^(7/2))/(7*e^5)]
    @test_int [(a + c*x^2)^2/(d + e*x)^(5/2), x, 2, (-2*(c*d^2 + a*e^2)^2)/(3*e^5*(d + e*x)^(3/2)) + (8*c*d*(c*d^2 + a*e^2))/(e^5*sqrt(d + e*x)) + (4*c*(3*c*d^2 + a*e^2)*sqrt(d + e*x))/e^5 - (8*c^2*d*(d + e*x)^(3/2))/(3*e^5) + (2*c^2*(d + e*x)^(5/2))/(5*e^5)]
    @test_int [(a + c*x^2)^2/(d + e*x)^(7/2), x, 2, (-2*(c*d^2 + a*e^2)^2)/(5*e^5*(d + e*x)^(5/2)) + (8*c*d*(c*d^2 + a*e^2))/(3*e^5*(d + e*x)^(3/2)) - (4*c*(3*c*d^2 + a*e^2))/(e^5*sqrt(d + e*x)) - (8*c^2*d*sqrt(d + e*x))/e^5 + (2*c^2*(d + e*x)^(3/2))/(3*e^5)]

    @test_int [(d + e*x)^(5/2)*(a + c*x^2)^3, x, 2, (2*(c*d^2 + a*e^2)^3*(d + e*x)^(7/2))/(7*e^7) - (4*c*d*(c*d^2 + a*e^2)^2*(d + e*x)^(9/2))/(3*e^7) + (6*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*(d + e*x)^(11/2))/(11*e^7) - (8*c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^(13/2))/(13*e^7) + (2*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^(15/2))/(5*e^7) - (12*c^3*d*(d + e*x)^(17/2))/(17*e^7) + (2*c^3*(d + e*x)^(19/2))/(19*e^7)]
    @test_int [(d + e*x)^(3/2)*(a + c*x^2)^3, x, 2, (2*(c*d^2 + a*e^2)^3*(d + e*x)^(5/2))/(5*e^7) - (12*c*d*(c*d^2 + a*e^2)^2*(d + e*x)^(7/2))/(7*e^7) + (2*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*(d + e*x)^(9/2))/(3*e^7) - (8*c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^(11/2))/(11*e^7) + (6*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^(13/2))/(13*e^7) - (4*c^3*d*(d + e*x)^(15/2))/(5*e^7) + (2*c^3*(d + e*x)^(17/2))/(17*e^7)]
    @test_int [sqrt(d + e*x)*(a + c*x^2)^3, x, 2, (2*(c*d^2 + a*e^2)^3*(d + e*x)^(3/2))/(3*e^7) - (12*c*d*(c*d^2 + a*e^2)^2*(d + e*x)^(5/2))/(5*e^7) + (6*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*(d + e*x)^(7/2))/(7*e^7) - (8*c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^(9/2))/(9*e^7) + (6*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^(11/2))/(11*e^7) - (12*c^3*d*(d + e*x)^(13/2))/(13*e^7) + (2*c^3*(d + e*x)^(15/2))/(15*e^7)]
    @test_int [(a + c*x^2)^3/sqrt(d + e*x), x, 2, (2*(c*d^2 + a*e^2)^3*sqrt(d + e*x))/e^7 - (4*c*d*(c*d^2 + a*e^2)^2*(d + e*x)^(3/2))/e^7 + (6*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*(d + e*x)^(5/2))/(5*e^7) - (8*c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^(7/2))/(7*e^7) + (2*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^(9/2))/(3*e^7) - (12*c^3*d*(d + e*x)^(11/2))/(11*e^7) + (2*c^3*(d + e*x)^(13/2))/(13*e^7)]
    @test_int [(a + c*x^2)^3/(d + e*x)^(3/2), x, 2, -((2*(c*d^2 + a*e^2)^3)/(e^7*sqrt(d + e*x))) - (12*c*d*(c*d^2 + a*e^2)^2*sqrt(d + e*x))/e^7 + (2*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*(d + e*x)^(3/2))/e^7 - (8*c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^(5/2))/(5*e^7) + (6*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^(7/2))/(7*e^7) - (4*c^3*d*(d + e*x)^(9/2))/(3*e^7) + (2*c^3*(d + e*x)^(11/2))/(11*e^7)]
    @test_int [(a + c*x^2)^3/(d + e*x)^(5/2), x, 2, -((2*(c*d^2 + a*e^2)^3)/(3*e^7*(d + e*x)^(3/2))) + (12*c*d*(c*d^2 + a*e^2)^2)/(e^7*sqrt(d + e*x)) + (6*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2)*sqrt(d + e*x))/e^7 - (8*c^2*d*(5*c*d^2 + 3*a*e^2)*(d + e*x)^(3/2))/(3*e^7) + (6*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^(5/2))/(5*e^7) - (12*c^3*d*(d + e*x)^(7/2))/(7*e^7) + (2*c^3*(d + e*x)^(9/2))/(9*e^7)]
    @test_int [(a + c*x^2)^3/(d + e*x)^(7/2), x, 2, -((2*(c*d^2 + a*e^2)^3)/(5*e^7*(d + e*x)^(5/2))) + (4*c*d*(c*d^2 + a*e^2)^2)/(e^7*(d + e*x)^(3/2)) - (6*c*(c*d^2 + a*e^2)*(5*c*d^2 + a*e^2))/(e^7*sqrt(d + e*x)) - (8*c^2*d*(5*c*d^2 + 3*a*e^2)*sqrt(d + e*x))/e^7 + (2*c^2*(5*c*d^2 + a*e^2)*(d + e*x)^(3/2))/e^7 - (12*c^3*d*(d + e*x)^(5/2))/(5*e^7) + (2*c^3*(d + e*x)^(7/2))/(7*e^7)]

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

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

    @test_int [(d + e*x)^(5/2)/(a + c*x^2), x, 12, (4*d*e*sqrt(d + e*x))/c + (2*e*(d + e*x)^(3/2))/(3*c) - (e*(2*c^(3/2)*d^3 + 2*a*sqrt(c)*d*e^2 - (3*c*d^2 - a*e^2)*sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(sqrt(2)*c^(7/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) + (e*(2*c^(3/2)*d^3 + 2*a*sqrt(c)*d*e^2 - (3*c*d^2 - a*e^2)*sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(sqrt(2)*c^(7/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) + (e*(2*c^(3/2)*d^3 + 2*a*sqrt(c)*d*e^2 + (3*c*d^2 - a*e^2)*sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(2*sqrt(2)*c^(7/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) - (e*(2*c^(3/2)*d^3 + 2*a*sqrt(c)*d*e^2 + (3*c*d^2 - a*e^2)*sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(2*sqrt(2)*c^(7/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]
    @test_int [(d + e*x)^(3/2)/(a + c*x^2), x, 11, (2*e*sqrt(d + e*x))/c - (e*(c*d^2 + a*e^2 - 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(sqrt(2)*c^(5/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) + (e*(c*d^2 + a*e^2 - 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(sqrt(2)*c^(5/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) + (e*(c*d^2 + a*e^2 + 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(2*sqrt(2)*c^(5/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) - (e*(c*d^2 + a*e^2 + 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(2*sqrt(2)*c^(5/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]
    @test_int [sqrt(d + e*x)/(a + c*x^2), x, 10, (e*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(sqrt(2)*c^(3/4)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (e*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(sqrt(2)*c^(3/4)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) + (e*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(2*sqrt(2)*c^(3/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) - (e*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(2*sqrt(2)*c^(3/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]
    @test_int [1/(sqrt(d + e*x)*(a + c*x^2)), x, 10, (e*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(sqrt(2)*c^(1/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (e*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(sqrt(2)*c^(1/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (e*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(2*sqrt(2)*c^(1/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) + (e*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(2*sqrt(2)*c^(1/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]
    @test_int [1/((d + e*x)^(3/2)*(a + c*x^2)), x, 11, (-2*e)/((c*d^2 + a*e^2)*sqrt(d + e*x)) + (c^(1/4)*e*(2*sqrt(c)*d - sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(sqrt(2)*(c*d^2 + a*e^2)^(3/2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (c^(1/4)*e*(2*sqrt(c)*d - sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(sqrt(2)*(c*d^2 + a*e^2)^(3/2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (c^(1/4)*e*(2*sqrt(c)*d + sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(2*sqrt(2)*(c*d^2 + a*e^2)^(3/2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) + (c^(1/4)*e*(2*sqrt(c)*d + sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(2*sqrt(2)*(c*d^2 + a*e^2)^(3/2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]
    @test_int [1/((d + e*x)^(5/2)*(a + c*x^2)), x, 12, (-2*e)/(3*(c*d^2 + a*e^2)*(d + e*x)^(3/2)) - (4*c*d*e)/((c*d^2 + a*e^2)^2*sqrt(d + e*x)) + (c^(3/4)*e*(3*c*d^2 - a*e^2 - 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(sqrt(2)*(c*d^2 + a*e^2)^(5/2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (c^(3/4)*e*(3*c*d^2 - a*e^2 - 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(sqrt(2)*(c*d^2 + a*e^2)^(5/2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (c^(3/4)*e*(3*c*d^2 - a*e^2 + 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(2*sqrt(2)*(c*d^2 + a*e^2)^(5/2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) + (c^(3/4)*e*(3*c*d^2 - a*e^2 + 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(2*sqrt(2)*(c*d^2 + a*e^2)^(5/2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]

    @test_int [(d + e*x)^(7/2)/(a - c*x^2)^2, x, 7, (e*(c*d^2 + 5*a*e^2)*sqrt(d + e*x))/(2*a*c^2) + (d*e*(d + e*x)^(3/2))/(2*a*c) + ((a*e + c*d*x)*(d + e*x)^(5/2))/(2*a*c*(a - c*x^2)) - ((sqrt(c)*d - sqrt(a)*e)^(5/2)*(2*sqrt(c)*d + 5*sqrt(a)*e)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(a)*e)))/(4*a^(3/2)*c^(9/4)) + ((2*sqrt(c)*d - 5*sqrt(a)*e)*(sqrt(c)*d + sqrt(a)*e)^(5/2)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d + sqrt(a)*e)))/(4*a^(3/2)*c^(9/4))]
    @test_int [(d + e*x)^(5/2)/(a - c*x^2)^2, x, 6, (d*e*sqrt(d + e*x))/(2*a*c) + ((a*e + c*d*x)*(d + e*x)^(3/2))/(2*a*c*(a - c*x^2)) - ((sqrt(c)*d - sqrt(a)*e)^(3/2)*(2*sqrt(c)*d + 3*sqrt(a)*e)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(a)*e)))/(4*a^(3/2)*c^(7/4)) + ((2*sqrt(c)*d - 3*sqrt(a)*e)*(sqrt(c)*d + sqrt(a)*e)^(3/2)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d + sqrt(a)*e)))/(4*a^(3/2)*c^(7/4))]
    @test_int [(d + e*x)^(3/2)/(a - c*x^2)^2, x, 5, ((a*e + c*d*x)*sqrt(d + e*x))/(2*a*c*(a - c*x^2)) - (sqrt(sqrt(c)*d - sqrt(a)*e)*(2*sqrt(c)*d + sqrt(a)*e)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(a)*e)))/(4*a^(3/2)*c^(5/4)) + ((2*sqrt(c)*d - sqrt(a)*e)*sqrt(sqrt(c)*d + sqrt(a)*e)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d + sqrt(a)*e)))/(4*a^(3/2)*c^(5/4))]
    @test_int [sqrt(d + e*x)/(a - c*x^2)^2, x, 5, (x*sqrt(d + e*x))/(2*a*(a - c*x^2)) - (((2*sqrt(c)*d)/sqrt(a) - e)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(a)*e)))/(4*a*c^(3/4)*sqrt(sqrt(c)*d - sqrt(a)*e)) + (((2*sqrt(c)*d)/sqrt(a) + e)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d + sqrt(a)*e)))/(4*a*c^(3/4)*sqrt(sqrt(c)*d + sqrt(a)*e))]
    @test_int [1/(sqrt(d + e*x)*(a - c*x^2)^2), x, 5, -((a*e - c*d*x)*sqrt(d + e*x))/(2*a*(c*d^2 - a*e^2)*(a - c*x^2)) - ((2*sqrt(c)*d - 3*sqrt(a)*e)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(a)*e)))/(4*a^(3/2)*c^(1/4)*(sqrt(c)*d - sqrt(a)*e)^(3/2)) + ((2*sqrt(c)*d + 3*sqrt(a)*e)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d + sqrt(a)*e)))/(4*a^(3/2)*c^(1/4)*(sqrt(c)*d + sqrt(a)*e)^(3/2))]
    @test_int [1/((d + e*x)^(3/2)*(a - c*x^2)^2), x, 6, -(e*(c*d^2 + 5*a*e^2))/(2*a*(c*d^2 - a*e^2)^2*sqrt(d + e*x)) - (a*e - c*d*x)/(2*a*(c*d^2 - a*e^2)*sqrt(d + e*x)*(a - c*x^2)) - (c^(1/4)*(2*sqrt(c)*d - 5*sqrt(a)*e)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(a)*e)))/(4*a^(3/2)*(sqrt(c)*d - sqrt(a)*e)^(5/2)) + (c^(1/4)*(2*sqrt(c)*d + 5*sqrt(a)*e)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d + sqrt(a)*e)))/(4*a^(3/2)*(sqrt(c)*d + sqrt(a)*e)^(5/2))]
    @test_int [1/((d + e*x)^(5/2)*(a - c*x^2)^2), x, 7, -(e*(3*c*d^2 + 7*a*e^2))/(6*a*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2)) - (c*d*e*(c*d^2 + 19*a*e^2))/(2*a*(c*d^2 - a*e^2)^3*sqrt(d + e*x)) - (a*e - c*d*x)/(2*a*(c*d^2 - a*e^2)*(d + e*x)^(3/2)*(a - c*x^2)) - (c^(3/4)*(2*sqrt(c)*d - 7*sqrt(a)*e)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(a)*e)))/(4*a^(3/2)*(sqrt(c)*d - sqrt(a)*e)^(7/2)) + (c^(3/4)*(2*sqrt(c)*d + 7*sqrt(a)*e)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d + sqrt(a)*e)))/(4*a^(3/2)*(sqrt(c)*d + sqrt(a)*e)^(7/2))]

    @test_int [(d + e*x)^(7/2)/(a + c*x^2)^2, x, 13, -(e*(c*d^2 - 5*a*e^2)*sqrt(d + e*x))/(2*a*c^2) - (d*e*(d + e*x)^(3/2))/(2*a*c) - ((a*e - c*d*x)*(d + e*x)^(5/2))/(2*a*c*(a + c*x^2)) + (e*(c^2*d^4 - 4*a*c*d^2*e^2 - 5*a^2*e^4 + sqrt(c)*d*sqrt(c*d^2 + a*e^2)*(c*d^2 + 13*a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(4*sqrt(2)*a*c^(9/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (e*(c^2*d^4 - 4*a*c*d^2*e^2 - 5*a^2*e^4 + sqrt(c)*d*sqrt(c*d^2 + a*e^2)*(c*d^2 + 13*a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(4*sqrt(2)*a*c^(9/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (e*(c^2*d^4 - 4*a*c*d^2*e^2 - 5*a^2*e^4 - sqrt(c)*d*sqrt(c*d^2 + a*e^2)*(c*d^2 + 13*a*e^2))*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(8*sqrt(2)*a*c^(9/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) + (e*(c^2*d^4 - 4*a*c*d^2*e^2 - 5*a^2*e^4 - sqrt(c)*d*sqrt(c*d^2 + a*e^2)*(c*d^2 + 13*a*e^2))*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(8*sqrt(2)*a*c^(9/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]
    @test_int [(d + e*x)^(5/2)/(a + c*x^2)^2, x, 12, -(d*e*sqrt(d + e*x))/(2*a*c) - ((a*e - c*d*x)*(d + e*x)^(3/2))/(2*a*c*(a + c*x^2)) + (e*(c^(3/2)*d^3 + a*sqrt(c)*d*e^2 + sqrt(c*d^2 + a*e^2)*(c*d^2 + 3*a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(4*sqrt(2)*a*c^(7/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (e*(c^(3/2)*d^3 + a*sqrt(c)*d*e^2 + sqrt(c*d^2 + a*e^2)*(c*d^2 + 3*a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(4*sqrt(2)*a*c^(7/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (e*(c^(3/2)*d^3 + a*sqrt(c)*d*e^2 - sqrt(c*d^2 + a*e^2)*(c*d^2 + 3*a*e^2))*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(8*sqrt(2)*a*c^(7/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) + (e*(c^(3/2)*d^3 + a*sqrt(c)*d*e^2 - sqrt(c*d^2 + a*e^2)*(c*d^2 + 3*a*e^2))*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(8*sqrt(2)*a*c^(7/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]
    @test_int [(d + e*x)^(3/2)/(a + c*x^2)^2, x, 11, -((a*e - c*d*x)*sqrt(d + e*x))/(2*a*c*(a + c*x^2)) + (e*(c*d^2 + a*e^2 + sqrt(c)*d*sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(4*sqrt(2)*a*c^(5/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (e*(c*d^2 + a*e^2 + sqrt(c)*d*sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(4*sqrt(2)*a*c^(5/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (e*(c*d^2 + a*e^2 - sqrt(c)*d*sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(8*sqrt(2)*a*c^(5/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) + (e*(c*d^2 + a*e^2 - sqrt(c)*d*sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(8*sqrt(2)*a*c^(5/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]
    @test_int [sqrt(d + e*x)/(a + c*x^2)^2, x, 11, (x*sqrt(d + e*x))/(2*a*(a + c*x^2)) + (e*(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(4*sqrt(2)*a*c^(3/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (e*(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(4*sqrt(2)*a*c^(3/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (e*(d - sqrt(c*d^2 + a*e^2)/sqrt(c))*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(8*sqrt(2)*a*c^(1/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) + (e*(d - sqrt(c*d^2 + a*e^2)/sqrt(c))*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(8*sqrt(2)*a*c^(1/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]
    @test_int [1/(sqrt(d + e*x)*(a + c*x^2)^2), x, 11, ((a*e + c*d*x)*sqrt(d + e*x))/(2*a*(c*d^2 + a*e^2)*(a + c*x^2)) + (e*(c*d^2 + 3*a*e^2 + sqrt(c)*d*sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(4*sqrt(2)*a*c^(1/4)*(c*d^2 + a*e^2)^(3/2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (e*(c*d^2 + 3*a*e^2 + sqrt(c)*d*sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(4*sqrt(2)*a*c^(1/4)*(c*d^2 + a*e^2)^(3/2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (e*(c*d^2 + 3*a*e^2 - sqrt(c)*d*sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(8*sqrt(2)*a*c^(1/4)*(c*d^2 + a*e^2)^(3/2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) + (e*(c*d^2 + 3*a*e^2 - sqrt(c)*d*sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(8*sqrt(2)*a*c^(1/4)*(c*d^2 + a*e^2)^(3/2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]
    @test_int [1/((d + e*x)^(3/2)*(a + c*x^2)^2), x, 12, (e*(c*d^2 - 5*a*e^2))/(2*a*(c*d^2 + a*e^2)^2*sqrt(d + e*x)) + (a*e + c*d*x)/(2*a*(c*d^2 + a*e^2)*sqrt(d + e*x)*(a + c*x^2)) + (c^(1/4)*e*(c^(3/2)*d^3 + 13*a*sqrt(c)*d*e^2 + (c*d^2 - 5*a*e^2)*sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(4*sqrt(2)*a*(c*d^2 + a*e^2)^(5/2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (c^(1/4)*e*(c^(3/2)*d^3 + 13*a*sqrt(c)*d*e^2 + (c*d^2 - 5*a*e^2)*sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(4*sqrt(2)*a*(c*d^2 + a*e^2)^(5/2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (c^(1/4)*e*(c^(3/2)*d^3 + 13*a*sqrt(c)*d*e^2 - (c*d^2 - 5*a*e^2)*sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(8*sqrt(2)*a*(c*d^2 + a*e^2)^(5/2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) + (c^(1/4)*e*(c^(3/2)*d^3 + 13*a*sqrt(c)*d*e^2 - (c*d^2 - 5*a*e^2)*sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(8*sqrt(2)*a*(c*d^2 + a*e^2)^(5/2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]
    @test_int [1/((d + e*x)^(5/2)*(a + c*x^2)^2), x, 13, (e*(3*c*d^2 - 7*a*e^2))/(6*a*(c*d^2 + a*e^2)^2*(d + e*x)^(3/2)) + (c*d*e*(c*d^2 - 19*a*e^2))/(2*a*(c*d^2 + a*e^2)^3*sqrt(d + e*x)) + (a*e + c*d*x)/(2*a*(c*d^2 + a*e^2)*(d + e*x)^(3/2)*(a + c*x^2)) + (c^(3/4)*e*(c^2*d^4 + 34*a*c*d^2*e^2 - 7*a^2*e^4 + sqrt(c)*d*(c*d^2 - 19*a*e^2)*sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(4*sqrt(2)*a*(c*d^2 + a*e^2)^(7/2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (c^(3/4)*e*(c^2*d^4 + 34*a*c*d^2*e^2 - 7*a^2*e^4 + sqrt(c)*d*(c*d^2 - 19*a*e^2)*sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(4*sqrt(2)*a*(c*d^2 + a*e^2)^(7/2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (c^(3/4)*e*(c^2*d^4 + 34*a*c*d^2*e^2 - 7*a^2*e^4 - sqrt(c)*d*(c*d^2 - 19*a*e^2)*sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(8*sqrt(2)*a*(c*d^2 + a*e^2)^(7/2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) + (c^(3/4)*e*(c^2*d^4 + 34*a*c*d^2*e^2 - 7*a^2*e^4 - sqrt(c)*d*(c*d^2 - 19*a*e^2)*sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(8*sqrt(2)*a*(c*d^2 + a*e^2)^(7/2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]

    @test_int [(d + e*x)^(7/2)/(a - c*x^2)^3, x, 6, ((a*e + c*d*x)*(d + e*x)^(5/2))/(4*a*c*(a - c*x^2)^2) + (sqrt(d + e*x)*(a*e*(7*c*d^2 - 5*a*e^2) + 2*c*d*(3*c*d^2 - 2*a*e^2)*x))/(16*a^2*c^2*(a - c*x^2)) - ((sqrt(c)*d - sqrt(a)*e)^(3/2)*(12*c*d^2 + 18*sqrt(a)*sqrt(c)*d*e + 5*a*e^2)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(a)*e)))/(32*a^(5/2)*c^(9/4)) + ((sqrt(c)*d + sqrt(a)*e)^(3/2)*(12*c*d^2 - 18*sqrt(a)*sqrt(c)*d*e + 5*a*e^2)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d + sqrt(a)*e)))/(32*a^(5/2)*c^(9/4))]
    @test_int [(d + e*x)^(5/2)/(a - c*x^2)^3, x, 6, ((a*e + c*d*x)*(d + e*x)^(3/2))/(4*a*c*(a - c*x^2)^2) + (3*sqrt(d + e*x)*(a*d*e + (2*c*d^2 - a*e^2)*x))/(16*a^2*c*(a - c*x^2)) - (3*sqrt(sqrt(c)*d - sqrt(a)*e)*(4*c*d^2 + 2*sqrt(a)*sqrt(c)*d*e - a*e^2)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(a)*e)))/(32*a^(5/2)*c^(7/4)) + (3*sqrt(sqrt(c)*d + sqrt(a)*e)*(4*c*d^2 - 2*sqrt(a)*sqrt(c)*d*e - a*e^2)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d + sqrt(a)*e)))/(32*a^(5/2)*c^(7/4))]
    @test_int [(d + e*x)^(3/2)/(a - c*x^2)^3, x, 6, ((a*e + c*d*x)*sqrt(d + e*x))/(4*a*c*(a - c*x^2)^2) - ((a*e - 6*c*d*x)*sqrt(d + e*x))/(16*a^2*c*(a - c*x^2)) - (3*(4*c*d^2 - 2*sqrt(a)*sqrt(c)*d*e - a*e^2)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(a)*e)))/(32*a^(5/2)*c^(5/4)*sqrt(sqrt(c)*d - sqrt(a)*e)) + (3*(4*c*d^2 + 2*sqrt(a)*sqrt(c)*d*e - a*e^2)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d + sqrt(a)*e)))/(32*a^(5/2)*c^(5/4)*sqrt(sqrt(c)*d + sqrt(a)*e))]
    @test_int [sqrt(d + e*x)/(a - c*x^2)^3, x, 6, (x*sqrt(d + e*x))/(4*a*(a - c*x^2)^2) - (sqrt(d + e*x)*(a*d*e - (6*c*d^2 - 5*a*e^2)*x))/(16*a^2*(c*d^2 - a*e^2)*(a - c*x^2)) - ((12*c*d^2 - 18*sqrt(a)*sqrt(c)*d*e + 5*a*e^2)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(a)*e)))/(32*a^(5/2)*c^(3/4)*(sqrt(c)*d - sqrt(a)*e)^(3/2)) + ((12*c*d^2 + 18*sqrt(a)*sqrt(c)*d*e + 5*a*e^2)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d + sqrt(a)*e)))/(32*a^(5/2)*c^(3/4)*(sqrt(c)*d + sqrt(a)*e)^(3/2))]
    @test_int [1/(sqrt(d + e*x)*(a - c*x^2)^3), x, 6, -((a*e - c*d*x)*sqrt(d + e*x))/(4*a*(c*d^2 - a*e^2)*(a - c*x^2)^2) - (sqrt(d + e*x)*(a*e*(c*d^2 - 7*a*e^2) - 6*c*d*(c*d^2 - 2*a*e^2)*x))/(16*a^2*(c*d^2 - a*e^2)^2*(a - c*x^2)) - (3*(4*c*d^2 - 10*sqrt(a)*sqrt(c)*d*e + 7*a*e^2)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(a)*e)))/(32*a^(5/2)*c^(1/4)*(sqrt(c)*d - sqrt(a)*e)^(5/2)) + (3*(4*c*d^2 + 10*sqrt(a)*sqrt(c)*d*e + 7*a*e^2)*atanh((c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d + sqrt(a)*e)))/(32*a^(5/2)*c^(1/4)*(sqrt(c)*d + sqrt(a)*e)^(5/2))]

    @test_int [(d + e*x)^(7/2)/(a + c*x^2)^3, x, 12, -((a*e - c*d*x)*(d + e*x)^(5/2))/(4*a*c*(a + c*x^2)^2) - (sqrt(d + e*x)*(a*e*(7*c*d^2 + 5*a*e^2) - 2*c*d*(3*c*d^2 + 2*a*e^2)*x))/(16*a^2*c^2*(a + c*x^2)) + (e*(6*c^2*d^4 + 11*a*c*d^2*e^2 + 5*a^2*e^4 + sqrt(c)*d*sqrt(c*d^2 + a*e^2)*(6*c*d^2 + 8*a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(32*sqrt(2)*a^2*c^(9/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (e*(6*c^2*d^4 + 11*a*c*d^2*e^2 + 5*a^2*e^4 + sqrt(c)*d*sqrt(c*d^2 + a*e^2)*(6*c*d^2 + 8*a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(32*sqrt(2)*a^2*c^(9/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (e*(6*c^2*d^4 + 11*a*c*d^2*e^2 + 5*a^2*e^4 - 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2)*(3*c*d^2 + 4*a*e^2))*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(64*sqrt(2)*a^2*c^(9/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) + (e*(6*c^2*d^4 + 11*a*c*d^2*e^2 + 5*a^2*e^4 - 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2)*(3*c*d^2 + 4*a*e^2))*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(64*sqrt(2)*a^2*c^(9/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]
    @test_int [(d + e*x)^(5/2)/(a + c*x^2)^3, x, 12, -((a*e - c*d*x)*(d + e*x)^(3/2))/(4*a*c*(a + c*x^2)^2) - (3*sqrt(d + e*x)*(a*d*e - (2*c*d^2 + a*e^2)*x))/(16*a^2*c*(a + c*x^2)) + (3*e*(2*c^(3/2)*d^3 + 2*a*sqrt(c)*d*e^2 + sqrt(c*d^2 + a*e^2)*(2*c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(32*sqrt(2)*a^2*c^(7/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (3*e*(2*c^(3/2)*d^3 + 2*a*sqrt(c)*d*e^2 + sqrt(c*d^2 + a*e^2)*(2*c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(32*sqrt(2)*a^2*c^(7/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (3*e*(2*c^(3/2)*d^3 + 2*a*sqrt(c)*d*e^2 - sqrt(c*d^2 + a*e^2)*(2*c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(64*sqrt(2)*a^2*c^(7/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) + (3*e*(2*c^(3/2)*d^3 + 2*a*sqrt(c)*d*e^2 - sqrt(c*d^2 + a*e^2)*(2*c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(64*sqrt(2)*a^2*c^(7/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]
    @test_int [(d + e*x)^(3/2)/(a + c*x^2)^3, x, 12, -((a*e - c*d*x)*sqrt(d + e*x))/(4*a*c*(a + c*x^2)^2) + ((a*e + 6*c*d*x)*sqrt(d + e*x))/(16*a^2*c*(a + c*x^2)) + (3*e*(2*c*d^2 + a*e^2 + 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(32*sqrt(2)*a^2*c^(5/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (3*e*(2*c*d^2 + a*e^2 + 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(32*sqrt(2)*a^2*c^(5/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (3*e*(2*c*d^2 + a*e^2 - 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(64*sqrt(2)*a^2*c^(5/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) + (3*e*(2*c*d^2 + a*e^2 - 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2))*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(64*sqrt(2)*a^2*c^(5/4)*sqrt(c*d^2 + a*e^2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]
    @test_int [sqrt(d + e*x)/(a + c*x^2)^3, x, 12, (x*sqrt(d + e*x))/(4*a*(a + c*x^2)^2) + (sqrt(d + e*x)*(a*d*e + (6*c*d^2 + 5*a*e^2)*x))/(16*a^2*(c*d^2 + a*e^2)*(a + c*x^2)) + (e*(6*c^(3/2)*d^3 + 8*a*sqrt(c)*d*e^2 + sqrt(c*d^2 + a*e^2)*(6*c*d^2 + 5*a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(32*sqrt(2)*a^2*c^(3/4)*(c*d^2 + a*e^2)^(3/2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (e*(6*c^(3/2)*d^3 + 8*a*sqrt(c)*d*e^2 + sqrt(c*d^2 + a*e^2)*(6*c*d^2 + 5*a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(32*sqrt(2)*a^2*c^(3/4)*(c*d^2 + a*e^2)^(3/2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (e*(6*c^(3/2)*d^3 + 8*a*sqrt(c)*d*e^2 - sqrt(c*d^2 + a*e^2)*(6*c*d^2 + 5*a*e^2))*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(64*sqrt(2)*a^2*c^(3/4)*(c*d^2 + a*e^2)^(3/2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) + (e*(6*c^(3/2)*d^3 + 8*a*sqrt(c)*d*e^2 - sqrt(c*d^2 + a*e^2)*(6*c*d^2 + 5*a*e^2))*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(64*sqrt(2)*a^2*c^(3/4)*(c*d^2 + a*e^2)^(3/2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]
    @test_int [1/(sqrt(d + e*x)*(a + c*x^2)^3), x, 12, ((a*e + c*d*x)*sqrt(d + e*x))/(4*a*(c*d^2 + a*e^2)*(a + c*x^2)^2) + (sqrt(d + e*x)*(a*e*(c*d^2 + 7*a*e^2) + 6*c*d*(c*d^2 + 2*a*e^2)*x))/(16*a^2*(c*d^2 + a*e^2)^2*(a + c*x^2)) + (3*e*(2*c^2*d^4 + 5*a*c*d^2*e^2 + 7*a^2*e^4 + 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2)*(c*d^2 + 2*a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) - sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(32*sqrt(2)*a^2*c^(1/4)*(c*d^2 + a*e^2)^(5/2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (3*e*(2*c^2*d^4 + 5*a*c*d^2*e^2 + 7*a^2*e^4 + 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2)*(c*d^2 + 2*a*e^2))*atanh((sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)) + sqrt(2)*c^(1/4)*sqrt(d + e*x))/sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))))/(32*sqrt(2)*a^2*c^(1/4)*(c*d^2 + a*e^2)^(5/2)*sqrt(sqrt(c)*d - sqrt(c*d^2 + a*e^2))) - (3*e*(2*c^2*d^4 + 5*a*c*d^2*e^2 + 7*a^2*e^4 - 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2)*(c*d^2 + 2*a*e^2))*log(sqrt(c*d^2 + a*e^2) - sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(64*sqrt(2)*a^2*c^(1/4)*(c*d^2 + a*e^2)^(5/2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))) + (3*e*(2*c^2*d^4 + 5*a*c*d^2*e^2 + 7*a^2*e^4 - 2*sqrt(c)*d*sqrt(c*d^2 + a*e^2)*(c*d^2 + 2*a*e^2))*log(sqrt(c*d^2 + a*e^2) + sqrt(2)*c^(1/4)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(64*sqrt(2)*a^2*c^(1/4)*(c*d^2 + a*e^2)^(5/2)*sqrt(sqrt(c)*d + sqrt(c*d^2 + a*e^2)))]

    @test_int [sqrt(2 + 3*x)/(1 + x^2), x, 10, -((3*atan((sqrt(2*(2 + sqrt(13))) - 2*sqrt(2 + 3*x))/sqrt(2*(-2 + sqrt(13)))))/sqrt(2*(-2 + sqrt(13)))) + (3*atan((sqrt(2*(2 + sqrt(13))) + 2*sqrt(2 + 3*x))/sqrt(2*(-2 + sqrt(13)))))/sqrt(2*(-2 + sqrt(13))) + (3*log(2 + sqrt(13) + 3*x - sqrt(2*(2 + sqrt(13)))*sqrt(2 + 3*x)))/(2*sqrt(2*(2 + sqrt(13)))) - (3*log(2 + sqrt(13) + 3*x + sqrt(2*(2 + sqrt(13)))*sqrt(2 + 3*x)))/(2*sqrt(2*(2 + sqrt(13))))]
    @test_int [sqrt(c + d*x)/(1 + x^2), x, 10, (d*atanh((sqrt(c + sqrt(c^2 + d^2)) - sqrt(2)*sqrt(c + d*x))/sqrt(c - sqrt(c^2 + d^2))))/(sqrt(2)*sqrt(c - sqrt(c^2 + d^2))) - (d*atanh((sqrt(c + sqrt(c^2 + d^2)) + sqrt(2)*sqrt(c + d*x))/sqrt(c - sqrt(c^2 + d^2))))/(sqrt(2)*sqrt(c - sqrt(c^2 + d^2))) + (d*log(c + sqrt(c^2 + d^2) + d*x - sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*sqrt(c + d*x)))/(2*sqrt(2)*sqrt(c + sqrt(c^2 + d^2))) - (d*log(c + sqrt(c^2 + d^2) + d*x + sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*sqrt(c + d*x)))/(2*sqrt(2)*sqrt(c + sqrt(c^2 + d^2)))]

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

    @test_int [sqrt(2 + 3*x)/(a + b*x^2), x, 10, (3*atanh((sqrt(2*sqrt(b) + sqrt(9*a + 4*b)) - sqrt(2)*b^(1/4)*sqrt(2 + 3*x))/sqrt(2*sqrt(b) - sqrt(9*a + 4*b))))/(sqrt(2)*b^(3/4)*sqrt(2*sqrt(b) - sqrt(9*a + 4*b))) - (3*atanh((sqrt(2*sqrt(b) + sqrt(9*a + 4*b)) + sqrt(2)*b^(1/4)*sqrt(2 + 3*x))/sqrt(2*sqrt(b) - sqrt(9*a + 4*b))))/(sqrt(2)*b^(3/4)*sqrt(2*sqrt(b) - sqrt(9*a + 4*b))) + (3*log(sqrt(9*a + 4*b) - sqrt(2)*b^(1/4)*sqrt(2*sqrt(b) + sqrt(9*a + 4*b))*sqrt(2 + 3*x) + sqrt(b)*(2 + 3*x)))/(2*sqrt(2)*b^(3/4)*sqrt(2*sqrt(b) + sqrt(9*a + 4*b))) - (3*log(sqrt(9*a + 4*b) + sqrt(2)*b^(1/4)*sqrt(2*sqrt(b) + sqrt(9*a + 4*b))*sqrt(2 + 3*x) + sqrt(b)*(2 + 3*x)))/(2*sqrt(2)*b^(3/4)*sqrt(2*sqrt(b) + sqrt(9*a + 4*b)))]
    @test_int [sqrt(2 + 3*x)/(a - b*x^2), x, 4, -((sqrt(3*sqrt(a) - 2*sqrt(b))*atan((b^(1/4)*sqrt(2 + 3*x))/sqrt(3*sqrt(a) - 2*sqrt(b))))/(sqrt(a)*b^(3/4))) + (sqrt(3*sqrt(a) + 2*sqrt(b))*atanh((b^(1/4)*sqrt(2 + 3*x))/sqrt(3*sqrt(a) + 2*sqrt(b))))/(sqrt(a)*b^(3/4))]

    @test_int [sqrt(1 + x)/(1 + x^2), x, 10, (-sqrt((1/2)*(1 + sqrt(2))))*atan((sqrt(2*(1 + sqrt(2))) - 2*sqrt(1 + x))/sqrt(2*(-1 + sqrt(2)))) + sqrt((1/2)*(1 + sqrt(2)))*atan((sqrt(2*(1 + sqrt(2))) + 2*sqrt(1 + x))/sqrt(2*(-1 + sqrt(2)))) + log(1 + sqrt(2) + x - sqrt(2*(1 + sqrt(2)))*sqrt(1 + x))/(2*sqrt(2*(1 + sqrt(2)))) - log(1 + sqrt(2) + x + sqrt(2*(1 + sqrt(2)))*sqrt(1 + x))/(2*sqrt(2*(1 + sqrt(2))))]
    @test_int [1/(sqrt(1 + x)*(1 + x^2)), x, 10, (-(1/2))*sqrt(1 + sqrt(2))*atan((sqrt(2*(1 + sqrt(2))) - 2*sqrt(1 + x))/sqrt(2*(-1 + sqrt(2)))) + (1/2)*sqrt(1 + sqrt(2))*atan((sqrt(2*(1 + sqrt(2))) + 2*sqrt(1 + x))/sqrt(2*(-1 + sqrt(2)))) - log(1 + sqrt(2) + x - sqrt(2*(1 + sqrt(2)))*sqrt(1 + x))/(4*sqrt(1 + sqrt(2))) + log(1 + sqrt(2) + x + sqrt(2*(1 + sqrt(2)))*sqrt(1 + x))/(4*sqrt(1 + sqrt(2)))]

    @test_int [sqrt(-1 + x)/(1 + x^2)^3, x, 12, (sqrt(-1 + x)*x)/(4*(1 + x^2)^2) - ((1 - 11*x)*sqrt(-1 + x))/(32*(1 + x^2)) - (1/64)*sqrt((1/2)*(-527 + 373*sqrt(2)))*atan((sqrt(2*(-1 + sqrt(2))) - 2*sqrt(-1 + x))/sqrt(2*(1 + sqrt(2)))) + (1/64)*sqrt((1/2)*(-527 + 373*sqrt(2)))*atan((sqrt(2*(-1 + sqrt(2))) + 2*sqrt(-1 + x))/sqrt(2*(1 + sqrt(2)))) - (1/128)*sqrt((1/2)*(527 + 373*sqrt(2)))*log(1 - sqrt(2) - sqrt(2*(-1 + sqrt(2)))*sqrt(-1 + x) - x) + (1/128)*sqrt((1/2)*(527 + 373*sqrt(2)))*log(1 - sqrt(2) + sqrt(2*(-1 + sqrt(2)))*sqrt(-1 + x) - x)]

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

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

    @test_int [(d + e*x)^(3/2)*sqrt(a + c*x^2), x, 7, (2*sqrt(d + e*x)*(3*c*d^2 - 5*a*e^2 + 24*c*d*e*x)*sqrt(a + c*x^2))/(105*c*e) + (2*e*sqrt(d + e*x)*(a + c*x^2)^(3/2))/(7*c) + (4*sqrt(-a)*d*(3*c*d^2 - 29*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(105*sqrt(c)*e^2*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (4*sqrt(-a)*(3*c*d^2 - 5*a*e^2)*(c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(105*c^(3/2)*e^2*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [sqrt(d + e*x)*sqrt(a + c*x^2), x, 7, (-4*d*sqrt(d + e*x)*sqrt(a + c*x^2))/(15*e) + (2*(d + e*x)^(3/2)*sqrt(a + c*x^2))/(5*e) + (4*sqrt(-a)*(c*d^2 - 3*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(15*sqrt(c)*e^2*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (4*sqrt(-a)*d*(c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(15*sqrt(c)*e^2*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [sqrt(a + c*x^2)/sqrt(d + e*x), x, 6, (2*sqrt(d + e*x)*sqrt(a + c*x^2))/(3*e) + (4*sqrt(-a)*sqrt(c)*d*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*e^2*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (4*sqrt(-a)*(c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*sqrt(c)*e^2*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [sqrt(a + c*x^2)/(d + e*x)^(3/2), x, 6, -((2*sqrt(a + c*x^2))/(e*sqrt(d + e*x))) - (4*sqrt(-a)*sqrt(c)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), -((2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e))))/(e^2*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + (4*sqrt(-a)*sqrt(c)*d*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), -((2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e))))/(e^2*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [sqrt(a + c*x^2)/(d + e*x)^(5/2), x, 7, (-2*sqrt(a + c*x^2))/(3*e*(d + e*x)^(3/2)) + (4*c*d*sqrt(a + c*x^2))/(3*e*(c*d^2 + a*e^2)*sqrt(d + e*x)) + (4*sqrt(-a)*c^(3/2)*d*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*e^2*(c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (4*sqrt(-a)*sqrt(c)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*e^2*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [sqrt(a + c*x^2)/(d + e*x)^(7/2), x, 8, (-2*sqrt(a + c*x^2))/(5*e*(d + e*x)^(5/2)) + (4*c*d*sqrt(a + c*x^2))/(15*e*(c*d^2 + a*e^2)*(d + e*x)^(3/2)) + (4*c*(c*d^2 - 3*a*e^2)*sqrt(a + c*x^2))/(15*e*(c*d^2 + a*e^2)^2*sqrt(d + e*x)) + (4*sqrt(-a)*c^(3/2)*(c*d^2 - 3*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(15*e^2*(c*d^2 + a*e^2)^2*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (4*sqrt(-a)*c^(3/2)*d*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(15*e^2*(c*d^2 + a*e^2)*sqrt(d + e*x)*sqrt(a + c*x^2))]

    @test_int [(d + e*x)^(3/2)*(a + c*x^2)^(3/2), x, 8, (4*sqrt(d + e*x)*(4*c^2*d^4 + 21*a*c*d^2*e^2 - 15*a^2*e^4 - 3*c*d*e*(c*d^2 - 31*a*e^2)*x)*sqrt(a + c*x^2))/(1155*c*e^3) + (2*sqrt(d + e*x)*(c*d^2 - 3*a*e^2 + 28*c*d*e*x)*(a + c*x^2)^(3/2))/(231*c*e) + (2*e*sqrt(d + e*x)*(a + c*x^2)^(5/2))/(11*c) + (32*sqrt(-a)*d*(c*d^2 - 3*a*e^2)*(c*d^2 + 9*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(1155*sqrt(c)*e^4*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (8*sqrt(-a)*(c*d^2 + a*e^2)*(4*c^2*d^4 + 21*a*c*d^2*e^2 - 15*a^2*e^4)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(1155*c^(3/2)*e^4*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [sqrt(d + e*x)*(a + c*x^2)^(3/2), x, 8, (4*sqrt(d + e*x)*(4*d*(c*d^2 + 3*a*e^2) - 3*e*(c*d^2 - 7*a*e^2)*x)*sqrt(a + c*x^2))/(315*e^3) - (4*d*sqrt(d + e*x)*(a + c*x^2)^(3/2))/(21*e) + (2*(d + e*x)^(3/2)*(a + c*x^2)^(3/2))/(9*e) + (8*sqrt(-a)*(4*c^2*d^4 + 15*a*c*d^2*e^2 - 21*a^2*e^4)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(315*sqrt(c)*e^4*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (32*sqrt(-a)*d*(c*d^2 + a*e^2)*(c*d^2 + 3*a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(315*sqrt(c)*e^4*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(a + c*x^2)^(3/2)/sqrt(d + e*x), x, 7, (4*sqrt(d + e*x)*(4*c*d^2 + 5*a*e^2 - 3*c*d*e*x)*sqrt(a + c*x^2))/(35*e^3) + (2*sqrt(d + e*x)*(a + c*x^2)^(3/2))/(7*e) + (32*sqrt(-a)*sqrt(c)*d*(c*d^2 + 2*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(35*e^4*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (8*sqrt(-a)*(c*d^2 + a*e^2)*(4*c*d^2 + 5*a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(35*sqrt(c)*e^4*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(a + c*x^2)^(3/2)/(d + e*x)^(3/2), x, 7, (-4*c*(4*d - 3*e*x)*sqrt(d + e*x)*sqrt(a + c*x^2))/(5*e^3) - (2*(a + c*x^2)^(3/2))/(e*sqrt(d + e*x)) - (8*sqrt(-a)*sqrt(c)*(4*c*d^2 + 3*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(5*e^4*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + (32*sqrt(-a)*sqrt(c)*d*(c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(5*e^4*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(a + c*x^2)^(3/2)/(d + e*x)^(5/2), x, 7, (4*c*(4*d + e*x)*sqrt(a + c*x^2))/(3*e^3*sqrt(d + e*x)) - (2*(a + c*x^2)^(3/2))/(3*e*(d + e*x)^(3/2)) + (32*sqrt(-a)*c^(3/2)*d*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*e^4*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (8*sqrt(-a)*sqrt(c)*(4*c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*e^4*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(a + c*x^2)^(3/2)/(d + e*x)^(7/2), x, 7, -((4*c*(2*d*(2*c*d^2 + a*e^2) + e*(5*c*d^2 + 3*a*e^2)*x)*sqrt(a + c*x^2))/(5*e^3*(c*d^2 + a*e^2)*(d + e*x)^(3/2))) - (2*(a + c*x^2)^(3/2))/(5*e*(d + e*x)^(5/2)) - (8*sqrt(-a)*c^(3/2)*(4*c*d^2 + 3*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), -((2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e))))/(5*e^4*(c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + (32*sqrt(-a)*c^(3/2)*d*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), -((2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e))))/(5*e^4*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(a + c*x^2)^(3/2)/(d + e*x)^(9/2), x, 8, (32*c^2*d*(c*d^2 + 2*a*e^2)*sqrt(a + c*x^2))/(35*e^3*(c*d^2 + a*e^2)^2*sqrt(d + e*x)) - (4*c*(2*d*(2*c*d^2 + a*e^2) + e*(7*c*d^2 + 5*a*e^2)*x)*sqrt(a + c*x^2))/(35*e^3*(c*d^2 + a*e^2)*(d + e*x)^(5/2)) - (2*(a + c*x^2)^(3/2))/(7*e*(d + e*x)^(7/2)) + (32*sqrt(-a)*c^(5/2)*d*(c*d^2 + 2*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), -((2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e))))/(35*e^4*(c*d^2 + a*e^2)^2*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (8*sqrt(-a)*c^(3/2)*(4*c*d^2 + 5*a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), -((2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e))))/(35*e^4*(c*d^2 + a*e^2)*sqrt(d + e*x)*sqrt(a + c*x^2))]

    @test_int [sqrt(d + e*x)*(a + c*x^2)^(5/2), x, 9, (8*sqrt(d + e*x)*(d*(32*c^2*d^4 + 113*a*c*d^2*e^2 + 177*a^2*e^4) - 3*e*(8*c^2*d^4 + 27*a*c*d^2*e^2 - 77*a^2*e^4)*x)*sqrt(a + c*x^2))/(9009*e^5) + (20*sqrt(d + e*x)*(4*d*(2*c*d^2 + 5*a*e^2) - 7*e*(c*d^2 - 11*a*e^2)*x)*(a + c*x^2)^(3/2))/(9009*e^3) - (20*d*sqrt(d + e*x)*(a + c*x^2)^(5/2))/(143*e) + (2*(d + e*x)^(3/2)*(a + c*x^2)^(5/2))/(13*e) + (16*sqrt(-a)*(32*c^3*d^6 + 137*a*c^2*d^4*e^2 + 258*a^2*c*d^2*e^4 - 231*a^3*e^6)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(9009*sqrt(c)*e^6*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (16*sqrt(-a)*d*(c*d^2 + a*e^2)*(32*c^2*d^4 + 113*a*c*d^2*e^2 + 177*a^2*e^4)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(9009*sqrt(c)*e^6*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(a + c*x^2)^(5/2)/sqrt(d + e*x), x, 8, (8*sqrt(d + e*x)*(32*c^2*d^4 + 69*a*c*d^2*e^2 + 45*a^2*e^4 - 24*c*d*e*(c*d^2 + 2*a*e^2)*x)*sqrt(a + c*x^2))/(693*e^5) + (20*sqrt(d + e*x)*(8*c*d^2 + 9*a*e^2 - 7*c*d*e*x)*(a + c*x^2)^(3/2))/(693*e^3) + (2*sqrt(d + e*x)*(a + c*x^2)^(5/2))/(11*e) + (16*sqrt(-a)*sqrt(c)*d*(32*c^2*d^4 + 93*a*c*d^2*e^2 + 93*a^2*e^4)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(693*e^6*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (16*sqrt(-a)*(c*d^2 + a*e^2)*(32*c^2*d^4 + 69*a*c*d^2*e^2 + 45*a^2*e^4)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(693*sqrt(c)*e^6*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(a + c*x^2)^(5/2)/(d + e*x)^(3/2), x, 8, (-8*c*sqrt(d + e*x)*(d*(32*c*d^2 + 33*a*e^2) - 3*e*(8*c*d^2 + 7*a*e^2)*x)*sqrt(a + c*x^2))/(63*e^5) - (20*c*(8*d - 7*e*x)*sqrt(d + e*x)*(a + c*x^2)^(3/2))/(63*e^3) - (2*(a + c*x^2)^(5/2))/(e*sqrt(d + e*x)) - (16*sqrt(-a)*sqrt(c)*(32*c^2*d^4 + 57*a*c*d^2*e^2 + 21*a^2*e^4)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(63*e^6*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + (16*sqrt(-a)*sqrt(c)*d*(c*d^2 + a*e^2)*(32*c*d^2 + 33*a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(63*e^6*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(a + c*x^2)^(5/2)/(d + e*x)^(5/2), x, 8, (8*c*sqrt(d + e*x)*(32*c*d^2 + 5*a*e^2 - 24*c*d*e*x)*sqrt(a + c*x^2))/(21*e^5) + (20*c*(8*d + e*x)*(a + c*x^2)^(3/2))/(21*e^3*sqrt(d + e*x)) - (2*(a + c*x^2)^(5/2))/(3*e*(d + e*x)^(3/2)) + (16*sqrt(-a)*c^(3/2)*d*(32*c*d^2 + 29*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(21*e^6*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (16*sqrt(-a)*sqrt(c)*(c*d^2 + a*e^2)*(32*c*d^2 + 5*a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(21*e^6*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(a + c*x^2)^(5/2)/(d + e*x)^(7/2), x, 8, (-8*c*(32*c*d^2 + 9*a*e^2 + 8*c*d*e*x)*sqrt(a + c*x^2))/(15*e^5*sqrt(d + e*x)) + (4*c*(8*d + 3*e*x)*(a + c*x^2)^(3/2))/(15*e^3*(d + e*x)^(3/2)) - (2*(a + c*x^2)^(5/2))/(5*e*(d + e*x)^(5/2)) - (16*sqrt(-a)*c^(3/2)*(32*c*d^2 + 9*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(15*e^6*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + (16*sqrt(-a)*c^(3/2)*d*(32*c*d^2 + 17*a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(15*e^6*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(a + c*x^2)^(5/2)/(d + e*x)^(9/2), x, 8, (8*c^2*(d*(32*c*d^2 + 29*a*e^2) + e*(8*c*d^2 + 5*a*e^2)*x)*sqrt(a + c*x^2))/(21*e^5*(c*d^2 + a*e^2)*sqrt(d + e*x)) - (4*c*(2*d*(4*c*d^2 + a*e^2) + e*(11*c*d^2 + 5*a*e^2)*x)*(a + c*x^2)^(3/2))/(21*e^3*(c*d^2 + a*e^2)*(d + e*x)^(5/2)) - (2*(a + c*x^2)^(5/2))/(7*e*(d + e*x)^(7/2)) + (16*sqrt(-a)*c^(5/2)*d*(32*c*d^2 + 29*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), -((2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e))))/(21*e^6*(c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (16*sqrt(-a)*c^(3/2)*(32*c*d^2 + 5*a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), -((2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e))))/(21*e^6*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(a + c*x^2)^(5/2)/(d + e*x)^(11/2), x, 8, -((8*c^2*(d*(32*c^2*d^4 + 49*a*c*d^2*e^2 + 9*a^2*e^4) + e*(40*c^2*d^4 + 69*a*c*d^2*e^2 + 21*a^2*e^4)*x)*sqrt(a + c*x^2))/(63*e^5*(c*d^2 + a*e^2)^2*(d + e*x)^(3/2))) - (4*c*(2*d*(4*c*d^2 + a*e^2) + e*(13*c*d^2 + 7*a*e^2)*x)*(a + c*x^2)^(3/2))/(63*e^3*(c*d^2 + a*e^2)*(d + e*x)^(7/2)) - (2*(a + c*x^2)^(5/2))/(9*e*(d + e*x)^(9/2)) - (16*sqrt(-a)*c^(5/2)*(32*c^2*d^4 + 57*a*c*d^2*e^2 + 21*a^2*e^4)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), -((2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e))))/(63*e^6*(c*d^2 + a*e^2)^2*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + (16*sqrt(-a)*c^(5/2)*d*(32*c*d^2 + 33*a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), -((2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e))))/(63*e^6*(c*d^2 + a*e^2)*sqrt(d + e*x)*sqrt(a + c*x^2))]

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

    @test_int [(d + e*x)^(7/2)/sqrt(a + c*x^2), x, 8, (2*e*(71*c*d^2 - 25*a*e^2)*sqrt(d + e*x)*sqrt(a + c*x^2))/(105*c^2) + (24*d*e*(d + e*x)^(3/2)*sqrt(a + c*x^2))/(35*c) + (2*e*(d + e*x)^(5/2)*sqrt(a + c*x^2))/(7*c) - (32*sqrt(-a)*d*(11*c*d^2 - 13*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(105*c^(3/2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + (2*sqrt(-a)*(71*c*d^2 - 25*a*e^2)*(c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(105*c^(5/2)*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(d + e*x)^(5/2)/sqrt(a + c*x^2), x, 7, (16*d*e*sqrt(d + e*x)*sqrt(a + c*x^2))/(15*c) + (2*e*(d + e*x)^(3/2)*sqrt(a + c*x^2))/(5*c) - (2*sqrt(-a)*(23*c*d^2 - 9*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(15*c^(3/2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + (16*sqrt(-a)*d*(c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(15*c^(3/2)*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(d + e*x)^(3/2)/sqrt(a + c*x^2), x, 6, (2*e*sqrt(d + e*x)*sqrt(a + c*x^2))/(3*c) - (8*sqrt(-a)*d*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*sqrt(c)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + (2*sqrt(-a)*(c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*c^(3/2)*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [sqrt(d + e*x)/sqrt(a + c*x^2), x, 2, (-2*sqrt(-a)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(sqrt(c)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2))]
    @test_int [1/(sqrt(d + e*x)*sqrt(a + c*x^2)), x, 2, (-2*sqrt(-a)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(sqrt(c)*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [1/((d + e*x)^(3/2)*sqrt(a + c*x^2)), x, 4, (-2*e*sqrt(a + c*x^2))/((c*d^2 + a*e^2)*sqrt(d + e*x)) - (2*sqrt(-a)*sqrt(c)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/((c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2))]
    @test_int [1/((d + e*x)^(5/2)*sqrt(a + c*x^2)), x, 7, (-2*e*sqrt(a + c*x^2))/(3*(c*d^2 + a*e^2)*(d + e*x)^(3/2)) - (8*c*d*e*sqrt(a + c*x^2))/(3*(c*d^2 + a*e^2)^2*sqrt(d + e*x)) - (8*sqrt(-a)*c^(3/2)*d*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*(c*d^2 + a*e^2)^2*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + (2*sqrt(-a)*sqrt(c)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*(c*d^2 + a*e^2)*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [1/((d + e*x)^(7/2)*sqrt(a + c*x^2)), x, 8, (-2*e*sqrt(a + c*x^2))/(5*(c*d^2 + a*e^2)*(d + e*x)^(5/2)) - (16*c*d*e*sqrt(a + c*x^2))/(15*(c*d^2 + a*e^2)^2*(d + e*x)^(3/2)) - (2*c*e*(23*c*d^2 - 9*a*e^2)*sqrt(a + c*x^2))/(15*(c*d^2 + a*e^2)^3*sqrt(d + e*x)) - (2*sqrt(-a)*c^(3/2)*(23*c*d^2 - 9*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(15*(c*d^2 + a*e^2)^3*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + (16*sqrt(-a)*c^(3/2)*d*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(15*(c*d^2 + a*e^2)^2*sqrt(d + e*x)*sqrt(a + c*x^2))]

    @test_int [(d + e*x)^(7/2)/(a + c*x^2)^(3/2), x, 8, -(((a*e - c*d*x)*(d + e*x)^(5/2))/(a*c*sqrt(a + c*x^2))) - (e*(3*c*d^2 - 5*a*e^2)*sqrt(d + e*x)*sqrt(a + c*x^2))/(3*a*c^2) - (d*e*(d + e*x)^(3/2)*sqrt(a + c*x^2))/(a*c) - (d*(3*c*d^2 - 29*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*sqrt(-a)*c^(3/2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + ((3*c*d^2 - 5*a*e^2)*(c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*sqrt(-a)*c^(5/2)*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(d + e*x)^(5/2)/(a + c*x^2)^(3/2), x, 7, -(((a*e - c*d*x)*(d + e*x)^(3/2))/(a*c*sqrt(a + c*x^2))) - (d*e*sqrt(d + e*x)*sqrt(a + c*x^2))/(a*c) - ((c*d^2 - 3*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(sqrt(-a)*c^(3/2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + (d*(c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(sqrt(-a)*c^(3/2)*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(d + e*x)^(3/2)/(a + c*x^2)^(3/2), x, 6, -(((a*e - c*d*x)*sqrt(d + e*x))/(a*c*sqrt(a + c*x^2))) - (d*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(sqrt(-a)*sqrt(c)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + ((c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(sqrt(-a)*c^(3/2)*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [sqrt(d + e*x)/(a + c*x^2)^(3/2), x, 7, (x*sqrt(d + e*x))/(a*sqrt(a + c*x^2)) - (sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), -((2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e))))/(sqrt(-a)*sqrt(c)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + (d*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), -((2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e))))/(sqrt(-a)*sqrt(c)*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [1/(sqrt(d + e*x)*(a + c*x^2)^(3/2)), x, 6, ((a*e + c*d*x)*sqrt(d + e*x))/(a*(c*d^2 + a*e^2)*sqrt(a + c*x^2)) - (sqrt(c)*d*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(sqrt(-a)*(c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + (sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(sqrt(-a)*sqrt(c)*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [1/((d + e*x)^(3/2)*(a + c*x^2)^(3/2)), x, 7, (a*e + c*d*x)/(a*(c*d^2 + a*e^2)*sqrt(d + e*x)*sqrt(a + c*x^2)) + (e*(c*d^2 - 3*a*e^2)*sqrt(a + c*x^2))/(a*(c*d^2 + a*e^2)^2*sqrt(d + e*x)) - (sqrt(c)*(c*d^2 - 3*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(sqrt(-a)*(c*d^2 + a*e^2)^2*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + (sqrt(c)*d*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(sqrt(-a)*(c*d^2 + a*e^2)*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [1/((d + e*x)^(5/2)*(a + c*x^2)^(3/2)), x, 8, (a*e + c*d*x)/(a*(c*d^2 + a*e^2)*(d + e*x)^(3/2)*sqrt(a + c*x^2)) + (e*(3*c*d^2 - 5*a*e^2)*sqrt(a + c*x^2))/(3*a*(c*d^2 + a*e^2)^2*(d + e*x)^(3/2)) + (c*d*e*(3*c*d^2 - 29*a*e^2)*sqrt(a + c*x^2))/(3*a*(c*d^2 + a*e^2)^3*sqrt(d + e*x)) - (c^(3/2)*d*(3*c*d^2 - 29*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*sqrt(-a)*(c*d^2 + a*e^2)^3*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) + (sqrt(c)*(3*c*d^2 - 5*a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*sqrt(-a)*(c*d^2 + a*e^2)^2*sqrt(d + e*x)*sqrt(a + c*x^2))]

    @test_int [(d + e*x)^(9/2)/(a + c*x^2)^(5/2), x, 8, -(((a*e - c*d*x)*(d + e*x)^(7/2))/(3*a*c*(a + c*x^2)^(3/2))) - ((d + e*x)^(3/2)*(a*e*(c*d^2 + 7*a*e^2) - 2*c*d*(2*c*d^2 + 5*a*e^2)*x))/(6*a^2*c^2*sqrt(a + c*x^2)) - (2*d*e*(c*d^2 + 3*a*e^2)*sqrt(d + e*x)*sqrt(a + c*x^2))/(3*a^2*c^2) + ((4*c^2*d^4 + 15*a*c*d^2*e^2 - 21*a^2*e^4)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), -((2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e))))/(6*(-a)^(3/2)*c^(5/2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (2*d*(c*d^2 + a*e^2)*(c*d^2 + 3*a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), -((2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e))))/(3*(-a)^(3/2)*c^(5/2)*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(d + e*x)^(7/2)/(a + c*x^2)^(5/2), x, 7, -(((a*e - c*d*x)*(d + e*x)^(5/2))/(3*a*c*(a + c*x^2)^(3/2))) - (sqrt(d + e*x)*(a*e*(3*c*d^2 + 5*a*e^2) - 2*c*d*(2*c*d^2 + 3*a*e^2)*x))/(6*a^2*c^2*sqrt(a + c*x^2)) + (2*d*(c*d^2 + 2*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), -((2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e))))/(3*(-a)^(3/2)*c^(3/2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - ((c*d^2 + a*e^2)*(4*c*d^2 + 5*a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), -((2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e))))/(6*(-a)^(3/2)*c^(5/2)*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(d + e*x)^(5/2)/(a + c*x^2)^(5/2), x, 7, -((a*e - c*d*x)*(d + e*x)^(3/2))/(3*a*c*(a + c*x^2)^(3/2)) - (sqrt(d + e*x)*(a*d*e - (4*c*d^2 + 3*a*e^2)*x))/(6*a^2*c*sqrt(a + c*x^2)) + ((4*c*d^2 + 3*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(6*(-a)^(3/2)*c^(3/2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (2*d*(c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*(-a)^(3/2)*c^(3/2)*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [(d + e*x)^(3/2)/(a + c*x^2)^(5/2), x, 7, -((a*e - c*d*x)*sqrt(d + e*x))/(3*a*c*(a + c*x^2)^(3/2)) + ((a*e + 4*c*d*x)*sqrt(d + e*x))/(6*a^2*c*sqrt(a + c*x^2)) + (2*d*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*(-a)^(3/2)*sqrt(c)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - ((4*c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(6*(-a)^(3/2)*c^(3/2)*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [sqrt(d + e*x)/(a + c*x^2)^(5/2), x, 7, (x*sqrt(d + e*x))/(3*a*(a + c*x^2)^(3/2)) + (sqrt(d + e*x)*(a*d*e + (4*c*d^2 + 3*a*e^2)*x))/(6*a^2*(c*d^2 + a*e^2)*sqrt(a + c*x^2)) + ((4*c*d^2 + 3*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(6*(-a)^(3/2)*sqrt(c)*(c*d^2 + a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (2*d*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*(-a)^(3/2)*sqrt(c)*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [1/(sqrt(d + e*x)*(a + c*x^2)^(5/2)), x, 7, ((a*e + c*d*x)*sqrt(d + e*x))/(3*a*(c*d^2 + a*e^2)*(a + c*x^2)^(3/2)) + (sqrt(d + e*x)*(a*e*(c*d^2 + 5*a*e^2) + 4*c*d*(c*d^2 + 2*a*e^2)*x))/(6*a^2*(c*d^2 + a*e^2)^2*sqrt(a + c*x^2)) + (2*sqrt(c)*d*(c*d^2 + 2*a*e^2)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*(-a)^(3/2)*(c*d^2 + a*e^2)^2*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - ((4*c*d^2 + 5*a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(6*(-a)^(3/2)*sqrt(c)*(c*d^2 + a*e^2)*sqrt(d + e*x)*sqrt(a + c*x^2))]
    @test_int [1/((d + e*x)^(3/2)*(a + c*x^2)^(5/2)), x, 8, (a*e + c*d*x)/(3*a*(c*d^2 + a*e^2)*sqrt(d + e*x)*(a + c*x^2)^(3/2)) - (a*e*(c*d^2 - 7*a*e^2) - 4*c*d*(c*d^2 + 3*a*e^2)*x)/(6*a^2*(c*d^2 + a*e^2)^2*sqrt(d + e*x)*sqrt(a + c*x^2)) + (e*(4*c^2*d^4 + 15*a*c*d^2*e^2 - 21*a^2*e^4)*sqrt(a + c*x^2))/(6*a^2*(c*d^2 + a*e^2)^3*sqrt(d + e*x)) + (sqrt(c)*(4*c^2*d^4 + 15*a*c*d^2*e^2 - 21*a^2*e^4)*sqrt(d + e*x)*sqrt(1 + (c*x^2)/a)*Elliptic.E(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(6*(-a)^(3/2)*(c*d^2 + a*e^2)^3*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(a + c*x^2)) - (2*sqrt(c)*d*(c*d^2 + 3*a*e^2)*sqrt((sqrt(c)*(d + e*x))/(sqrt(c)*d + sqrt(-a)*e))*sqrt(1 + (c*x^2)/a)*Elliptic.F(asin(sqrt(1 - (sqrt(c)*x)/sqrt(-a))/sqrt(2)), (-2*a*e)/(sqrt(-a)*sqrt(c)*d - a*e)))/(3*(-a)^(3/2)*(c*d^2 + a*e^2)^2*sqrt(d + e*x)*sqrt(a + c*x^2))]

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

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

    @test_int [(2 + 3*x)^3/(4 + 27*x^2)^(1/3), x, 6, (1/30)*(2 + 3*x)^2*(4 + 27*x^2)^(2/3) + (4/35)*(7 + 4*x)*(4 + 27*x^2)^(2/3) - (96*x)/(7*(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))) + (16*2^(1/3)*sqrt(2 + sqrt(3))*(2^(2/3) - (4 + 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2)*Elliptic.E(asin((2^(2/3)*(1 + sqrt(3)) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(21*3^(3/4)*x*sqrt(-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2))) - (32*2^(5/6)*(2^(2/3) - (4 + 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2)*Elliptic.F(asin((2^(2/3)*(1 + sqrt(3)) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(63*3^(1/4)*x*sqrt(-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2)))]
    @test_int [(2 + 3*x)^2/(4 + 27*x^2)^(1/3), x, 6, (5/21)*(4 + 27*x^2)^(2/3) + (1/21)*(2 + 3*x)*(4 + 27*x^2)^(2/3) - (72*x)/(7*(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))) + (4*2^(1/3)*sqrt(2 + sqrt(3))*(2^(2/3) - (4 + 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2)*Elliptic.E(asin((2^(2/3)*(1 + sqrt(3)) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(7*3^(3/4)*x*sqrt(-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2))) - (8*2^(5/6)*(2^(2/3) - (4 + 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2)*Elliptic.F(asin((2^(2/3)*(1 + sqrt(3)) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(21*3^(1/4)*x*sqrt(-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2)))]
    @test_int [(2 + 3*x)^1/(4 + 27*x^2)^(1/3), x, 5, (1/12)*(4 + 27*x^2)^(2/3) - (6*x)/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3)) + (2^(1/3)*sqrt(2 + sqrt(3))*(2^(2/3) - (4 + 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2)*Elliptic.E(asin((2^(2/3)*(1 + sqrt(3)) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(3*3^(3/4)*x*sqrt(-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2))) - (2*2^(5/6)*(2^(2/3) - (4 + 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2)*Elliptic.F(asin((2^(2/3)*(1 + sqrt(3)) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(9*3^(1/4)*x*sqrt(-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2)))]
    @test_int [1/((2 + 3*x)^1*(4 + 27*x^2)^(1/3)), x, 1, -(atan(1/sqrt(3) + (2^(1/3)*(2 - 3*x))/(sqrt(3)*(4 + 27*x^2)^(1/3)))/(6*2^(1/3)*sqrt(3))) - log(2 + 3*x)/(12*2^(1/3)) + log(54 - 81*x - 27*2^(2/3)*(4 + 27*x^2)^(1/3))/(12*2^(1/3))]
    @test_int [1/((2 + 3*x)^2*(4 + 27*x^2)^(1/3)), x, 7, -((4 + 27*x^2)^(2/3)/(48*(2 + 3*x))) - (3*x)/(16*(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))) - atan(1/sqrt(3) + (2^(1/3)*(2 - 3*x))/(sqrt(3)*(4 + 27*x^2)^(1/3)))/(24*2^(1/3)*sqrt(3)) + (sqrt(2 + sqrt(3))*(2^(2/3) - (4 + 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2)*Elliptic.E(asin((2^(2/3)*(1 + sqrt(3)) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(48*2^(2/3)*3^(3/4)*x*sqrt(-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2))) - ((2^(2/3) - (4 + 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2)*Elliptic.F(asin((2^(2/3)*(1 + sqrt(3)) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(72*2^(1/6)*3^(1/4)*x*sqrt(-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2))) - log(2 + 3*x)/(48*2^(1/3)) + log(54 - 81*x - 27*2^(2/3)*(4 + 27*x^2)^(1/3))/(48*2^(1/3))]
    @test_int [1/((2 + 3*x)^3*(4 + 27*x^2)^(1/3)), x, 8, -((4 + 27*x^2)^(2/3)/(96*(2 + 3*x)^2)) - (4 + 27*x^2)^(2/3)/(96*(2 + 3*x)) - (3*x)/(32*(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))) - atan(1/sqrt(3) + (2^(1/3)*(2 - 3*x))/(sqrt(3)*(4 + 27*x^2)^(1/3)))/(96*2^(1/3)*sqrt(3)) + (sqrt(2 + sqrt(3))*(2^(2/3) - (4 + 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2)*Elliptic.E(asin((2^(2/3)*(1 + sqrt(3)) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(96*2^(2/3)*3^(3/4)*x*sqrt(-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2))) - ((2^(2/3) - (4 + 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 + 27*x^2)^(1/3) + (4 + 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2)*Elliptic.F(asin((2^(2/3)*(1 + sqrt(3)) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(144*2^(1/6)*3^(1/4)*x*sqrt(-((2^(2/3) - (4 + 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 + 27*x^2)^(1/3))^2))) - log(2 + 3*x)/(192*2^(1/3)) + log(54 - 81*x - 27*2^(2/3)*(4 + 27*x^2)^(1/3))/(192*2^(1/3))]

    @test_int [(2 + 3*im*x)^3/(4 - 27*x^2)^(1/3), x, 6, (-(4/35))*(7*im - 4*x)*(4 - 27*x^2)^(2/3) - (1/30)*im*(2 + 3*im*x)^2*(4 - 27*x^2)^(2/3) - (96*x)/(7*(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))) - (16*2^(1/3)*sqrt(2 + sqrt(3))*(2^(2/3) - (4 - 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2)*Elliptic.E(asin((2^(2/3)*(1 + sqrt(3)) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(21*3^(3/4)*x*sqrt(-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2))) + (32*2^(5/6)*(2^(2/3) - (4 - 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2)*Elliptic.F(asin((2^(2/3)*(1 + sqrt(3)) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(63*3^(1/4)*x*sqrt(-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2)))]
    @test_int [(2 + 3*im*x)^2/(4 - 27*x^2)^(1/3), x, 6, (-(5/21))*im*(4 - 27*x^2)^(2/3) - (1/21)*im*(2 + 3*im*x)*(4 - 27*x^2)^(2/3) - (72*x)/(7*(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))) - (4*2^(1/3)*sqrt(2 + sqrt(3))*(2^(2/3) - (4 - 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2)*Elliptic.E(asin((2^(2/3)*(1 + sqrt(3)) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(7*3^(3/4)*x*sqrt(-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2))) + (8*2^(5/6)*(2^(2/3) - (4 - 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2)*Elliptic.F(asin((2^(2/3)*(1 + sqrt(3)) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(21*3^(1/4)*x*sqrt(-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2)))]
    @test_int [(2 + 3*im*x)^1/(4 - 27*x^2)^(1/3), x, 5, (-(1/12))*im*(4 - 27*x^2)^(2/3) - (6*x)/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3)) - (2^(1/3)*sqrt(2 + sqrt(3))*(2^(2/3) - (4 - 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2)*Elliptic.E(asin((2^(2/3)*(1 + sqrt(3)) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(3*3^(3/4)*x*sqrt(-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2))) + (2*2^(5/6)*(2^(2/3) - (4 - 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2)*Elliptic.F(asin((2^(2/3)*(1 + sqrt(3)) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(9*3^(1/4)*x*sqrt(-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2)))]
    @test_int [1/((2 + 3*im*x)^1*(4 - 27*x^2)^(1/3)), x, 1, (im*atan(1/sqrt(3) + (2^(1/3)*(2 - 3*im*x))/(sqrt(3)*(4 - 27*x^2)^(1/3))))/(6*2^(1/3)*sqrt(3)) + (im*log(2 + 3*im*x))/(12*2^(1/3)) - (im*log(-54 + 81*im*x + 27*2^(2/3)*(4 - 27*x^2)^(1/3)))/(12*2^(1/3))]
    @test_int [1/((2 + 3*im*x)^2*(4 - 27*x^2)^(1/3)), x, 7, (im*(4 - 27*x^2)^(2/3))/(48*(2 + 3*im*x)) - (3*x)/(16*(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))) + (im*atan(1/sqrt(3) + (2^(1/3)*(2 - 3*im*x))/(sqrt(3)*(4 - 27*x^2)^(1/3))))/(24*2^(1/3)*sqrt(3)) - (sqrt(2 + sqrt(3))*(2^(2/3) - (4 - 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2)*Elliptic.E(asin((2^(2/3)*(1 + sqrt(3)) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(48*2^(2/3)*3^(3/4)*x*sqrt(-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2))) + ((2^(2/3) - (4 - 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2)*Elliptic.F(asin((2^(2/3)*(1 + sqrt(3)) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(72*2^(1/6)*3^(1/4)*x*sqrt(-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2))) + (im*log(2 + 3*im*x))/(48*2^(1/3)) - (im*log(-54 + 81*im*x + 27*2^(2/3)*(4 - 27*x^2)^(1/3)))/(48*2^(1/3))]
    @test_int [1/((2 + 3*im*x)^3*(4 - 27*x^2)^(1/3)), x, 8, (im*(4 - 27*x^2)^(2/3))/(96*(2 + 3*im*x)^2) + (im*(4 - 27*x^2)^(2/3))/(96*(2 + 3*im*x)) - (3*x)/(32*(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))) + (im*atan(1/sqrt(3) + (2^(1/3)*(2 - 3*im*x))/(sqrt(3)*(4 - 27*x^2)^(1/3))))/(96*2^(1/3)*sqrt(3)) - (sqrt(2 + sqrt(3))*(2^(2/3) - (4 - 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2)*Elliptic.E(asin((2^(2/3)*(1 + sqrt(3)) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(96*2^(2/3)*3^(3/4)*x*sqrt(-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2))) + ((2^(2/3) - (4 - 27*x^2)^(1/3))*sqrt((2*2^(1/3) + 2^(2/3)*(4 - 27*x^2)^(1/3) + (4 - 27*x^2)^(2/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2)*Elliptic.F(asin((2^(2/3)*(1 + sqrt(3)) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))), -7 + 4*sqrt(3)))/(144*2^(1/6)*3^(1/4)*x*sqrt(-((2^(2/3) - (4 - 27*x^2)^(1/3))/(2^(2/3)*(1 - sqrt(3)) - (4 - 27*x^2)^(1/3))^2))) + (im*log(2 + 3*im*x))/(192*2^(1/3)) - (im*log(-54 + 81*im*x + 27*2^(2/3)*(4 - 27*x^2)^(1/3)))/(192*2^(1/3))]

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(d+e*x)^m*(a+c*x^2)^(p/3)*with*c*d^2+9*a*e^2=0=#

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

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

    @test_int [1/((d + e*x)*(d^2 - 9*e^2*x^2)^(1/3)), x, 3, (sqrt(3)*(1 - (9*e^2*x^2)/d^2)^(1/3)*atan(1/sqrt(3) - (1 - (3*e*x)/d)^(2/3)/(sqrt(3)*(1 + (3*e*x)/d)^(1/3))))/(4*e*(d^2 - 9*e^2*x^2)^(1/3)) + ((1 - (9*e^2*x^2)/d^2)^(1/3)*log(d + e*x))/(4*e*(d^2 - 9*e^2*x^2)^(1/3)) - (3*(1 - (9*e^2*x^2)/d^2)^(1/3)*log((-(1/2))*(1 - (3*e*x)/d)^(2/3) - (1 + (3*e*x)/d)^(1/3)))/(8*e*(d^2 - 9*e^2*x^2)^(1/3))]

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

    @test_int [1/((a + b*x)*(c + d*x^2)^(1/4)), x, 10, atan((sqrt(b)*(c + d*x^2)^(1/4))/(b^2*c + a^2*d)^(1/4))/(sqrt(b)*(b^2*c + a^2*d)^(1/4)) - atanh((sqrt(b)*(c + d*x^2)^(1/4))/(b^2*c + a^2*d)^(1/4))/(sqrt(b)*(b^2*c + a^2*d)^(1/4)) - (a*c^(1/4)*sqrt(-((d*x^2)/c))*Elliptic.Pi(-((b*sqrt(c))/sqrt(b^2*c + a^2*d)), asin((c + d*x^2)^(1/4)/c^(1/4)), -1))/(b*sqrt(b^2*c + a^2*d)*x) + (a*c^(1/4)*sqrt(-((d*x^2)/c))*Elliptic.Pi((b*sqrt(c))/sqrt(b^2*c + a^2*d), asin((c + d*x^2)^(1/4)/c^(1/4)), -1))/(b*sqrt(b^2*c + a^2*d)*x)]

    @test_int [1/((a + b*x)*(c + d*x^2)^(3/4)), x, 11, -((sqrt(b)*atan((sqrt(b)*(c + d*x^2)^(1/4))/(b^2*c + a^2*d)^(1/4)))/(b^2*c + a^2*d)^(3/4)) - (sqrt(b)*atanh((sqrt(b)*(c + d*x^2)^(1/4))/(b^2*c + a^2*d)^(1/4)))/(b^2*c + a^2*d)^(3/4) + (a*c^(1/4)*sqrt(-((d*x^2)/c))*Elliptic.Pi(-((b*sqrt(c))/sqrt(b^2*c + a^2*d)), asin((c + d*x^2)^(1/4)/c^(1/4)), -1))/((b^2*c + a^2*d)*x) + (a*c^(1/4)*sqrt(-((d*x^2)/c))*Elliptic.Pi((b*sqrt(c))/sqrt(b^2*c + a^2*d), asin((c + d*x^2)^(1/4)/c^(1/4)), -1))/((b^2*c + a^2*d)*x)]

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(d+e*x)^m*(a+c*x^2)^(p/6)=#

    @test_int [1/((1 + x)*(1 + x^2)^(1/6)), x, 15, x*AppellF1(1/2, 1, 1/6, 3/2, x^2, -x^2) - (sqrt(3)*atan((1 - 2^(5/6)*(1 + x^2)^(1/6))/sqrt(3)))/(2*2^(1/6)) + (sqrt(3)*atan((1 + 2^(5/6)*(1 + x^2)^(1/6))/sqrt(3)))/(2*2^(1/6)) - atanh((1 + x^2)^(1/6)/2^(1/6))/2^(1/6) + log(2^(1/3) - 2^(1/6)*(1 + x^2)^(1/6) + (1 + x^2)^(1/3))/(4*2^(1/6)) - log(2^(1/3) + 2^(1/6)*(1 + x^2)^(1/6) + (1 + x^2)^(1/3))/(4*2^(1/6))]

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

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

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

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

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

    @test_int [(a + c*x^2)^p*(d + e*x)^3, x, 4, (e*(d + e*x)^2*(a + c*x^2)^(1 + p))/(2*c*(2 + p)) - (e*((3 + 2*p)*(a*e^2 - c*d^2*(5 + 2*p)) - 2*c*d*e*(1 + p)*(3 + p)*x)*(a + c*x^2)^(1 + p))/(2*c^2*(2 + p)*(3 + 5*p + 2*p^2)) - (d*(3*a*e^2 - c*d^2*(3 + 2*p))*x*(a + c*x^2)^p*HypergeometricFunctions._₂F₁(1/2, -p, 3/2, -((c*x^2)/a)))/((1 + (c*x^2)/a)^p*(c*(3 + 2*p)))]
    @test_int [(a + c*x^2)^p*(d + e*x)^2, x, 4, If(13>=8, (d*e*(2 + p)*(a + c*x^2)^(1 + p))/(c*(1 + p)*(3 + 2*p)) + (e*(d + e*x)*(a + c*x^2)^(1 + p))/(c*(3 + 2*p)) - ((a*e^2 - c*d^2*(3 + 2*p))*x*(a + c*x^2)^p*HypergeometricFunctions._₂F₁(1/2, -p, 3/2, -((c*x^2)/a)))/((1 + (c*x^2)/a)^p*(c*(3 + 2*p))), (d*e*(2 + p)*(a + c*x^2)^(1 + p))/(c*(3 + 5*p + 2*p^2)) + (e*(d + e*x)*(a + c*x^2)^(1 + p))/(c*(3 + 2*p)) - ((a*e^2 - c*d^2*(3 + 2*p))*x*(a + c*x^2)^p*HypergeometricFunctions._₂F₁(1/2, -p, 3/2, -((c*x^2)/a)))/((1 + (c*x^2)/a)^p*(c*(3 + 2*p))))]
    @test_int [(a + c*x^2)^p*(d + e*x)^1, x, 3, (e*(a + c*x^2)^(1 + p))/(2*c*(1 + p)) + (d*x*(a + c*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(1, 3/2 + p, 3/2, -((c*x^2)/a)))/a, (e*(a + c*x^2)^(1 + p))/(2*c*(1 + p)) + (d*x*(a + c*x^2)^p*HypergeometricFunctions._₂F₁(1/2, -p, 3/2, -((c*x^2)/a)))/(1 + (c*x^2)/a)^p]
    @test_int [(a + c*x^2)^p*(d + e*x)^0, x, 2, (x*(a + c*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(1, 3/2 + p, 3/2, -((c*x^2)/a)))/a, (x*(a + c*x^2)^p*HypergeometricFunctions._₂F₁(1/2, -p, 3/2, -((c*x^2)/a)))/(1 + (c*x^2)/a)^p]
    @test_int [(a + c*x^2)^p/(d + e*x)^1, x, 6, (x*(a + c*x^2)^p*AppellF1(1/2, -p, 1, 3/2, -((c*x^2)/a), (e^2*x^2)/d^2))/((1 + (c*x^2)/a)^p*d) - (e*(a + c*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(1, 1 + p, 2 + p, (e^2*(a + c*x^2))/(c*d^2 + a*e^2)))/(2*(c*d^2 + a*e^2)*(1 + p))]
    @test_int [(a + c*x^2)^p/(d + e*x)^2, x, 8, (x*(a + c*x^2)^p*AppellF1(1/2, -p, 2, 3/2, -((c*x^2)/a), (e^2*x^2)/d^2))/((1 + (c*x^2)/a)^p*d^2) + (e^2*x^3*(a + c*x^2)^p*AppellF1(3/2, -p, 2, 5/2, -((c*x^2)/a), (e^2*x^2)/d^2))/((1 + (c*x^2)/a)^p*(3*d^4)) - (c*d*e*(a + c*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(2, 1 + p, 2 + p, (e^2*(a + c*x^2))/(c*d^2 + a*e^2)))/((c*d^2 + a*e^2)^2*(1 + p))]
    @test_int [(a + c*x^2)^p/(d + e*x)^3, x, 11, -((d^2*e*(a + c*x^2)^(1 + p))/(4*(c*d^2 + a*e^2)*(d^2 - e^2*x^2)^2)) + (x*(a + c*x^2)^p*AppellF1(1/2, -p, 3, 3/2, -((c*x^2)/a), (e^2*x^2)/d^2))/((1 + (c*x^2)/a)^p*d^3) + (e^2*x^3*(a + c*x^2)^p*AppellF1(3/2, -p, 3, 5/2, -((c*x^2)/a), (e^2*x^2)/d^2))/((1 + (c*x^2)/a)^p*d^5) + (c*e*(2*a*e^2 + c*d^2*(1 + p))*(a + c*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(2, 1 + p, 2 + p, (e^2*(a + c*x^2))/(c*d^2 + a*e^2)))/(4*(c*d^2 + a*e^2)^3*(1 + p)) - (3*c^2*d^2*e*(a + c*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(3, 1 + p, 2 + p, (e^2*(a + c*x^2))/(c*d^2 + a*e^2)))/(2*(c*d^2 + a*e^2)^3*(1 + p))]

    @test_int [(a + c*x^2)^p/(d + e*x)^(2*p + 0), x, 2, ((d + e*x)^(1 - 2*p)*(a + c*x^2)^p*AppellF1(1 - 2*p, -p, -p, 2 - 2*p, (d + e*x)/(d - (sqrt(-a)*e)/sqrt(c)), (d + e*x)/(d + (sqrt(-a)*e)/sqrt(c))))/((1 - (d + e*x)/(d - (sqrt(-a)*e)/sqrt(c)))^p*(1 - (d + e*x)/(d + (sqrt(-a)*e)/sqrt(c)))^p*(e*(1 - 2*p)))]
    @test_int [(a + c*x^2)^p/(d + e*x)^(2*p + 1), x, 2, -(((a + c*x^2)^p*AppellF1(-2*p, -p, -p, 1 - 2*p, (d + e*x)/(d - (sqrt(-a)*e)/sqrt(c)), (d + e*x)/(d + (sqrt(-a)*e)/sqrt(c))))/((d + e*x)^(2*p)*(1 - (d + e*x)/(d - (sqrt(-a)*e)/sqrt(c)))^p*(1 - (d + e*x)/(d + (sqrt(-a)*e)/sqrt(c)))^p*(2*e*p)))]
    @test_int [(a + c*x^2)^p/(d + e*x)^(2*p + 2), x, 1, -(((sqrt(-a) - sqrt(c)*x)*(d + e*x)^(-1 - 2*p)*(a + c*x^2)^p*HypergeometricFunctions._₂F₁(-1 - 2*p, -p, -2*p, (2*sqrt(-a)*sqrt(c)*(d + e*x))/((sqrt(c)*d - sqrt(-a)*e)*(sqrt(-a) - sqrt(c)*x))))/((-(((sqrt(c)*d + sqrt(-a)*e)*(sqrt(-a) + sqrt(c)*x))/((sqrt(c)*d - sqrt(-a)*e)*(sqrt(-a) - sqrt(c)*x))))^p*((sqrt(c)*d + sqrt(-a)*e)*(1 + 2*p))))]
    @test_int [(a + c*x^2)^p/(d + e*x)^(2*p + 3), x, 2, -((e*(a + c*x^2)^(1 + p))/((d + e*x)^(2*(1 + p))*(2*(c*d^2 + a*e^2)*(1 + p)))) - (c*d*(sqrt(-a) - sqrt(c)*x)*(d + e*x)^(-1 - 2*p)*(a + c*x^2)^p*HypergeometricFunctions._₂F₁(-1 - 2*p, -p, -2*p, (2*sqrt(-a)*sqrt(c)*(d + e*x))/((sqrt(c)*d - sqrt(-a)*e)*(sqrt(-a) - sqrt(c)*x))))/((-(((sqrt(c)*d + sqrt(-a)*e)*(sqrt(-a) + sqrt(c)*x))/((sqrt(c)*d - sqrt(-a)*e)*(sqrt(-a) - sqrt(c)*x))))^p*((sqrt(c)*d + sqrt(-a)*e)*(c*d^2 + a*e^2)*(1 + 2*p)))]
    @test_int [(a + c*x^2)^p/(d + e*x)^(2*p + 4), x, 3, -((e*(d + e*x)^(-3 - 2*p)*(a + c*x^2)^(1 + p))/((c*d^2 + a*e^2)*(3 + 2*p))) - (c*d*e*(2 + p)*(a + c*x^2)^(1 + p))/((d + e*x)^(2*(1 + p))*((c*d^2 + a*e^2)^2*(1 + p)*(3 + 2*p))) + (c*(a*e^2 - c*d^2*(3 + 2*p))*(sqrt(-a) - sqrt(c)*x)*(d + e*x)^(-1 - 2*p)*(a + c*x^2)^p*HypergeometricFunctions._₂F₁(-1 - 2*p, -p, -2*p, (2*sqrt(-a)*sqrt(c)*(d + e*x))/((sqrt(c)*d - sqrt(-a)*e)*(sqrt(-a) - sqrt(c)*x))))/((-(((sqrt(c)*d + sqrt(-a)*e)*(sqrt(-a) + sqrt(c)*x))/((sqrt(c)*d - sqrt(-a)*e)*(sqrt(-a) - sqrt(c)*x))))^p*((sqrt(c)*d + sqrt(-a)*e)*(c*d^2 + a*e^2)^2*(1 + 2*p)*(3 + 2*p)))]
    @test_int [(a + c*x^2)^p/(d + e*x)^(2*p + 5), x, 4, -((c*d*e*(3 + p)*(d + e*x)^(-3 - 2*p)*(a + c*x^2)^(1 + p))/((c*d^2 + a*e^2)^2*(2 + p)*(3 + 2*p))) + (c*e*(a*e^2*(3 + 2*p) - c*d^2*(9 + 8*p + 2*p^2))*(a + c*x^2)^(1 + p))/((d + e*x)^(2*(1 + p))*(2*(c*d^2 + a*e^2)^3*(1 + p)*(2 + p)*(3 + 2*p))) - (e*(a + c*x^2)^(1 + p))/((d + e*x)^(2*(2 + p))*(2*(c*d^2 + a*e^2)*(2 + p))) + (c^2*d*(3*a*e^2 - c*d^2*(3 + 2*p))*(sqrt(-a) - sqrt(c)*x)*(d + e*x)^(-1 - 2*p)*(a + c*x^2)^p*HypergeometricFunctions._₂F₁(-1 - 2*p, -p, -2*p, (2*sqrt(-a)*sqrt(c)*(d + e*x))/((sqrt(c)*d - sqrt(-a)*e)*(sqrt(-a) - sqrt(c)*x))))/((-(((sqrt(c)*d + sqrt(-a)*e)*(sqrt(-a) + sqrt(c)*x))/((sqrt(c)*d - sqrt(-a)*e)*(sqrt(-a) - sqrt(c)*x))))^p*((sqrt(c)*d + sqrt(-a)*e)*(c*d^2 + a*e^2)^3*(1 + 2*p)*(3 + 2*p)))]
    @test_int [(a + c*x^2)^p/(d + e*x)^(2*p + 6), x, 5, -((e*(d + e*x)^(-5 - 2*p)*(a + c*x^2)^(1 + p))/((c*d^2 + a*e^2)*(5 + 2*p))) + (c*e*(3*a*e^2*(2 + p) - c*d^2*(18 + 11*p + 2*p^2))*(d + e*x)^(-3 - 2*p)*(a + c*x^2)^(1 + p))/((c*d^2 + a*e^2)^3*(2 + p)*(3 + 2*p)*(5 + 2*p)) + (c^2*d*e*(3 + p)*(a*e^2*(8 + 5*p) - c*d^2*(8 + 7*p + 2*p^2))*(a + c*x^2)^(1 + p))/((d + e*x)^(2*(1 + p))*((c*d^2 + a*e^2)^4*(1 + p)*(2 + p)*(3 + 2*p)*(5 + 2*p))) - (c*d*e*(4 + p)*(a + c*x^2)^(1 + p))/((d + e*x)^(2*(2 + p))*((c*d^2 + a*e^2)^2*(2 + p)*(5 + 2*p))) - (c^2*(3*a^2*e^4 - 6*a*c*d^2*e^2*(5 + 2*p) + c^2*d^4*(15 + 16*p + 4*p^2))*(sqrt(-a) - sqrt(c)*x)*(d + e*x)^(-1 - 2*p)*(a + c*x^2)^p*HypergeometricFunctions._₂F₁(-1 - 2*p, -p, -2*p, (2*sqrt(-a)*sqrt(c)*(d + e*x))/((sqrt(c)*d - sqrt(-a)*e)*(sqrt(-a) - sqrt(c)*x))))/(-(((sqrt(c)*d + sqrt(-a)*e)*(sqrt(-a) + sqrt(c)*x))/((sqrt(c)*d - sqrt(-a)*e)*(sqrt(-a) - sqrt(c)*x))))^p/((sqrt(c)*d + sqrt(-a)*e)*(c*d^2 + a*e^2)^4*(1 + 2*p)*(3 + 2*p)*(5 + 2*p))]

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

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(d+e*x)^m*(d^2 - e^2*x^2)^p=#

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

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

    @test_int [(a + b*x)^6/(a^2 - b^2*x^2), x, 3, -16*a^4*x - (4*a^3*(a + b*x)^2)/b - (4*a^2*(a + b*x)^3)/(3*b) - (a*(a + b*x)^4)/(2*b) - (a + b*x)^5/(5*b) - (32*a^5*log(a - b*x))/b]
    @test_int [(a + b*x)^5/(a^2 - b^2*x^2), x, 3, -8*a^3*x - (2*a^2*(a + b*x)^2)/b - (2*a*(a + b*x)^3)/(3*b) - (a + b*x)^4/(4*b) - (16*a^4*log(a - b*x))/b]
    @test_int [(a + b*x)^4/(a^2 - b^2*x^2), x, 3, -4*a^2*x - (a*(a + b*x)^2)/b - (a + b*x)^3/(3*b) - (8*a^3*log(a - b*x))/b]
    @test_int [(a + b*x)^3/(a^2 - b^2*x^2), x, 3, -3*a*x - (b*x^2)/2 - (4*a^2*log(a - b*x))/b]
    @test_int [(a + b*x)^2/(a^2 - b^2*x^2), x, 3, -x - (2*a*log(a - b*x))/b]
    @test_int [(a + b*x)^1/(a^2 - b^2*x^2), x, 2, -(log(a - b*x)/b)]
    @test_int [1/((a + b*x)^1*(a^2 - b^2*x^2)), x, 4, -(1/(2*a*b*(a + b*x))) + atanh((b*x)/a)/(2*a^2*b)]
    @test_int [1/((a + b*x)^2*(a^2 - b^2*x^2)), x, 4, -(1/(4*a*b*(a + b*x)^2)) - 1/(4*a^2*b*(a + b*x)) + atanh((b*x)/a)/(4*a^3*b)]
    @test_int [1/((a + b*x)^3*(a^2 - b^2*x^2)), x, 4, -(1/(6*a*b*(a + b*x)^3)) - 1/(8*a^2*b*(a + b*x)^2) - 1/(8*a^3*b*(a + b*x)) + atanh((b*x)/a)/(8*a^4*b)]
    @test_int [1/((a + b*x)^4*(a^2 - b^2*x^2)), x, 4, -(1/(8*a*b*(a + b*x)^4)) - 1/(12*a^2*b*(a + b*x)^3) - 1/(16*a^3*b*(a + b*x)^2) - 1/(16*a^4*b*(a + b*x)) + atanh((b*x)/a)/(16*a^5*b)]

    @test_int [(a + b*x)^7/(a^2 - b^2*x^2)^2, x, 3, 49*a^3*x + (23/2)*a^2*b*x^2 + (7/3)*a*b^2*x^3 + (b^3*x^4)/4 + (32*a^5)/(b*(a - b*x)) + (80*a^4*log(a - b*x))/b]
    @test_int [(a + b*x)^6/(a^2 - b^2*x^2)^2, x, 3, 17*a^2*x + 3*a*b*x^2 + (b^2*x^3)/3 + (16*a^4)/(b*(a - b*x)) + (32*a^3*log(a - b*x))/b]
    @test_int [(a + b*x)^5/(a^2 - b^2*x^2)^2, x, 3, 5*a*x + (b*x^2)/2 + (8*a^3)/(b*(a - b*x)) + (12*a^2*log(a - b*x))/b]
    @test_int [(a + b*x)^4/(a^2 - b^2*x^2)^2, x, 3, x + (4*a^2)/(b*(a - b*x)) + (4*a*log(a - b*x))/b]
    @test_int [(a + b*x)^3/(a^2 - b^2*x^2)^2, x, 3, (2*a)/(b*(a - b*x)) + log(a - b*x)/b]
    @test_int [(a + b*x)^2/(a^2 - b^2*x^2)^2, x, 2, 1/(b*(a - b*x))]
    @test_int [(a + b*x)^1/(a^2 - b^2*x^2)^2, x, 4, 1/(2*a*b*(a - b*x)) + atanh((b*x)/a)/(2*a^2*b)]
    @test_int [1/((a + b*x)^1*(a^2 - b^2*x^2)^2), x, 4, 1/(8*a^3*b*(a - b*x)) - 1/(8*a^2*b*(a + b*x)^2) - 1/(4*a^3*b*(a + b*x)) + (3*atanh((b*x)/a))/(8*a^4*b)]
    @test_int [1/((a + b*x)^2*(a^2 - b^2*x^2)^2), x, 4, 1/(16*a^4*b*(a - b*x)) - 1/(12*a^2*b*(a + b*x)^3) - 1/(8*a^3*b*(a + b*x)^2) - 3/(16*a^4*b*(a + b*x)) + atanh((b*x)/a)/(4*a^5*b)]
    @test_int [1/((a + b*x)^3*(a^2 - b^2*x^2)^2), x, 4, 1/(32*a^5*b*(a - b*x)) - 1/(16*a^2*b*(a + b*x)^4) - 1/(12*a^3*b*(a + b*x)^3) - 3/(32*a^4*b*(a + b*x)^2) - 1/(8*a^5*b*(a + b*x)) + (5*atanh((b*x)/a))/(32*a^6*b)]

    @test_int [(a + b*x)^8/(a^2 - b^2*x^2)^3, x, 3, -31*a^2*x - 4*a*b*x^2 - (b^2*x^3)/3 + (16*a^5)/(b*(a - b*x)^2) - (80*a^4)/(b*(a - b*x)) - (80*a^3*log(a - b*x))/b]
    @test_int [(a + b*x)^7/(a^2 - b^2*x^2)^3, x, 3, -7*a*x - (b*x^2)/2 + (8*a^4)/(b*(a - b*x)^2) - (32*a^3)/(b*(a - b*x)) - (24*a^2*log(a - b*x))/b]
    @test_int [(a + b*x)^6/(a^2 - b^2*x^2)^3, x, 3, -x + (4*a^3)/(b*(a - b*x)^2) - (12*a^2)/(b*(a - b*x)) - (6*a*log(a - b*x))/b]
    @test_int [(a + b*x)^5/(a^2 - b^2*x^2)^3, x, 3, (2*a^2)/(b*(a - b*x)^2) - (4*a)/(b*(a - b*x)) - log(a - b*x)/b]
    @test_int [(a + b*x)^4/(a^2 - b^2*x^2)^3, x, 2, x/(a - b*x)^2]
    @test_int [(a + b*x)^3/(a^2 - b^2*x^2)^3, x, 2, 1/(2*b*(a - b*x)^2)]
    @test_int [(a + b*x)^2/(a^2 - b^2*x^2)^3, x, 4, 1/(4*a*b*(a - b*x)^2) + 1/(4*a^2*b*(a - b*x)) + atanh((b*x)/a)/(4*a^3*b)]
    @test_int [(a + b*x)^1/(a^2 - b^2*x^2)^3, x, 4, 1/(8*a^2*b*(a - b*x)^2) + 1/(4*a^3*b*(a - b*x)) - 1/(8*a^3*b*(a + b*x)) + (3*atanh((b*x)/a))/(8*a^4*b)]
    @test_int [1/((a + b*x)^1*(a^2 - b^2*x^2)^3), x, 4, 1/(32*a^4*b*(a - b*x)^2) + 1/(8*a^5*b*(a - b*x)) - 1/(24*a^3*b*(a + b*x)^3) - 3/(32*a^4*b*(a + b*x)^2) - 3/(16*a^5*b*(a + b*x)) + (5*atanh((b*x)/a))/(16*a^6*b)]
    @test_int [1/((a + b*x)^2*(a^2 - b^2*x^2)^3), x, 4, 1/(64*a^5*b*(a - b*x)^2) + 5/(64*a^6*b*(a - b*x)) - 1/(32*a^3*b*(a + b*x)^4) - 1/(16*a^4*b*(a + b*x)^3) - 3/(32*a^5*b*(a + b*x)^2) - 5/(32*a^6*b*(a + b*x)) + (15*atanh((b*x)/a))/(64*a^7*b)]

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

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

    @test_int [sqrt(a^2 - b^2*x^2)*(a + b*x)^4, x, 7, (21/16)*a^4*x*sqrt(a^2 - b^2*x^2) - (7*a^3*(a^2 - b^2*x^2)^(3/2))/(8*b) - (21*a^2*(a + b*x)*(a^2 - b^2*x^2)^(3/2))/(40*b) - (3*a*(a + b*x)^2*(a^2 - b^2*x^2)^(3/2))/(10*b) - ((a + b*x)^3*(a^2 - b^2*x^2)^(3/2))/(6*b) + (21*a^6*atan((b*x)/sqrt(a^2 - b^2*x^2)))/(16*b)]
    @test_int [sqrt(a^2 - b^2*x^2)*(a + b*x)^3, x, 6, (7/8)*a^3*x*sqrt(a^2 - b^2*x^2) - (7*a^2*(a^2 - b^2*x^2)^(3/2))/(12*b) - (7*a*(a + b*x)*(a^2 - b^2*x^2)^(3/2))/(20*b) - ((a + b*x)^2*(a^2 - b^2*x^2)^(3/2))/(5*b) + (7*a^5*atan((b*x)/sqrt(a^2 - b^2*x^2)))/(8*b)]
    @test_int [sqrt(a^2 - b^2*x^2)*(a + b*x)^2, x, 5, (5/8)*a^2*x*sqrt(a^2 - b^2*x^2) - (5*a*(a^2 - b^2*x^2)^(3/2))/(12*b) - ((a + b*x)*(a^2 - b^2*x^2)^(3/2))/(4*b) + (5*a^4*atan((b*x)/sqrt(a^2 - b^2*x^2)))/(8*b)]
    @test_int [sqrt(a^2 - b^2*x^2)*(a + b*x)^1, x, 4, (1/2)*a*x*sqrt(a^2 - b^2*x^2) - (a^2 - b^2*x^2)^(3/2)/(3*b) + (a^3*atan((b*x)/sqrt(a^2 - b^2*x^2)))/(2*b)]
    @test_int [sqrt(a^2 - b^2*x^2)/(a + b*x)^1, x, 3, sqrt(a^2 - b^2*x^2)/b + (a*atan((b*x)/sqrt(a^2 - b^2*x^2)))/b]
    @test_int [sqrt(a^2 - b^2*x^2)/(a + b*x)^2, x, 3, -((2*sqrt(a^2 - b^2*x^2))/(b*(a + b*x))) - atan((b*x)/sqrt(a^2 - b^2*x^2))/b]
    @test_int [sqrt(a^2 - b^2*x^2)/(a + b*x)^3, x, 1, -((a^2 - b^2*x^2)^(3/2)/(3*a*b*(a + b*x)^3))]
    @test_int [sqrt(a^2 - b^2*x^2)/(a + b*x)^4, x, 2, -((a^2 - b^2*x^2)^(3/2)/(5*a*b*(a + b*x)^4)) - (a^2 - b^2*x^2)^(3/2)/(15*a^2*b*(a + b*x)^3)]
    @test_int [sqrt(a^2 - b^2*x^2)/(a + b*x)^5, x, 3, -((a^2 - b^2*x^2)^(3/2)/(7*a*b*(a + b*x)^5)) - (2*(a^2 - b^2*x^2)^(3/2))/(35*a^2*b*(a + b*x)^4) - (2*(a^2 - b^2*x^2)^(3/2))/(105*a^3*b*(a + b*x)^3)]
    @test_int [sqrt(a^2 - b^2*x^2)/(a + b*x)^6, x, 4, -((a^2 - b^2*x^2)^(3/2)/(9*a*b*(a + b*x)^6)) - (a^2 - b^2*x^2)^(3/2)/(21*a^2*b*(a + b*x)^5) - (2*(a^2 - b^2*x^2)^(3/2))/(105*a^3*b*(a + b*x)^4) - (2*(a^2 - b^2*x^2)^(3/2))/(315*a^4*b*(a + b*x)^3)]
    @test_int [sqrt(a^2 - b^2*x^2)/(a + b*x)^7, x, 5, -((a^2 - b^2*x^2)^(3/2)/(11*a*b*(a + b*x)^7)) - (4*(a^2 - b^2*x^2)^(3/2))/(99*a^2*b*(a + b*x)^6) - (4*(a^2 - b^2*x^2)^(3/2))/(231*a^3*b*(a + b*x)^5) - (8*(a^2 - b^2*x^2)^(3/2))/(1155*a^4*b*(a + b*x)^4) - (8*(a^2 - b^2*x^2)^(3/2))/(3465*a^5*b*(a + b*x)^3)]

    @test_int [(a^2 - b^2*x^2)^(3/2)*(a + b*x)^3, x, 7, (9/16)*a^5*x*sqrt(a^2 - b^2*x^2) + (3/8)*a^3*x*(a^2 - b^2*x^2)^(3/2) - (3*a^2*(a^2 - b^2*x^2)^(5/2))/(10*b) - (3*a*(a + b*x)*(a^2 - b^2*x^2)^(5/2))/(14*b) - ((a + b*x)^2*(a^2 - b^2*x^2)^(5/2))/(7*b) + (9*a^7*atan((b*x)/sqrt(a^2 - b^2*x^2)))/(16*b)]
    @test_int [(a^2 - b^2*x^2)^(3/2)*(a + b*x)^2, x, 6, (7/16)*a^4*x*sqrt(a^2 - b^2*x^2) + (7/24)*a^2*x*(a^2 - b^2*x^2)^(3/2) - (7*a*(a^2 - b^2*x^2)^(5/2))/(30*b) - ((a + b*x)*(a^2 - b^2*x^2)^(5/2))/(6*b) + (7*a^6*atan((b*x)/sqrt(a^2 - b^2*x^2)))/(16*b)]
    @test_int [(a^2 - b^2*x^2)^(3/2)*(a + b*x)^1, x, 5, (3/8)*a^3*x*sqrt(a^2 - b^2*x^2) + (1/4)*a*x*(a^2 - b^2*x^2)^(3/2) - (a^2 - b^2*x^2)^(5/2)/(5*b) + (3*a^5*atan((b*x)/sqrt(a^2 - b^2*x^2)))/(8*b)]
    @test_int [(a^2 - b^2*x^2)^(3/2)/(a + b*x)^1, x, 4, (1/2)*a*x*sqrt(a^2 - b^2*x^2) + (a^2 - b^2*x^2)^(3/2)/(3*b) + (a^3*atan((b*x)/sqrt(a^2 - b^2*x^2)))/(2*b)]
    @test_int [(a^2 - b^2*x^2)^(3/2)/(a + b*x)^2, x, 4, (3*a*sqrt(a^2 - b^2*x^2))/(2*b) + (a^2 - b^2*x^2)^(3/2)/(2*b*(a + b*x)) + (3*a^2*atan((b*x)/sqrt(a^2 - b^2*x^2)))/(2*b)]
    @test_int [(a^2 - b^2*x^2)^(3/2)/(a + b*x)^3, x, 4, -((3*sqrt(a^2 - b^2*x^2))/b) - (2*(a^2 - b^2*x^2)^(3/2))/(b*(a + b*x)^2) - (3*a*atan((b*x)/sqrt(a^2 - b^2*x^2)))/b]
    @test_int [(a^2 - b^2*x^2)^(3/2)/(a + b*x)^4, x, 4, (2*sqrt(a^2 - b^2*x^2))/(b*(a + b*x)) - (2*(a^2 - b^2*x^2)^(3/2))/(3*b*(a + b*x)^3) + atan((b*x)/sqrt(a^2 - b^2*x^2))/b]
    @test_int [(a^2 - b^2*x^2)^(3/2)/(a + b*x)^5, x, 1, -((a^2 - b^2*x^2)^(5/2)/(5*a*b*(a + b*x)^5))]
    @test_int [(a^2 - b^2*x^2)^(3/2)/(a + b*x)^6, x, 2, -((a^2 - b^2*x^2)^(5/2)/(7*a*b*(a + b*x)^6)) - (a^2 - b^2*x^2)^(5/2)/(35*a^2*b*(a + b*x)^5)]
    @test_int [(a^2 - b^2*x^2)^(3/2)/(a + b*x)^7, x, 3, -((a^2 - b^2*x^2)^(5/2)/(9*a*b*(a + b*x)^7)) - (2*(a^2 - b^2*x^2)^(5/2))/(63*a^2*b*(a + b*x)^6) - (2*(a^2 - b^2*x^2)^(5/2))/(315*a^3*b*(a + b*x)^5)]
    @test_int [(a^2 - b^2*x^2)^(3/2)/(a + b*x)^8, x, 4, -((a^2 - b^2*x^2)^(5/2)/(11*a*b*(a + b*x)^8)) - (a^2 - b^2*x^2)^(5/2)/(33*a^2*b*(a + b*x)^7) - (2*(a^2 - b^2*x^2)^(5/2))/(231*a^3*b*(a + b*x)^6) - (2*(a^2 - b^2*x^2)^(5/2))/(1155*a^4*b*(a + b*x)^5)]
    @test_int [(a^2 - b^2*x^2)^(3/2)/(a + b*x)^9, x, 5, -((a^2 - b^2*x^2)^(5/2)/(13*a*b*(a + b*x)^9)) - (4*(a^2 - b^2*x^2)^(5/2))/(143*a^2*b*(a + b*x)^8) - (4*(a^2 - b^2*x^2)^(5/2))/(429*a^3*b*(a + b*x)^7) - (8*(a^2 - b^2*x^2)^(5/2))/(3003*a^4*b*(a + b*x)^6) - (8*(a^2 - b^2*x^2)^(5/2))/(15015*a^5*b*(a + b*x)^5)]

    @test_int [(d^2 - e^2*x^2)^(7/2)*(d + e*x)^3, x, 9, (91/256)*d^9*x*sqrt(d^2 - e^2*x^2) + (91/384)*d^7*x*(d^2 - e^2*x^2)^(3/2) + (91/480)*d^5*x*(d^2 - e^2*x^2)^(5/2) + (13/80)*d^3*x*(d^2 - e^2*x^2)^(7/2) - (13*d^2*(d^2 - e^2*x^2)^(9/2))/(90*e) - (13*d*(d + e*x)*(d^2 - e^2*x^2)^(9/2))/(110*e) - ((d + e*x)^2*(d^2 - e^2*x^2)^(9/2))/(11*e) + (91*d^11*atan((e*x)/sqrt(d^2 - e^2*x^2)))/(256*e)]
    @test_int [(d^2 - e^2*x^2)^(7/2)*(d + e*x)^2, x, 8, (77/256)*d^8*x*sqrt(d^2 - e^2*x^2) + (77/384)*d^6*x*(d^2 - e^2*x^2)^(3/2) + (77/480)*d^4*x*(d^2 - e^2*x^2)^(5/2) + (11/80)*d^2*x*(d^2 - e^2*x^2)^(7/2) - (11*d*(d^2 - e^2*x^2)^(9/2))/(90*e) - ((d + e*x)*(d^2 - e^2*x^2)^(9/2))/(10*e) + (77*d^10*atan((e*x)/sqrt(d^2 - e^2*x^2)))/(256*e)]
    @test_int [(d^2 - e^2*x^2)^(7/2)*(d + e*x)^1, x, 7, (35/128)*d^7*x*sqrt(d^2 - e^2*x^2) + (35/192)*d^5*x*(d^2 - e^2*x^2)^(3/2) + (7/48)*d^3*x*(d^2 - e^2*x^2)^(5/2) + (1/8)*d*x*(d^2 - e^2*x^2)^(7/2) - (d^2 - e^2*x^2)^(9/2)/(9*e) + (35*d^9*atan((e*x)/sqrt(d^2 - e^2*x^2)))/(128*e)]
    @test_int [(d^2 - e^2*x^2)^(7/2)/(d + e*x)^1, x, 6, (5/16)*d^5*x*sqrt(d^2 - e^2*x^2) + (5/24)*d^3*x*(d^2 - e^2*x^2)^(3/2) + (1/6)*d*x*(d^2 - e^2*x^2)^(5/2) + (d^2 - e^2*x^2)^(7/2)/(7*e) + (5*d^7*atan((e*x)/sqrt(d^2 - e^2*x^2)))/(16*e)]
    @test_int [(d^2 - e^2*x^2)^(7/2)/(d + e*x)^2, x, 7, (7/16)*d^4*x*sqrt(d^2 - e^2*x^2) + (7/24)*d^2*x*(d^2 - e^2*x^2)^(3/2) + (7*d*(d^2 - e^2*x^2)^(5/2))/(30*e) + ((d - e*x)*(d^2 - e^2*x^2)^(5/2))/(6*e) + (7*d^6*atan((e*x)/sqrt(d^2 - e^2*x^2)))/(16*e)]
    @test_int [(d^2 - e^2*x^2)^(7/2)/(d + e*x)^3, x, 7, (7/8)*d^3*x*sqrt(d^2 - e^2*x^2) + (7*d^2*(d^2 - e^2*x^2)^(3/2))/(12*e) + (7*d*(d - e*x)*(d^2 - e^2*x^2)^(3/2))/(20*e) + ((d - e*x)^2*(d^2 - e^2*x^2)^(3/2))/(5*e) + (7*d^5*atan((e*x)/sqrt(d^2 - e^2*x^2)))/(8*e)]
    @test_int [(d^2 - e^2*x^2)^(7/2)/(d + e*x)^4, x, 7, (35/8)*d^2*x*sqrt(d^2 - e^2*x^2) + (35*d*(d^2 - e^2*x^2)^(3/2))/(12*e) + (7*(d - e*x)*(d^2 - e^2*x^2)^(3/2))/(4*e) + (2*(d^2 - e^2*x^2)^(7/2))/(e*(d + e*x)^3) + (35*d^4*atan((e*x)/sqrt(d^2 - e^2*x^2)))/(8*e)]
    @test_int [(d^2 - e^2*x^2)^(7/2)/(d + e*x)^5, x, 6, (-(35/2))*d*x*sqrt(d^2 - e^2*x^2) - (35*(d^2 - e^2*x^2)^(3/2))/(3*e) - (14*(d^2 - e^2*x^2)^(5/2))/(e*(d + e*x)^2) - (2*(d^2 - e^2*x^2)^(7/2))/(e*(d + e*x)^4) - (35*d^3*atan((e*x)/sqrt(d^2 - e^2*x^2)))/(2*e)]
    @test_int [(d^2 - e^2*x^2)^(7/2)/(d + e*x)^6, x, 6, (35*d*sqrt(d^2 - e^2*x^2))/(2*e) + (35*(d^2 - e^2*x^2)^(3/2))/(6*e*(d + e*x)) + (14*(d^2 - e^2*x^2)^(5/2))/(3*e*(d + e*x)^3) - (2*(d^2 - e^2*x^2)^(7/2))/(3*e*(d + e*x)^5) + (35*d^2*atan((e*x)/sqrt(d^2 - e^2*x^2)))/(2*e)]
    @test_int [(d^2 - e^2*x^2)^(7/2)/(d + e*x)^7, x, 6, -((7*sqrt(d^2 - e^2*x^2))/e) - (14*(d^2 - e^2*x^2)^(3/2))/(3*e*(d + e*x)^2) + (14*(d^2 - e^2*x^2)^(5/2))/(15*e*(d + e*x)^4) - (2*(d^2 - e^2*x^2)^(7/2))/(5*e*(d + e*x)^6) - (7*d*atan((e*x)/sqrt(d^2 - e^2*x^2)))/e]
    @test_int [(d^2 - e^2*x^2)^(7/2)/(d + e*x)^8, x, 6, (2*sqrt(d^2 - e^2*x^2))/(e*(d + e*x)) - (2*(d^2 - e^2*x^2)^(3/2))/(3*e*(d + e*x)^3) + (2*(d^2 - e^2*x^2)^(5/2))/(5*e*(d + e*x)^5) - (2*(d^2 - e^2*x^2)^(7/2))/(7*e*(d + e*x)^7) + atan((e*x)/sqrt(d^2 - e^2*x^2))/e]
    @test_int [(d^2 - e^2*x^2)^(7/2)/(d + e*x)^9, x, 1, -((d^2 - e^2*x^2)^(9/2)/(9*d*e*(d + e*x)^9))]
    @test_int [(d^2 - e^2*x^2)^(7/2)/(d + e*x)^10, x, 2, -((d^2 - e^2*x^2)^(9/2)/(11*d*e*(d + e*x)^10)) - (d^2 - e^2*x^2)^(9/2)/(99*d^2*e*(d + e*x)^9)]
    @test_int [(d^2 - e^2*x^2)^(7/2)/(d + e*x)^11, x, 3, -((d^2 - e^2*x^2)^(9/2)/(13*d*e*(d + e*x)^11)) - (2*(d^2 - e^2*x^2)^(9/2))/(143*d^2*e*(d + e*x)^10) - (2*(d^2 - e^2*x^2)^(9/2))/(1287*d^3*e*(d + e*x)^9)]
    @test_int [(d^2 - e^2*x^2)^(7/2)/(d + e*x)^12, x, 4, -((d^2 - e^2*x^2)^(9/2)/(15*d*e*(d + e*x)^12)) - (d^2 - e^2*x^2)^(9/2)/(65*d^2*e*(d + e*x)^11) - (2*(d^2 - e^2*x^2)^(9/2))/(715*d^3*e*(d + e*x)^10) - (2*(d^2 - e^2*x^2)^(9/2))/(6435*d^4*e*(d + e*x)^9)]
    @test_int [(d^2 - e^2*x^2)^(7/2)/(d + e*x)^13, x, 5, -((d^2 - e^2*x^2)^(9/2)/(17*d*e*(d + e*x)^13)) - (4*(d^2 - e^2*x^2)^(9/2))/(255*d^2*e*(d + e*x)^12) - (4*(d^2 - e^2*x^2)^(9/2))/(1105*d^3*e*(d + e*x)^11) - (8*(d^2 - e^2*x^2)^(9/2))/(12155*d^4*e*(d + e*x)^10) - (8*(d^2 - e^2*x^2)^(9/2))/(109395*d^5*e*(d + e*x)^9)]

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

    @test_int [(a + b*x)^2*sqrt(-((a^2*c)/b^2) + c*x^2), x, 5, (5/8)*a^2*x*sqrt(-((a^2*c)/b^2) + c*x^2) + (5*a*b*(-((a^2*c)/b^2) + c*x^2)^(3/2))/(12*c) + (b*(a + b*x)*(-((a^2*c)/b^2) + c*x^2)^(3/2))/(4*c) - (5*a^4*sqrt(c)*atanh((sqrt(c)*x)/sqrt(-((a^2*c)/b^2) + c*x^2)))/(8*b^2)]
    @test_int [(a + b*x)^3*sqrt(-((a^2*c)/b^2) + c*x^2), x, 6, (7/8)*a^3*x*sqrt(-((a^2*c)/b^2) + c*x^2) + (7*a^2*b*(-((a^2*c)/b^2) + c*x^2)^(3/2))/(12*c) + (7*a*b*(a + b*x)*(-((a^2*c)/b^2) + c*x^2)^(3/2))/(20*c) + (b*(a + b*x)^2*(-((a^2*c)/b^2) + c*x^2)^(3/2))/(5*c) - (7*a^5*sqrt(c)*atanh((sqrt(c)*x)/sqrt(-((a^2*c)/b^2) + c*x^2)))/(8*b^2)]

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

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

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

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

    @test_int [(d + e*x)^5/sqrt(d^2 - e^2*x^2), x, 7, -((63*d^4*sqrt(d^2 - e^2*x^2))/(8*e)) - (21*d^3*(d + e*x)*sqrt(d^2 - e^2*x^2))/(8*e) - (21*d^2*(d + e*x)^2*sqrt(d^2 - e^2*x^2))/(20*e) - (9*d*(d + e*x)^3*sqrt(d^2 - e^2*x^2))/(20*e) - ((d + e*x)^4*sqrt(d^2 - e^2*x^2))/(5*e) + (63*d^5*atan((e*x)/sqrt(d^2 - e^2*x^2)))/(8*e)]
    @test_int [(d + e*x)^4/sqrt(d^2 - e^2*x^2), x, 6, -((35*d^3*sqrt(d^2 - e^2*x^2))/(8*e)) - (35*d^2*(d + e*x)*sqrt(d^2 - e^2*x^2))/(24*e) - (7*d*(d + e*x)^2*sqrt(d^2 - e^2*x^2))/(12*e) - ((d + e*x)^3*sqrt(d^2 - e^2*x^2))/(4*e) + (35*d^4*atan((e*x)/sqrt(d^2 - e^2*x^2)))/(8*e)]
    @test_int [(d + e*x)^3/sqrt(d^2 - e^2*x^2), x, 5, -((5*d^2*sqrt(d^2 - e^2*x^2))/(2*e)) - (5*d*(d + e*x)*sqrt(d^2 - e^2*x^2))/(6*e) - ((d + e*x)^2*sqrt(d^2 - e^2*x^2))/(3*e) + (5*d^3*atan((e*x)/sqrt(d^2 - e^2*x^2)))/(2*e)]
    @test_int [(d + e*x)^2/sqrt(d^2 - e^2*x^2), x, 4, -((2*d*sqrt(d^2 - e^2*x^2))/e) - (1/2)*x*sqrt(d^2 - e^2*x^2) + (3*d^2*atan((e*x)/sqrt(d^2 - e^2*x^2)))/(2*e), -((3*d*sqrt(d^2 - e^2*x^2))/(2*e)) - ((d + e*x)*sqrt(d^2 - e^2*x^2))/(2*e) + (3*d^2*atan((e*x)/sqrt(d^2 - e^2*x^2)))/(2*e)]
    @test_int [(d + e*x)^1/sqrt(d^2 - e^2*x^2), x, 3, -(sqrt(d^2 - e^2*x^2)/e) + (d*atan((e*x)/sqrt(d^2 - e^2*x^2)))/e]
    @test_int [1/((d + e*x)^1*sqrt(d^2 - e^2*x^2)), x, 1, -(sqrt(d^2 - e^2*x^2)/(d*e*(d + e*x)))]
    @test_int [1/((d + e*x)^2*sqrt(d^2 - e^2*x^2)), x, 2, -(sqrt(d^2 - e^2*x^2)/(3*d*e*(d + e*x)^2)) - sqrt(d^2 - e^2*x^2)/(3*d^2*e*(d + e*x))]
    @test_int [1/((d + e*x)^3*sqrt(d^2 - e^2*x^2)), x, 3, -(sqrt(d^2 - e^2*x^2)/(5*d*e*(d + e*x)^3)) - (2*sqrt(d^2 - e^2*x^2))/(15*d^2*e*(d + e*x)^2) - (2*sqrt(d^2 - e^2*x^2))/(15*d^3*e*(d + e*x))]
    @test_int [1/((d + e*x)^4*sqrt(d^2 - e^2*x^2)), x, 4, -(sqrt(d^2 - e^2*x^2)/(7*d*e*(d + e*x)^4)) - (3*sqrt(d^2 - e^2*x^2))/(35*d^2*e*(d + e*x)^3) - (2*sqrt(d^2 - e^2*x^2))/(35*d^3*e*(d + e*x)^2) - (2*sqrt(d^2 - e^2*x^2))/(35*d^4*e*(d + e*x))]
    @test_int [1/((d + e*x)^5*sqrt(d^2 - e^2*x^2)), x, 5, -(sqrt(d^2 - e^2*x^2)/(9*d*e*(d + e*x)^5)) - (4*sqrt(d^2 - e^2*x^2))/(63*d^2*e*(d + e*x)^4) - (4*sqrt(d^2 - e^2*x^2))/(105*d^3*e*(d + e*x)^3) - (8*sqrt(d^2 - e^2*x^2))/(315*d^4*e*(d + e*x)^2) - (8*sqrt(d^2 - e^2*x^2))/(315*d^5*e*(d + e*x))]

    @test_int [(d + e*x)^6/(d^2 - e^2*x^2)^(5/2), x, 6, (2*(d + e*x)^5)/(3*e*(d^2 - e^2*x^2)^(3/2)) - (14*(d + e*x)^3)/(3*e*sqrt(d^2 - e^2*x^2)) - (35*d*sqrt(d^2 - e^2*x^2))/(2*e) - (35*(d + e*x)*sqrt(d^2 - e^2*x^2))/(6*e) + (35*d^2*atan((e*x)/sqrt(d^2 - e^2*x^2)))/(2*e)]
    @test_int [(d + e*x)^5/(d^2 - e^2*x^2)^(5/2), x, 5, (2*(d + e*x)^4)/(3*e*(d^2 - e^2*x^2)^(3/2)) - (10*(d + e*x)^2)/(3*e*sqrt(d^2 - e^2*x^2)) - (5*sqrt(d^2 - e^2*x^2))/e + (5*d*atan((e*x)/sqrt(d^2 - e^2*x^2)))/e]
    @test_int [(d + e*x)^4/(d^2 - e^2*x^2)^(5/2), x, 4, (2*(d + e*x)^3)/(3*e*(d^2 - e^2*x^2)^(3/2)) - (2*(d + e*x))/(e*sqrt(d^2 - e^2*x^2)) + atan((e*x)/sqrt(d^2 - e^2*x^2))/e]
    @test_int [(d + e*x)^3/(d^2 - e^2*x^2)^(5/2), x, 1, (d + e*x)^3/(3*d*e*(d^2 - e^2*x^2)^(3/2))]
    @test_int [(d + e*x)^2/(d^2 - e^2*x^2)^(5/2), x, 2, (2*(d + e*x))/(3*e*(d^2 - e^2*x^2)^(3/2)) + x/(3*d^2*sqrt(d^2 - e^2*x^2))]
    @test_int [(d + e*x)^1/(d^2 - e^2*x^2)^(5/2), x, 2, (d + e*x)/(3*d*e*(d^2 - e^2*x^2)^(3/2)) + (2*x)/(3*d^3*sqrt(d^2 - e^2*x^2))]
    @test_int [1/((d + e*x)^1*(d^2 - e^2*x^2)^(5/2)), x, 3, (4*x)/(15*d^3*(d^2 - e^2*x^2)^(3/2)) - 1/(5*d*e*(d + e*x)*(d^2 - e^2*x^2)^(3/2)) + (8*x)/(15*d^5*sqrt(d^2 - e^2*x^2))]
    @test_int [1/((d + e*x)^2*(d^2 - e^2*x^2)^(5/2)), x, 4, (4*x)/(21*d^4*(d^2 - e^2*x^2)^(3/2)) - 1/(7*d*e*(d + e*x)^2*(d^2 - e^2*x^2)^(3/2)) - 1/(7*d^2*e*(d + e*x)*(d^2 - e^2*x^2)^(3/2)) + (8*x)/(21*d^6*sqrt(d^2 - e^2*x^2))]
    @test_int [1/((d + e*x)^3*(d^2 - e^2*x^2)^(5/2)), x, 5, (8*x)/(63*d^5*(d^2 - e^2*x^2)^(3/2)) - 1/(9*d*e*(d + e*x)^3*(d^2 - e^2*x^2)^(3/2)) - 2/(21*d^2*e*(d + e*x)^2*(d^2 - e^2*x^2)^(3/2)) - 2/(21*d^3*e*(d + e*x)*(d^2 - e^2*x^2)^(3/2)) + (16*x)/(63*d^7*sqrt(d^2 - e^2*x^2))]
    @test_int [1/((d + e*x)^4*(d^2 - e^2*x^2)^(5/2)), x, 6, (8*x)/(99*d^6*(d^2 - e^2*x^2)^(3/2)) - 1/(11*d*e*(d + e*x)^4*(d^2 - e^2*x^2)^(3/2)) - 7/(99*d^2*e*(d + e*x)^3*(d^2 - e^2*x^2)^(3/2)) - 2/(33*d^3*e*(d + e*x)^2*(d^2 - e^2*x^2)^(3/2)) - 2/(33*d^4*e*(d + e*x)*(d^2 - e^2*x^2)^(3/2)) + (16*x)/(99*d^8*sqrt(d^2 - e^2*x^2))]

    @test_int [(d + e*x)^9/(d^2 - e^2*x^2)^(7/2), x, 8, (2*(d + e*x)^8)/(5*e*(d^2 - e^2*x^2)^(5/2)) - (22*(d + e*x)^6)/(15*e*(d^2 - e^2*x^2)^(3/2)) + (66*(d + e*x)^4)/(5*e*sqrt(d^2 - e^2*x^2)) + (231*d^2*sqrt(d^2 - e^2*x^2))/(2*e) + (77*d*(d + e*x)*sqrt(d^2 - e^2*x^2))/(2*e) + (77*(d + e*x)^2*sqrt(d^2 - e^2*x^2))/(5*e) - (231*d^3*atan((e*x)/sqrt(d^2 - e^2*x^2)))/(2*e)]
    @test_int [(d + e*x)^8/(d^2 - e^2*x^2)^(7/2), x, 7, (2*(d + e*x)^7)/(5*e*(d^2 - e^2*x^2)^(5/2)) - (6*(d + e*x)^5)/(5*e*(d^2 - e^2*x^2)^(3/2)) + (42*(d + e*x)^3)/(5*e*sqrt(d^2 - e^2*x^2)) + (63*d*sqrt(d^2 - e^2*x^2))/(2*e) + (21*(d + e*x)*sqrt(d^2 - e^2*x^2))/(2*e) - (63*d^2*atan((e*x)/sqrt(d^2 - e^2*x^2)))/(2*e)]
    @test_int [(d + e*x)^7/(d^2 - e^2*x^2)^(7/2), x, 6, (2*(d + e*x)^6)/(5*e*(d^2 - e^2*x^2)^(5/2)) - (14*(d + e*x)^4)/(15*e*(d^2 - e^2*x^2)^(3/2)) + (14*(d + e*x)^2)/(3*e*sqrt(d^2 - e^2*x^2)) + (7*sqrt(d^2 - e^2*x^2))/e - (7*d*atan((e*x)/sqrt(d^2 - e^2*x^2)))/e]
    @test_int [(d + e*x)^6/(d^2 - e^2*x^2)^(7/2), x, 5, (2*(d + e*x)^5)/(5*e*(d^2 - e^2*x^2)^(5/2)) - (2*(d + e*x)^3)/(3*e*(d^2 - e^2*x^2)^(3/2)) + (2*(d + e*x))/(e*sqrt(d^2 - e^2*x^2)) - atan((e*x)/sqrt(d^2 - e^2*x^2))/e]
    @test_int [(d + e*x)^5/(d^2 - e^2*x^2)^(7/2), x, 1, (d + e*x)^5/(5*d*e*(d^2 - e^2*x^2)^(5/2))]
    @test_int [(d + e*x)^4/(d^2 - e^2*x^2)^(7/2), x, 2, (d + e*x)^4/(3*d*e*(d^2 - e^2*x^2)^(5/2)) - (d + e*x)^5/(15*d^2*e*(d^2 - e^2*x^2)^(5/2))]
    @test_int [(d + e*x)^3/(d^2 - e^2*x^2)^(7/2), x, 4, sqrt(d^2 - e^2*x^2)/(5*d*e*(d - e*x)^3) + (2*sqrt(d^2 - e^2*x^2))/(15*d^2*e*(d - e*x)^2) + (2*sqrt(d^2 - e^2*x^2))/(15*d^3*e*(d - e*x))]
    @test_int [(d + e*x)^2/(d^2 - e^2*x^2)^(7/2), x, 3, (2*(d + e*x))/(5*e*(d^2 - e^2*x^2)^(5/2)) + x/(5*d^2*(d^2 - e^2*x^2)^(3/2)) + (2*x)/(5*d^4*sqrt(d^2 - e^2*x^2))]
    @test_int [(d + e*x)^1/(d^2 - e^2*x^2)^(7/2), x, 3, (d + e*x)/(5*d*e*(d^2 - e^2*x^2)^(5/2)) + (4*x)/(15*d^3*(d^2 - e^2*x^2)^(3/2)) + (8*x)/(15*d^5*sqrt(d^2 - e^2*x^2))]
    @test_int [1/((d + e*x)^1*(d^2 - e^2*x^2)^(7/2)), x, 4, (6*x)/(35*d^3*(d^2 - e^2*x^2)^(5/2)) - 1/(7*d*e*(d + e*x)*(d^2 - e^2*x^2)^(5/2)) + (8*x)/(35*d^5*(d^2 - e^2*x^2)^(3/2)) + (16*x)/(35*d^7*sqrt(d^2 - e^2*x^2))]
    @test_int [1/((d + e*x)^2*(d^2 - e^2*x^2)^(7/2)), x, 5, (2*x)/(15*d^4*(d^2 - e^2*x^2)^(5/2)) - 1/(9*d*e*(d + e*x)^2*(d^2 - e^2*x^2)^(5/2)) - 1/(9*d^2*e*(d + e*x)*(d^2 - e^2*x^2)^(5/2)) + (8*x)/(45*d^6*(d^2 - e^2*x^2)^(3/2)) + (16*x)/(45*d^8*sqrt(d^2 - e^2*x^2))]
    @test_int [1/((d + e*x)^3*(d^2 - e^2*x^2)^(7/2)), x, 6, (16*x)/(165*d^5*(d^2 - e^2*x^2)^(5/2)) - 1/(11*d*e*(d + e*x)^3*(d^2 - e^2*x^2)^(5/2)) - 8/(99*d^2*e*(d + e*x)^2*(d^2 - e^2*x^2)^(5/2)) - 8/(99*d^3*e*(d + e*x)*(d^2 - e^2*x^2)^(5/2)) + (64*x)/(495*d^7*(d^2 - e^2*x^2)^(3/2)) + (128*x)/(495*d^9*sqrt(d^2 - e^2*x^2))]
    @test_int [1/((d + e*x)^4*(d^2 - e^2*x^2)^(7/2)), x, 7, (48*x)/(715*d^6*(d^2 - e^2*x^2)^(5/2)) - 1/(13*d*e*(d + e*x)^4*(d^2 - e^2*x^2)^(5/2)) - 9/(143*d^2*e*(d + e*x)^3*(d^2 - e^2*x^2)^(5/2)) - 8/(143*d^3*e*(d + e*x)^2*(d^2 - e^2*x^2)^(5/2)) - 8/(143*d^4*e*(d + e*x)*(d^2 - e^2*x^2)^(5/2)) + (64*x)/(715*d^8*(d^2 - e^2*x^2)^(3/2)) + (128*x)/(715*d^10*sqrt(d^2 - e^2*x^2))]
    @test_int [1/((d + e*x)^5*(d^2 - e^2*x^2)^(7/2)), x, 8, (32*x)/(715*d^7*(d^2 - e^2*x^2)^(5/2)) - 1/(15*d*e*(d + e*x)^5*(d^2 - e^2*x^2)^(5/2)) - 2/(39*d^2*e*(d + e*x)^4*(d^2 - e^2*x^2)^(5/2)) - 6/(143*d^3*e*(d + e*x)^3*(d^2 - e^2*x^2)^(5/2)) - 16/(429*d^4*e*(d + e*x)^2*(d^2 - e^2*x^2)^(5/2)) - 16/(429*d^5*e*(d + e*x)*(d^2 - e^2*x^2)^(5/2)) + (128*x)/(2145*d^9*(d^2 - e^2*x^2)^(3/2)) + (256*x)/(2145*d^11*sqrt(d^2 - e^2*x^2))]

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

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

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

    @test_int [(d + e*x)^(5/2)*(c*d^2 - c*e^2*x^2)^(1/2), x, 4, -((256*d^3*(c*d^2 - c*e^2*x^2)^(3/2))/(315*c*e*(d + e*x)^(3/2))) - (64*d^2*(c*d^2 - c*e^2*x^2)^(3/2))/(105*c*e*sqrt(d + e*x)) - (8*d*sqrt(d + e*x)*(c*d^2 - c*e^2*x^2)^(3/2))/(21*c*e) - (2*(d + e*x)^(3/2)*(c*d^2 - c*e^2*x^2)^(3/2))/(9*c*e)]
    @test_int [(d + e*x)^(3/2)*(c*d^2 - c*e^2*x^2)^(1/2), x, 3, -((64*d^2*(c*d^2 - c*e^2*x^2)^(3/2))/(105*c*e*(d + e*x)^(3/2))) - (16*d*(c*d^2 - c*e^2*x^2)^(3/2))/(35*c*e*sqrt(d + e*x)) - (2*sqrt(d + e*x)*(c*d^2 - c*e^2*x^2)^(3/2))/(7*c*e)]
    @test_int [(d + e*x)^(1/2)*(c*d^2 - c*e^2*x^2)^(1/2), x, 2, -((8*d*(c*d^2 - c*e^2*x^2)^(3/2))/(15*c*e*(d + e*x)^(3/2))) - (2*(c*d^2 - c*e^2*x^2)^(3/2))/(5*c*e*sqrt(d + e*x))]
    @test_int [1/(d + e*x)^(1/2)*(c*d^2 - c*e^2*x^2)^(1/2), x, 1, -((2*(c*d^2 - c*e^2*x^2)^(3/2))/(3*c*e*(d + e*x)^(3/2)))]
    @test_int [1/(d + e*x)^(3/2)*(c*d^2 - c*e^2*x^2)^(1/2), x, 3, (2*sqrt(c*d^2 - c*e^2*x^2))/(e*sqrt(d + e*x)) - (2*sqrt(2)*sqrt(c)*sqrt(d)*atanh(sqrt(c*d^2 - c*e^2*x^2)/(sqrt(2)*sqrt(c)*sqrt(d)*sqrt(d + e*x))))/e]
    @test_int [1/(d + e*x)^(5/2)*(c*d^2 - c*e^2*x^2)^(1/2), x, 3, -(sqrt(c*d^2 - c*e^2*x^2)/(e*(d + e*x)^(3/2))) + (sqrt(c)*atanh(sqrt(c*d^2 - c*e^2*x^2)/(sqrt(2)*sqrt(c)*sqrt(d)*sqrt(d + e*x))))/(sqrt(2)*sqrt(d)*e)]
    @test_int [1/(d + e*x)^(7/2)*(c*d^2 - c*e^2*x^2)^(1/2), x, 4, -(sqrt(c*d^2 - c*e^2*x^2)/(2*e*(d + e*x)^(5/2))) + sqrt(c*d^2 - c*e^2*x^2)/(8*d*e*(d + e*x)^(3/2)) + (sqrt(c)*atanh(sqrt(c*d^2 - c*e^2*x^2)/(sqrt(2)*sqrt(c)*sqrt(d)*sqrt(d + e*x))))/(8*sqrt(2)*d^(3/2)*e)]

    @test_int [(d + e*x)^(5/2)*(c*d^2 - c*e^2*x^2)^(3/2), x, 5, -((4096*d^4*(c*d^2 - c*e^2*x^2)^(5/2))/(15015*c*e*(d + e*x)^(5/2))) - (1024*d^3*(c*d^2 - c*e^2*x^2)^(5/2))/(3003*c*e*(d + e*x)^(3/2)) - (128*d^2*(c*d^2 - c*e^2*x^2)^(5/2))/(429*c*e*sqrt(d + e*x)) - (32*d*sqrt(d + e*x)*(c*d^2 - c*e^2*x^2)^(5/2))/(143*c*e) - (2*(d + e*x)^(3/2)*(c*d^2 - c*e^2*x^2)^(5/2))/(13*c*e)]
    @test_int [(d + e*x)^(3/2)*(c*d^2 - c*e^2*x^2)^(3/2), x, 4, -((256*d^3*(c*d^2 - c*e^2*x^2)^(5/2))/(1155*c*e*(d + e*x)^(5/2))) - (64*d^2*(c*d^2 - c*e^2*x^2)^(5/2))/(231*c*e*(d + e*x)^(3/2)) - (8*d*(c*d^2 - c*e^2*x^2)^(5/2))/(33*c*e*sqrt(d + e*x)) - (2*sqrt(d + e*x)*(c*d^2 - c*e^2*x^2)^(5/2))/(11*c*e)]
    @test_int [(d + e*x)^(1/2)*(c*d^2 - c*e^2*x^2)^(3/2), x, 3, -((64*d^2*(c*d^2 - c*e^2*x^2)^(5/2))/(315*c*e*(d + e*x)^(5/2))) - (16*d*(c*d^2 - c*e^2*x^2)^(5/2))/(63*c*e*(d + e*x)^(3/2)) - (2*(c*d^2 - c*e^2*x^2)^(5/2))/(9*c*e*sqrt(d + e*x))]
    @test_int [1/(d + e*x)^(1/2)*(c*d^2 - c*e^2*x^2)^(3/2), x, 2, -((8*d*(c*d^2 - c*e^2*x^2)^(5/2))/(35*c*e*(d + e*x)^(5/2))) - (2*(c*d^2 - c*e^2*x^2)^(5/2))/(7*c*e*(d + e*x)^(3/2))]
    @test_int [1/(d + e*x)^(3/2)*(c*d^2 - c*e^2*x^2)^(3/2), x, 1, -((2*(c*d^2 - c*e^2*x^2)^(5/2))/(5*c*e*(d + e*x)^(5/2)))]
    @test_int [1/(d + e*x)^(5/2)*(c*d^2 - c*e^2*x^2)^(3/2), x, 4, (4*c*d*sqrt(c*d^2 - c*e^2*x^2))/(e*sqrt(d + e*x)) + (2*(c*d^2 - c*e^2*x^2)^(3/2))/(3*e*(d + e*x)^(3/2)) - (4*sqrt(2)*c^(3/2)*d^(3/2)*atanh(sqrt(c*d^2 - c*e^2*x^2)/(sqrt(2)*sqrt(c)*sqrt(d)*sqrt(d + e*x))))/e]
    @test_int [1/(d + e*x)^(7/2)*(c*d^2 - c*e^2*x^2)^(3/2), x, 4, -((3*c*sqrt(c*d^2 - c*e^2*x^2))/(e*sqrt(d + e*x))) - (c*d^2 - c*e^2*x^2)^(3/2)/(e*(d + e*x)^(5/2)) + (3*sqrt(2)*c^(3/2)*sqrt(d)*atanh(sqrt(c*d^2 - c*e^2*x^2)/(sqrt(2)*sqrt(c)*sqrt(d)*sqrt(d + e*x))))/e]
    @test_int [1/(d + e*x)^(9/2)*(c*d^2 - c*e^2*x^2)^(3/2), x, 4, (3*c*sqrt(c*d^2 - c*e^2*x^2))/(4*e*(d + e*x)^(3/2)) - (c*d^2 - c*e^2*x^2)^(3/2)/(2*e*(d + e*x)^(7/2)) - (3*c^(3/2)*atanh(sqrt(c*d^2 - c*e^2*x^2)/(sqrt(2)*sqrt(c)*sqrt(d)*sqrt(d + e*x))))/(4*sqrt(2)*sqrt(d)*e)]
    @test_int [1/(d + e*x)^(11/2)*(c*d^2 - c*e^2*x^2)^(3/2), x, 5, (c*sqrt(c*d^2 - c*e^2*x^2))/(4*e*(d + e*x)^(5/2)) - (c*sqrt(c*d^2 - c*e^2*x^2))/(16*d*e*(d + e*x)^(3/2)) - (c*d^2 - c*e^2*x^2)^(3/2)/(3*e*(d + e*x)^(9/2)) - (c^(3/2)*atanh(sqrt(c*d^2 - c*e^2*x^2)/(sqrt(2)*sqrt(c)*sqrt(d)*sqrt(d + e*x))))/(16*sqrt(2)*d^(3/2)*e)]
    @test_int [1/(d + e*x)^(13/2)*(c*d^2 - c*e^2*x^2)^(3/2), x, 6, (c*sqrt(c*d^2 - c*e^2*x^2))/(8*e*(d + e*x)^(7/2)) - (c*sqrt(c*d^2 - c*e^2*x^2))/(64*d*e*(d + e*x)^(5/2)) - (3*c*sqrt(c*d^2 - c*e^2*x^2))/(256*d^2*e*(d + e*x)^(3/2)) - (c*d^2 - c*e^2*x^2)^(3/2)/(4*e*(d + e*x)^(11/2)) - (3*c^(3/2)*atanh(sqrt(c*d^2 - c*e^2*x^2)/(sqrt(2)*sqrt(c)*sqrt(d)*sqrt(d + e*x))))/(256*sqrt(2)*d^(5/2)*e)]

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

    @test_int [(d + e*x)^(7/2)/(c*d^2 - c*e^2*x^2)^(1/2), x, 4, -((256*d^3*sqrt(c*d^2 - c*e^2*x^2))/(35*c*e*sqrt(d + e*x))) - (64*d^2*sqrt(d + e*x)*sqrt(c*d^2 - c*e^2*x^2))/(35*c*e) - (24*d*(d + e*x)^(3/2)*sqrt(c*d^2 - c*e^2*x^2))/(35*c*e) - (2*(d + e*x)^(5/2)*sqrt(c*d^2 - c*e^2*x^2))/(7*c*e)]
    @test_int [(d + e*x)^(5/2)/(c*d^2 - c*e^2*x^2)^(1/2), x, 3, -((64*d^2*sqrt(c*d^2 - c*e^2*x^2))/(15*c*e*sqrt(d + e*x))) - (16*d*sqrt(d + e*x)*sqrt(c*d^2 - c*e^2*x^2))/(15*c*e) - (2*(d + e*x)^(3/2)*sqrt(c*d^2 - c*e^2*x^2))/(5*c*e)]
    @test_int [(d + e*x)^(3/2)/(c*d^2 - c*e^2*x^2)^(1/2), x, 2, -((8*d*sqrt(c*d^2 - c*e^2*x^2))/(3*c*e*sqrt(d + e*x))) - (2*sqrt(d + e*x)*sqrt(c*d^2 - c*e^2*x^2))/(3*c*e)]
    @test_int [(d + e*x)^(1/2)/(c*d^2 - c*e^2*x^2)^(1/2), x, 1, -((2*sqrt(c*d^2 - c*e^2*x^2))/(c*e*sqrt(d + e*x)))]
    @test_int [1/(d + e*x)^(1/2)/(c*d^2 - c*e^2*x^2)^(1/2), x, 2, -((sqrt(2)*atanh(sqrt(c*d^2 - c*e^2*x^2)/(sqrt(2)*sqrt(c)*sqrt(d)*sqrt(d + e*x))))/(sqrt(c)*sqrt(d)*e))]
    @test_int [1/(d + e*x)^(3/2)/(c*d^2 - c*e^2*x^2)^(1/2), x, 3, -(sqrt(c*d^2 - c*e^2*x^2)/(2*c*d*e*(d + e*x)^(3/2))) - atanh(sqrt(c*d^2 - c*e^2*x^2)/(sqrt(2)*sqrt(c)*sqrt(d)*sqrt(d + e*x)))/(2*sqrt(2)*sqrt(c)*d^(3/2)*e)]
    @test_int [1/(d + e*x)^(5/2)/(c*d^2 - c*e^2*x^2)^(1/2), x, 4, -(sqrt(c*d^2 - c*e^2*x^2)/(4*c*d*e*(d + e*x)^(5/2))) - (3*sqrt(c*d^2 - c*e^2*x^2))/(16*c*d^2*e*(d + e*x)^(3/2)) - (3*atanh(sqrt(c*d^2 - c*e^2*x^2)/(sqrt(2)*sqrt(c)*sqrt(d)*sqrt(d + e*x))))/(16*sqrt(2)*sqrt(c)*d^(5/2)*e)]

    @test_int [(d + e*x)^(9/2)/(c*d^2 - c*e^2*x^2)^(3/2), x, 4, (256*d^3*sqrt(d + e*x))/(5*c*e*sqrt(c*d^2 - c*e^2*x^2)) - (64*d^2*(d + e*x)^(3/2))/(5*c*e*sqrt(c*d^2 - c*e^2*x^2)) - (8*d*(d + e*x)^(5/2))/(5*c*e*sqrt(c*d^2 - c*e^2*x^2)) - (2*(d + e*x)^(7/2))/(5*c*e*sqrt(c*d^2 - c*e^2*x^2))]
    @test_int [(d + e*x)^(7/2)/(c*d^2 - c*e^2*x^2)^(3/2), x, 3, (64*d^2*sqrt(d + e*x))/(3*c*e*sqrt(c*d^2 - c*e^2*x^2)) - (16*d*(d + e*x)^(3/2))/(3*c*e*sqrt(c*d^2 - c*e^2*x^2)) - (2*(d + e*x)^(5/2))/(3*c*e*sqrt(c*d^2 - c*e^2*x^2))]
    @test_int [(d + e*x)^(5/2)/(c*d^2 - c*e^2*x^2)^(3/2), x, 2, (8*d*sqrt(d + e*x))/(c*e*sqrt(c*d^2 - c*e^2*x^2)) - (2*(d + e*x)^(3/2))/(c*e*sqrt(c*d^2 - c*e^2*x^2))]
    @test_int [(d + e*x)^(3/2)/(c*d^2 - c*e^2*x^2)^(3/2), x, 1, (2*sqrt(d + e*x))/(c*e*sqrt(c*d^2 - c*e^2*x^2))]
    @test_int [(d + e*x)^(1/2)/(c*d^2 - c*e^2*x^2)^(3/2), x, 3, sqrt(d + e*x)/(c*d*e*sqrt(c*d^2 - c*e^2*x^2)) - atanh(sqrt(c*d^2 - c*e^2*x^2)/(sqrt(2)*sqrt(c)*sqrt(d)*sqrt(d + e*x)))/(sqrt(2)*c^(3/2)*d^(3/2)*e)]
    @test_int [1/(d + e*x)^(1/2)/(c*d^2 - c*e^2*x^2)^(3/2), x, 4, -(1/(2*c*d*e*sqrt(d + e*x)*sqrt(c*d^2 - c*e^2*x^2))) + (3*sqrt(d + e*x))/(4*c*d^2*e*sqrt(c*d^2 - c*e^2*x^2)) - (3*atanh(sqrt(c*d^2 - c*e^2*x^2)/(sqrt(2)*sqrt(c)*sqrt(d)*sqrt(d + e*x))))/(4*sqrt(2)*c^(3/2)*d^(5/2)*e)]
    @test_int [1/(d + e*x)^(3/2)/(c*d^2 - c*e^2*x^2)^(3/2), x, 5, -(1/(4*c*d*e*(d + e*x)^(3/2)*sqrt(c*d^2 - c*e^2*x^2))) - 5/(16*c*d^2*e*sqrt(d + e*x)*sqrt(c*d^2 - c*e^2*x^2)) + (15*sqrt(d + e*x))/(32*c*d^3*e*sqrt(c*d^2 - c*e^2*x^2)) - (15*atanh(sqrt(c*d^2 - c*e^2*x^2)/(sqrt(2)*sqrt(c)*sqrt(d)*sqrt(d + e*x))))/(32*sqrt(2)*c^(3/2)*d^(7/2)*e)]

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

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

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

    @test_int [(2 + e*x)^(5/2)*(12 - 3*e^2*x^2)^(1/2), x, 3, -((128*(2 - e*x)^(3/2))/(sqrt(3)*e)) + (96*sqrt(3)*(2 - e*x)^(5/2))/(5*e) - (24*sqrt(3)*(2 - e*x)^(7/2))/(7*e) + (2*(2 - e*x)^(9/2))/(3*sqrt(3)*e)]
    @test_int [(2 + e*x)^(3/2)*(12 - 3*e^2*x^2)^(1/2), x, 3, -((32*(2 - e*x)^(3/2))/(sqrt(3)*e)) + (16*sqrt(3)*(2 - e*x)^(5/2))/(5*e) - (2*sqrt(3)*(2 - e*x)^(7/2))/(7*e)]
    @test_int [(2 + e*x)^(1/2)*(12 - 3*e^2*x^2)^(1/2), x, 3, -((8*(2 - e*x)^(3/2))/(sqrt(3)*e)) + (2*sqrt(3)*(2 - e*x)^(5/2))/(5*e)]
    @test_int [1/(2 + e*x)^(1/2)*(12 - 3*e^2*x^2)^(1/2), x, 2, -((2*(2 - e*x)^(3/2))/(sqrt(3)*e))]
    @test_int [1/(2 + e*x)^(3/2)*(12 - 3*e^2*x^2)^(1/2), x, 4, (2*sqrt(3)*sqrt(2 - e*x))/e - (4*sqrt(3)*atanh((1/2)*sqrt(2 - e*x)))/e]
    @test_int [1/(2 + e*x)^(5/2)*(12 - 3*e^2*x^2)^(1/2), x, 4, -((sqrt(3)*sqrt(2 - e*x))/(e*(2 + e*x))) + (sqrt(3)*atanh((1/2)*sqrt(2 - e*x)))/(2*e)]
    @test_int [1/(2 + e*x)^(7/2)*(12 - 3*e^2*x^2)^(1/2), x, 5, -((sqrt(3)*sqrt(2 - e*x))/(2*e*(2 + e*x)^2)) + (sqrt(3)*sqrt(2 - e*x))/(16*e*(2 + e*x)) + (sqrt(3)*atanh((1/2)*sqrt(2 - e*x)))/(32*e)]

    @test_int [(2 + e*x)^(5/2)*(12 - 3*e^2*x^2)^(3/2), x, 3, -((1536*sqrt(3)*(2 - e*x)^(5/2))/(5*e)) + (1536*sqrt(3)*(2 - e*x)^(7/2))/(7*e) - (64*sqrt(3)*(2 - e*x)^(9/2))/e + (96*sqrt(3)*(2 - e*x)^(11/2))/(11*e) - (6*sqrt(3)*(2 - e*x)^(13/2))/(13*e)]
    @test_int [(2 + e*x)^(3/2)*(12 - 3*e^2*x^2)^(3/2), x, 3, -((384*sqrt(3)*(2 - e*x)^(5/2))/(5*e)) + (288*sqrt(3)*(2 - e*x)^(7/2))/(7*e) - (8*sqrt(3)*(2 - e*x)^(9/2))/e + (6*sqrt(3)*(2 - e*x)^(11/2))/(11*e)]
    @test_int [(2 + e*x)^(1/2)*(12 - 3*e^2*x^2)^(3/2), x, 3, -((96*sqrt(3)*(2 - e*x)^(5/2))/(5*e)) + (48*sqrt(3)*(2 - e*x)^(7/2))/(7*e) - (2*(2 - e*x)^(9/2))/(sqrt(3)*e)]
    @test_int [1/(2 + e*x)^(1/2)*(12 - 3*e^2*x^2)^(3/2), x, 3, -((24*sqrt(3)*(2 - e*x)^(5/2))/(5*e)) + (6*sqrt(3)*(2 - e*x)^(7/2))/(7*e)]
    @test_int [1/(2 + e*x)^(3/2)*(12 - 3*e^2*x^2)^(3/2), x, 2, -((6*sqrt(3)*(2 - e*x)^(5/2))/(5*e))]
    @test_int [1/(2 + e*x)^(5/2)*(12 - 3*e^2*x^2)^(3/2), x, 5, (24*sqrt(3)*sqrt(2 - e*x))/e + (2*sqrt(3)*(2 - e*x)^(3/2))/e - (48*sqrt(3)*atanh((1/2)*sqrt(2 - e*x)))/e]
    @test_int [1/(2 + e*x)^(7/2)*(12 - 3*e^2*x^2)^(3/2), x, 5, -((9*sqrt(3)*sqrt(2 - e*x))/e) - (3*sqrt(3)*(2 - e*x)^(3/2))/(e*(2 + e*x)) + (18*sqrt(3)*atanh((1/2)*sqrt(2 - e*x)))/e]
    @test_int [1/(2 + e*x)^(9/2)*(12 - 3*e^2*x^2)^(3/2), x, 5, -((3*sqrt(3)*(2 - e*x)^(3/2))/(2*e*(2 + e*x)^2)) + (9*sqrt(3)*sqrt(2 - e*x))/(4*e*(2 + e*x)) - (9*sqrt(3)*atanh((1/2)*sqrt(2 - e*x)))/(8*e)]
    @test_int [1/(2 + e*x)^(11/2)*(12 - 3*e^2*x^2)^(3/2), x, 6, -((sqrt(3)*(2 - e*x)^(3/2))/(e*(2 + e*x)^3)) + (3*sqrt(3)*sqrt(2 - e*x))/(4*e*(2 + e*x)^2) - (3*sqrt(3)*sqrt(2 - e*x))/(32*e*(2 + e*x)) - (3*sqrt(3)*atanh((1/2)*sqrt(2 - e*x)))/(64*e)]
    @test_int [1/(2 + e*x)^(13/2)*(12 - 3*e^2*x^2)^(3/2), x, 7, -((3*sqrt(3)*(2 - e*x)^(3/2))/(4*e*(2 + e*x)^4)) + (3*sqrt(3)*sqrt(2 - e*x))/(8*e*(2 + e*x)^3) - (3*sqrt(3)*sqrt(2 - e*x))/(128*e*(2 + e*x)^2) - (9*sqrt(3)*sqrt(2 - e*x))/(1024*e*(2 + e*x)) - (9*sqrt(3)*atanh((1/2)*sqrt(2 - e*x)))/(2048*e)]

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

    @test_int [(2 + e*x)^(7/2)/(12 - 3*e^2*x^2)^(1/2), x, 3, -((128*sqrt(2 - e*x))/(sqrt(3)*e)) + (32*(2 - e*x)^(3/2))/(sqrt(3)*e) - (8*sqrt(3)*(2 - e*x)^(5/2))/(5*e) + (2*(2 - e*x)^(7/2))/(7*sqrt(3)*e)]
    @test_int [(2 + e*x)^(5/2)/(12 - 3*e^2*x^2)^(1/2), x, 3, -((32*sqrt(2 - e*x))/(sqrt(3)*e)) + (16*(2 - e*x)^(3/2))/(3*sqrt(3)*e) - (2*(2 - e*x)^(5/2))/(5*sqrt(3)*e)]
    @test_int [(2 + e*x)^(3/2)/(12 - 3*e^2*x^2)^(1/2), x, 3, -((8*sqrt(2 - e*x))/(sqrt(3)*e)) + (2*(2 - e*x)^(3/2))/(3*sqrt(3)*e)]
    @test_int [(2 + e*x)^(1/2)/(12 - 3*e^2*x^2)^(1/2), x, 2, -((2*sqrt(2 - e*x))/(sqrt(3)*e))]
    @test_int [1/(2 + e*x)^(1/2)/(12 - 3*e^2*x^2)^(1/2), x, 3, -(atanh((1/2)*sqrt(2 - e*x))/(sqrt(3)*e))]
    @test_int [1/(2 + e*x)^(3/2)/(12 - 3*e^2*x^2)^(1/2), x, 4, -(sqrt(2 - e*x)/(4*sqrt(3)*e*(2 + e*x))) - atanh((1/2)*sqrt(2 - e*x))/(8*sqrt(3)*e)]
    @test_int [1/(2 + e*x)^(5/2)/(12 - 3*e^2*x^2)^(1/2), x, 5, -(sqrt(2 - e*x)/(8*sqrt(3)*e*(2 + e*x)^2)) - (sqrt(3)*sqrt(2 - e*x))/(64*e*(2 + e*x)) - (sqrt(3)*atanh((1/2)*sqrt(2 - e*x)))/(128*e)]

    @test_int [(2 + e*x)^(11/2)/(12 - 3*e^2*x^2)^(3/2), x, 3, 512/(3*sqrt(3)*e*sqrt(2 - e*x)) + (512*sqrt(2 - e*x))/(3*sqrt(3)*e) - (64*(2 - e*x)^(3/2))/(3*sqrt(3)*e) + (32*(2 - e*x)^(5/2))/(15*sqrt(3)*e) - (2*(2 - e*x)^(7/2))/(21*sqrt(3)*e)]
    @test_int [(2 + e*x)^(9/2)/(12 - 3*e^2*x^2)^(3/2), x, 3, 128/(3*sqrt(3)*e*sqrt(2 - e*x)) + (32*sqrt(2 - e*x))/(sqrt(3)*e) - (8*(2 - e*x)^(3/2))/(3*sqrt(3)*e) + (2*(2 - e*x)^(5/2))/(15*sqrt(3)*e)]
    @test_int [(2 + e*x)^(7/2)/(12 - 3*e^2*x^2)^(3/2), x, 3, 32/(3*sqrt(3)*e*sqrt(2 - e*x)) + (16*sqrt(2 - e*x))/(3*sqrt(3)*e) - (2*(2 - e*x)^(3/2))/(9*sqrt(3)*e)]
    @test_int [(2 + e*x)^(5/2)/(12 - 3*e^2*x^2)^(3/2), x, 3, 8/(3*sqrt(3)*e*sqrt(2 - e*x)) + (2*sqrt(2 - e*x))/(3*sqrt(3)*e)]
    @test_int [(2 + e*x)^(3/2)/(12 - 3*e^2*x^2)^(3/2), x, 2, 2/(3*sqrt(3)*e*sqrt(2 - e*x))]
    @test_int [(2 + e*x)^(1/2)/(12 - 3*e^2*x^2)^(3/2), x, 4, 1/(6*sqrt(3)*e*sqrt(2 - e*x)) - atanh((1/2)*sqrt(2 - e*x))/(12*sqrt(3)*e)]
    @test_int [1/(2 + e*x)^(1/2)/(12 - 3*e^2*x^2)^(3/2), x, 5, 1/(16*sqrt(3)*e*sqrt(2 - e*x)) - 1/(12*sqrt(3)*e*sqrt(2 - e*x)*(2 + e*x)) - atanh((1/2)*sqrt(2 - e*x))/(32*sqrt(3)*e)]
    @test_int [1/(2 + e*x)^(3/2)/(12 - 3*e^2*x^2)^(3/2), x, 6, 5/(256*sqrt(3)*e*sqrt(2 - e*x)) - 1/(24*sqrt(3)*e*sqrt(2 - e*x)*(2 + e*x)^2) - 5/(192*sqrt(3)*e*sqrt(2 - e*x)*(2 + e*x)) - (5*atanh((1/2)*sqrt(2 - e*x)))/(512*sqrt(3)*e)]

    #= The*following*pairs*of*integrands*are*equal: =#
    @test_int [1/(sqrt(1 - x)*(1 + x)), x, 2, (-sqrt(2))*atanh(sqrt(1 - x)/sqrt(2))]
    @test_int [1/(sqrt(1 + x)*sqrt(1 - x^2)), x, 3, (-sqrt(2))*atanh(sqrt(1 - x)/sqrt(2))]

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(d+e*x)^(m/2)*(c*d^2 - c*e^2*x^2)^(p/4)*when*d>0*and*c>0=#

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

    @test_int [(12 - 3*e^2*x^2)^(1/4)*(2 + e*x)^(1/2), x, 14, If(13>=8, (3*3^(1/4)*(2 - e*x)^(1/4)*(2 + e*x)^(3/4))/(2*e) - (3^(1/4)*(2 - e*x)^(5/4)*(2 + e*x)^(3/4))/(2*e) + (3*3^(1/4)*atan(1 - (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(sqrt(2)*e) - (3*3^(1/4)*atan(1 + (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(sqrt(2)*e) + (3*3^(1/4)*log((sqrt(6 - 3*e*x) - sqrt(6)*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + sqrt(3)*sqrt(2 + e*x))/sqrt(2 + e*x)))/(2*sqrt(2)*e) - (3*3^(1/4)*log((sqrt(6 - 3*e*x) + sqrt(6)*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + sqrt(3)*sqrt(2 + e*x))/sqrt(2 + e*x)))/(2*sqrt(2)*e), (3*3^(1/4)*(2 - e*x)^(1/4)*(2 + e*x)^(3/4))/(2*e) - (3^(1/4)*(2 - e*x)^(5/4)*(2 + e*x)^(3/4))/(2*e) + (3*3^(1/4)*atan(1 - (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(sqrt(2)*e) - (3*3^(1/4)*atan(1 + (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(sqrt(2)*e) + (3*3^(1/4)*log(sqrt(3) + (sqrt(3)*sqrt(2 - e*x))/sqrt(2 + e*x) - (sqrt(6)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(2*sqrt(2)*e) - (3*3^(1/4)*log(sqrt(3) + (sqrt(3)*sqrt(2 - e*x))/sqrt(2 + e*x) + (sqrt(6)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(2*sqrt(2)*e))]
    @test_int [(12 - 3*e^2*x^2)^(1/4)/(2 + e*x)^(1/2), x, 13, If(13>=8, (3^(1/4)*(2 - e*x)^(1/4)*(2 + e*x)^(3/4))/e + (sqrt(2)*3^(1/4)*atan(1 - (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/e - (sqrt(2)*3^(1/4)*atan(1 + (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/e + (3^(1/4)*log((sqrt(6 - 3*e*x) - sqrt(6)*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + sqrt(3)*sqrt(2 + e*x))/sqrt(2 + e*x)))/(sqrt(2)*e) - (3^(1/4)*log((sqrt(6 - 3*e*x) + sqrt(6)*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + sqrt(3)*sqrt(2 + e*x))/sqrt(2 + e*x)))/(sqrt(2)*e), (3^(1/4)*(2 - e*x)^(1/4)*(2 + e*x)^(3/4))/e + (sqrt(2)*3^(1/4)*atan(1 - (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/e - (sqrt(2)*3^(1/4)*atan(1 + (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/e + (3^(1/4)*log(sqrt(3) + (sqrt(3)*sqrt(2 - e*x))/sqrt(2 + e*x) - (sqrt(6)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(sqrt(2)*e) - (3^(1/4)*log(sqrt(3) + (sqrt(3)*sqrt(2 - e*x))/sqrt(2 + e*x) + (sqrt(6)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(sqrt(2)*e))]
    @test_int [(12 - 3*e^2*x^2)^(1/4)/(2 + e*x)^(3/2), x, 13, If(13>=8, -((4*3^(1/4)*(2 - e*x)^(1/4))/(e*(2 + e*x)^(1/4))) - (sqrt(2)*3^(1/4)*atan(1 - (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/e + (sqrt(2)*3^(1/4)*atan(1 + (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/e - (3^(1/4)*log((sqrt(6 - 3*e*x) - sqrt(6)*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + sqrt(3)*sqrt(2 + e*x))/sqrt(2 + e*x)))/(sqrt(2)*e) + (3^(1/4)*log((sqrt(6 - 3*e*x) + sqrt(6)*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + sqrt(3)*sqrt(2 + e*x))/sqrt(2 + e*x)))/(sqrt(2)*e), -((4*3^(1/4)*(2 - e*x)^(1/4))/(e*(2 + e*x)^(1/4))) - (sqrt(2)*3^(1/4)*atan(1 - (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/e + (sqrt(2)*3^(1/4)*atan(1 + (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/e - (3^(1/4)*log(sqrt(3) + (sqrt(3)*sqrt(2 - e*x))/sqrt(2 + e*x) - (sqrt(6)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(sqrt(2)*e) + (3^(1/4)*log(sqrt(3) + (sqrt(3)*sqrt(2 - e*x))/sqrt(2 + e*x) + (sqrt(6)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(sqrt(2)*e))]
    @test_int [(12 - 3*e^2*x^2)^(1/4)/(2 + e*x)^(5/2), x, 1, -((3^(1/4)*(4 - e^2*x^2)^(5/4))/(5*e*(2 + e*x)^(5/2)))]
    @test_int [(12 - 3*e^2*x^2)^(1/4)/(2 + e*x)^(7/2), x, 2, -((4 - e^2*x^2)^(5/4)/(3*3^(3/4)*e*(2 + e*x)^(7/2))) - (4 - e^2*x^2)^(5/4)/(15*3^(3/4)*e*(2 + e*x)^(5/2))]
    @test_int [(12 - 3*e^2*x^2)^(1/4)/(2 + e*x)^(9/2), x, 3, -((3^(1/4)*(4 - e^2*x^2)^(5/4))/(13*e*(2 + e*x)^(9/2))) - (2*(4 - e^2*x^2)^(5/4))/(39*3^(3/4)*e*(2 + e*x)^(7/2)) - (2*(4 - e^2*x^2)^(5/4))/(195*3^(3/4)*e*(2 + e*x)^(5/2))]
    @test_int [(12 - 3*e^2*x^2)^(1/4)/(2 + e*x)^(11/2), x, 4, -((3^(1/4)*(4 - e^2*x^2)^(5/4))/(17*e*(2 + e*x)^(11/2))) - (3*3^(1/4)*(4 - e^2*x^2)^(5/4))/(221*e*(2 + e*x)^(9/2)) - (2*(4 - e^2*x^2)^(5/4))/(221*3^(3/4)*e*(2 + e*x)^(7/2)) - (2*(4 - e^2*x^2)^(5/4))/(1105*3^(3/4)*e*(2 + e*x)^(5/2))]

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

    @test_int [(2 + e*x)^(5/2)/(12 - 3*e^2*x^2)^(1/4), x, 15, If(13>=8, -((5*3^(3/4)*(2 - e*x)^(3/4)*(2 + e*x)^(1/4))/(2*e)) - (3^(3/4)*(2 - e*x)^(3/4)*(2 + e*x)^(5/4))/(2*e) - ((2 - e*x)^(3/4)*(2 + e*x)^(9/4))/(3*3^(1/4)*e) + (5*3^(3/4)*atan(1 - (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(sqrt(2)*e) - (5*3^(3/4)*atan(1 + (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(sqrt(2)*e) - (5*3^(3/4)*log((sqrt(6 - 3*e*x) - sqrt(6)*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + sqrt(3)*sqrt(2 + e*x))/sqrt(2 + e*x)))/(2*sqrt(2)*e) + (5*3^(3/4)*log((sqrt(6 - 3*e*x) + sqrt(6)*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + sqrt(3)*sqrt(2 + e*x))/sqrt(2 + e*x)))/(2*sqrt(2)*e), -((5*3^(3/4)*(2 - e*x)^(3/4)*(2 + e*x)^(1/4))/(2*e)) - (3^(3/4)*(2 - e*x)^(3/4)*(2 + e*x)^(5/4))/(2*e) - ((2 - e*x)^(3/4)*(2 + e*x)^(9/4))/(3*3^(1/4)*e) + (5*3^(3/4)*atan(1 - (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(sqrt(2)*e) - (5*3^(3/4)*atan(1 + (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(sqrt(2)*e) - (5*3^(3/4)*log(sqrt(3) + (sqrt(3)*sqrt(2 - e*x))/sqrt(2 + e*x) - (sqrt(6)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(2*sqrt(2)*e) + (5*3^(3/4)*log(sqrt(3) + (sqrt(3)*sqrt(2 - e*x))/sqrt(2 + e*x) + (sqrt(6)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(2*sqrt(2)*e))]
    @test_int [(2 + e*x)^(3/2)/(12 - 3*e^2*x^2)^(1/4), x, 14, If(13>=8, -((5*(2 - e*x)^(3/4)*(2 + e*x)^(1/4))/(2*3^(1/4)*e)) - ((2 - e*x)^(3/4)*(2 + e*x)^(5/4))/(2*3^(1/4)*e) + (5*atan(1 - (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(sqrt(2)*3^(1/4)*e) - (5*atan(1 + (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(sqrt(2)*3^(1/4)*e) - (5*log((sqrt(6 - 3*e*x) - sqrt(6)*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + sqrt(3)*sqrt(2 + e*x))/sqrt(2 + e*x)))/(2*sqrt(2)*3^(1/4)*e) + (5*log((sqrt(6 - 3*e*x) + sqrt(6)*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + sqrt(3)*sqrt(2 + e*x))/sqrt(2 + e*x)))/(2*sqrt(2)*3^(1/4)*e), -((5*(2 - e*x)^(3/4)*(2 + e*x)^(1/4))/(2*3^(1/4)*e)) - ((2 - e*x)^(3/4)*(2 + e*x)^(5/4))/(2*3^(1/4)*e) + (5*atan(1 - (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(sqrt(2)*3^(1/4)*e) - (5*atan(1 + (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(sqrt(2)*3^(1/4)*e) - (5*log(sqrt(3) + (sqrt(3)*sqrt(2 - e*x))/sqrt(2 + e*x) - (sqrt(6)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(2*sqrt(2)*3^(1/4)*e) + (5*log(sqrt(3) + (sqrt(3)*sqrt(2 - e*x))/sqrt(2 + e*x) + (sqrt(6)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(2*sqrt(2)*3^(1/4)*e))]
    @test_int [(2 + e*x)^(1/2)/(12 - 3*e^2*x^2)^(1/4), x, 13, If(13>=8, -(((2 - e*x)^(3/4)*(2 + e*x)^(1/4))/(3^(1/4)*e)) + (sqrt(2)*atan(1 - (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(3^(1/4)*e) - (sqrt(2)*atan(1 + (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(3^(1/4)*e) - log((sqrt(6 - 3*e*x) - sqrt(6)*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + sqrt(3)*sqrt(2 + e*x))/sqrt(2 + e*x))/(sqrt(2)*3^(1/4)*e) + log((sqrt(6 - 3*e*x) + sqrt(6)*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + sqrt(3)*sqrt(2 + e*x))/sqrt(2 + e*x))/(sqrt(2)*3^(1/4)*e), -(((2 - e*x)^(3/4)*(2 + e*x)^(1/4))/(3^(1/4)*e)) + (sqrt(2)*atan(1 - (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(3^(1/4)*e) - (sqrt(2)*atan(1 + (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(3^(1/4)*e) - log(sqrt(3) + (sqrt(3)*sqrt(2 - e*x))/sqrt(2 + e*x) - (sqrt(6)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4))/(sqrt(2)*3^(1/4)*e) + log(sqrt(3) + (sqrt(3)*sqrt(2 - e*x))/sqrt(2 + e*x) + (sqrt(6)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4))/(sqrt(2)*3^(1/4)*e))]
    @test_int [1/((2 + e*x)^(1/2)*(12 - 3*e^2*x^2)^(1/4)), x, 12, If(13>=8, (sqrt(2)*atan(1 - (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(3^(1/4)*e) - (sqrt(2)*atan(1 + (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(3^(1/4)*e) - log((sqrt(6 - 3*e*x) - sqrt(6)*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + sqrt(3)*sqrt(2 + e*x))/sqrt(2 + e*x))/(sqrt(2)*3^(1/4)*e) + log((sqrt(6 - 3*e*x) + sqrt(6)*(2 - e*x)^(1/4)*(2 + e*x)^(1/4) + sqrt(3)*sqrt(2 + e*x))/sqrt(2 + e*x))/(sqrt(2)*3^(1/4)*e), (sqrt(2)*atan(1 - (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(3^(1/4)*e) - (sqrt(2)*atan(1 + (sqrt(2)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4)))/(3^(1/4)*e) - log(sqrt(3) + (sqrt(3)*sqrt(2 - e*x))/sqrt(2 + e*x) - (sqrt(6)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4))/(sqrt(2)*3^(1/4)*e) + log(sqrt(3) + (sqrt(3)*sqrt(2 - e*x))/sqrt(2 + e*x) + (sqrt(6)*(2 - e*x)^(1/4))/(2 + e*x)^(1/4))/(sqrt(2)*3^(1/4)*e))]
    @test_int [1/((2 + e*x)^(3/2)*(12 - 3*e^2*x^2)^(1/4)), x, 1, -((4 - e^2*x^2)^(3/4)/(3*3^(1/4)*e*(2 + e*x)^(3/2)))]
    @test_int [1/((2 + e*x)^(5/2)*(12 - 3*e^2*x^2)^(1/4)), x, 2, -((4 - e^2*x^2)^(3/4)/(7*3^(1/4)*e*(2 + e*x)^(5/2))) - (4 - e^2*x^2)^(3/4)/(21*3^(1/4)*e*(2 + e*x)^(3/2))]
    @test_int [1/((2 + e*x)^(7/2)*(12 - 3*e^2*x^2)^(1/4)), x, 3, -((4 - e^2*x^2)^(3/4)/(11*3^(1/4)*e*(2 + e*x)^(7/2))) - (2*(4 - e^2*x^2)^(3/4))/(77*3^(1/4)*e*(2 + e*x)^(5/2)) - (2*(4 - e^2*x^2)^(3/4))/(231*3^(1/4)*e*(2 + e*x)^(3/2))]
    @test_int [1/((2 + e*x)^(9/2)*(12 - 3*e^2*x^2)^(1/4)), x, 4, -((4 - e^2*x^2)^(3/4)/(15*3^(1/4)*e*(2 + e*x)^(9/2))) - (4 - e^2*x^2)^(3/4)/(55*3^(1/4)*e*(2 + e*x)^(7/2)) - (2*(4 - e^2*x^2)^(3/4))/(385*3^(1/4)*e*(2 + e*x)^(5/2)) - (2*(4 - e^2*x^2)^(3/4))/(1155*3^(1/4)*e*(2 + e*x)^(3/2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(d+e*x)^m*(d^2 - e^2*x^2)^p*when*m*symbolic=#

    @test_int [(a + b*x)^m*(a^2 - b^2*x^2)^3, x, 3, (8*a^3*(a + b*x)^(4 + m))/(b*(4 + m)) - (12*a^2*(a + b*x)^(5 + m))/(b*(5 + m)) + (6*a*(a + b*x)^(6 + m))/(b*(6 + m)) - (a + b*x)^(7 + m)/(b*(7 + m))]
    @test_int [(a + b*x)^m*(a^2 - b^2*x^2)^2, x, 3, (4*a^2*(a + b*x)^(3 + m))/(b*(3 + m)) - (4*a*(a + b*x)^(4 + m))/(b*(4 + m)) + (a + b*x)^(5 + m)/(b*(5 + m))]
    @test_int [(a + b*x)^m*(a^2 - b^2*x^2)^1, x, 3, (2*a*(a + b*x)^(2 + m))/(b*(2 + m)) - (a + b*x)^(3 + m)/(b*(3 + m))]
    @test_int [(a + b*x)^m/(a^2 - b^2*x^2)^1, x, 2, ((a + b*x)^m*HypergeometricFunctions._₂F₁(1, m, 1 + m, (a + b*x)/(2*a)))/(2*a*b*m)]
    @test_int [(a + b*x)^m/(a^2 - b^2*x^2)^2, x, 2, -(((a + b*x)^(-1 + m)*HypergeometricFunctions._₂F₁(2, -1 + m, m, (a + b*x)/(2*a)))/(4*a^2*b*(1 - m)))]
    @test_int [(a + b*x)^m/(a^2 - b^2*x^2)^3, x, 2, -(((a + b*x)^(-2 + m)*HypergeometricFunctions._₂F₁(3, -2 + m, -1 + m, (a + b*x)/(2*a)))/(8*a^3*b*(2 - m)))]

    @test_int [(d + e*x)^m*(d^2 - e^2*x^2)^(7/2), x, 3, ((d + e*x)^m*(d^2 - e^2*x^2)^(9/2)*HypergeometricFunctions._₂F₁(1, 9 + m, 11/2 + m, (d + e*x)/(2*d)))/(d*e*(9 + 2*m)), -((2^(9/2 + m)*(d + e*x)^m*(1 + (e*x)/d)^(-(9/2) - m)*(d^2 - e^2*x^2)^(9/2)*HypergeometricFunctions._₂F₁(9/2, -(7/2) - m, 11/2, (d - e*x)/(2*d)))/(9*d*e))]
    @test_int [(d + e*x)^m*(d^2 - e^2*x^2)^(5/2), x, 3, -((2^(7/2 + m)*(d + e*x)^m*(1 + (e*x)/d)^(-(7/2) - m)*(d^2 - e^2*x^2)^(7/2)*HypergeometricFunctions._₂F₁(7/2, -(5/2) - m, 9/2, (d - e*x)/(2*d)))/(7*d*e))]
    @test_int [(d + e*x)^m*(d^2 - e^2*x^2)^(3/2), x, 3, ((d + e*x)^m*(d^2 - e^2*x^2)^(5/2)*HypergeometricFunctions._₂F₁(1, 5 + m, 7/2 + m, (d + e*x)/(2*d)))/(d*e*(5 + 2*m)), -((2^(5/2 + m)*(d + e*x)^m*(1 + (e*x)/d)^(-(5/2) - m)*(d^2 - e^2*x^2)^(5/2)*HypergeometricFunctions._₂F₁(5/2, -(3/2) - m, 7/2, (d - e*x)/(2*d)))/(5*d*e))]
    @test_int [(d + e*x)^m*(d^2 - e^2*x^2)^(1/2), x, 3, ((d - e*x)*(d + e*x)^(1 + m)*sqrt(d^2 - e^2*x^2)*HypergeometricFunctions._₂F₁(1, 3 + m, 5/2 + m, (d + e*x)/(2*d)))/(d*e*(3 + 2*m)), -((2^(3/2 + m)*(d + e*x)^m*(1 + (e*x)/d)^(-(3/2) - m)*(d^2 - e^2*x^2)^(3/2)*HypergeometricFunctions._₂F₁(3/2, -(1/2) - m, 5/2, (d - e*x)/(2*d)))/(3*d*e))]
    @test_int [(d + e*x)^m/(d^2 - e^2*x^2)^(1/2), x, 3, ((d - e*x)*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 3/2 + m, (d + e*x)/(2*d)))/(d*e*(1 + 2*m)*sqrt(d^2 - e^2*x^2)), -((2^(1/2 + m)*(d + e*x)^m*(1 + (e*x)/d)^(-(1/2) - m)*sqrt(d^2 - e^2*x^2)*HypergeometricFunctions._₂F₁(1/2, 1/2 - m, 3/2, (d - e*x)/(2*d)))/(d*e))]
    @test_int [(d + e*x)^m/(d^2 - e^2*x^2)^(3/2), x, 3, (2^(-(1/2) + m)*(d + e*x)^m*(1 + (e*x)/d)^(1/2 - m)*HypergeometricFunctions._₂F₁(-(1/2), 3/2 - m, 1/2, (d - e*x)/(2*d)))/(d*e*sqrt(d^2 - e^2*x^2))]
    @test_int [(d + e*x)^m/(d^2 - e^2*x^2)^(5/2), x, 3, -(((d + e*x)^m*HypergeometricFunctions._₂F₁(1, -3 + m, -(1/2) + m, (d + e*x)/(2*d)))/(d*e*(3 - 2*m)*(d^2 - e^2*x^2)^(3/2))), (2^(-(3/2) + m)*(d + e*x)^m*(1 + (e*x)/d)^(3/2 - m)*HypergeometricFunctions._₂F₁(-(3/2), 5/2 - m, -(1/2), (d - e*x)/(2*d)))/(3*d*e*(d^2 - e^2*x^2)^(3/2))]
    @test_int [(d + e*x)^m/(d^2 - e^2*x^2)^(7/2), x, 3, -(((d - e*x)*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, -5 + m, -(3/2) + m, (d + e*x)/(2*d)))/(d*e*(5 - 2*m)*(d^2 - e^2*x^2)^(7/2))), (2^(-(5/2) + m)*(d + e*x)^m*(1 + (e*x)/d)^(5/2 - m)*HypergeometricFunctions._₂F₁(-(5/2), 7/2 - m, -(3/2), (d - e*x)/(2*d)))/(5*d*e*(d^2 - e^2*x^2)^(5/2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(d+e*x)^m*(d^2 - e^2*x^2)^p*when*p*symbolic=#

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

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

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

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

    @test_int [(a^2 - b^2*x^2)^p*(a + b*x) - a*(a^2 - b^2*x^2)^p, x, 6, -((a^2 - b^2*x^2)^(1 + p)/(2*b*(1 + p)))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(d+e*x)^m*(a+b*x+c*x^2)^p*when*b^2-4*a*c=0*and*2*c*d-b*e=0=#

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

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

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

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

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

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

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

    @test_int [(d + e*x)^9/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3, x, 3, (d + e*x)^4/(4*c^3*e)]
    @test_int [(d + e*x)^8/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3, x, 3, (d + e*x)^3/(3*c^3*e)]
    @test_int [(d + e*x)^7/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3, x, 2, (d + e*x)^2/(2*c^3*e)]
    @test_int [(d + e*x)^6/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3, x, 2, x/c^3]
    @test_int [(d + e*x)^5/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3, x, 3, log(d + e*x)/(c^3*e)]
    @test_int [(d + e*x)^4/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3, x, 3, -(1/(c^3*e*(d + e*x)))]
    @test_int [(d + e*x)^3/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3, x, 3, -(1/(2*c^3*e*(d + e*x)^2))]
    @test_int [(d + e*x)^2/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3, x, 3, -(1/(3*c^3*e*(d + e*x)^3))]
    @test_int [(d + e*x)^1/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3, x, 3, -(1/(4*c^3*e*(d + e*x)^4))]
    @test_int [(d + e*x)^0/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3, x, 3, -(1/(5*c^3*e*(d + e*x)^5))]
    @test_int [1/((d + e*x)^1*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3), x, 3, -(1/(6*c^3*e*(d + e*x)^6))]
    @test_int [1/((d + e*x)^2*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3), x, 3, -(1/(7*c^3*e*(d + e*x)^7))]

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

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

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

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

    @test_int [(d + e*x)^3*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2), x, 2, (c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(9/2)/(9*c^2*e)]
    @test_int [(d + e*x)^2*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2), x, 2, ((d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(7/2))/(8*c*e)]
    @test_int [(d + e*x)^1*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2), x, 1, (c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(7/2)/(7*c*e)]
    @test_int [(d + e*x)^0*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2), x, 1, ((d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2))/(6*e)]
    @test_int [(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^1, x, 2, (c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(5*e)]
    @test_int [(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^2, x, 2, (c*(d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2))/(4*e)]
    @test_int [(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^3, x, 2, (c*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(3/2))/(3*e)]
    @test_int [(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^4, x, 2, (c^2*(d + e*x)*sqrt(c*d^2 + 2*c*d*e*x + c*e^2*x^2))/(2*e)]
    @test_int [(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^5, x, 2, (c^2*sqrt(c*d^2 + 2*c*d*e*x + c*e^2*x^2))/e]
    @test_int [(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^6, x, 3, (c^3*(d + e*x)*log(d + e*x))/(e*sqrt(c*d^2 + 2*c*d*e*x + c*e^2*x^2))]
    @test_int [(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^7, x, 2, -(c^3/(e*sqrt(c*d^2 + 2*c*d*e*x + c*e^2*x^2)))]
    @test_int [(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(5/2)/(d + e*x)^8, x, 2, -c^3/(2*e*(d + e*x)*sqrt(c*d^2 + 2*c*d*e*x + c*e^2*x^2))]

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

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

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

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

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

    @test_int [(d + e*x)^m*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2, x, 3, (c^2*(d + e*x)^(5 + m))/(e*(5 + m))]
    @test_int [(d + e*x)^m*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^1, x, 3, (c*(d + e*x)^(3 + m))/(e*(3 + m))]
    @test_int [(d + e*x)^m/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^1, x, 3, -((d + e*x)^(-1 + m)/(c*e*(1 - m)))]
    @test_int [(d + e*x)^m/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^2, x, 3, -((d + e*x)^(-3 + m)/(c^2*e*(3 - m)))]
    @test_int [(d + e*x)^m/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3, x, 3, -((d + e*x)^(-5 + m)/(c^3*e*(5 - m)))]

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

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

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

    @test_int [(d + e*x)^3*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p, x, 2, (c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(2 + p)/(2*c^2*e*(2 + p))]
    @test_int [(d + e*x)^2*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p, x, 2, ((d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(1 + p))/(c*e*(3 + 2*p))]
    @test_int [(d + e*x)^1*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p, x, 1, (c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(1 + p)/(2*c*e*(1 + p))]
    @test_int [(d + e*x)^0*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p, x, 1, ((d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p)/(e*(1 + 2*p))]
    @test_int [(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p/(d + e*x)^1, x, 2, (c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p/(2*e*p)]
    @test_int [(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p/(d + e*x)^2, x, 2, -((c*(d + e*x)*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(-1 + p))/(e*(1 - 2*p)))]
    @test_int [(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p/(d + e*x)^3, x, 2, -((c*(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^(-1 + p))/(2*e*(1 - p)))]

    @test_int [(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p/(d + e*x)^(2*p + 1), x, 2, ((c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p*log(d + e*x))/((d + e*x)^(2*p)*e)]
    @test_int [(d + e*x)^(2*p - 1)/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p, x, 2, ((d + e*x)^(2*p)*log(d + e*x))/((c*d^2 + 2*c*d*e*x + c*e^2*x^2)^p*e)]

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

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

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

    @test_int [(b*d + 2*c*d*x)^4*(a + b*x + c*x^2), x, 2, -(((b^2 - 4*a*c)*d^4*(b + 2*c*x)^5)/(40*c^2)) + (d^4*(b + 2*c*x)^7)/(56*c^2)]
    @test_int [(b*d + 2*c*d*x)^3*(a + b*x + c*x^2), x, 2, -(((b^2 - 4*a*c)*d^3*(b + 2*c*x)^4)/(32*c^2)) + (d^3*(b + 2*c*x)^6)/(48*c^2)]
    @test_int [(b*d + 2*c*d*x)^2*(a + b*x + c*x^2), x, 2, -(((b^2 - 4*a*c)*d^2*(b + 2*c*x)^3)/(24*c^2)) + (d^2*(b + 2*c*x)^5)/(40*c^2)]
    @test_int [(b*d + 2*c*d*x)^1*(a + b*x + c*x^2), x, 1, (1/2)*d*(a + b*x + c*x^2)^2]
    @test_int [(a + b*x + c*x^2)/(b*d + 2*c*d*x)^1, x, 2, (b*x)/(4*c*d) + x^2/(4*d) - ((b^2 - 4*a*c)*log(b + 2*c*x))/(8*c^2*d)]
    @test_int [(a + b*x + c*x^2)/(b*d + 2*c*d*x)^2, x, 2, x/(4*c*d^2) + (b^2 - 4*a*c)/(8*c^2*d^2*(b + 2*c*x))]
    @test_int [(a + b*x + c*x^2)/(b*d + 2*c*d*x)^3, x, 2, (b^2 - 4*a*c)/(16*c^2*d^3*(b + 2*c*x)^2) + log(b + 2*c*x)/(8*c^2*d^3)]
    @test_int [(a + b*x + c*x^2)/(b*d + 2*c*d*x)^4, x, 2, (b^2 - 4*a*c)/(24*c^2*d^4*(b + 2*c*x)^3) - 1/(8*c^2*d^4*(b + 2*c*x))]
    @test_int [(a + b*x + c*x^2)/(b*d + 2*c*d*x)^5, x, 1, (a + b*x + c*x^2)^2/(2*(b^2 - 4*a*c)*d^5*(b + 2*c*x)^4)]
    @test_int [(a + b*x + c*x^2)/(b*d + 2*c*d*x)^6, x, 2, (b^2 - 4*a*c)/(40*c^2*d^6*(b + 2*c*x)^5) - 1/(24*c^2*d^6*(b + 2*c*x)^3)]
    @test_int [(a + b*x + c*x^2)/(b*d + 2*c*d*x)^7, x, 2, (b^2 - 4*a*c)/(48*c^2*d^7*(b + 2*c*x)^6) - 1/(32*c^2*d^7*(b + 2*c*x)^4)]
    @test_int [(a + b*x + c*x^2)/(b*d + 2*c*d*x)^8, x, 2, (b^2 - 4*a*c)/(56*c^2*d^8*(b + 2*c*x)^7) - 1/(40*c^2*d^8*(b + 2*c*x)^5)]

    @test_int [(b*d + 2*c*d*x)^5*(a + b*x + c*x^2)^2, x, 2, ((b^2 - 4*a*c)^2*d^5*(b + 2*c*x)^6)/(192*c^3) - ((b^2 - 4*a*c)*d^5*(b + 2*c*x)^8)/(128*c^3) + (d^5*(b + 2*c*x)^10)/(320*c^3)]
    @test_int [(b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^2, x, 2, ((b^2 - 4*a*c)^2*d^4*(b + 2*c*x)^5)/(160*c^3) - ((b^2 - 4*a*c)*d^4*(b + 2*c*x)^7)/(112*c^3) + (d^4*(b + 2*c*x)^9)/(288*c^3)]
    @test_int [(b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^2, x, 2, (1/12)*(b^2 - 4*a*c)*d^3*(a + b*x + c*x^2)^3 + (1/4)*d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)^3]
    @test_int [(b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^2, x, 2, ((b^2 - 4*a*c)^2*d^2*(b + 2*c*x)^3)/(96*c^3) - ((b^2 - 4*a*c)*d^2*(b + 2*c*x)^5)/(80*c^3) + (d^2*(b + 2*c*x)^7)/(224*c^3)]
    @test_int [(b*d + 2*c*d*x)^1*(a + b*x + c*x^2)^2, x, 1, (1/3)*d*(a + b*x + c*x^2)^3]
    @test_int [(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^1, x, 2, -(((b^2 - 4*a*c)*(b + 2*c*x)^2)/(32*c^3*d)) + (b + 2*c*x)^4/(128*c^3*d) + ((b^2 - 4*a*c)^2*log(b + 2*c*x))/(32*c^3*d)]
    @test_int [(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^2, x, 2, -(((b^2 - 8*a*c)*x)/(16*c^2*d^2)) + (b*x^2)/(8*c*d^2) + x^3/(12*d^2) - (b^2 - 4*a*c)^2/(32*c^3*d^2*(b + 2*c*x))]
    @test_int [(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^3, x, 2, (b*x)/(16*c^2*d^3) + x^2/(16*c*d^3) - (b^2 - 4*a*c)^2/(64*c^3*d^3*(b + 2*c*x)^2) - ((b^2 - 4*a*c)*log(b + 2*c*x))/(16*c^3*d^3)]
    @test_int [(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^4, x, 2, x/(16*c^2*d^4) - (b^2 - 4*a*c)^2/(96*c^3*d^4*(b + 2*c*x)^3) + (b^2 - 4*a*c)/(16*c^3*d^4*(b + 2*c*x))]
    @test_int [(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^5, x, 2, -((b^2 - 4*a*c)^2/(128*c^3*d^5*(b + 2*c*x)^4)) + (b^2 - 4*a*c)/(32*c^3*d^5*(b + 2*c*x)^2) + log(b + 2*c*x)/(32*c^3*d^5)]
    @test_int [(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^6, x, 2, -((b^2 - 4*a*c)^2/(160*c^3*d^6*(b + 2*c*x)^5)) + (b^2 - 4*a*c)/(48*c^3*d^6*(b + 2*c*x)^3) - 1/(32*c^3*d^6*(b + 2*c*x))]
    @test_int [(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^7, x, 1, (a + b*x + c*x^2)^3/(3*(b^2 - 4*a*c)*d^7*(b + 2*c*x)^6)]
    @test_int [(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^8, x, 2, -((b^2 - 4*a*c)^2/(224*c^3*d^8*(b + 2*c*x)^7)) + (b^2 - 4*a*c)/(80*c^3*d^8*(b + 2*c*x)^5) - 1/(96*c^3*d^8*(b + 2*c*x)^3)]
    @test_int [(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^9, x, 2, -((b^2 - 4*a*c)^2/(256*c^3*d^9*(b + 2*c*x)^8)) + (b^2 - 4*a*c)/(96*c^3*d^9*(b + 2*c*x)^6) - 1/(128*c^3*d^9*(b + 2*c*x)^4)]
    @test_int [(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^10, x, 2, -((b^2 - 4*a*c)^2/(288*c^3*d^10*(b + 2*c*x)^9)) + (b^2 - 4*a*c)/(112*c^3*d^10*(b + 2*c*x)^7) - 1/(160*c^3*d^10*(b + 2*c*x)^5)]
    @test_int [(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^11, x, 2, -((b^2 - 4*a*c)^2/(320*c^3*d^11*(b + 2*c*x)^10)) + (b^2 - 4*a*c)/(128*c^3*d^11*(b + 2*c*x)^8) - 1/(192*c^3*d^11*(b + 2*c*x)^6)]

    @test_int [(b*d + 2*c*d*x)^5*(a + b*x + c*x^2)^3, x, 2, -(((b^2 - 4*a*c)^3*d^5*(b + 2*c*x)^6)/(768*c^4)) + (3*(b^2 - 4*a*c)^2*d^5*(b + 2*c*x)^8)/(1024*c^4) - (3*(b^2 - 4*a*c)*d^5*(b + 2*c*x)^10)/(1280*c^4) + (d^5*(b + 2*c*x)^12)/(1536*c^4)]
    @test_int [(b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^3, x, 2, -(((b^2 - 4*a*c)^3*d^4*(b + 2*c*x)^5)/(640*c^4)) + (3*(b^2 - 4*a*c)^2*d^4*(b + 2*c*x)^7)/(896*c^4) - ((b^2 - 4*a*c)*d^4*(b + 2*c*x)^9)/(384*c^4) + (d^4*(b + 2*c*x)^11)/(1408*c^4)]
    @test_int [(b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^3, x, 2, (1/20)*(b^2 - 4*a*c)*d^3*(a + b*x + c*x^2)^4 + (1/5)*d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)^4]
    @test_int [(b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^3, x, 2, -(((b^2 - 4*a*c)^3*d^2*(b + 2*c*x)^3)/(384*c^4)) + (3*(b^2 - 4*a*c)^2*d^2*(b + 2*c*x)^5)/(640*c^4) - (3*(b^2 - 4*a*c)*d^2*(b + 2*c*x)^7)/(896*c^4) + (d^2*(b + 2*c*x)^9)/(1152*c^4)]
    @test_int [(b*d + 2*c*d*x)^1*(a + b*x + c*x^2)^3, x, 1, (1/4)*d*(a + b*x + c*x^2)^4]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^1, x, 2, (3*(b^2 - 4*a*c)^2*(b + 2*c*x)^2)/(256*c^4*d) - (3*(b^2 - 4*a*c)*(b + 2*c*x)^4)/(512*c^4*d) + (b + 2*c*x)^6/(768*c^4*d) - ((b^2 - 4*a*c)^3*log(b + 2*c*x))/(128*c^4*d)]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^2, x, 2, (3*(b^2 - 4*a*c)^2*x)/(64*c^3*d^2) + (b^2 - 4*a*c)^3/(128*c^4*d^2*(b + 2*c*x)) - ((b^2 - 4*a*c)*(b + 2*c*x)^3)/(128*c^4*d^2) + (b + 2*c*x)^5/(640*c^4*d^2)]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^3, x, 2, (b^2 - 4*a*c)^3/(256*c^4*d^3*(b + 2*c*x)^2) - (3*(b^2 - 4*a*c)*(b + 2*c*x)^2)/(256*c^4*d^3) + (b + 2*c*x)^4/(512*c^4*d^3) + (3*(b^2 - 4*a*c)^2*log(b + 2*c*x))/(128*c^4*d^3)]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^4, x, 2, -(((b^2 - 6*a*c)*x)/(32*c^3*d^4)) + (b*x^2)/(32*c^2*d^4) + x^3/(48*c*d^4) + (b^2 - 4*a*c)^3/(384*c^4*d^4*(b + 2*c*x)^3) - (3*(b^2 - 4*a*c)^2)/(128*c^4*d^4*(b + 2*c*x))]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^5, x, 2, (b*x)/(64*c^3*d^5) + x^2/(64*c^2*d^5) + (b^2 - 4*a*c)^3/(512*c^4*d^5*(b + 2*c*x)^4) - (3*(b^2 - 4*a*c)^2)/(256*c^4*d^5*(b + 2*c*x)^2) - (3*(b^2 - 4*a*c)*log(b + 2*c*x))/(128*c^4*d^5)]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^6, x, 2, x/(64*c^3*d^6) + (b^2 - 4*a*c)^3/(640*c^4*d^6*(b + 2*c*x)^5) - (b^2 - 4*a*c)^2/(128*c^4*d^6*(b + 2*c*x)^3) + (3*(b^2 - 4*a*c))/(128*c^4*d^6*(b + 2*c*x))]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^7, x, 2, (b^2 - 4*a*c)^3/(768*c^4*d^7*(b + 2*c*x)^6) - (3*(b^2 - 4*a*c)^2)/(512*c^4*d^7*(b + 2*c*x)^4) + (3*(b^2 - 4*a*c))/(256*c^4*d^7*(b + 2*c*x)^2) + log(b + 2*c*x)/(128*c^4*d^7)]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^8, x, 2, (b^2 - 4*a*c)^3/(896*c^4*d^8*(b + 2*c*x)^7) - (3*(b^2 - 4*a*c)^2)/(640*c^4*d^8*(b + 2*c*x)^5) + (b^2 - 4*a*c)/(128*c^4*d^8*(b + 2*c*x)^3) - 1/(128*c^4*d^8*(b + 2*c*x))]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^9, x, 1, (a + b*x + c*x^2)^4/(4*(b^2 - 4*a*c)*d^9*(b + 2*c*x)^8)]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^10, x, 2, (b^2 - 4*a*c)^3/(1152*c^4*d^10*(b + 2*c*x)^9) - (3*(b^2 - 4*a*c)^2)/(896*c^4*d^10*(b + 2*c*x)^7) + (3*(b^2 - 4*a*c))/(640*c^4*d^10*(b + 2*c*x)^5) - 1/(384*c^4*d^10*(b + 2*c*x)^3)]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^11, x, 2, (b^2 - 4*a*c)^3/(1280*c^4*d^11*(b + 2*c*x)^10) - (3*(b^2 - 4*a*c)^2)/(1024*c^4*d^11*(b + 2*c*x)^8) + (b^2 - 4*a*c)/(256*c^4*d^11*(b + 2*c*x)^6) - 1/(512*c^4*d^11*(b + 2*c*x)^4)]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^12, x, 2, (b^2 - 4*a*c)^3/(1408*c^4*d^12*(b + 2*c*x)^11) - (b^2 - 4*a*c)^2/(384*c^4*d^12*(b + 2*c*x)^9) + (3*(b^2 - 4*a*c))/(896*c^4*d^12*(b + 2*c*x)^7) - 1/(640*c^4*d^12*(b + 2*c*x)^5)]

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

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

    @test_int [(b*d + 2*c*d*x)^8/(a + b*x + c*x^2)^2, x, 6, 28*c*(b^2 - 4*a*c)^2*d^8*(b + 2*c*x) + (28/3)*c*(b^2 - 4*a*c)*d^8*(b + 2*c*x)^3 + (28/5)*c*d^8*(b + 2*c*x)^5 - (d^8*(b + 2*c*x)^7)/(a + b*x + c*x^2) - 28*c*(b^2 - 4*a*c)^(5/2)*d^8*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c))]
    @test_int [(b*d + 2*c*d*x)^7/(a + b*x + c*x^2)^2, x, 4, 12*c*(b^2 - 4*a*c)*d^7*(b + 2*c*x)^2 + 6*c*d^7*(b + 2*c*x)^4 - (d^7*(b + 2*c*x)^6)/(a + b*x + c*x^2) + 12*c*(b^2 - 4*a*c)^2*d^7*log(a + b*x + c*x^2)]
    @test_int [(b*d + 2*c*d*x)^6/(a + b*x + c*x^2)^2, x, 5, 20*c*(b^2 - 4*a*c)*d^6*(b + 2*c*x) + (20/3)*c*d^6*(b + 2*c*x)^3 - (d^6*(b + 2*c*x)^5)/(a + b*x + c*x^2) - 20*c*(b^2 - 4*a*c)^(3/2)*d^6*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c))]
    @test_int [(b*d + 2*c*d*x)^5/(a + b*x + c*x^2)^2, x, 3, 8*c*d^5*(b + 2*c*x)^2 - (d^5*(b + 2*c*x)^4)/(a + b*x + c*x^2) + 8*c*(b^2 - 4*a*c)*d^5*log(a + b*x + c*x^2)]
    @test_int [(b*d + 2*c*d*x)^4/(a + b*x + c*x^2)^2, x, 4, 12*c*d^4*(b + 2*c*x) - (d^4*(b + 2*c*x)^3)/(a + b*x + c*x^2) - 12*c*sqrt(b^2 - 4*a*c)*d^4*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c))]
    @test_int [(b*d + 2*c*d*x)^3/(a + b*x + c*x^2)^2, x, 2, -((d^3*(b + 2*c*x)^2)/(a + b*x + c*x^2)) + 4*c*d^3*log(a + b*x + c*x^2)]
    @test_int [(b*d + 2*c*d*x)^2/(a + b*x + c*x^2)^2, x, 3, -((d^2*(b + 2*c*x))/(a + b*x + c*x^2)) - (4*c*d^2*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/sqrt(b^2 - 4*a*c)]
    @test_int [(b*d + 2*c*d*x)^1/(a + b*x + c*x^2)^2, x, 1, -(d/(a + b*x + c*x^2))]
    @test_int [1/((b*d + 2*c*d*x)^1*(a + b*x + c*x^2)^2), x, 4, -(1/((b^2 - 4*a*c)*d*(a + b*x + c*x^2))) + (8*c*log(b + 2*c*x))/((b^2 - 4*a*c)^2*d) - (4*c*log(a + b*x + c*x^2))/((b^2 - 4*a*c)^2*d)]
    @test_int [1/((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^2), x, 4, -((12*c)/((b^2 - 4*a*c)^2*d^2*(b + 2*c*x))) - 1/((b^2 - 4*a*c)*d^2*(b + 2*c*x)*(a + b*x + c*x^2)) + (12*c*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/((b^2 - 4*a*c)^(5/2)*d^2)]
    @test_int [1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^2), x, 5, -((8*c)/((b^2 - 4*a*c)^2*d^3*(b + 2*c*x)^2)) - 1/((b^2 - 4*a*c)*d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)) + (16*c*log(b + 2*c*x))/((b^2 - 4*a*c)^3*d^3) - (8*c*log(a + b*x + c*x^2))/((b^2 - 4*a*c)^3*d^3)]

    @test_int [(b*d + 2*c*d*x)^10/(a + b*x + c*x^2)^3, x, 7, 252*c^2*(b^2 - 4*a*c)^2*d^10*(b + 2*c*x) + 84*c^2*(b^2 - 4*a*c)*d^10*(b + 2*c*x)^3 + (252/5)*c^2*d^10*(b + 2*c*x)^5 - (d^10*(b + 2*c*x)^9)/(2*(a + b*x + c*x^2)^2) - (9*c*d^10*(b + 2*c*x)^7)/(a + b*x + c*x^2) - 252*c^2*(b^2 - 4*a*c)^(5/2)*d^10*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c))]
    @test_int [(b*d + 2*c*d*x)^9/(a + b*x + c*x^2)^3, x, 5, 96*c^2*(b^2 - 4*a*c)*d^9*(b + 2*c*x)^2 + 48*c^2*d^9*(b + 2*c*x)^4 - (d^9*(b + 2*c*x)^8)/(2*(a + b*x + c*x^2)^2) - (8*c*d^9*(b + 2*c*x)^6)/(a + b*x + c*x^2) + 96*c^2*(b^2 - 4*a*c)^2*d^9*log(a + b*x + c*x^2)]
    @test_int [(b*d + 2*c*d*x)^8/(a + b*x + c*x^2)^3, x, 6, 140*c^2*(b^2 - 4*a*c)*d^8*(b + 2*c*x) + (140/3)*c^2*d^8*(b + 2*c*x)^3 - (d^8*(b + 2*c*x)^7)/(2*(a + b*x + c*x^2)^2) - (7*c*d^8*(b + 2*c*x)^5)/(a + b*x + c*x^2) - 140*c^2*(b^2 - 4*a*c)^(3/2)*d^8*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c))]
    @test_int [(b*d + 2*c*d*x)^7/(a + b*x + c*x^2)^3, x, 4, 48*c^2*d^7*(b + 2*c*x)^2 - (d^7*(b + 2*c*x)^6)/(2*(a + b*x + c*x^2)^2) - (6*c*d^7*(b + 2*c*x)^4)/(a + b*x + c*x^2) + 48*c^2*(b^2 - 4*a*c)*d^7*log(a + b*x + c*x^2)]
    @test_int [(b*d + 2*c*d*x)^6/(a + b*x + c*x^2)^3, x, 5, 60*c^2*d^6*(b + 2*c*x) - (d^6*(b + 2*c*x)^5)/(2*(a + b*x + c*x^2)^2) - (5*c*d^6*(b + 2*c*x)^3)/(a + b*x + c*x^2) - 60*c^2*sqrt(b^2 - 4*a*c)*d^6*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c))]
    @test_int [(b*d + 2*c*d*x)^5/(a + b*x + c*x^2)^3, x, 3, -((d^5*(b + 2*c*x)^4)/(2*(a + b*x + c*x^2)^2)) - (4*c*d^5*(b + 2*c*x)^2)/(a + b*x + c*x^2) + 16*c^2*d^5*log(a + b*x + c*x^2)]
    @test_int [(b*d + 2*c*d*x)^4/(a + b*x + c*x^2)^3, x, 4, -((d^4*(b + 2*c*x)^3)/(2*(a + b*x + c*x^2)^2)) - (3*c*d^4*(b + 2*c*x))/(a + b*x + c*x^2) - (12*c^2*d^4*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/sqrt(b^2 - 4*a*c)]
    @test_int [(b*d + 2*c*d*x)^3/(a + b*x + c*x^2)^3, x, 1, -((d^3*(b + 2*c*x)^4)/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2))]
    @test_int [(b*d + 2*c*d*x)^2/(a + b*x + c*x^2)^3, x, 4, -((d^2*(b + 2*c*x))/(2*(a + b*x + c*x^2)^2)) - (c*d^2*(b + 2*c*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + (4*c^2*d^2*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(3/2)]
    @test_int [(b*d + 2*c*d*x)^1/(a + b*x + c*x^2)^3, x, 1, -(d/(2*(a + b*x + c*x^2)^2))]
    @test_int [1/((b*d + 2*c*d*x)^1*(a + b*x + c*x^2)^3), x, 5, -(1/(2*(b^2 - 4*a*c)*d*(a + b*x + c*x^2)^2)) + (4*c)/((b^2 - 4*a*c)^2*d*(a + b*x + c*x^2)) - (32*c^2*log(b + 2*c*x))/((b^2 - 4*a*c)^3*d) + (16*c^2*log(a + b*x + c*x^2))/((b^2 - 4*a*c)^3*d)]
    @test_int [1/((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^3), x, 5, (60*c^2)/((b^2 - 4*a*c)^3*d^2*(b + 2*c*x)) - 1/(2*(b^2 - 4*a*c)*d^2*(b + 2*c*x)*(a + b*x + c*x^2)^2) + (5*c)/((b^2 - 4*a*c)^2*d^2*(b + 2*c*x)*(a + b*x + c*x^2)) - (60*c^2*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/((b^2 - 4*a*c)^(7/2)*d^2)]
    @test_int [1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^3), x, 6, (48*c^2)/((b^2 - 4*a*c)^3*d^3*(b + 2*c*x)^2) - 1/(2*(b^2 - 4*a*c)*d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)^2) + (6*c)/((b^2 - 4*a*c)^2*d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)) - (96*c^2*log(b + 2*c*x))/((b^2 - 4*a*c)^4*d^3) + (48*c^2*log(a + b*x + c*x^2))/((b^2 - 4*a*c)^4*d^3)]
    @test_int [1/((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^3), x, 6, (140*c^2)/(3*(b^2 - 4*a*c)^3*d^4*(b + 2*c*x)^3) + (140*c^2)/((b^2 - 4*a*c)^4*d^4*(b + 2*c*x)) - 1/(2*(b^2 - 4*a*c)*d^4*(b + 2*c*x)^3*(a + b*x + c*x^2)^2) + (7*c)/((b^2 - 4*a*c)^2*d^4*(b + 2*c*x)^3*(a + b*x + c*x^2)) - (140*c^2*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/((b^2 - 4*a*c)^(9/2)*d^4)]

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

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

    @test_int [(b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^(1/2), x, 5, -(((b^2 - 4*a*c)^2*d^4*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(32*c)) - ((b^2 - 4*a*c)*d^4*(b + 2*c*x)^3*sqrt(a + b*x + c*x^2))/(48*c) + (d^4*(b + 2*c*x)^5*sqrt(a + b*x + c*x^2))/(12*c) - ((b^2 - 4*a*c)^3*d^4*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(64*c^(3/2))]
    @test_int [(b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(1/2), x, 2, (4/15)*(b^2 - 4*a*c)*d^3*(a + b*x + c*x^2)^(3/2) + (2/5)*d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)^(3/2)]
    @test_int [(b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^(1/2), x, 4, -(((b^2 - 4*a*c)*d^2*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(16*c)) + (d^2*(b + 2*c*x)^3*sqrt(a + b*x + c*x^2))/(8*c) - ((b^2 - 4*a*c)^2*d^2*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(32*c^(3/2))]
    @test_int [(b*d + 2*c*d*x)^1*(a + b*x + c*x^2)^(1/2), x, 1, (2/3)*d*(a + b*x + c*x^2)^(3/2)]
    @test_int [(a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^1, x, 3, sqrt(a + b*x + c*x^2)/(2*c*d) - (sqrt(b^2 - 4*a*c)*atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c)))/(4*c^(3/2)*d)]
    @test_int [(a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^2, x, 3, -(sqrt(a + b*x + c*x^2)/(2*c*d^2*(b + 2*c*x))) + atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2)))/(4*c^(3/2)*d^2)]
    @test_int [(a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^3, x, 3, -(sqrt(a + b*x + c*x^2)/(4*c*d^3*(b + 2*c*x)^2)) + atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))/(8*c^(3/2)*sqrt(b^2 - 4*a*c)*d^3)]
    @test_int [(a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^4, x, 1, (2*(a + b*x + c*x^2)^(3/2))/(3*(b^2 - 4*a*c)*d^4*(b + 2*c*x)^3)]
    @test_int [(a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^5, x, 4, -(sqrt(a + b*x + c*x^2)/(8*c*d^5*(b + 2*c*x)^4)) + sqrt(a + b*x + c*x^2)/(16*c*(b^2 - 4*a*c)*d^5*(b + 2*c*x)^2) + atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))/(32*c^(3/2)*(b^2 - 4*a*c)^(3/2)*d^5)]
    @test_int [(a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^6, x, 2, (2*(a + b*x + c*x^2)^(3/2))/(5*(b^2 - 4*a*c)*d^6*(b + 2*c*x)^5) + (4*(a + b*x + c*x^2)^(3/2))/(15*(b^2 - 4*a*c)^2*d^6*(b + 2*c*x)^3)]
    @test_int [(a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^7, x, 5, -(sqrt(a + b*x + c*x^2)/(12*c*d^7*(b + 2*c*x)^6)) + sqrt(a + b*x + c*x^2)/(48*c*(b^2 - 4*a*c)*d^7*(b + 2*c*x)^4) + sqrt(a + b*x + c*x^2)/(32*c*(b^2 - 4*a*c)^2*d^7*(b + 2*c*x)^2) + atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))/(64*c^(3/2)*(b^2 - 4*a*c)^(5/2)*d^7)]

    @test_int [(b*d + 2*c*d*x)^5*(a + b*x + c*x^2)^(3/2), x, 3, (16/315)*(b^2 - 4*a*c)^2*d^5*(a + b*x + c*x^2)^(5/2) + (8/63)*(b^2 - 4*a*c)*d^5*(b + 2*c*x)^2*(a + b*x + c*x^2)^(5/2) + (2/9)*d^5*(b + 2*c*x)^4*(a + b*x + c*x^2)^(5/2)]
    @test_int [(b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^(3/2), x, 6, (3*(b^2 - 4*a*c)^3*d^4*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(1024*c^2) + ((b^2 - 4*a*c)^2*d^4*(b + 2*c*x)^3*sqrt(a + b*x + c*x^2))/(512*c^2) - ((b^2 - 4*a*c)*d^4*(b + 2*c*x)^5*sqrt(a + b*x + c*x^2))/(128*c^2) + (d^4*(b + 2*c*x)^5*(a + b*x + c*x^2)^(3/2))/(16*c) + (3*(b^2 - 4*a*c)^4*d^4*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(2048*c^(5/2))]
    @test_int [(b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(3/2), x, 2, (4/35)*(b^2 - 4*a*c)*d^3*(a + b*x + c*x^2)^(5/2) + (2/7)*d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)^(5/2)]
    @test_int [(b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^(3/2), x, 5, ((b^2 - 4*a*c)^2*d^2*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(128*c^2) - ((b^2 - 4*a*c)*d^2*(b + 2*c*x)^3*sqrt(a + b*x + c*x^2))/(64*c^2) + (d^2*(b + 2*c*x)^3*(a + b*x + c*x^2)^(3/2))/(12*c) + ((b^2 - 4*a*c)^3*d^2*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(256*c^(5/2))]
    @test_int [(b*d + 2*c*d*x)^1*(a + b*x + c*x^2)^(3/2), x, 1, (2/5)*d*(a + b*x + c*x^2)^(5/2)]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^1, x, 4, -(((b^2 - 4*a*c)*sqrt(a + b*x + c*x^2))/(8*c^2*d)) + (a + b*x + c*x^2)^(3/2)/(6*c*d) + ((b^2 - 4*a*c)^(3/2)*atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c)))/(16*c^(5/2)*d)]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^2, x, 4, (3*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(16*c^2*d^2) - (a + b*x + c*x^2)^(3/2)/(2*c*d^2*(b + 2*c*x)) - (3*(b^2 - 4*a*c)*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(32*c^(5/2)*d^2)]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^3, x, 4, (3*sqrt(a + b*x + c*x^2))/(16*c^2*d^3) - (a + b*x + c*x^2)^(3/2)/(4*c*d^3*(b + 2*c*x)^2) - (3*sqrt(b^2 - 4*a*c)*atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c)))/(32*c^(5/2)*d^3)]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^4, x, 4, -(sqrt(a + b*x + c*x^2)/(8*c^2*d^4*(b + 2*c*x))) - (a + b*x + c*x^2)^(3/2)/(6*c*d^4*(b + 2*c*x)^3) + atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2)))/(16*c^(5/2)*d^4)]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^5, x, 4, -((3*sqrt(a + b*x + c*x^2))/(64*c^2*d^5*(b + 2*c*x)^2)) - (a + b*x + c*x^2)^(3/2)/(8*c*d^5*(b + 2*c*x)^4) + (3*atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c)))/(128*c^(5/2)*sqrt(b^2 - 4*a*c)*d^5)]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^6, x, 1, (2*(a + b*x + c*x^2)^(5/2))/(5*(b^2 - 4*a*c)*d^6*(b + 2*c*x)^5)]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^7, x, 5, -(sqrt(a + b*x + c*x^2)/(64*c^2*d^7*(b + 2*c*x)^4)) + sqrt(a + b*x + c*x^2)/(128*c^2*(b^2 - 4*a*c)*d^7*(b + 2*c*x)^2) - (a + b*x + c*x^2)^(3/2)/(12*c*d^7*(b + 2*c*x)^6) + atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))/(256*c^(5/2)*(b^2 - 4*a*c)^(3/2)*d^7)]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^8, x, 2, (2*(a + b*x + c*x^2)^(5/2))/(7*(b^2 - 4*a*c)*d^8*(b + 2*c*x)^7) + (4*(a + b*x + c*x^2)^(5/2))/(35*(b^2 - 4*a*c)^2*d^8*(b + 2*c*x)^5)]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^9, x, 6, -(sqrt(a + b*x + c*x^2)/(128*c^2*d^9*(b + 2*c*x)^6)) + sqrt(a + b*x + c*x^2)/(512*c^2*(b^2 - 4*a*c)*d^9*(b + 2*c*x)^4) + (3*sqrt(a + b*x + c*x^2))/(1024*c^2*(b^2 - 4*a*c)^2*d^9*(b + 2*c*x)^2) - (a + b*x + c*x^2)^(3/2)/(16*c*d^9*(b + 2*c*x)^8) + (3*atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c)))/(2048*c^(5/2)*(b^2 - 4*a*c)^(5/2)*d^9)]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^10, x, 3, (2*(a + b*x + c*x^2)^(5/2))/(9*(b^2 - 4*a*c)*d^10*(b + 2*c*x)^9) + (8*(a + b*x + c*x^2)^(5/2))/(63*(b^2 - 4*a*c)^2*d^10*(b + 2*c*x)^7) + (16*(a + b*x + c*x^2)^(5/2))/(315*(b^2 - 4*a*c)^3*d^10*(b + 2*c*x)^5)]

    @test_int [(b*d + 2*c*d*x)^5*(a + b*x + c*x^2)^(5/2), x, 3, (16/693)*(b^2 - 4*a*c)^2*d^5*(a + b*x + c*x^2)^(7/2) + (8/99)*(b^2 - 4*a*c)*d^5*(b + 2*c*x)^2*(a + b*x + c*x^2)^(7/2) + (2/11)*d^5*(b + 2*c*x)^4*(a + b*x + c*x^2)^(7/2)]
    @test_int [(b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^(5/2), x, 7, -((3*(b^2 - 4*a*c)^4*d^4*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(8192*c^3)) - ((b^2 - 4*a*c)^3*d^4*(b + 2*c*x)^3*sqrt(a + b*x + c*x^2))/(4096*c^3) + ((b^2 - 4*a*c)^2*d^4*(b + 2*c*x)^5*sqrt(a + b*x + c*x^2))/(1024*c^3) - ((b^2 - 4*a*c)*d^4*(b + 2*c*x)^5*(a + b*x + c*x^2)^(3/2))/(128*c^2) + (d^4*(b + 2*c*x)^5*(a + b*x + c*x^2)^(5/2))/(20*c) - (3*(b^2 - 4*a*c)^5*d^4*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(16384*c^(7/2))]
    @test_int [(b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(5/2), x, 2, (4/63)*(b^2 - 4*a*c)*d^3*(a + b*x + c*x^2)^(7/2) + (2/9)*d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)^(7/2)]
    @test_int [(b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^(5/2), x, 6, -((5*(b^2 - 4*a*c)^3*d^2*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(4096*c^3)) + (5*(b^2 - 4*a*c)^2*d^2*(b + 2*c*x)^3*sqrt(a + b*x + c*x^2))/(2048*c^3) - (5*(b^2 - 4*a*c)*d^2*(b + 2*c*x)^3*(a + b*x + c*x^2)^(3/2))/(384*c^2) + (d^2*(b + 2*c*x)^3*(a + b*x + c*x^2)^(5/2))/(16*c) - (5*(b^2 - 4*a*c)^4*d^2*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(8192*c^(7/2))]
    @test_int [(b*d + 2*c*d*x)^1*(a + b*x + c*x^2)^(5/2), x, 1, (2/7)*d*(a + b*x + c*x^2)^(7/2)]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^1, x, 5, ((b^2 - 4*a*c)^2*sqrt(a + b*x + c*x^2))/(32*c^3*d) - ((b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2))/(24*c^2*d) + (a + b*x + c*x^2)^(5/2)/(10*c*d) - ((b^2 - 4*a*c)^(5/2)*atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c)))/(64*c^(7/2)*d)]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^2, x, 5, -((15*(b^2 - 4*a*c)*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(256*c^3*d^2)) + (5*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(32*c^2*d^2) - (a + b*x + c*x^2)^(5/2)/(2*c*d^2*(b + 2*c*x)) + (15*(b^2 - 4*a*c)^2*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(512*c^(7/2)*d^2)]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^3, x, 5, -((5*(b^2 - 4*a*c)*sqrt(a + b*x + c*x^2))/(64*c^3*d^3)) + (5*(a + b*x + c*x^2)^(3/2))/(48*c^2*d^3) - (a + b*x + c*x^2)^(5/2)/(4*c*d^3*(b + 2*c*x)^2) + (5*(b^2 - 4*a*c)^(3/2)*atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c)))/(128*c^(7/2)*d^3)]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^4, x, 5, (5*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(64*c^3*d^4) - (5*(a + b*x + c*x^2)^(3/2))/(24*c^2*d^4*(b + 2*c*x)) - (a + b*x + c*x^2)^(5/2)/(6*c*d^4*(b + 2*c*x)^3) - (5*(b^2 - 4*a*c)*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(128*c^(7/2)*d^4)]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^5, x, 5, (15*sqrt(a + b*x + c*x^2))/(256*c^3*d^5) - (5*(a + b*x + c*x^2)^(3/2))/(64*c^2*d^5*(b + 2*c*x)^2) - (a + b*x + c*x^2)^(5/2)/(8*c*d^5*(b + 2*c*x)^4) - (15*sqrt(b^2 - 4*a*c)*atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c)))/(512*c^(7/2)*d^5)]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^6, x, 5, -(sqrt(a + b*x + c*x^2)/(32*c^3*d^6*(b + 2*c*x))) - (a + b*x + c*x^2)^(3/2)/(24*c^2*d^6*(b + 2*c*x)^3) - (a + b*x + c*x^2)^(5/2)/(10*c*d^6*(b + 2*c*x)^5) + atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2)))/(64*c^(7/2)*d^6)]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^7, x, 5, -((5*sqrt(a + b*x + c*x^2))/(512*c^3*d^7*(b + 2*c*x)^2)) - (5*(a + b*x + c*x^2)^(3/2))/(192*c^2*d^7*(b + 2*c*x)^4) - (a + b*x + c*x^2)^(5/2)/(12*c*d^7*(b + 2*c*x)^6) + (5*atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c)))/(1024*c^(7/2)*sqrt(b^2 - 4*a*c)*d^7)]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^8, x, 1, (2*(a + b*x + c*x^2)^(7/2))/(7*(b^2 - 4*a*c)*d^8*(b + 2*c*x)^7)]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^9, x, 6, -((5*sqrt(a + b*x + c*x^2))/(2048*c^3*d^9*(b + 2*c*x)^4)) + (5*sqrt(a + b*x + c*x^2))/(4096*c^3*(b^2 - 4*a*c)*d^9*(b + 2*c*x)^2) - (5*(a + b*x + c*x^2)^(3/2))/(384*c^2*d^9*(b + 2*c*x)^6) - (a + b*x + c*x^2)^(5/2)/(16*c*d^9*(b + 2*c*x)^8) + (5*atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c)))/(8192*c^(7/2)*(b^2 - 4*a*c)^(3/2)*d^9)]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^10, x, 2, (2*(a + b*x + c*x^2)^(7/2))/(9*(b^2 - 4*a*c)*d^10*(b + 2*c*x)^9) + (4*(a + b*x + c*x^2)^(7/2))/(63*(b^2 - 4*a*c)^2*d^10*(b + 2*c*x)^7)]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^11, x, 7, -(sqrt(a + b*x + c*x^2)/(1024*c^3*d^11*(b + 2*c*x)^6)) + sqrt(a + b*x + c*x^2)/(4096*c^3*(b^2 - 4*a*c)*d^11*(b + 2*c*x)^4) + (3*sqrt(a + b*x + c*x^2))/(8192*c^3*(b^2 - 4*a*c)^2*d^11*(b + 2*c*x)^2) - (a + b*x + c*x^2)^(3/2)/(128*c^2*d^11*(b + 2*c*x)^8) - (a + b*x + c*x^2)^(5/2)/(20*c*d^11*(b + 2*c*x)^10) + (3*atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c)))/(16384*c^(7/2)*(b^2 - 4*a*c)^(5/2)*d^11)]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^12, x, 3, (2*(a + b*x + c*x^2)^(7/2))/(11*(b^2 - 4*a*c)*d^12*(b + 2*c*x)^11) + (8*(a + b*x + c*x^2)^(7/2))/(99*(b^2 - 4*a*c)^2*d^12*(b + 2*c*x)^9) + (16*(a + b*x + c*x^2)^(7/2))/(693*(b^2 - 4*a*c)^3*d^12*(b + 2*c*x)^7)]

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

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

    @test_int [(b*d + 2*c*d*x)^4/(a + b*x + c*x^2)^(3/2), x, 4, -((2*d^4*(b + 2*c*x)^3)/sqrt(a + b*x + c*x^2)) + 12*c*d^4*(b + 2*c*x)*sqrt(a + b*x + c*x^2) + 6*sqrt(c)*(b^2 - 4*a*c)*d^4*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2)))]
    @test_int [(b*d + 2*c*d*x)^3/(a + b*x + c*x^2)^(3/2), x, 2, -((2*d^3*(b + 2*c*x)^2)/sqrt(a + b*x + c*x^2)) + 16*c*d^3*sqrt(a + b*x + c*x^2)]
    @test_int [(b*d + 2*c*d*x)^2/(a + b*x + c*x^2)^(3/2), x, 3, -((2*d^2*(b + 2*c*x))/sqrt(a + b*x + c*x^2)) + 4*sqrt(c)*d^2*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2)))]
    @test_int [(b*d + 2*c*d*x)^1/(a + b*x + c*x^2)^(3/2), x, 1, -((2*d)/sqrt(a + b*x + c*x^2))]
    @test_int [1/((b*d + 2*c*d*x)^1*(a + b*x + c*x^2)^(3/2)), x, 3, -(2/((b^2 - 4*a*c)*d*sqrt(a + b*x + c*x^2))) - (4*sqrt(c)*atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c)))/((b^2 - 4*a*c)^(3/2)*d)]
    @test_int [1/((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^(3/2)), x, 2, -(2/((b^2 - 4*a*c)*d^2*(b + 2*c*x)*sqrt(a + b*x + c*x^2))) - (16*c*sqrt(a + b*x + c*x^2))/((b^2 - 4*a*c)^2*d^2*(b + 2*c*x))]
    @test_int [1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(3/2)), x, 4, -(2/((b^2 - 4*a*c)*d^3*(b + 2*c*x)^2*sqrt(a + b*x + c*x^2))) - (12*c*sqrt(a + b*x + c*x^2))/((b^2 - 4*a*c)^2*d^3*(b + 2*c*x)^2) - (6*sqrt(c)*atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c)))/((b^2 - 4*a*c)^(5/2)*d^3)]
    @test_int [1/((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^(3/2)), x, 3, -(2/((b^2 - 4*a*c)*d^4*(b + 2*c*x)^3*sqrt(a + b*x + c*x^2))) - (32*c*sqrt(a + b*x + c*x^2))/(3*(b^2 - 4*a*c)^2*d^4*(b + 2*c*x)^3) - (64*c*sqrt(a + b*x + c*x^2))/(3*(b^2 - 4*a*c)^3*d^4*(b + 2*c*x))]

    @test_int [(b*d + 2*c*d*x)^6/(a + b*x + c*x^2)^(5/2), x, 5, -((2*d^6*(b + 2*c*x)^5)/(3*(a + b*x + c*x^2)^(3/2))) - (40*c*d^6*(b + 2*c*x)^3)/(3*sqrt(a + b*x + c*x^2)) + 80*c^2*d^6*(b + 2*c*x)*sqrt(a + b*x + c*x^2) + 40*c^(3/2)*(b^2 - 4*a*c)*d^6*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2)))]
    @test_int [(b*d + 2*c*d*x)^5/(a + b*x + c*x^2)^(5/2), x, 3, -((2*d^5*(b + 2*c*x)^4)/(3*(a + b*x + c*x^2)^(3/2))) - (32*c*d^5*(b + 2*c*x)^2)/(3*sqrt(a + b*x + c*x^2)) + (256/3)*c^2*d^5*sqrt(a + b*x + c*x^2)]
    @test_int [(b*d + 2*c*d*x)^4/(a + b*x + c*x^2)^(5/2), x, 4, -((2*d^4*(b + 2*c*x)^3)/(3*(a + b*x + c*x^2)^(3/2))) - (8*c*d^4*(b + 2*c*x))/sqrt(a + b*x + c*x^2) + 16*c^(3/2)*d^4*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2)))]
    @test_int [(b*d + 2*c*d*x)^3/(a + b*x + c*x^2)^(5/2), x, 2, -((2*d^3*(b + 2*c*x)^2)/(3*(a + b*x + c*x^2)^(3/2))) - (16*c*d^3)/(3*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^2/(a + b*x + c*x^2)^(5/2), x, 1, -((2*d^2*(b + 2*c*x)^3)/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)))]
    @test_int [(b*d + 2*c*d*x)^1/(a + b*x + c*x^2)^(5/2), x, 1, -((2*d)/(3*(a + b*x + c*x^2)^(3/2)))]
    @test_int [1/((b*d + 2*c*d*x)^1*(a + b*x + c*x^2)^(5/2)), x, 4, -(2/(3*(b^2 - 4*a*c)*d*(a + b*x + c*x^2)^(3/2))) + (8*c)/((b^2 - 4*a*c)^2*d*sqrt(a + b*x + c*x^2)) + (16*c^(3/2)*atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c)))/((b^2 - 4*a*c)^(5/2)*d)]
    @test_int [1/((b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^(5/2)), x, 3, -(2/(3*(b^2 - 4*a*c)*d^2*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))) + (32*c)/(3*(b^2 - 4*a*c)^2*d^2*(b + 2*c*x)*sqrt(a + b*x + c*x^2)) + (256*c^2*sqrt(a + b*x + c*x^2))/(3*(b^2 - 4*a*c)^3*d^2*(b + 2*c*x))]
    @test_int [1/((b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^(5/2)), x, 5, -(2/(3*(b^2 - 4*a*c)*d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)^(3/2))) + (40*c)/(3*(b^2 - 4*a*c)^2*d^3*(b + 2*c*x)^2*sqrt(a + b*x + c*x^2)) + (80*c^2*sqrt(a + b*x + c*x^2))/((b^2 - 4*a*c)^3*d^3*(b + 2*c*x)^2) + (40*c^(3/2)*atan((2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c)))/((b^2 - 4*a*c)^(7/2)*d^3)]
    @test_int [1/((b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^(5/2)), x, 4, -(2/(3*(b^2 - 4*a*c)*d^4*(b + 2*c*x)^3*(a + b*x + c*x^2)^(3/2))) + (16*c)/((b^2 - 4*a*c)^2*d^4*(b + 2*c*x)^3*sqrt(a + b*x + c*x^2)) + (256*c^2*sqrt(a + b*x + c*x^2))/(3*(b^2 - 4*a*c)^3*d^4*(b + 2*c*x)^3) + (512*c^2*sqrt(a + b*x + c*x^2))/(3*(b^2 - 4*a*c)^4*d^4*(b + 2*c*x))]

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

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

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

    @test_int [(b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2), x, 2, -(((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(7/2))/(28*c^2*d)) + (b*d + 2*c*d*x)^(11/2)/(44*c^2*d^3)]
    @test_int [(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2), x, 2, -(((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(5/2))/(20*c^2*d)) + (b*d + 2*c*d*x)^(9/2)/(36*c^2*d^3)]
    @test_int [(b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2), x, 2, -(((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(3/2))/(12*c^2*d)) + (b*d + 2*c*d*x)^(7/2)/(28*c^2*d^3)]
    @test_int [(a + b*x + c*x^2)/(b*d + 2*c*d*x)^(1/2), x, 2, -(((b^2 - 4*a*c)*sqrt(b*d + 2*c*d*x))/(4*c^2*d)) + (b*d + 2*c*d*x)^(5/2)/(20*c^2*d^3)]
    @test_int [(a + b*x + c*x^2)/(b*d + 2*c*d*x)^(3/2), x, 2, (b^2 - 4*a*c)/(4*c^2*d*sqrt(b*d + 2*c*d*x)) + (b*d + 2*c*d*x)^(3/2)/(12*c^2*d^3)]
    @test_int [(a + b*x + c*x^2)/(b*d + 2*c*d*x)^(5/2), x, 2, (b^2 - 4*a*c)/(12*c^2*d*(b*d + 2*c*d*x)^(3/2)) + sqrt(b*d + 2*c*d*x)/(4*c^2*d^3)]
    @test_int [(a + b*x + c*x^2)/(b*d + 2*c*d*x)^(7/2), x, 2, (b^2 - 4*a*c)/(20*c^2*d*(b*d + 2*c*d*x)^(5/2)) - 1/(4*c^2*d^3*sqrt(b*d + 2*c*d*x))]
    @test_int [(a + b*x + c*x^2)/(b*d + 2*c*d*x)^(9/2), x, 2, (b^2 - 4*a*c)/(28*c^2*d*(b*d + 2*c*d*x)^(7/2)) - 1/(12*c^2*d^3*(b*d + 2*c*d*x)^(3/2))]

    @test_int [(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^2, x, 2, ((b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(5/2))/(80*c^3*d) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(9/2))/(72*c^3*d^3) + (b*d + 2*c*d*x)^(13/2)/(208*c^3*d^5)]
    @test_int [(b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^2, x, 2, ((b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(3/2))/(48*c^3*d) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(7/2))/(56*c^3*d^3) + (b*d + 2*c*d*x)^(11/2)/(176*c^3*d^5)]
    @test_int [(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^(1/2), x, 2, ((b^2 - 4*a*c)^2*sqrt(b*d + 2*c*d*x))/(16*c^3*d) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(5/2))/(40*c^3*d^3) + (b*d + 2*c*d*x)^(9/2)/(144*c^3*d^5)]
    @test_int [(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^(3/2), x, 2, -((b^2 - 4*a*c)^2/(16*c^3*d*sqrt(b*d + 2*c*d*x))) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(3/2))/(24*c^3*d^3) + (b*d + 2*c*d*x)^(7/2)/(112*c^3*d^5)]
    @test_int [(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^(5/2), x, 2, -((b^2 - 4*a*c)^2/(48*c^3*d*(b*d + 2*c*d*x)^(3/2))) - ((b^2 - 4*a*c)*sqrt(b*d + 2*c*d*x))/(8*c^3*d^3) + (b*d + 2*c*d*x)^(5/2)/(80*c^3*d^5)]
    @test_int [(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^(7/2), x, 2, -((b^2 - 4*a*c)^2/(80*c^3*d*(b*d + 2*c*d*x)^(5/2))) + (b^2 - 4*a*c)/(8*c^3*d^3*sqrt(b*d + 2*c*d*x)) + (b*d + 2*c*d*x)^(3/2)/(48*c^3*d^5)]
    @test_int [(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^(9/2), x, 2, -((b^2 - 4*a*c)^2/(112*c^3*d*(b*d + 2*c*d*x)^(7/2))) + (b^2 - 4*a*c)/(24*c^3*d^3*(b*d + 2*c*d*x)^(3/2)) + sqrt(b*d + 2*c*d*x)/(16*c^3*d^5)]
    @test_int [(a + b*x + c*x^2)^2/(b*d + 2*c*d*x)^(11/2), x, 2, -((b^2 - 4*a*c)^2/(144*c^3*d*(b*d + 2*c*d*x)^(9/2))) + (b^2 - 4*a*c)/(40*c^3*d^3*(b*d + 2*c*d*x)^(5/2)) - 1/(16*c^3*d^5*sqrt(b*d + 2*c*d*x))]

    @test_int [(b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^3, x, 2, -(((b^2 - 4*a*c)^3*(b*d + 2*c*d*x)^(3/2))/(192*c^4*d)) + (3*(b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(7/2))/(448*c^4*d^3) - (3*(b^2 - 4*a*c)*(b*d + 2*c*d*x)^(11/2))/(704*c^4*d^5) + (b*d + 2*c*d*x)^(15/2)/(960*c^4*d^7)]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(1/2), x, 2, -(((b^2 - 4*a*c)^3*sqrt(b*d + 2*c*d*x))/(64*c^4*d)) + (3*(b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(5/2))/(320*c^4*d^3) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(9/2))/(192*c^4*d^5) + (b*d + 2*c*d*x)^(13/2)/(832*c^4*d^7)]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(3/2), x, 2, (b^2 - 4*a*c)^3/(64*c^4*d*sqrt(b*d + 2*c*d*x)) + ((b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(3/2))/(64*c^4*d^3) - (3*(b^2 - 4*a*c)*(b*d + 2*c*d*x)^(7/2))/(448*c^4*d^5) + (b*d + 2*c*d*x)^(11/2)/(704*c^4*d^7)]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(5/2), x, 2, (b^2 - 4*a*c)^3/(192*c^4*d*(b*d + 2*c*d*x)^(3/2)) + (3*(b^2 - 4*a*c)^2*sqrt(b*d + 2*c*d*x))/(64*c^4*d^3) - (3*(b^2 - 4*a*c)*(b*d + 2*c*d*x)^(5/2))/(320*c^4*d^5) + (b*d + 2*c*d*x)^(9/2)/(576*c^4*d^7)]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(7/2), x, 2, (b^2 - 4*a*c)^3/(320*c^4*d*(b*d + 2*c*d*x)^(5/2)) - (3*(b^2 - 4*a*c)^2)/(64*c^4*d^3*sqrt(b*d + 2*c*d*x)) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(3/2))/(64*c^4*d^5) + (b*d + 2*c*d*x)^(7/2)/(448*c^4*d^7)]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(9/2), x, 2, (b^2 - 4*a*c)^3/(448*c^4*d*(b*d + 2*c*d*x)^(7/2)) - (b^2 - 4*a*c)^2/(64*c^4*d^3*(b*d + 2*c*d*x)^(3/2)) - (3*(b^2 - 4*a*c)*sqrt(b*d + 2*c*d*x))/(64*c^4*d^5) + (b*d + 2*c*d*x)^(5/2)/(320*c^4*d^7)]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(11/2), x, 2, (b^2 - 4*a*c)^3/(576*c^4*d*(b*d + 2*c*d*x)^(9/2)) - (3*(b^2 - 4*a*c)^2)/(320*c^4*d^3*(b*d + 2*c*d*x)^(5/2)) + (3*(b^2 - 4*a*c))/(64*c^4*d^5*sqrt(b*d + 2*c*d*x)) + (b*d + 2*c*d*x)^(3/2)/(192*c^4*d^7)]
    @test_int [(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^(13/2), x, 2, (b^2 - 4*a*c)^3/(704*c^4*d*(b*d + 2*c*d*x)^(11/2)) - (3*(b^2 - 4*a*c)^2)/(448*c^4*d^3*(b*d + 2*c*d*x)^(7/2)) + (b^2 - 4*a*c)/(64*c^4*d^5*(b*d + 2*c*d*x)^(3/2)) + sqrt(b*d + 2*c*d*x)/(64*c^4*d^7)]

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

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

    @test_int [(b*d + 2*c*d*x)^(15/2)/(a + b*x + c*x^2)^2, x, 9, 52*c*(b^2 - 4*a*c)^2*d^7*sqrt(b*d + 2*c*d*x) + (52/5)*c*(b^2 - 4*a*c)*d^5*(b*d + 2*c*d*x)^(5/2) + (52/9)*c*d^3*(b*d + 2*c*d*x)^(9/2) - (d*(b*d + 2*c*d*x)^(13/2))/(a + b*x + c*x^2) - 26*c*(b^2 - 4*a*c)^(9/4)*d^(15/2)*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))) - 26*c*(b^2 - 4*a*c)^(9/4)*d^(15/2)*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d)))]
    @test_int [(b*d + 2*c*d*x)^(13/2)/(a + b*x + c*x^2)^2, x, 8, (44/3)*c*(b^2 - 4*a*c)*d^5*(b*d + 2*c*d*x)^(3/2) + (44/7)*c*d^3*(b*d + 2*c*d*x)^(7/2) - (d*(b*d + 2*c*d*x)^(11/2))/(a + b*x + c*x^2) + 22*c*(b^2 - 4*a*c)^(7/4)*d^(13/2)*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))) - 22*c*(b^2 - 4*a*c)^(7/4)*d^(13/2)*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d)))]
    @test_int [(b*d + 2*c*d*x)^(11/2)/(a + b*x + c*x^2)^2, x, 8, 36*c*(b^2 - 4*a*c)*d^5*sqrt(b*d + 2*c*d*x) + (36/5)*c*d^3*(b*d + 2*c*d*x)^(5/2) - (d*(b*d + 2*c*d*x)^(9/2))/(a + b*x + c*x^2) - 18*c*(b^2 - 4*a*c)^(5/4)*d^(11/2)*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))) - 18*c*(b^2 - 4*a*c)^(5/4)*d^(11/2)*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d)))]
    @test_int [(b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2)^2, x, 7, (28/3)*c*d^3*(b*d + 2*c*d*x)^(3/2) - (d*(b*d + 2*c*d*x)^(7/2))/(a + b*x + c*x^2) + 14*c*(b^2 - 4*a*c)^(3/4)*d^(9/2)*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))) - 14*c*(b^2 - 4*a*c)^(3/4)*d^(9/2)*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d)))]
    @test_int [(b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2)^2, x, 7, 20*c*d^3*sqrt(b*d + 2*c*d*x) - (d*(b*d + 2*c*d*x)^(5/2))/(a + b*x + c*x^2) - 10*c*(b^2 - 4*a*c)^(1/4)*d^(7/2)*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))) - 10*c*(b^2 - 4*a*c)^(1/4)*d^(7/2)*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d)))]
    @test_int [(b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2)^2, x, 6, -((d*(b*d + 2*c*d*x)^(3/2))/(a + b*x + c*x^2)) + (6*c*d^(5/2)*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/(b^2 - 4*a*c)^(1/4) - (6*c*d^(5/2)*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/(b^2 - 4*a*c)^(1/4)]
    @test_int [(b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2)^2, x, 6, -((d*sqrt(b*d + 2*c*d*x))/(a + b*x + c*x^2)) - (2*c*d^(3/2)*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/(b^2 - 4*a*c)^(3/4) - (2*c*d^(3/2)*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/(b^2 - 4*a*c)^(3/4)]
    @test_int [(b*d + 2*c*d*x)^(1/2)/(a + b*x + c*x^2)^2, x, 6, -((b*d + 2*c*d*x)^(3/2)/((b^2 - 4*a*c)*d*(a + b*x + c*x^2))) - (2*c*sqrt(d)*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/(b^2 - 4*a*c)^(5/4) + (2*c*sqrt(d)*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/(b^2 - 4*a*c)^(5/4)]
    @test_int [1/((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^2), x, 6, -(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)*d*(a + b*x + c*x^2))) + (6*c*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/((b^2 - 4*a*c)^(7/4)*sqrt(d)) + (6*c*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/((b^2 - 4*a*c)^(7/4)*sqrt(d))]
    @test_int [1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^2), x, 7, -((20*c)/((b^2 - 4*a*c)^2*d*sqrt(b*d + 2*c*d*x))) - 1/((b^2 - 4*a*c)*d*sqrt(b*d + 2*c*d*x)*(a + b*x + c*x^2)) - (10*c*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/((b^2 - 4*a*c)^(9/4)*d^(3/2)) + (10*c*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/((b^2 - 4*a*c)^(9/4)*d^(3/2))]
    @test_int [1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^2), x, 7, -((28*c)/(3*(b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(3/2))) - 1/((b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)) + (14*c*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/((b^2 - 4*a*c)^(11/4)*d^(5/2)) + (14*c*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/((b^2 - 4*a*c)^(11/4)*d^(5/2))]
    @test_int [1/((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^2), x, 8, -((36*c)/(5*(b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(5/2))) - (36*c)/((b^2 - 4*a*c)^3*d^3*sqrt(b*d + 2*c*d*x)) - 1/((b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)) - (18*c*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/((b^2 - 4*a*c)^(13/4)*d^(7/2)) + (18*c*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/((b^2 - 4*a*c)^(13/4)*d^(7/2))]

    @test_int [(b*d + 2*c*d*x)^(17/2)/(a + b*x + c*x^2)^3, x, 9, 110*c^2*(b^2 - 4*a*c)*d^7*(b*d + 2*c*d*x)^(3/2) + (330/7)*c^2*d^5*(b*d + 2*c*d*x)^(7/2) - (d*(b*d + 2*c*d*x)^(15/2))/(2*(a + b*x + c*x^2)^2) - (15*c*d^3*(b*d + 2*c*d*x)^(11/2))/(2*(a + b*x + c*x^2)) + 165*c^2*(b^2 - 4*a*c)^(7/4)*d^(17/2)*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))) - 165*c^2*(b^2 - 4*a*c)^(7/4)*d^(17/2)*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d)))]
    @test_int [(b*d + 2*c*d*x)^(15/2)/(a + b*x + c*x^2)^3, x, 9, 234*c^2*(b^2 - 4*a*c)*d^7*sqrt(b*d + 2*c*d*x) + (234/5)*c^2*d^5*(b*d + 2*c*d*x)^(5/2) - (d*(b*d + 2*c*d*x)^(13/2))/(2*(a + b*x + c*x^2)^2) - (13*c*d^3*(b*d + 2*c*d*x)^(9/2))/(2*(a + b*x + c*x^2)) - 117*c^2*(b^2 - 4*a*c)^(5/4)*d^(15/2)*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))) - 117*c^2*(b^2 - 4*a*c)^(5/4)*d^(15/2)*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d)))]
    @test_int [(b*d + 2*c*d*x)^(13/2)/(a + b*x + c*x^2)^3, x, 8, (154/3)*c^2*d^5*(b*d + 2*c*d*x)^(3/2) - (d*(b*d + 2*c*d*x)^(11/2))/(2*(a + b*x + c*x^2)^2) - (11*c*d^3*(b*d + 2*c*d*x)^(7/2))/(2*(a + b*x + c*x^2)) + 77*c^2*(b^2 - 4*a*c)^(3/4)*d^(13/2)*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))) - 77*c^2*(b^2 - 4*a*c)^(3/4)*d^(13/2)*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d)))]
    @test_int [(b*d + 2*c*d*x)^(11/2)/(a + b*x + c*x^2)^3, x, 8, 90*c^2*d^5*sqrt(b*d + 2*c*d*x) - (d*(b*d + 2*c*d*x)^(9/2))/(2*(a + b*x + c*x^2)^2) - (9*c*d^3*(b*d + 2*c*d*x)^(5/2))/(2*(a + b*x + c*x^2)) - 45*c^2*(b^2 - 4*a*c)^(1/4)*d^(11/2)*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))) - 45*c^2*(b^2 - 4*a*c)^(1/4)*d^(11/2)*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d)))]
    @test_int [(b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2)^3, x, 7, -((d*(b*d + 2*c*d*x)^(7/2))/(2*(a + b*x + c*x^2)^2)) - (7*c*d^3*(b*d + 2*c*d*x)^(3/2))/(2*(a + b*x + c*x^2)) + (21*c^2*d^(9/2)*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/(b^2 - 4*a*c)^(1/4) - (21*c^2*d^(9/2)*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/(b^2 - 4*a*c)^(1/4)]
    @test_int [(b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2)^3, x, 7, -((d*(b*d + 2*c*d*x)^(5/2))/(2*(a + b*x + c*x^2)^2)) - (5*c*d^3*sqrt(b*d + 2*c*d*x))/(2*(a + b*x + c*x^2)) - (5*c^2*d^(7/2)*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/(b^2 - 4*a*c)^(3/4) - (5*c^2*d^(7/2)*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/(b^2 - 4*a*c)^(3/4)]
    @test_int [(b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2)^3, x, 7, -((d*(b*d + 2*c*d*x)^(3/2))/(2*(a + b*x + c*x^2)^2)) - (3*c*d*(b*d + 2*c*d*x)^(3/2))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)) - (3*c^2*d^(5/2)*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/(b^2 - 4*a*c)^(5/4) + (3*c^2*d^(5/2)*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/(b^2 - 4*a*c)^(5/4)]
    @test_int [(b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2)^3, x, 7, -((d*sqrt(b*d + 2*c*d*x))/(2*(a + b*x + c*x^2)^2)) - (c*d*sqrt(b*d + 2*c*d*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)) + (3*c^2*d^(3/2)*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/(b^2 - 4*a*c)^(7/4) + (3*c^2*d^(3/2)*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/(b^2 - 4*a*c)^(7/4)]
    @test_int [(b*d + 2*c*d*x)^(1/2)/(a + b*x + c*x^2)^3, x, 7, -((b*d + 2*c*d*x)^(3/2)/(2*(b^2 - 4*a*c)*d*(a + b*x + c*x^2)^2)) + (5*c*(b*d + 2*c*d*x)^(3/2))/(2*(b^2 - 4*a*c)^2*d*(a + b*x + c*x^2)) + (5*c^2*sqrt(d)*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/(b^2 - 4*a*c)^(9/4) - (5*c^2*sqrt(d)*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/(b^2 - 4*a*c)^(9/4)]
    @test_int [1/((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^3), x, 7, -(sqrt(b*d + 2*c*d*x)/(2*(b^2 - 4*a*c)*d*(a + b*x + c*x^2)^2)) + (7*c*sqrt(b*d + 2*c*d*x))/(2*(b^2 - 4*a*c)^2*d*(a + b*x + c*x^2)) - (21*c^2*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/((b^2 - 4*a*c)^(11/4)*sqrt(d)) - (21*c^2*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/((b^2 - 4*a*c)^(11/4)*sqrt(d))]
    @test_int [1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^3), x, 8, (90*c^2)/((b^2 - 4*a*c)^3*d*sqrt(b*d + 2*c*d*x)) - 1/(2*(b^2 - 4*a*c)*d*sqrt(b*d + 2*c*d*x)*(a + b*x + c*x^2)^2) + (9*c)/(2*(b^2 - 4*a*c)^2*d*sqrt(b*d + 2*c*d*x)*(a + b*x + c*x^2)) + (45*c^2*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/((b^2 - 4*a*c)^(13/4)*d^(3/2)) - (45*c^2*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/((b^2 - 4*a*c)^(13/4)*d^(3/2))]
    @test_int [1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^3), x, 8, (154*c^2)/(3*(b^2 - 4*a*c)^3*d*(b*d + 2*c*d*x)^(3/2)) - 1/(2*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^2) + (11*c)/(2*(b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)) - (77*c^2*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/((b^2 - 4*a*c)^(15/4)*d^(5/2)) - (77*c^2*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/((b^2 - 4*a*c)^(15/4)*d^(5/2))]
    @test_int [1/((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^3), x, 9, (234*c^2)/(5*(b^2 - 4*a*c)^3*d*(b*d + 2*c*d*x)^(5/2)) + (234*c^2)/((b^2 - 4*a*c)^4*d^3*sqrt(b*d + 2*c*d*x)) - 1/(2*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^2) + (13*c)/(2*(b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)) + (117*c^2*atan(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/((b^2 - 4*a*c)^(17/4)*d^(7/2)) - (117*c^2*atanh(sqrt(d*(b + 2*c*x))/((b^2 - 4*a*c)^(1/4)*sqrt(d))))/((b^2 - 4*a*c)^(17/4)*d^(7/2))]

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

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

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

    @test_int [(b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(1/2), x, 6, -((10*(b^2 - 4*a*c)^2*d^3*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2))/(231*c)) - (2*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(5/2)*sqrt(a + b*x + c*x^2))/(77*c) + ((b*d + 2*c*d*x)^(9/2)*sqrt(a + b*x + c*x^2))/(11*c*d) - (5*(b^2 - 4*a*c)^(13/4)*d^(7/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(231*c^2*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(1/2), x, 5, -((2*(b^2 - 4*a*c)*d*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2))/(21*c)) + ((b*d + 2*c*d*x)^(5/2)*sqrt(a + b*x + c*x^2))/(7*c*d) - ((b^2 - 4*a*c)^(9/4)*d^(3/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(21*c^2*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(1/2), x, 4, (sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2))/(3*c*d) - ((b^2 - 4*a*c)^(5/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(3*c^2*sqrt(d)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(5/2), x, 4, -(sqrt(a + b*x + c*x^2)/(3*c*d*(b*d + 2*c*d*x)^(3/2))) + ((b^2 - 4*a*c)^(1/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(3*c^2*d^(5/2)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(9/2), x, 5, -(sqrt(a + b*x + c*x^2)/(7*c*d*(b*d + 2*c*d*x)^(7/2))) + (2*sqrt(a + b*x + c*x^2))/(21*c*(b^2 - 4*a*c)*d^3*(b*d + 2*c*d*x)^(3/2)) + (sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(21*c^2*(b^2 - 4*a*c)^(3/4)*d^(9/2)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(13/2), x, 6, -(sqrt(a + b*x + c*x^2)/(11*c*d*(b*d + 2*c*d*x)^(11/2))) + (2*sqrt(a + b*x + c*x^2))/(77*c*(b^2 - 4*a*c)*d^3*(b*d + 2*c*d*x)^(7/2)) + (10*sqrt(a + b*x + c*x^2))/(231*c*(b^2 - 4*a*c)^2*d^5*(b*d + 2*c*d*x)^(3/2)) + (5*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(231*c^2*(b^2 - 4*a*c)^(7/4)*d^(13/2)*sqrt(a + b*x + c*x^2))]

    @test_int [(b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(1/2), x, 8, -((2*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(3/2)*sqrt(a + b*x + c*x^2))/(45*c)) + ((b*d + 2*c*d*x)^(7/2)*sqrt(a + b*x + c*x^2))/(9*c*d) - ((b^2 - 4*a*c)^(11/4)*d^(5/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(15*c^2*sqrt(a + b*x + c*x^2)) + ((b^2 - 4*a*c)^(11/4)*d^(5/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(15*c^2*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(1/2), x, 7, ((b*d + 2*c*d*x)^(3/2)*sqrt(a + b*x + c*x^2))/(5*c*d) - ((b^2 - 4*a*c)^(7/4)*sqrt(d)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(5*c^2*sqrt(a + b*x + c*x^2)) + ((b^2 - 4*a*c)^(7/4)*sqrt(d)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(5*c^2*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(3/2), x, 7, -(sqrt(a + b*x + c*x^2)/(c*d*sqrt(b*d + 2*c*d*x))) + ((b^2 - 4*a*c)^(3/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(c^2*d^(3/2)*sqrt(a + b*x + c*x^2)) - ((b^2 - 4*a*c)^(3/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(c^2*d^(3/2)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(1/2)/(b*d + 2*c*d*x)^(7/2), x, 8, -(sqrt(a + b*x + c*x^2)/(5*c*d*(b*d + 2*c*d*x)^(5/2))) + (2*sqrt(a + b*x + c*x^2))/(5*c*(b^2 - 4*a*c)*d^3*sqrt(b*d + 2*c*d*x)) - (sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(5*c^2*(b^2 - 4*a*c)^(1/4)*d^(7/2)*sqrt(a + b*x + c*x^2)) + (sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(5*c^2*(b^2 - 4*a*c)^(1/4)*d^(7/2)*sqrt(a + b*x + c*x^2))]

    @test_int [(b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(3/2), x, 7, ((b^2 - 4*a*c)^3*d^3*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2))/(231*c^2) + ((b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(5/2)*sqrt(a + b*x + c*x^2))/(385*c^2) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(9/2)*sqrt(a + b*x + c*x^2))/(110*c^2*d) + ((b*d + 2*c*d*x)^(9/2)*(a + b*x + c*x^2)^(3/2))/(15*c*d) + ((b^2 - 4*a*c)^(17/4)*d^(7/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(462*c^3*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(3/2), x, 6, ((b^2 - 4*a*c)^2*d*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2))/(77*c^2) - (3*(b^2 - 4*a*c)*(b*d + 2*c*d*x)^(5/2)*sqrt(a + b*x + c*x^2))/(154*c^2*d) + ((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(3/2))/(11*c*d) + ((b^2 - 4*a*c)^(13/4)*d^(3/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(154*c^3*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(1/2), x, 5, -(((b^2 - 4*a*c)*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2))/(14*c^2*d)) + (sqrt(b*d + 2*c*d*x)*(a + b*x + c*x^2)^(3/2))/(7*c*d) + ((b^2 - 4*a*c)^(9/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(14*c^3*sqrt(d)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(5/2), x, 5, (sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2))/(6*c^2*d^3) - (a + b*x + c*x^2)^(3/2)/(3*c*d*(b*d + 2*c*d*x)^(3/2)) - ((b^2 - 4*a*c)^(5/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(6*c^3*d^(5/2)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(9/2), x, 5, -(sqrt(a + b*x + c*x^2)/(14*c^2*d^3*(b*d + 2*c*d*x)^(3/2))) - (a + b*x + c*x^2)^(3/2)/(7*c*d*(b*d + 2*c*d*x)^(7/2)) + ((b^2 - 4*a*c)^(1/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(14*c^3*d^(9/2)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(13/2), x, 6, -((3*sqrt(a + b*x + c*x^2))/(154*c^2*d^3*(b*d + 2*c*d*x)^(7/2))) + sqrt(a + b*x + c*x^2)/(77*c^2*(b^2 - 4*a*c)*d^5*(b*d + 2*c*d*x)^(3/2)) - (a + b*x + c*x^2)^(3/2)/(11*c*d*(b*d + 2*c*d*x)^(11/2)) + (sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(154*c^3*(b^2 - 4*a*c)^(3/4)*d^(13/2)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(17/2), x, 7, -(sqrt(a + b*x + c*x^2)/(110*c^2*d^3*(b*d + 2*c*d*x)^(11/2))) + sqrt(a + b*x + c*x^2)/(385*c^2*(b^2 - 4*a*c)*d^5*(b*d + 2*c*d*x)^(7/2)) + sqrt(a + b*x + c*x^2)/(231*c^2*(b^2 - 4*a*c)^2*d^7*(b*d + 2*c*d*x)^(3/2)) - (a + b*x + c*x^2)^(3/2)/(15*c*d*(b*d + 2*c*d*x)^(15/2)) + (sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(462*c^3*(b^2 - 4*a*c)^(7/4)*d^(17/2)*sqrt(a + b*x + c*x^2))]

    @test_int [(b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(3/2), x, 9, ((b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(3/2)*sqrt(a + b*x + c*x^2))/(195*c^2) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(7/2)*sqrt(a + b*x + c*x^2))/(78*c^2*d) + ((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(3/2))/(13*c*d) + ((b^2 - 4*a*c)^(15/4)*d^(5/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(130*c^3*sqrt(a + b*x + c*x^2)) - ((b^2 - 4*a*c)^(15/4)*d^(5/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(130*c^3*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(3/2), x, 8, -(((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(3/2)*sqrt(a + b*x + c*x^2))/(30*c^2*d)) + ((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(3/2))/(9*c*d) + ((b^2 - 4*a*c)^(11/4)*sqrt(d)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(30*c^3*sqrt(a + b*x + c*x^2)) - ((b^2 - 4*a*c)^(11/4)*sqrt(d)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(30*c^3*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(3/2), x, 8, (3*(b*d + 2*c*d*x)^(3/2)*sqrt(a + b*x + c*x^2))/(10*c^2*d^3) - (a + b*x + c*x^2)^(3/2)/(c*d*sqrt(b*d + 2*c*d*x)) - (3*(b^2 - 4*a*c)^(7/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(10*c^3*d^(3/2)*sqrt(a + b*x + c*x^2)) + (3*(b^2 - 4*a*c)^(7/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(10*c^3*d^(3/2)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(7/2), x, 8, -((3*sqrt(a + b*x + c*x^2))/(10*c^2*d^3*sqrt(b*d + 2*c*d*x))) - (a + b*x + c*x^2)^(3/2)/(5*c*d*(b*d + 2*c*d*x)^(5/2)) + (3*(b^2 - 4*a*c)^(3/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(10*c^3*d^(7/2)*sqrt(a + b*x + c*x^2)) - (3*(b^2 - 4*a*c)^(3/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(10*c^3*d^(7/2)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(b*d + 2*c*d*x)^(11/2), x, 9, -(sqrt(a + b*x + c*x^2)/(30*c^2*d^3*(b*d + 2*c*d*x)^(5/2))) + sqrt(a + b*x + c*x^2)/(15*c^2*(b^2 - 4*a*c)*d^5*sqrt(b*d + 2*c*d*x)) - (a + b*x + c*x^2)^(3/2)/(9*c*d*(b*d + 2*c*d*x)^(9/2)) - (sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(30*c^3*(b^2 - 4*a*c)^(1/4)*d^(11/2)*sqrt(a + b*x + c*x^2)) + (sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(30*c^3*(b^2 - 4*a*c)^(1/4)*d^(11/2)*sqrt(a + b*x + c*x^2))]

    @test_int [(b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(5/2), x, 8, -((5*(b^2 - 4*a*c)^4*d^3*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2))/(8778*c^3)) - ((b^2 - 4*a*c)^3*d*(b*d + 2*c*d*x)^(5/2)*sqrt(a + b*x + c*x^2))/(2926*c^3) + ((b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(9/2)*sqrt(a + b*x + c*x^2))/(836*c^3*d) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(9/2)*(a + b*x + c*x^2)^(3/2))/(114*c^2*d) + ((b*d + 2*c*d*x)^(9/2)*(a + b*x + c*x^2)^(5/2))/(19*c*d) - (5*(b^2 - 4*a*c)^(21/4)*d^(7/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(17556*c^4*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(5/2), x, 7, -(((b^2 - 4*a*c)^3*d*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2))/(462*c^3)) + ((b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(5/2)*sqrt(a + b*x + c*x^2))/(308*c^3*d) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(3/2))/(66*c^2*d) + ((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(5/2))/(15*c*d) - ((b^2 - 4*a*c)^(17/4)*d^(3/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(924*c^4*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(1/2), x, 6, (5*(b^2 - 4*a*c)^2*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2))/(308*c^3*d) - (5*(b^2 - 4*a*c)*sqrt(b*d + 2*c*d*x)*(a + b*x + c*x^2)^(3/2))/(154*c^2*d) + (sqrt(b*d + 2*c*d*x)*(a + b*x + c*x^2)^(5/2))/(11*c*d) - (5*(b^2 - 4*a*c)^(13/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(308*c^4*sqrt(d)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(5/2), x, 6, -((5*(b^2 - 4*a*c)*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2))/(84*c^3*d^3)) + (5*sqrt(b*d + 2*c*d*x)*(a + b*x + c*x^2)^(3/2))/(42*c^2*d^3) - (a + b*x + c*x^2)^(5/2)/(3*c*d*(b*d + 2*c*d*x)^(3/2)) + (5*(b^2 - 4*a*c)^(9/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(84*c^4*d^(5/2)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(9/2), x, 6, (5*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2))/(84*c^3*d^5) - (5*(a + b*x + c*x^2)^(3/2))/(42*c^2*d^3*(b*d + 2*c*d*x)^(3/2)) - (a + b*x + c*x^2)^(5/2)/(7*c*d*(b*d + 2*c*d*x)^(7/2)) - (5*(b^2 - 4*a*c)^(5/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(84*c^4*d^(9/2)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(13/2), x, 6, -((5*sqrt(a + b*x + c*x^2))/(308*c^3*d^5*(b*d + 2*c*d*x)^(3/2))) - (5*(a + b*x + c*x^2)^(3/2))/(154*c^2*d^3*(b*d + 2*c*d*x)^(7/2)) - (a + b*x + c*x^2)^(5/2)/(11*c*d*(b*d + 2*c*d*x)^(11/2)) + (5*(b^2 - 4*a*c)^(1/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(308*c^4*d^(13/2)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(17/2), x, 7, -(sqrt(a + b*x + c*x^2)/(308*c^3*d^5*(b*d + 2*c*d*x)^(7/2))) + sqrt(a + b*x + c*x^2)/(462*c^3*(b^2 - 4*a*c)*d^7*(b*d + 2*c*d*x)^(3/2)) - (a + b*x + c*x^2)^(3/2)/(66*c^2*d^3*(b*d + 2*c*d*x)^(11/2)) - (a + b*x + c*x^2)^(5/2)/(15*c*d*(b*d + 2*c*d*x)^(15/2)) + (sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(924*c^4*(b^2 - 4*a*c)^(3/4)*d^(17/2)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(21/2), x, 8, -(sqrt(a + b*x + c*x^2)/(836*c^3*d^5*(b*d + 2*c*d*x)^(11/2))) + sqrt(a + b*x + c*x^2)/(2926*c^3*(b^2 - 4*a*c)*d^7*(b*d + 2*c*d*x)^(7/2)) + (5*sqrt(a + b*x + c*x^2))/(8778*c^3*(b^2 - 4*a*c)^2*d^9*(b*d + 2*c*d*x)^(3/2)) - (a + b*x + c*x^2)^(3/2)/(114*c^2*d^3*(b*d + 2*c*d*x)^(15/2)) - (a + b*x + c*x^2)^(5/2)/(19*c*d*(b*d + 2*c*d*x)^(19/2)) + (5*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(17556*c^4*(b^2 - 4*a*c)^(7/4)*d^(21/2)*sqrt(a + b*x + c*x^2))]

    @test_int [(b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(5/2), x, 10, -(((b^2 - 4*a*c)^3*d*(b*d + 2*c*d*x)^(3/2)*sqrt(a + b*x + c*x^2))/(1326*c^3)) + (5*(b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(7/2)*sqrt(a + b*x + c*x^2))/(2652*c^3*d) - (5*(b^2 - 4*a*c)*(b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(3/2))/(442*c^2*d) + ((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(5/2))/(17*c*d) - ((b^2 - 4*a*c)^(19/4)*d^(5/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(884*c^4*sqrt(a + b*x + c*x^2)) + ((b^2 - 4*a*c)^(19/4)*d^(5/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(884*c^4*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(5/2), x, 9, ((b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(3/2)*sqrt(a + b*x + c*x^2))/(156*c^3*d) - (5*(b^2 - 4*a*c)*(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(3/2))/(234*c^2*d) + ((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(5/2))/(13*c*d) - ((b^2 - 4*a*c)^(15/4)*sqrt(d)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(156*c^4*sqrt(a + b*x + c*x^2)) + ((b^2 - 4*a*c)^(15/4)*sqrt(d)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(156*c^4*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(3/2), x, 9, -(((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(3/2)*sqrt(a + b*x + c*x^2))/(12*c^3*d^3)) + (5*(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(3/2))/(18*c^2*d^3) - (a + b*x + c*x^2)^(5/2)/(c*d*sqrt(b*d + 2*c*d*x)) + ((b^2 - 4*a*c)^(11/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(12*c^4*d^(3/2)*sqrt(a + b*x + c*x^2)) - ((b^2 - 4*a*c)^(11/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(12*c^4*d^(3/2)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(7/2), x, 9, (3*(b*d + 2*c*d*x)^(3/2)*sqrt(a + b*x + c*x^2))/(20*c^3*d^5) - (a + b*x + c*x^2)^(3/2)/(2*c^2*d^3*sqrt(b*d + 2*c*d*x)) - (a + b*x + c*x^2)^(5/2)/(5*c*d*(b*d + 2*c*d*x)^(5/2)) - (3*(b^2 - 4*a*c)^(7/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(20*c^4*d^(7/2)*sqrt(a + b*x + c*x^2)) + (3*(b^2 - 4*a*c)^(7/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(20*c^4*d^(7/2)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(11/2), x, 9, -(sqrt(a + b*x + c*x^2)/(12*c^3*d^5*sqrt(b*d + 2*c*d*x))) - (a + b*x + c*x^2)^(3/2)/(18*c^2*d^3*(b*d + 2*c*d*x)^(5/2)) - (a + b*x + c*x^2)^(5/2)/(9*c*d*(b*d + 2*c*d*x)^(9/2)) + ((b^2 - 4*a*c)^(3/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(12*c^4*d^(11/2)*sqrt(a + b*x + c*x^2)) - ((b^2 - 4*a*c)^(3/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(12*c^4*d^(11/2)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(b*d + 2*c*d*x)^(15/2), x, 10, -(sqrt(a + b*x + c*x^2)/(156*c^3*d^5*(b*d + 2*c*d*x)^(5/2))) + sqrt(a + b*x + c*x^2)/(78*c^3*(b^2 - 4*a*c)*d^7*sqrt(b*d + 2*c*d*x)) - (5*(a + b*x + c*x^2)^(3/2))/(234*c^2*d^3*(b*d + 2*c*d*x)^(9/2)) - (a + b*x + c*x^2)^(5/2)/(13*c*d*(b*d + 2*c*d*x)^(13/2)) - (sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(156*c^4*(b^2 - 4*a*c)^(1/4)*d^(15/2)*sqrt(a + b*x + c*x^2)) + (sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(156*c^4*(b^2 - 4*a*c)^(1/4)*d^(15/2)*sqrt(a + b*x + c*x^2))]

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

    @test_int [(b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2)^(1/2), x, 5, (20/21)*(b^2 - 4*a*c)*d^3*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2) + (4/7)*d*(b*d + 2*c*d*x)^(5/2)*sqrt(a + b*x + c*x^2) + (10*(b^2 - 4*a*c)^(9/4)*d^(7/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(21*c*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2)^(1/2), x, 4, (4/3)*d*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2) + (2*(b^2 - 4*a*c)^(5/4)*d^(3/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(3*c*sqrt(a + b*x + c*x^2))]
    @test_int [1/((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(1/2)), x, 3, (2*(b^2 - 4*a*c)^(1/4)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(c*sqrt(d)*sqrt(a + b*x + c*x^2))]
    @test_int [1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(1/2)), x, 4, (4*sqrt(a + b*x + c*x^2))/(3*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(3/2)) + (2*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(3*c*(b^2 - 4*a*c)^(3/4)*d^(5/2)*sqrt(a + b*x + c*x^2))]
    @test_int [1/((b*d + 2*c*d*x)^(9/2)*(a + b*x + c*x^2)^(1/2)), x, 5, (4*sqrt(a + b*x + c*x^2))/(7*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(7/2)) + (20*sqrt(a + b*x + c*x^2))/(21*(b^2 - 4*a*c)^2*d^3*(b*d + 2*c*d*x)^(3/2)) + (10*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(21*c*(b^2 - 4*a*c)^(7/4)*d^(9/2)*sqrt(a + b*x + c*x^2))]

    @test_int [(b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2)^(1/2), x, 8, (28/45)*(b^2 - 4*a*c)*d^3*(b*d + 2*c*d*x)^(3/2)*sqrt(a + b*x + c*x^2) + (4/9)*d*(b*d + 2*c*d*x)^(7/2)*sqrt(a + b*x + c*x^2) + (14*(b^2 - 4*a*c)^(11/4)*d^(9/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(15*c*sqrt(a + b*x + c*x^2)) - (14*(b^2 - 4*a*c)^(11/4)*d^(9/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(15*c*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2)^(1/2), x, 7, (4/5)*d*(b*d + 2*c*d*x)^(3/2)*sqrt(a + b*x + c*x^2) + (6*(b^2 - 4*a*c)^(7/4)*d^(5/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(5*c*sqrt(a + b*x + c*x^2)) - (6*(b^2 - 4*a*c)^(7/4)*d^(5/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(5*c*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^(1/2)/(a + b*x + c*x^2)^(1/2), x, 6, (2*(b^2 - 4*a*c)^(3/4)*sqrt(d)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(c*sqrt(a + b*x + c*x^2)) - (2*(b^2 - 4*a*c)^(3/4)*sqrt(d)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(c*sqrt(a + b*x + c*x^2))]
    @test_int [1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(1/2)), x, 7, (4*sqrt(a + b*x + c*x^2))/((b^2 - 4*a*c)*d*sqrt(b*d + 2*c*d*x)) - (2*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(c*(b^2 - 4*a*c)^(1/4)*d^(3/2)*sqrt(a + b*x + c*x^2)) + (2*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(c*(b^2 - 4*a*c)^(1/4)*d^(3/2)*sqrt(a + b*x + c*x^2))]
    @test_int [1/((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(1/2)), x, 8, (4*sqrt(a + b*x + c*x^2))/(5*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(5/2)) + (12*sqrt(a + b*x + c*x^2))/(5*(b^2 - 4*a*c)^2*d^3*sqrt(b*d + 2*c*d*x)) - (6*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(5*c*(b^2 - 4*a*c)^(5/4)*d^(7/2)*sqrt(a + b*x + c*x^2)) + (6*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(5*c*(b^2 - 4*a*c)^(5/4)*d^(7/2)*sqrt(a + b*x + c*x^2))]

    @test_int [(3 - 2*x)^(3/2)/sqrt(1 - 3*x + x^2), x, 4, (-(4/3))*sqrt(3 - 2*x)*sqrt(1 - 3*x + x^2) - (2*5^(3/4)*sqrt(-1 + 3*x - x^2)*Elliptic.F(asin(sqrt(3 - 2*x)/5^(1/4)), -1))/(3*sqrt(1 - 3*x + x^2))]
    @test_int [1/((3 - 2*x)^(1/2)*sqrt(1 - 3*x + x^2)), x, 3, -((2*sqrt(-1 + 3*x - x^2)*Elliptic.F(asin(sqrt(3 - 2*x)/5^(1/4)), -1))/(5^(1/4)*sqrt(1 - 3*x + x^2)))]
    @test_int [1/((3 - 2*x)^(5/2)*sqrt(1 - 3*x + x^2)), x, 4, -((4*sqrt(1 - 3*x + x^2))/(15*(3 - 2*x)^(3/2))) - (2*sqrt(-1 + 3*x - x^2)*Elliptic.F(asin(sqrt(3 - 2*x)/5^(1/4)), -1))/(15*5^(1/4)*sqrt(1 - 3*x + x^2))]

    @test_int [(3 - 2*x)^(5/2)/sqrt(1 - 3*x + x^2), x, 8, (-(4/5))*(3 - 2*x)^(3/2)*sqrt(1 - 3*x + x^2) - (6*5^(1/4)*sqrt(-1 + 3*x - x^2)*Elliptic.E(asin(sqrt(3 - 2*x)/5^(1/4)), -1))/sqrt(1 - 3*x + x^2) + (6*5^(1/4)*sqrt(-1 + 3*x - x^2)*Elliptic.F(asin(sqrt(3 - 2*x)/5^(1/4)), -1))/sqrt(1 - 3*x + x^2)]
    @test_int [(3 - 2*x)^(1/2)/sqrt(1 - 3*x + x^2), x, 7, -((2*5^(1/4)*sqrt(-1 + 3*x - x^2)*Elliptic.E(asin(sqrt(3 - 2*x)/5^(1/4)), -1))/sqrt(1 - 3*x + x^2)) + (2*5^(1/4)*sqrt(-1 + 3*x - x^2)*Elliptic.F(asin(sqrt(3 - 2*x)/5^(1/4)), -1))/sqrt(1 - 3*x + x^2)]
    @test_int [1/((3 - 2*x)^(3/2)*sqrt(1 - 3*x + x^2)), x, 8, -((4*sqrt(1 - 3*x + x^2))/(5*sqrt(3 - 2*x))) + (2*sqrt(-1 + 3*x - x^2)*Elliptic.E(asin(sqrt(3 - 2*x)/5^(1/4)), -1))/(5^(3/4)*sqrt(1 - 3*x + x^2)) - (2*sqrt(-1 + 3*x - x^2)*Elliptic.F(asin(sqrt(3 - 2*x)/5^(1/4)), -1))/(5^(3/4)*sqrt(1 - 3*x + x^2))]

    @test_int [(b*d + 2*c*d*x)^(11/2)/(a + b*x + c*x^2)^(3/2), x, 6, -((2*d*(b*d + 2*c*d*x)^(9/2))/sqrt(a + b*x + c*x^2)) + (120/7)*c*(b^2 - 4*a*c)*d^5*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2) + (72/7)*c*d^3*(b*d + 2*c*d*x)^(5/2)*sqrt(a + b*x + c*x^2) + (60*(b^2 - 4*a*c)^(9/4)*d^(11/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(7*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2)^(3/2), x, 5, -((2*d*(b*d + 2*c*d*x)^(5/2))/sqrt(a + b*x + c*x^2)) + (40/3)*c*d^3*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2) + (20*(b^2 - 4*a*c)^(5/4)*d^(7/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(3*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2)^(3/2), x, 4, -((2*d*sqrt(b*d + 2*c*d*x))/sqrt(a + b*x + c*x^2)) + (4*(b^2 - 4*a*c)^(1/4)*d^(3/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/sqrt(a + b*x + c*x^2)]
    @test_int [1/((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(3/2)), x, 4, -((2*sqrt(b*d + 2*c*d*x))/((b^2 - 4*a*c)*d*sqrt(a + b*x + c*x^2))) - (4*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/((b^2 - 4*a*c)^(3/4)*sqrt(d)*sqrt(a + b*x + c*x^2))]
    @test_int [1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(3/2)), x, 5, -(2/((b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(3/2)*sqrt(a + b*x + c*x^2))) - (40*c*sqrt(a + b*x + c*x^2))/(3*(b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(3/2)) - (20*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(3*(b^2 - 4*a*c)^(7/4)*d^(5/2)*sqrt(a + b*x + c*x^2))]

    @test_int [(b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2)^(3/2), x, 8, -((2*d*(b*d + 2*c*d*x)^(7/2))/sqrt(a + b*x + c*x^2)) + (56/5)*c*d^3*(b*d + 2*c*d*x)^(3/2)*sqrt(a + b*x + c*x^2) + (84*(b^2 - 4*a*c)^(7/4)*d^(9/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(5*sqrt(a + b*x + c*x^2)) - (84*(b^2 - 4*a*c)^(7/4)*d^(9/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(5*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2)^(3/2), x, 7, -((2*d*(b*d + 2*c*d*x)^(3/2))/sqrt(a + b*x + c*x^2)) + (12*(b^2 - 4*a*c)^(3/4)*d^(5/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/sqrt(a + b*x + c*x^2) - (12*(b^2 - 4*a*c)^(3/4)*d^(5/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/sqrt(a + b*x + c*x^2)]
    @test_int [(b*d + 2*c*d*x)^(1/2)/(a + b*x + c*x^2)^(3/2), x, 7, -((2*(b*d + 2*c*d*x)^(3/2))/((b^2 - 4*a*c)*d*sqrt(a + b*x + c*x^2))) + (4*sqrt(d)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/((b^2 - 4*a*c)^(1/4)*sqrt(a + b*x + c*x^2)) - (4*sqrt(d)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/((b^2 - 4*a*c)^(1/4)*sqrt(a + b*x + c*x^2))]
    @test_int [1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(3/2)), x, 8, -(2/((b^2 - 4*a*c)*d*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2))) - (24*c*sqrt(a + b*x + c*x^2))/((b^2 - 4*a*c)^2*d*sqrt(b*d + 2*c*d*x)) + (12*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/((b^2 - 4*a*c)^(5/4)*d^(3/2)*sqrt(a + b*x + c*x^2)) - (12*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/((b^2 - 4*a*c)^(5/4)*d^(3/2)*sqrt(a + b*x + c*x^2))]
    @test_int [1/((b*d + 2*c*d*x)^(7/2)*(a + b*x + c*x^2)^(3/2)), x, 9, -(2/((b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(5/2)*sqrt(a + b*x + c*x^2))) - (56*c*sqrt(a + b*x + c*x^2))/(5*(b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(5/2)) - (168*c*sqrt(a + b*x + c*x^2))/(5*(b^2 - 4*a*c)^3*d^3*sqrt(b*d + 2*c*d*x)) + (84*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(5*(b^2 - 4*a*c)^(9/4)*d^(7/2)*sqrt(a + b*x + c*x^2)) - (84*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(5*(b^2 - 4*a*c)^(9/4)*d^(7/2)*sqrt(a + b*x + c*x^2))]

    @test_int [(b*d + 2*c*d*x)^(15/2)/(a + b*x + c*x^2)^(5/2), x, 7, -((2*d*(b*d + 2*c*d*x)^(13/2))/(3*(a + b*x + c*x^2)^(3/2))) - (52*c*d^3*(b*d + 2*c*d*x)^(9/2))/(3*sqrt(a + b*x + c*x^2)) + (1040/7)*c^2*(b^2 - 4*a*c)*d^7*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2) + (624/7)*c^2*d^5*(b*d + 2*c*d*x)^(5/2)*sqrt(a + b*x + c*x^2) + (520*c*(b^2 - 4*a*c)^(9/4)*d^(15/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(7*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^(11/2)/(a + b*x + c*x^2)^(5/2), x, 6, -((2*d*(b*d + 2*c*d*x)^(9/2))/(3*(a + b*x + c*x^2)^(3/2))) - (12*c*d^3*(b*d + 2*c*d*x)^(5/2))/sqrt(a + b*x + c*x^2) + 80*c^2*d^5*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2) + (40*c*(b^2 - 4*a*c)^(5/4)*d^(11/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/sqrt(a + b*x + c*x^2)]
    @test_int [(b*d + 2*c*d*x)^(7/2)/(a + b*x + c*x^2)^(5/2), x, 5, -((2*d*(b*d + 2*c*d*x)^(5/2))/(3*(a + b*x + c*x^2)^(3/2))) - (20*c*d^3*sqrt(b*d + 2*c*d*x))/(3*sqrt(a + b*x + c*x^2)) + (40*c*(b^2 - 4*a*c)^(1/4)*d^(7/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(3*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^(3/2)/(a + b*x + c*x^2)^(5/2), x, 5, -((2*d*sqrt(b*d + 2*c*d*x))/(3*(a + b*x + c*x^2)^(3/2))) - (4*c*d*sqrt(b*d + 2*c*d*x))/(3*(b^2 - 4*a*c)*sqrt(a + b*x + c*x^2)) - (8*c*d^(3/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(3*(b^2 - 4*a*c)^(3/4)*sqrt(a + b*x + c*x^2))]
    @test_int [1/((b*d + 2*c*d*x)^(1/2)*(a + b*x + c*x^2)^(5/2)), x, 5, -((2*sqrt(b*d + 2*c*d*x))/(3*(b^2 - 4*a*c)*d*(a + b*x + c*x^2)^(3/2))) + (20*c*sqrt(b*d + 2*c*d*x))/(3*(b^2 - 4*a*c)^2*d*sqrt(a + b*x + c*x^2)) + (40*c*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(3*(b^2 - 4*a*c)^(7/4)*sqrt(d)*sqrt(a + b*x + c*x^2))]
    @test_int [1/((b*d + 2*c*d*x)^(5/2)*(a + b*x + c*x^2)^(5/2)), x, 6, -(2/(3*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(3/2))) + (12*c)/((b^2 - 4*a*c)^2*d*(b*d + 2*c*d*x)^(3/2)*sqrt(a + b*x + c*x^2)) + (80*c^2*sqrt(a + b*x + c*x^2))/((b^2 - 4*a*c)^3*d*(b*d + 2*c*d*x)^(3/2)) + (40*c*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/((b^2 - 4*a*c)^(11/4)*d^(5/2)*sqrt(a + b*x + c*x^2))]

    @test_int [(b*d + 2*c*d*x)^(13/2)/(a + b*x + c*x^2)^(5/2), x, 9, -((2*d*(b*d + 2*c*d*x)^(11/2))/(3*(a + b*x + c*x^2)^(3/2))) - (44*c*d^3*(b*d + 2*c*d*x)^(7/2))/(3*sqrt(a + b*x + c*x^2)) + (1232/15)*c^2*d^5*(b*d + 2*c*d*x)^(3/2)*sqrt(a + b*x + c*x^2) + (616*c*(b^2 - 4*a*c)^(7/4)*d^(13/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(5*sqrt(a + b*x + c*x^2)) - (616*c*(b^2 - 4*a*c)^(7/4)*d^(13/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/(5*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^(9/2)/(a + b*x + c*x^2)^(5/2), x, 8, -((2*d*(b*d + 2*c*d*x)^(7/2))/(3*(a + b*x + c*x^2)^(3/2))) - (28*c*d^3*(b*d + 2*c*d*x)^(3/2))/(3*sqrt(a + b*x + c*x^2)) + (56*c*(b^2 - 4*a*c)^(3/4)*d^(9/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/sqrt(a + b*x + c*x^2) - (56*c*(b^2 - 4*a*c)^(3/4)*d^(9/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/sqrt(a + b*x + c*x^2)]
    @test_int [(b*d + 2*c*d*x)^(5/2)/(a + b*x + c*x^2)^(5/2), x, 8, -((2*d*(b*d + 2*c*d*x)^(3/2))/(3*(a + b*x + c*x^2)^(3/2))) - (4*c*d*(b*d + 2*c*d*x)^(3/2))/((b^2 - 4*a*c)*sqrt(a + b*x + c*x^2)) + (8*c*d^(5/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/((b^2 - 4*a*c)^(1/4)*sqrt(a + b*x + c*x^2)) - (8*c*d^(5/2)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/((b^2 - 4*a*c)^(1/4)*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^(1/2)/(a + b*x + c*x^2)^(5/2), x, 8, -((2*(b*d + 2*c*d*x)^(3/2))/(3*(b^2 - 4*a*c)*d*(a + b*x + c*x^2)^(3/2))) + (4*c*(b*d + 2*c*d*x)^(3/2))/((b^2 - 4*a*c)^2*d*sqrt(a + b*x + c*x^2)) - (8*c*sqrt(d)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/((b^2 - 4*a*c)^(5/4)*sqrt(a + b*x + c*x^2)) + (8*c*sqrt(d)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/((b^2 - 4*a*c)^(5/4)*sqrt(a + b*x + c*x^2))]
    @test_int [1/((b*d + 2*c*d*x)^(3/2)*(a + b*x + c*x^2)^(5/2)), x, 9, -(2/(3*(b^2 - 4*a*c)*d*sqrt(b*d + 2*c*d*x)*(a + b*x + c*x^2)^(3/2))) + (28*c)/(3*(b^2 - 4*a*c)^2*d*sqrt(b*d + 2*c*d*x)*sqrt(a + b*x + c*x^2)) + (112*c^2*sqrt(a + b*x + c*x^2))/((b^2 - 4*a*c)^3*d*sqrt(b*d + 2*c*d*x)) - (56*c*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/((b^2 - 4*a*c)^(9/4)*d^(3/2)*sqrt(a + b*x + c*x^2)) + (56*c*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt(b*d + 2*c*d*x)/((b^2 - 4*a*c)^(1/4)*sqrt(d))), -1))/((b^2 - 4*a*c)^(9/4)*d^(3/2)*sqrt(a + b*x + c*x^2))]

    @test_int [(c*e + d*e*x)^(11/2)/sqrt(1 - c^2 - 2*c*d*x - d^2*x^2), x, 5, -((30*e^5*sqrt(c*e + d*e*x)*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(77*d)) - (18*e^3*(c*e + d*e*x)^(5/2)*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(77*d) - (2*e*(c*e + d*e*x)^(9/2)*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(11*d) + (30*e^(11/2)*Elliptic.F(asin(sqrt(c*e + d*e*x)/sqrt(e)), -1))/(77*d)]
    @test_int [(c*e + d*e*x)^(7/2)/sqrt(1 - c^2 - 2*c*d*x - d^2*x^2), x, 4, -((10*e^3*sqrt(c*e + d*e*x)*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(21*d)) - (2*e*(c*e + d*e*x)^(5/2)*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(7*d) + (10*e^(7/2)*Elliptic.F(asin(sqrt(c*e + d*e*x)/sqrt(e)), -1))/(21*d)]
    @test_int [(c*e + d*e*x)^(3/2)/sqrt(1 - c^2 - 2*c*d*x - d^2*x^2), x, 3, -((2*e*sqrt(c*e + d*e*x)*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(3*d)) + (2*e^(3/2)*Elliptic.F(asin(sqrt(c*e + d*e*x)/sqrt(e)), -1))/(3*d)]
    @test_int [1/((c*e + d*e*x)^(1/2)*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2)), x, 2, (2*Elliptic.F(asin(sqrt(c*e + d*e*x)/sqrt(e)), -1))/(d*sqrt(e))]
    @test_int [1/((c*e + d*e*x)^(5/2)*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2)), x, 3, -((2*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(3*d*e*(c*e + d*e*x)^(3/2))) + (2*Elliptic.F(asin(sqrt(c*e + d*e*x)/sqrt(e)), -1))/(3*d*e^(5/2))]
    @test_int [1/((c*e + d*e*x)^(9/2)*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2)), x, 4, -((2*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(7*d*e*(c*e + d*e*x)^(7/2))) - (10*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(21*d*e^3*(c*e + d*e*x)^(3/2)) + (10*Elliptic.F(asin(sqrt(c*e + d*e*x)/sqrt(e)), -1))/(21*d*e^(9/2))]
    @test_int [1/((c*e + d*e*x)^(13/2)*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2)), x, 5, -((2*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(11*d*e*(c*e + d*e*x)^(11/2))) - (18*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(77*d*e^3*(c*e + d*e*x)^(7/2)) - (30*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(77*d*e^5*(c*e + d*e*x)^(3/2)) + (30*Elliptic.F(asin(sqrt(c*e + d*e*x)/sqrt(e)), -1))/(77*d*e^(13/2))]

    @test_int [(c*e + d*e*x)^(9/2)/sqrt(1 - c^2 - 2*c*d*x - d^2*x^2), x, 7, -((14*e^3*(c*e + d*e*x)^(3/2)*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(45*d)) - (2*e*(c*e + d*e*x)^(7/2)*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(9*d) + (14*e^(9/2)*Elliptic.E(asin(sqrt(c*e + d*e*x)/sqrt(e)), -1))/(15*d) - (14*e^(9/2)*Elliptic.F(asin(sqrt(c*e + d*e*x)/sqrt(e)), -1))/(15*d)]
    @test_int [(c*e + d*e*x)^(5/2)/sqrt(1 - c^2 - 2*c*d*x - d^2*x^2), x, 6, -((2*e*(c*e + d*e*x)^(3/2)*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(5*d)) + (6*e^(5/2)*Elliptic.E(asin(sqrt(c*e + d*e*x)/sqrt(e)), -1))/(5*d) - (6*e^(5/2)*Elliptic.F(asin(sqrt(c*e + d*e*x)/sqrt(e)), -1))/(5*d)]
    @test_int [(c*e + d*e*x)^(1/2)/sqrt(1 - c^2 - 2*c*d*x - d^2*x^2), x, 5, (2*sqrt(e)*Elliptic.E(asin(sqrt(c*e + d*e*x)/sqrt(e)), -1))/d - (2*sqrt(e)*Elliptic.F(asin(sqrt(c*e + d*e*x)/sqrt(e)), -1))/d]
    @test_int [1/((c*e + d*e*x)^(3/2)*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2)), x, 6, -((2*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(d*e*sqrt(c*e + d*e*x))) - (2*Elliptic.E(asin(sqrt(c*e + d*e*x)/sqrt(e)), -1))/(d*e^(3/2)) + (2*Elliptic.F(asin(sqrt(c*e + d*e*x)/sqrt(e)), -1))/(d*e^(3/2))]
    @test_int [1/((c*e + d*e*x)^(7/2)*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2)), x, 7, -((2*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(5*d*e*(c*e + d*e*x)^(5/2))) - (6*sqrt(1 - c^2 - 2*c*d*x - d^2*x^2))/(5*d*e^3*sqrt(c*e + d*e*x)) - (6*Elliptic.E(asin(sqrt(c*e + d*e*x)/sqrt(e)), -1))/(5*d*e^(7/2)) + (6*Elliptic.F(asin(sqrt(c*e + d*e*x)/sqrt(e)), -1))/(5*d*e^(7/2))]

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

    @test_int [(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(11/3), x, 8, -((3*(d*(b + 2*c*x))^(4/3)*(a + b*x + c*x^2)^(1/3))/(16*c^2*(b^2 - 4*a*c)*d^5)) + (9*(d*(b + 2*c*x))^(4/3)*(a + b*x + c*x^2)^(4/3))/(16*c*(b^2 - 4*a*c)^2*d^5) + (3*(a + b*x + c*x^2)^(7/3))/(4*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(8/3)) - (9*(a + b*x + c*x^2)^(7/3))/(4*(b^2 - 4*a*c)^2*d^3*(b*d + 2*c*d*x)^(2/3)) - (sqrt(3)*atan((1 + (2^(1/3)*(d*(b + 2*c*x))^(2/3))/(c^(1/3)*d^(2/3)*(a + b*x + c*x^2)^(1/3)))/sqrt(3)))/(16*2^(2/3)*c^(7/3)*d^(11/3)) - (3*log((d*(b + 2*c*x))^(2/3) - 2^(2/3)*c^(1/3)*d^(2/3)*(a + b*x + c*x^2)^(1/3)))/(32*2^(2/3)*c^(7/3)*d^(11/3))]
    @test_int [(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(17/3), x, 1, (3*(a + b*x + c*x^2)^(7/3))/(7*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(14/3))]
    @test_int [(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(23/3), x, 2, (3*(a + b*x + c*x^2)^(7/3))/(10*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(20/3)) + (9*(a + b*x + c*x^2)^(7/3))/(70*(b^2 - 4*a*c)^2*d^3*(b*d + 2*c*d*x)^(14/3))]
    @test_int [(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(29/3), x, 3, (3*(a + b*x + c*x^2)^(7/3))/(13*(b^2 - 4*a*c)*d*(b*d + 2*c*d*x)^(26/3)) + (9*(a + b*x + c*x^2)^(7/3))/(65*(b^2 - 4*a*c)^2*d^3*(b*d + 2*c*d*x)^(20/3)) + (27*(a + b*x + c*x^2)^(7/3))/(455*(b^2 - 4*a*c)^3*d^5*(b*d + 2*c*d*x)^(14/3))]

    @test_int [(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(2/3), x, 6, -(((b^2 - 4*a*c)*(d*(b + 2*c*x))^(1/3)*(a + b*x + c*x^2)^(1/3))/(9*c^2*d)) + ((d*(b + 2*c*x))^(1/3)*(a + b*x + c*x^2)^(4/3))/(6*c*d) + ((b^2 - 4*a*c)*(d*(b + 2*c*x))^(1/3)*(b^2 - 4*a*c - (b + 2*c*x)^2)*(2*c^(1/3)*d^(2/3) - (2^(1/3)*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))*sqrt((2*2^(1/3)*c^(2/3)*d^(4/3) + (d*(b + 2*c*x))^(4/3)/(a + b*x + c*x^2)^(2/3) + (2^(2/3)*c^(1/3)*d^(2/3)*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))/(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + sqrt(3))*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))^2)*Elliptic.F(acos((2^(2/3)*c^(1/3)*d^(2/3) - ((1 - sqrt(3))*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))/(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + sqrt(3))*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))), (1/4)*(2 + sqrt(3))))/(72*3^(1/4)*c^(10/3)*d^(5/3)*(a + b*x + c*x^2)^(2/3)*sqrt(-(((d*(b + 2*c*x))^(2/3)*(2^(2/3)*c^(1/3)*d^(2/3) - (d*(b + 2*c*x))^(2/3)/(a + b*x + c*x^2)^(1/3)))/((a + b*x + c*x^2)^(1/3)*(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + sqrt(3))*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))^2))))]
    @test_int [(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(8/3), x, 6, ((d*(b + 2*c*x))^(1/3)*(a + b*x + c*x^2)^(1/3))/(5*c^2*d^3) - (3*(a + b*x + c*x^2)^(4/3))/(10*c*d*(d*(b + 2*c*x))^(5/3)) - ((d*(b + 2*c*x))^(1/3)*(b^2 - 4*a*c - (b + 2*c*x)^2)*(2*c^(1/3)*d^(2/3) - (2^(1/3)*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))*sqrt((2*2^(1/3)*c^(2/3)*d^(4/3) + (d*(b + 2*c*x))^(4/3)/(a + b*x + c*x^2)^(2/3) + (2^(2/3)*c^(1/3)*d^(2/3)*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))/(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + sqrt(3))*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))^2)*Elliptic.F(acos((2^(2/3)*c^(1/3)*d^(2/3) - ((1 - sqrt(3))*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))/(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + sqrt(3))*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))), (1/4)*(2 + sqrt(3))))/(40*3^(1/4)*c^(10/3)*d^(11/3)*(a + b*x + c*x^2)^(2/3)*sqrt(-(((d*(b + 2*c*x))^(2/3)*(2^(2/3)*c^(1/3)*d^(2/3) - (d*(b + 2*c*x))^(2/3)/(a + b*x + c*x^2)^(1/3)))/((a + b*x + c*x^2)^(1/3)*(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + sqrt(3))*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))^2))))]
    @test_int [(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(14/3), x, 6, -((3*(a + b*x + c*x^2)^(1/3))/(55*c^2*d^3*(d*(b + 2*c*x))^(5/3))) - (3*(a + b*x + c*x^2)^(4/3))/(22*c*d*(d*(b + 2*c*x))^(11/3)) + (3^(3/4)*(d*(b + 2*c*x))^(1/3)*(b^2 - 4*a*c - (b + 2*c*x)^2)*(2*c^(1/3)*d^(2/3) - (2^(1/3)*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))*sqrt((2*2^(1/3)*c^(2/3)*d^(4/3) + (d*(b + 2*c*x))^(4/3)/(a + b*x + c*x^2)^(2/3) + (2^(2/3)*c^(1/3)*d^(2/3)*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))/(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + sqrt(3))*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))^2)*Elliptic.F(acos((2^(2/3)*c^(1/3)*d^(2/3) - ((1 - sqrt(3))*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))/(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + sqrt(3))*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))), (1/4)*(2 + sqrt(3))))/(440*c^(10/3)*(b^2 - 4*a*c)*d^(17/3)*(a + b*x + c*x^2)^(2/3)*sqrt(-(((d*(b + 2*c*x))^(2/3)*(2^(2/3)*c^(1/3)*d^(2/3) - (d*(b + 2*c*x))^(2/3)/(a + b*x + c*x^2)^(1/3)))/((a + b*x + c*x^2)^(1/3)*(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + sqrt(3))*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))^2))))]
    @test_int [(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(20/3), x, 7, -((3*(a + b*x + c*x^2)^(1/3))/(187*c^2*d^3*(d*(b + 2*c*x))^(11/3))) + (6*(a + b*x + c*x^2)^(1/3))/(935*c^2*(b^2 - 4*a*c)*d^5*(d*(b + 2*c*x))^(5/3)) - (3*(a + b*x + c*x^2)^(4/3))/(34*c*d*(d*(b + 2*c*x))^(17/3)) + (3*3^(3/4)*(d*(b + 2*c*x))^(1/3)*(b^2 - 4*a*c - (b + 2*c*x)^2)*(2*c^(1/3)*d^(2/3) - (2^(1/3)*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))*sqrt((2*2^(1/3)*c^(2/3)*d^(4/3) + (d*(b + 2*c*x))^(4/3)/(a + b*x + c*x^2)^(2/3) + (2^(2/3)*c^(1/3)*d^(2/3)*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))/(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + sqrt(3))*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))^2)*Elliptic.F(acos((2^(2/3)*c^(1/3)*d^(2/3) - ((1 - sqrt(3))*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))/(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + sqrt(3))*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))), (1/4)*(2 + sqrt(3))))/(7480*c^(10/3)*(b^2 - 4*a*c)^2*d^(23/3)*(a + b*x + c*x^2)^(2/3)*sqrt(-(((d*(b + 2*c*x))^(2/3)*(2^(2/3)*c^(1/3)*d^(2/3) - (d*(b + 2*c*x))^(2/3)/(a + b*x + c*x^2)^(1/3)))/((a + b*x + c*x^2)^(1/3)*(2^(2/3)*c^(1/3)*d^(2/3) - ((1 + sqrt(3))*(d*(b + 2*c*x))^(2/3))/(a + b*x + c*x^2)^(1/3))^2))))]

    @test_int [(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(4/3), x, 3, (3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(1/3)*HypergeometricFunctions._₂F₁(-(4/3), -(1/6), 5/6, (b + 2*c*x)^2/(b^2 - 4*a*c)))/(8*c^2*d*(d*(b + 2*c*x))^(1/3)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/3))]
    @test_int [(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(10/3), x, 3, (3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(1/3)*HypergeometricFunctions._₂F₁(-(4/3), -(7/6), -(1/6), (b + 2*c*x)^2/(b^2 - 4*a*c)))/(56*c^2*d*(d*(b + 2*c*x))^(7/3)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/3))]
    @test_int [(a + b*x + c*x^2)^(4/3)/(b*d + 2*c*d*x)^(16/3), x, 3, (3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(1/3)*HypergeometricFunctions._₂F₁(-(13/6), -(4/3), -(7/6), (b + 2*c*x)^2/(b^2 - 4*a*c)))/(104*c^2*d*(d*(b + 2*c*x))^(13/3)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/3))]

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

    @test_int [(b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^3, x, 2, -(((b^2 - 4*a*c)^3*(b*d + 2*c*d*x)^(1 + m))/(128*c^4*d*(1 + m))) + (3*(b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(3 + m))/(128*c^4*d^3*(3 + m)) - (3*(b^2 - 4*a*c)*(b*d + 2*c*d*x)^(5 + m))/(128*c^4*d^5*(5 + m)) + (b*d + 2*c*d*x)^(7 + m)/(128*c^4*d^7*(7 + m))]
    @test_int [(b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^2, x, 2, ((b^2 - 4*a*c)^2*(b*d + 2*c*d*x)^(1 + m))/(32*c^3*d*(1 + m)) - ((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(3 + m))/(16*c^3*d^3*(3 + m)) + (b*d + 2*c*d*x)^(5 + m)/(32*c^3*d^5*(5 + m))]
    @test_int [(b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^1, x, 2, -(((b^2 - 4*a*c)*(b*d + 2*c*d*x)^(1 + m))/(8*c^2*d*(1 + m))) + (b*d + 2*c*d*x)^(3 + m)/(8*c^2*d^3*(3 + m))]
    @test_int [(b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^1, x, 2, -((2*(d*(b + 2*c*x))^(1 + m)*HypergeometricFunctions._₂F₁(1, (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/((b^2 - 4*a*c)*d*(1 + m)))]
    @test_int [(b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^2, x, 2, (8*c*(d*(b + 2*c*x))^(1 + m)*HypergeometricFunctions._₂F₁(2, (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/((b^2 - 4*a*c)^2*d*(1 + m))]
    @test_int [(b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^3, x, 2, -((32*c^2*(d*(b + 2*c*x))^(1 + m)*HypergeometricFunctions._₂F₁(3, (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/((b^2 - 4*a*c)^3*d*(1 + m)))]

    @test_int [(b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^(5/2), x, 3, -((2*(b*d + 2*c*d*x)^(1 + m)*(a + b*x + c*x^2)^(7/2)*HypergeometricFunctions._₂F₁(1, (8 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/((b^2 - 4*a*c)*d*(1 + m))), ((b^2 - 4*a*c)^2*(d*(b + 2*c*x))^(1 + m)*sqrt(a + b*x + c*x^2)*HypergeometricFunctions._₂F₁(-(5/2), (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/(32*c^3*d*(1 + m)*sqrt(1 - (b + 2*c*x)^2/(b^2 - 4*a*c)))]
    @test_int [(b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^(3/2), x, 3, -(((b*d + 2*c*d*x)^(1 + m)*(4*a - b^2/c + (b + 2*c*x)^2/c)^(5/2)*HypergeometricFunctions._₂F₁(1, (6 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/(16*(b^2 - 4*a*c)*d*(1 + m))), -(((b^2 - 4*a*c)*(d*(b + 2*c*x))^(1 + m)*sqrt(a + b*x + c*x^2)*HypergeometricFunctions._₂F₁(-(3/2), (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/(8*c^2*d*(1 + m)*sqrt(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))))]
    @test_int [(b*d + 2*c*d*x)^m*(a + b*x + c*x^2)^(1/2), x, 3, -(((b*d + 2*c*d*x)^(1 + m)*(4*a - b^2/c + (b + 2*c*x)^2/c)^(3/2)*HypergeometricFunctions._₂F₁(1, (4 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/(4*(b^2 - 4*a*c)*d*(1 + m))), ((d*(b + 2*c*x))^(1 + m)*sqrt(a + b*x + c*x^2)*HypergeometricFunctions._₂F₁(-(1/2), (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/(2*c*d*(1 + m)*sqrt(1 - (b + 2*c*x)^2/(b^2 - 4*a*c)))]
    @test_int [(b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^(1/2), x, 3, -(((b*d + 2*c*d*x)^(1 + m)*sqrt(4*a - b^2/c + (b + 2*c*x)^2/c)*HypergeometricFunctions._₂F₁(1, (2 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/((b^2 - 4*a*c)*d*(1 + m))), ((d*(b + 2*c*x))^(1 + m)*sqrt(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/(2*c*d*(1 + m)*sqrt(a + b*x + c*x^2))]
    @test_int [(b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^(3/2), x, 3, -((4*(b*d + 2*c*d*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, m/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/((b^2 - 4*a*c)*d*(1 + m)*sqrt(4*a - b^2/c + (b + 2*c*x)^2/c))), -((2*(d*(b + 2*c*x))^(1 + m)*sqrt(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))*HypergeometricFunctions._₂F₁(3/2, (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/((b^2 - 4*a*c)*d*(1 + m)*sqrt(a + b*x + c*x^2)))]
    @test_int [(b*d + 2*c*d*x)^m/(a + b*x + c*x^2)^(5/2), x, 3, -((16*(b*d + 2*c*d*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, (1/2)*(-2 + m), (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/((b^2 - 4*a*c)*d*(1 + m)*(4*a - b^2/c + (b + 2*c*x)^2/c)^(3/2))), (8*c*(d*(b + 2*c*x))^(1 + m)*sqrt(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))*HypergeometricFunctions._₂F₁(5/2, (1 + m)/2, (3 + m)/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/((b^2 - 4*a*c)^2*d*(1 + m)*sqrt(a + b*x + c*x^2))]

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

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

    @test_int [(b*d + 2*c*d*x)^5*(a + b*x + c*x^2)^p, x, 3, If(13>=8, (2*(b^2 - 4*a*c)^2*d^5*(a + b*x + c*x^2)^(1 + p))/((1 + p)*(2 + p)*(3 + p)) + (2*(b^2 - 4*a*c)*d^5*(b + 2*c*x)^2*(a + b*x + c*x^2)^(1 + p))/((2 + p)*(3 + p)) + (d^5*(b + 2*c*x)^4*(a + b*x + c*x^2)^(1 + p))/(3 + p), (2*(b^2 - 4*a*c)^2*d^5*(a + b*x + c*x^2)^(1 + p))/((3 + p)*(2 + 3*p + p^2)) + (2*(b^2 - 4*a*c)*d^5*(b + 2*c*x)^2*(a + b*x + c*x^2)^(1 + p))/(6 + 5*p + p^2) + (d^5*(b + 2*c*x)^4*(a + b*x + c*x^2)^(1 + p))/(3 + p))]
    @test_int [(b*d + 2*c*d*x)^4*(a + b*x + c*x^2)^p, x, 3, -((2*d^4*(b + 2*c*x)^5*((1/4)*(4*a - b^2/c) + (b + 2*c*x)^2/(4*c))^(1 + p)*HypergeometricFunctions._₂F₁(1, 7/2 + p, 7/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/(5*(b^2 - 4*a*c))), (d^4*(b + 2*c*x)^5*(a + b*x + c*x^2)^p*HypergeometricFunctions._₂F₁(5/2, -p, 7/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^p*(10*c))]
    @test_int [(b*d + 2*c*d*x)^3*(a + b*x + c*x^2)^p, x, 2, If(13>=8, ((b^2 - 4*a*c)*d^3*(a + b*x + c*x^2)^(1 + p))/((1 + p)*(2 + p)) + (d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)^(1 + p))/(2 + p), ((b^2 - 4*a*c)*d^3*(a + b*x + c*x^2)^(1 + p))/(2 + 3*p + p^2) + (d^3*(b + 2*c*x)^2*(a + b*x + c*x^2)^(1 + p))/(2 + p))]
    @test_int [(b*d + 2*c*d*x)^2*(a + b*x + c*x^2)^p, x, 3, -((2*d^2*(b + 2*c*x)^3*((1/4)*(4*a - b^2/c) + (b + 2*c*x)^2/(4*c))^(1 + p)*HypergeometricFunctions._₂F₁(1, 5/2 + p, 5/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/(3*(b^2 - 4*a*c))), (d^2*(b + 2*c*x)^3*(a + b*x + c*x^2)^p*HypergeometricFunctions._₂F₁(3/2, -p, 5/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^p*(6*c))]
    @test_int [(b*d + 2*c*d*x)^1*(a + b*x + c*x^2)^p, x, 1, (d*(a + b*x + c*x^2)^(1 + p))/(1 + p)]
    @test_int [(a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^1, x, 3, ((a + b*x + c*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(1, 1 + p, 2 + p, 1 - (b + 2*c*x)^2/(b^2 - 4*a*c)))/((b^2 - 4*a*c)*d*(1 + p))]
    @test_int [(a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^2, x, 3, (2*((1/4)*(4*a - b^2/c) + (b + 2*c*x)^2/(4*c))^(1 + p)*HypergeometricFunctions._₂F₁(1, 1/2 + p, 1/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/((b^2 - 4*a*c)*d^2*(b + 2*c*x)), -(((a + b*x + c*x^2)^p*HypergeometricFunctions._₂F₁(-(1/2), -p, 1/2, (b + 2*c*x)^2/(b^2 - 4*a*c)))/((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^p*(2*c*d^2*(b + 2*c*x))))]
    @test_int [(a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^3, x, 3, ((a + b*x + c*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(2, 1 + p, 2 + p, 1 - (b + 2*c*x)^2/(b^2 - 4*a*c)))/((b^2 - 4*a*c)^2*d^3*(1 + p))]
    @test_int [(a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^4, x, 3, (2*((1/4)*(4*a - b^2/c) + (b + 2*c*x)^2/(4*c))^(1 + p)*HypergeometricFunctions._₂F₁(1, -(1/2) + p, -(1/2), (b + 2*c*x)^2/(b^2 - 4*a*c)))/(3*(b^2 - 4*a*c)*d^4*(b + 2*c*x)^3), -(((a + b*x + c*x^2)^p*HypergeometricFunctions._₂F₁(-(3/2), -p, -(1/2), (b + 2*c*x)^2/(b^2 - 4*a*c)))/((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^p*(6*c*d^4*(b + 2*c*x)^3)))]
    @test_int [(a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^5, x, 3, ((a + b*x + c*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(3, 1 + p, 2 + p, 1 - (b + 2*c*x)^2/(b^2 - 4*a*c)))/((b^2 - 4*a*c)^3*d^5*(1 + p))]
    @test_int [(a + b*x + c*x^2)^p/(b*d + 2*c*d*x)^6, x, 3, (2*((1/4)*(4*a - b^2/c) + (b + 2*c*x)^2/(4*c))^(1 + p)*HypergeometricFunctions._₂F₁(1, -(3/2) + p, -(3/2), (b + 2*c*x)^2/(b^2 - 4*a*c)))/(5*(b^2 - 4*a*c)*d^6*(b + 2*c*x)^5), -(((a + b*x + c*x^2)^p*HypergeometricFunctions._₂F₁(-(5/2), -p, -(3/2), (b + 2*c*x)^2/(b^2 - 4*a*c)))/((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^p*(10*c*d^6*(b + 2*c*x)^5)))]

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

    @test_int [(1 + x)^m*(1 + 2*x + x^2)^n, x, 2, ((1 + x)^(1 + m)*(1 + 2*x + x^2)^n)/(1 + m + 2*n)]

    @test_int [((b*e)/(2*c) + e*x)^m*(b^2/(4*c) + b*x + c*x^2)^n, x, 2, (((b*e)/(2*c) + e*x)^(1 + m)*(b^2/(4*c) + b*x + c*x^2)^n)/(e*(1 + m + 2*n))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(d+e*x)^m*(a+b*x+c*x^2)^p*when*b^2-4*a*c=0=#

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

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

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

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

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

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

    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^6, x, 2, (a + b*x)^5/(5*(b*d - a*e)*(d + e*x)^5)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^7, x, 3, (a + b*x)^5/(6*(b*d - a*e)*(d + e*x)^6) + (b*(a + b*x)^5)/(30*(b*d - a*e)^2*(d + e*x)^5)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^8, x, 4, (a + b*x)^5/(7*(b*d - a*e)*(d + e*x)^7) + (b*(a + b*x)^5)/(21*(b*d - a*e)^2*(d + e*x)^6) + (b^2*(a + b*x)^5)/(105*(b*d - a*e)^3*(d + e*x)^5)]

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

    @test_int [(d + e*x)^8*(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, ((b*d - a*e)^6*(d + e*x)^9)/(9*e^7) - (3*b*(b*d - a*e)^5*(d + e*x)^10)/(5*e^7) + (15*b^2*(b*d - a*e)^4*(d + e*x)^11)/(11*e^7) - (5*b^3*(b*d - a*e)^3*(d + e*x)^12)/(3*e^7) + (15*b^4*(b*d - a*e)^2*(d + e*x)^13)/(13*e^7) - (3*b^5*(b*d - a*e)*(d + e*x)^14)/(7*e^7) + (b^6*(d + e*x)^15)/(15*e^7)]
    @test_int [(d + e*x)^7*(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, ((b*d - a*e)^6*(d + e*x)^8)/(8*e^7) - (2*b*(b*d - a*e)^5*(d + e*x)^9)/(3*e^7) + (3*b^2*(b*d - a*e)^4*(d + e*x)^10)/(2*e^7) - (20*b^3*(b*d - a*e)^3*(d + e*x)^11)/(11*e^7) + (5*b^4*(b*d - a*e)^2*(d + e*x)^12)/(4*e^7) - (6*b^5*(b*d - a*e)*(d + e*x)^13)/(13*e^7) + (b^6*(d + e*x)^14)/(14*e^7)]
    @test_int [(d + e*x)^6*(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, ((b*d - a*e)^6*(a + b*x)^7)/(7*b^7) + (3*e*(b*d - a*e)^5*(a + b*x)^8)/(4*b^7) + (5*e^2*(b*d - a*e)^4*(a + b*x)^9)/(3*b^7) + (2*e^3*(b*d - a*e)^3*(a + b*x)^10)/b^7 + (15*e^4*(b*d - a*e)^2*(a + b*x)^11)/(11*b^7) + (e^5*(b*d - a*e)*(a + b*x)^12)/(2*b^7) + (e^6*(a + b*x)^13)/(13*b^7)]

    @test_int [(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, ((b*d - a*e)^5*(a + b*x)^7)/(7*b^6) + (5*e*(b*d - a*e)^4*(a + b*x)^8)/(8*b^6) + (10*e^2*(b*d - a*e)^3*(a + b*x)^9)/(9*b^6) + (e^3*(b*d - a*e)^2*(a + b*x)^10)/b^6 + (5*e^4*(b*d - a*e)*(a + b*x)^11)/(11*b^6) + (e^5*(a + b*x)^12)/(12*b^6)]
    @test_int [(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, ((b*d - a*e)^4*(a + b*x)^7)/(7*b^5) + (e*(b*d - a*e)^3*(a + b*x)^8)/(2*b^5) + (2*e^2*(b*d - a*e)^2*(a + b*x)^9)/(3*b^5) + (2*e^3*(b*d - a*e)*(a + b*x)^10)/(5*b^5) + (e^4*(a + b*x)^11)/(11*b^5)]
    @test_int [(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, ((b*d - a*e)^3*(a + b*x)^7)/(7*b^4) + (3*e*(b*d - a*e)^2*(a + b*x)^8)/(8*b^4) + (e^2*(b*d - a*e)*(a + b*x)^9)/(3*b^4) + (e^3*(a + b*x)^10)/(10*b^4)]
    @test_int [(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, ((b*d - a*e)^2*(a + b*x)^7)/(7*b^3) + (e*(b*d - a*e)*(a + b*x)^8)/(4*b^3) + (e^2*(a + b*x)^9)/(9*b^3)]
    @test_int [(d + e*x)^1*(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, ((b*d - a*e)*(a + b*x)^7)/(7*b^2) + (e*(a + b*x)^8)/(8*b^2)]
    @test_int [(d + e*x)^0*(a^2 + 2*a*b*x + b^2*x^2)^3, x, 2, (a + b*x)^7/(7*b)]

    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^1, x, 3, -((b*(b*d - a*e)^5*x)/e^6) + ((b*d - a*e)^4*(a + b*x)^2)/(2*e^5) - ((b*d - a*e)^3*(a + b*x)^3)/(3*e^4) + ((b*d - a*e)^2*(a + b*x)^4)/(4*e^3) - ((b*d - a*e)*(a + b*x)^5)/(5*e^2) + (a + b*x)^6/(6*e) + ((b*d - a*e)^6*log(d + e*x))/e^7]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^2, x, 3, (15*b^2*(b*d - a*e)^4*x)/e^6 - (b*d - a*e)^6/(e^7*(d + e*x)) - (10*b^3*(b*d - a*e)^3*(d + e*x)^2)/e^7 + (5*b^4*(b*d - a*e)^2*(d + e*x)^3)/e^7 - (3*b^5*(b*d - a*e)*(d + e*x)^4)/(2*e^7) + (b^6*(d + e*x)^5)/(5*e^7) - (6*b*(b*d - a*e)^5*log(d + e*x))/e^7]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^3, x, 3, -((20*b^3*(b*d - a*e)^3*x)/e^6) - (b*d - a*e)^6/(2*e^7*(d + e*x)^2) + (6*b*(b*d - a*e)^5)/(e^7*(d + e*x)) + (15*b^4*(b*d - a*e)^2*(d + e*x)^2)/(2*e^7) - (2*b^5*(b*d - a*e)*(d + e*x)^3)/e^7 + (b^6*(d + e*x)^4)/(4*e^7) + (15*b^2*(b*d - a*e)^4*log(d + e*x))/e^7]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^4, x, 3, (15*b^4*(b*d - a*e)^2*x)/e^6 - (b*d - a*e)^6/(3*e^7*(d + e*x)^3) + (3*b*(b*d - a*e)^5)/(e^7*(d + e*x)^2) - (15*b^2*(b*d - a*e)^4)/(e^7*(d + e*x)) - (3*b^5*(b*d - a*e)*(d + e*x)^2)/e^7 + (b^6*(d + e*x)^3)/(3*e^7) - (20*b^3*(b*d - a*e)^3*log(d + e*x))/e^7]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^5, x, 3, -((b^5*(5*b*d - 6*a*e)*x)/e^6) + (b^6*x^2)/(2*e^5) - (b*d - a*e)^6/(4*e^7*(d + e*x)^4) + (2*b*(b*d - a*e)^5)/(e^7*(d + e*x)^3) - (15*b^2*(b*d - a*e)^4)/(2*e^7*(d + e*x)^2) + (20*b^3*(b*d - a*e)^3)/(e^7*(d + e*x)) + (15*b^4*(b*d - a*e)^2*log(d + e*x))/e^7]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^6, x, 3, (b^6*x)/e^6 - (b*d - a*e)^6/(5*e^7*(d + e*x)^5) + (3*b*(b*d - a*e)^5)/(2*e^7*(d + e*x)^4) - (5*b^2*(b*d - a*e)^4)/(e^7*(d + e*x)^3) + (10*b^3*(b*d - a*e)^3)/(e^7*(d + e*x)^2) - (15*b^4*(b*d - a*e)^2)/(e^7*(d + e*x)) - (6*b^5*(b*d - a*e)*log(d + e*x))/e^7]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^7, x, 3, -((b*d - a*e)^6/(6*e^7*(d + e*x)^6)) + (6*b*(b*d - a*e)^5)/(5*e^7*(d + e*x)^5) - (15*b^2*(b*d - a*e)^4)/(4*e^7*(d + e*x)^4) + (20*b^3*(b*d - a*e)^3)/(3*e^7*(d + e*x)^3) - (15*b^4*(b*d - a*e)^2)/(2*e^7*(d + e*x)^2) + (6*b^5*(b*d - a*e))/(e^7*(d + e*x)) + (b^6*log(d + e*x))/e^7]

    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^8, x, 2, (a + b*x)^7/(7*(b*d - a*e)*(d + e*x)^7)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^9, x, 3, (a + b*x)^7/(8*(b*d - a*e)*(d + e*x)^8) + (b*(a + b*x)^7)/(56*(b*d - a*e)^2*(d + e*x)^7)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^10, x, 4, (a + b*x)^7/(9*(b*d - a*e)*(d + e*x)^9) + (b*(a + b*x)^7)/(36*(b*d - a*e)^2*(d + e*x)^8) + (b^2*(a + b*x)^7)/(252*(b*d - a*e)^3*(d + e*x)^7)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^11, x, 5, (a + b*x)^7/(10*(b*d - a*e)*(d + e*x)^10) + (b*(a + b*x)^7)/(30*(b*d - a*e)^2*(d + e*x)^9) + (b^2*(a + b*x)^7)/(120*(b*d - a*e)^3*(d + e*x)^8) + (b^3*(a + b*x)^7)/(840*(b*d - a*e)^4*(d + e*x)^7)]

    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^12, x, 3, -((b*d - a*e)^6/(11*e^7*(d + e*x)^11)) + (3*b*(b*d - a*e)^5)/(5*e^7*(d + e*x)^10) - (5*b^2*(b*d - a*e)^4)/(3*e^7*(d + e*x)^9) + (5*b^3*(b*d - a*e)^3)/(2*e^7*(d + e*x)^8) - (15*b^4*(b*d - a*e)^2)/(7*e^7*(d + e*x)^7) + (b^5*(b*d - a*e))/(e^7*(d + e*x)^6) - b^6/(5*e^7*(d + e*x)^5)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^13, x, 3, -((b*d - a*e)^6/(12*e^7*(d + e*x)^12)) + (6*b*(b*d - a*e)^5)/(11*e^7*(d + e*x)^11) - (3*b^2*(b*d - a*e)^4)/(2*e^7*(d + e*x)^10) + (20*b^3*(b*d - a*e)^3)/(9*e^7*(d + e*x)^9) - (15*b^4*(b*d - a*e)^2)/(8*e^7*(d + e*x)^8) + (6*b^5*(b*d - a*e))/(7*e^7*(d + e*x)^7) - b^6/(6*e^7*(d + e*x)^6)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^14, x, 3, -((b*d - a*e)^6/(13*e^7*(d + e*x)^13)) + (b*(b*d - a*e)^5)/(2*e^7*(d + e*x)^12) - (15*b^2*(b*d - a*e)^4)/(11*e^7*(d + e*x)^11) + (2*b^3*(b*d - a*e)^3)/(e^7*(d + e*x)^10) - (5*b^4*(b*d - a*e)^2)/(3*e^7*(d + e*x)^9) + (3*b^5*(b*d - a*e))/(4*e^7*(d + e*x)^8) - b^6/(7*e^7*(d + e*x)^7)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^15, x, 3, -((b*d - a*e)^6/(14*e^7*(d + e*x)^14)) + (6*b*(b*d - a*e)^5)/(13*e^7*(d + e*x)^13) - (5*b^2*(b*d - a*e)^4)/(4*e^7*(d + e*x)^12) + (20*b^3*(b*d - a*e)^3)/(11*e^7*(d + e*x)^11) - (3*b^4*(b*d - a*e)^2)/(2*e^7*(d + e*x)^10) + (2*b^5*(b*d - a*e))/(3*e^7*(d + e*x)^9) - b^6/(8*e^7*(d + e*x)^8)]

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

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

    @test_int [(d + e*x)^6/(a^2 + 2*a*b*x + b^2*x^2)^2, x, 3, (15*e^4*(b*d - a*e)^2*x)/b^6 - (b*d - a*e)^6/(3*b^7*(a + b*x)^3) - (3*e*(b*d - a*e)^5)/(b^7*(a + b*x)^2) - (15*e^2*(b*d - a*e)^4)/(b^7*(a + b*x)) + (3*e^5*(b*d - a*e)*(a + b*x)^2)/b^7 + (e^6*(a + b*x)^3)/(3*b^7) + (20*e^3*(b*d - a*e)^3*log(a + b*x))/b^7]
    @test_int [(d + e*x)^5/(a^2 + 2*a*b*x + b^2*x^2)^2, x, 3, (e^4*(5*b*d - 4*a*e)*x)/b^5 + (e^5*x^2)/(2*b^4) - (b*d - a*e)^5/(3*b^6*(a + b*x)^3) - (5*e*(b*d - a*e)^4)/(2*b^6*(a + b*x)^2) - (10*e^2*(b*d - a*e)^3)/(b^6*(a + b*x)) + (10*e^3*(b*d - a*e)^2*log(a + b*x))/b^6]
    @test_int [(d + e*x)^4/(a^2 + 2*a*b*x + b^2*x^2)^2, x, 3, (e^4*x)/b^4 - (b*d - a*e)^4/(3*b^5*(a + b*x)^3) - (2*e*(b*d - a*e)^3)/(b^5*(a + b*x)^2) - (6*e^2*(b*d - a*e)^2)/(b^5*(a + b*x)) + (4*e^3*(b*d - a*e)*log(a + b*x))/b^5]
    @test_int [(d + e*x)^3/(a^2 + 2*a*b*x + b^2*x^2)^2, x, 3, -((b*d - a*e)^3/(3*b^4*(a + b*x)^3)) - (3*e*(b*d - a*e)^2)/(2*b^4*(a + b*x)^2) - (3*e^2*(b*d - a*e))/(b^4*(a + b*x)) + (e^3*log(a + b*x))/b^4]
    @test_int [(d + e*x)^2/(a^2 + 2*a*b*x + b^2*x^2)^2, x, 2, -((d + e*x)^3/(3*(b*d - a*e)*(a + b*x)^3))]
    @test_int [(d + e*x)^1/(a^2 + 2*a*b*x + b^2*x^2)^2, x, 3, -((b*d - a*e)/(3*b^2*(a + b*x)^3)) - e/(2*b^2*(a + b*x)^2)]
    @test_int [(d + e*x)^0/(a^2 + 2*a*b*x + b^2*x^2)^2, x, 2, -(1/(3*b*(a + b*x)^3))]
    @test_int [1/((d + e*x)^1*(a^2 + 2*a*b*x + b^2*x^2)^2), x, 3, -(1/(3*(b*d - a*e)*(a + b*x)^3)) + e/(2*(b*d - a*e)^2*(a + b*x)^2) - e^2/((b*d - a*e)^3*(a + b*x)) - (e^3*log(a + b*x))/(b*d - a*e)^4 + (e^3*log(d + e*x))/(b*d - a*e)^4]
    @test_int [1/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^2), x, 3, -(b/(3*(b*d - a*e)^2*(a + b*x)^3)) + (b*e)/((b*d - a*e)^3*(a + b*x)^2) - (3*b*e^2)/((b*d - a*e)^4*(a + b*x)) - e^3/((b*d - a*e)^4*(d + e*x)) - (4*b*e^3*log(a + b*x))/(b*d - a*e)^5 + (4*b*e^3*log(d + e*x))/(b*d - a*e)^5]
    @test_int [1/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^2), x, 3, -(b^2/(3*(b*d - a*e)^3*(a + b*x)^3)) + (3*b^2*e)/(2*(b*d - a*e)^4*(a + b*x)^2) - (6*b^2*e^2)/((b*d - a*e)^5*(a + b*x)) - e^3/(2*(b*d - a*e)^4*(d + e*x)^2) - (4*b*e^3)/((b*d - a*e)^5*(d + e*x)) - (10*b^2*e^3*log(a + b*x))/(b*d - a*e)^6 + (10*b^2*e^3*log(d + e*x))/(b*d - a*e)^6]

    @test_int [(d + e*x)^8/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, (28*e^6*(b*d - a*e)^2*x)/b^8 - (b*d - a*e)^8/(5*b^9*(a + b*x)^5) - (2*e*(b*d - a*e)^7)/(b^9*(a + b*x)^4) - (28*e^2*(b*d - a*e)^6)/(3*b^9*(a + b*x)^3) - (28*e^3*(b*d - a*e)^5)/(b^9*(a + b*x)^2) - (70*e^4*(b*d - a*e)^4)/(b^9*(a + b*x)) + (4*e^7*(b*d - a*e)*(a + b*x)^2)/b^9 + (e^8*(a + b*x)^3)/(3*b^9) + (56*e^5*(b*d - a*e)^3*log(a + b*x))/b^9]
    @test_int [(d + e*x)^7/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, (e^6*(7*b*d - 6*a*e)*x)/b^7 + (e^7*x^2)/(2*b^6) - (b*d - a*e)^7/(5*b^8*(a + b*x)^5) - (7*e*(b*d - a*e)^6)/(4*b^8*(a + b*x)^4) - (7*e^2*(b*d - a*e)^5)/(b^8*(a + b*x)^3) - (35*e^3*(b*d - a*e)^4)/(2*b^8*(a + b*x)^2) - (35*e^4*(b*d - a*e)^3)/(b^8*(a + b*x)) + (21*e^5*(b*d - a*e)^2*log(a + b*x))/b^8]
    @test_int [(d + e*x)^6/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, (e^6*x)/b^6 - (b*d - a*e)^6/(5*b^7*(a + b*x)^5) - (3*e*(b*d - a*e)^5)/(2*b^7*(a + b*x)^4) - (5*e^2*(b*d - a*e)^4)/(b^7*(a + b*x)^3) - (10*e^3*(b*d - a*e)^3)/(b^7*(a + b*x)^2) - (15*e^4*(b*d - a*e)^2)/(b^7*(a + b*x)) + (6*e^5*(b*d - a*e)*log(a + b*x))/b^7]
    @test_int [(d + e*x)^5/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, -((b*d - a*e)^5/(5*b^6*(a + b*x)^5)) - (5*e*(b*d - a*e)^4)/(4*b^6*(a + b*x)^4) - (10*e^2*(b*d - a*e)^3)/(3*b^6*(a + b*x)^3) - (5*e^3*(b*d - a*e)^2)/(b^6*(a + b*x)^2) - (5*e^4*(b*d - a*e))/(b^6*(a + b*x)) + (e^5*log(a + b*x))/b^6]
    @test_int [(d + e*x)^4/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 2, -((d + e*x)^5/(5*(b*d - a*e)*(a + b*x)^5))]
    @test_int [(d + e*x)^3/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, -((d + e*x)^4/(5*(b*d - a*e)*(a + b*x)^5)) + (e*(d + e*x)^4)/(20*(b*d - a*e)^2*(a + b*x)^4)]
    @test_int [(d + e*x)^2/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, -((b*d - a*e)^2/(5*b^3*(a + b*x)^5)) - (e*(b*d - a*e))/(2*b^3*(a + b*x)^4) - e^2/(3*b^3*(a + b*x)^3)]
    @test_int [(d + e*x)^1/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, -((b*d - a*e)/(5*b^2*(a + b*x)^5)) - e/(4*b^2*(a + b*x)^4)]
    @test_int [(d + e*x)^0/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 2, -(1/(5*b*(a + b*x)^5))]
    @test_int [1/((d + e*x)^1*(a^2 + 2*a*b*x + b^2*x^2)^3), x, 3, -(1/(5*(b*d - a*e)*(a + b*x)^5)) + e/(4*(b*d - a*e)^2*(a + b*x)^4) - e^2/(3*(b*d - a*e)^3*(a + b*x)^3) + e^3/(2*(b*d - a*e)^4*(a + b*x)^2) - e^4/((b*d - a*e)^5*(a + b*x)) - (e^5*log(a + b*x))/(b*d - a*e)^6 + (e^5*log(d + e*x))/(b*d - a*e)^6]
    @test_int [1/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^3), x, 3, -(b/(5*(b*d - a*e)^2*(a + b*x)^5)) + (b*e)/(2*(b*d - a*e)^3*(a + b*x)^4) - (b*e^2)/((b*d - a*e)^4*(a + b*x)^3) + (2*b*e^3)/((b*d - a*e)^5*(a + b*x)^2) - (5*b*e^4)/((b*d - a*e)^6*(a + b*x)) - e^5/((b*d - a*e)^6*(d + e*x)) - (6*b*e^5*log(a + b*x))/(b*d - a*e)^7 + (6*b*e^5*log(d + e*x))/(b*d - a*e)^7]
    @test_int [1/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^3), x, 3, -(b^2/(5*(b*d - a*e)^3*(a + b*x)^5)) + (3*b^2*e)/(4*(b*d - a*e)^4*(a + b*x)^4) - (2*b^2*e^2)/((b*d - a*e)^5*(a + b*x)^3) + (5*b^2*e^3)/((b*d - a*e)^6*(a + b*x)^2) - (15*b^2*e^4)/((b*d - a*e)^7*(a + b*x)) - e^5/(2*(b*d - a*e)^6*(d + e*x)^2) - (6*b*e^5)/((b*d - a*e)^7*(d + e*x)) - (21*b^2*e^5*log(a + b*x))/(b*d - a*e)^8 + (21*b^2*e^5*log(d + e*x))/(b*d - a*e)^8]

    @test_int [(d + e*x)*(9 + 12*x + 4*x^2)^3, x, 3, (1/28)*(2*d - 3*e)*(3 + 2*x)^7 + (1/32)*e*(3 + 2*x)^8]
    @test_int [(d + e*x)*(9 + 12*x + 4*x^2)^2, x, 3, (1/20)*(2*d - 3*e)*(3 + 2*x)^5 + (1/24)*e*(3 + 2*x)^6]
    @test_int [(d + e*x)*(9 + 12*x + 4*x^2)^1, x, 3, (1/12)*(2*d - 3*e)*(3 + 2*x)^3 + (1/16)*e*(3 + 2*x)^4]
    @test_int [(d + e*x)/(9 + 12*x + 4*x^2)^1, x, 3, -((2*d - 3*e)/(4*(3 + 2*x))) + (1/4)*e*log(3 + 2*x)]
    @test_int [(d + e*x)/(9 + 12*x + 4*x^2)^2, x, 3, -((2*d - 3*e)/(12*(3 + 2*x)^3)) - e/(8*(3 + 2*x)^2)]
    @test_int [(d + e*x)/(9 + 12*x + 4*x^2)^3, x, 3, -((2*d - 3*e)/(20*(3 + 2*x)^5)) - e/(16*(3 + 2*x)^4)]

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

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

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

    @test_int [(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 3, -((b*d - a*e)^3*(d + e*x)^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*e^4*(a + b*x)) + (3*b*(b*d - a*e)^2*(d + e*x)^7*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*e^4*(a + b*x)) - (3*b^2*(b*d - a*e)*(d + e*x)^8*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(8*e^4*(a + b*x)) + (b^3*(d + e*x)^9*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*e^4*(a + b*x))]
    @test_int [(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 3, -((b*d - a*e)^3*(d + e*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*e^4*(a + b*x)) + (b*(b*d - a*e)^2*(d + e*x)^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*e^4*(a + b*x)) - (3*b^2*(b*d - a*e)*(d + e*x)^7*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*e^4*(a + b*x)) + (b^3*(d + e*x)^8*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(8*e^4*(a + b*x))]
    @test_int [(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 3, ((b*d - a*e)^3*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*b^4) + (3*e*(b*d - a*e)^2*(a + b*x)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*b^4) + (e^2*(b*d - a*e)*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*b^4) + (e^3*(a + b*x)^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*b^4)]
    @test_int [(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 2, ((b*d - a*e)^2*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(4*b^3) + (2*e*(b*d - a*e)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(5*b^3) + (e^2*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(6*b^3), ((b*d - a*e)^2*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*b^3) + (2*e*(b*d - a*e)*(a + b*x)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*b^3) + (e^2*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*b^3)]
    @test_int [(d + e*x)^1*(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 2, ((b*d - a*e)*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(4*b^2) + (e*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(5*b^2)]
    @test_int [(d + e*x)^0*(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 1, ((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(4*b)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^1, x, 3, (b*(b*d - a*e)^2*x*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^3*(a + b*x)) - ((b*d - a*e)*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*e^2) + ((a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e) - ((b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(d + e*x))/(e^4*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^2, x, 3, -((b^2*(2*b*d - 3*a*e)*x*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^3*(a + b*x))) + (b^3*x^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*e^2*(a + b*x)) + ((b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^4*(a + b*x)*(d + e*x)) + (3*b*(b*d - a*e)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(d + e*x))/(e^4*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^3, x, 3, (b^3*x*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^3*(a + b*x)) + ((b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*e^4*(a + b*x)*(d + e*x)^2) - (3*b*(b*d - a*e)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^4*(a + b*x)*(d + e*x)) - (3*b^2*(b*d - a*e)*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(d + e*x))/(e^4*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^4, x, 3, ((b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^4*(a + b*x)*(d + e*x)^3) - (3*b*(b*d - a*e)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*e^4*(a + b*x)*(d + e*x)^2) + (3*b^2*(b*d - a*e)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^4*(a + b*x)*(d + e*x)) + (b^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(d + e*x))/(e^4*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^5, x, 2, ((a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*(b*d - a*e)*(d + e*x)^4)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^6, x, 3, ((a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*(b*d - a*e)*(d + e*x)^5) + (b*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(20*(b*d - a*e)^2*(d + e*x)^4)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^7, x, 3, ((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(6*(b*d - a*e)*(d + e*x)^6) + (b*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(15*(b*d - a*e)^2*(d + e*x)^5) + (b^2*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(60*(b*d - a*e)^3*(d + e*x)^4), ((b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*e^4*(a + b*x)*(d + e*x)^6) - (3*b*(b*d - a*e)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*e^4*(a + b*x)*(d + e*x)^5) + (3*b^2*(b*d - a*e)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*e^4*(a + b*x)*(d + e*x)^4) - (b^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^4*(a + b*x)*(d + e*x)^3)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^8, x, 3, ((b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*e^4*(a + b*x)*(d + e*x)^7) - (b*(b*d - a*e)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*e^4*(a + b*x)*(d + e*x)^6) + (3*b^2*(b*d - a*e)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*e^4*(a + b*x)*(d + e*x)^5) - (b^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*e^4*(a + b*x)*(d + e*x)^4)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(d + e*x)^9, x, 3, ((b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(8*e^4*(a + b*x)*(d + e*x)^8) - (3*b*(b*d - a*e)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*e^4*(a + b*x)*(d + e*x)^7) + (b^2*(b*d - a*e)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*e^4*(a + b*x)*(d + e*x)^6) - (b^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*e^4*(a + b*x)*(d + e*x)^5)]

    @test_int [(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, ((b*d - a*e)^5*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*b^6) + (5*e*(b*d - a*e)^4*(a + b*x)^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*b^6) + (5*e^2*(b*d - a*e)^3*(a + b*x)^7*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*b^6) + (10*e^3*(b*d - a*e)^2*(a + b*x)^8*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*b^6) + (e^4*(b*d - a*e)*(a + b*x)^9*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*b^6) + (e^5*(a + b*x)^10*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(11*b^6)]
    @test_int [(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 2, ((b*d - a*e)^4*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*b^5) + (4*e*(b*d - a*e)^3*(a + b*x)^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*b^5) + (3*e^2*(b*d - a*e)^2*(a + b*x)^7*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*b^5) + (4*e^3*(b*d - a*e)*(a + b*x)^8*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*b^5) + (e^4*(a + b*x)^9*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(10*b^5)]
    @test_int [(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, ((b*d - a*e)^3*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*b^4) + (3*e*(b*d - a*e)^2*(a + b*x)^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*b^4) + (3*e^2*(b*d - a*e)*(a + b*x)^7*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(8*b^4) + (e^3*(a + b*x)^8*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*b^4)]
    @test_int [(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, ((b*d - a*e)^2*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*b^3) + (2*e*(b*d - a*e)*(a + b*x)^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*b^3) + (e^2*(a + b*x)^7*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(8*b^3)]
    @test_int [(d + e*x)^1*(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 2, ((b*d - a*e)*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(6*b^2) + (e*(a^2 + 2*a*b*x + b^2*x^2)^(7/2))/(7*b^2)]
    @test_int [(d + e*x)^0*(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 1, ((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(6*b)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^1, x, 3, (b*(b*d - a*e)^4*x*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^5*(a + b*x)) - ((b*d - a*e)^3*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*e^4) + ((b*d - a*e)^2*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^3) - ((b*d - a*e)*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*e^2) + ((a + b*x)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*e) - ((b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(d + e*x))/(e^6*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^2, x, 3, (-10*b^2*(b*d - a*e)^3*x*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^5*(a + b*x)) + ((b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)*(d + e*x)) + (5*b^3*(b*d - a*e)^2*(d + e*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)) - (5*b^4*(b*d - a*e)*(d + e*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x)) + (b^5*(d + e*x)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*e^6*(a + b*x)) + (5*b*(b*d - a*e)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(d + e*x))/(e^6*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^3, x, 3, (10*b^3*(b*d - a*e)^2*x*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^5*(a + b*x)) + ((b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*e^6*(a + b*x)*(d + e*x)^2) - (5*b*(b*d - a*e)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)*(d + e*x)) - (5*b^4*(b*d - a*e)*(d + e*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*e^6*(a + b*x)) + (b^5*(d + e*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x)) - (10*b^2*(b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(d + e*x))/(e^6*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^4, x, 3, -((b^4*(4*b*d - 5*a*e)*x*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^5*(a + b*x))) + (b^5*x^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*e^4*(a + b*x)) + ((b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x)*(d + e*x)^3) - (5*b*(b*d - a*e)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*e^6*(a + b*x)*(d + e*x)^2) + (10*b^2*(b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)*(d + e*x)) + (10*b^3*(b*d - a*e)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(d + e*x))/(e^6*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^5, x, 3, (b^5*x*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^5*(a + b*x)) + ((b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*e^6*(a + b*x)*(d + e*x)^4) - (5*b*(b*d - a*e)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x)*(d + e*x)^3) + (5*b^2*(b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)*(d + e*x)^2) - (10*b^3*(b*d - a*e)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)*(d + e*x)) - (5*b^4*(b*d - a*e)*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(d + e*x))/(e^6*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^6, x, 3, ((b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*e^6*(a + b*x)*(d + e*x)^5) - (5*b*(b*d - a*e)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*e^6*(a + b*x)*(d + e*x)^4) + (10*b^2*(b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x)*(d + e*x)^3) - (5*b^3*(b*d - a*e)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)*(d + e*x)^2) + (5*b^4*(b*d - a*e)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)*(d + e*x)) + (b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)*log(d + e*x))/(e^6*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^7, x, 2, ((a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*(b*d - a*e)*(d + e*x)^6)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^8, x, 3, ((a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*(b*d - a*e)*(d + e*x)^7) + (b*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(42*(b*d - a*e)^2*(d + e*x)^6)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^9, x, 4, ((a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(8*(b*d - a*e)*(d + e*x)^8) + (b*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(28*(b*d - a*e)^2*(d + e*x)^7) + (b^2*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(168*(b*d - a*e)^3*(d + e*x)^6)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^10, x, 5, ((a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*(b*d - a*e)*(d + e*x)^9) + (b*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(24*(b*d - a*e)^2*(d + e*x)^8) + (b^2*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(84*(b*d - a*e)^3*(d + e*x)^7) + (b^3*(a + b*x)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(504*(b*d - a*e)^4*(d + e*x)^6)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^11, x, 3, ((b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(10*e^6*(a + b*x)*(d + e*x)^10) - (5*b*(b*d - a*e)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*e^6*(a + b*x)*(d + e*x)^9) + (5*b^2*(b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*e^6*(a + b*x)*(d + e*x)^8) - (10*b^3*(b*d - a*e)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*e^6*(a + b*x)*(d + e*x)^7) + (5*b^4*(b*d - a*e)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*e^6*(a + b*x)*(d + e*x)^6) - (b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*e^6*(a + b*x)*(d + e*x)^5)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^12, x, 3, ((b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(11*e^6*(a + b*x)*(d + e*x)^11) - (b*(b*d - a*e)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(2*e^6*(a + b*x)*(d + e*x)^10) + (10*b^2*(b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*e^6*(a + b*x)*(d + e*x)^9) - (5*b^3*(b*d - a*e)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(4*e^6*(a + b*x)*(d + e*x)^8) + (5*b^4*(b*d - a*e)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*e^6*(a + b*x)*(d + e*x)^7) - (b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(6*e^6*(a + b*x)*(d + e*x)^6)]

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

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

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

    @test_int [(d + e*x)^6/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, (-20*e^3*(b*d - a*e)^3)/(b^7*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (b*d - a*e)^6/(4*b^7*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (2*e*(b*d - a*e)^5)/(b^7*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (15*e^2*(b*d - a*e)^4)/(2*b^7*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (e^5*(6*b*d - 5*a*e)*x*(a + b*x))/(b^6*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (e^6*x^2*(a + b*x))/(2*b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (15*e^4*(b*d - a*e)^2*(a + b*x)*log(a + b*x))/(b^7*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [(d + e*x)^5/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, (-10*e^3*(b*d - a*e)^2)/(b^6*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (b*d - a*e)^5/(4*b^6*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (5*e*(b*d - a*e)^4)/(3*b^6*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (5*e^2*(b*d - a*e)^3)/(b^6*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (e^5*x*(a + b*x))/(b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (5*e^4*(b*d - a*e)*(a + b*x)*log(a + b*x))/(b^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [(d + e*x)^4/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, (-4*e^3*(b*d - a*e))/(b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (b*d - a*e)^4/(4*b^5*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (4*e*(b*d - a*e)^3)/(3*b^5*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (3*e^2*(b*d - a*e)^2)/(b^5*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (e^4*(a + b*x)*log(a + b*x))/(b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [(d + e*x)^3/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 2, -((d + e*x)^4/(4*(b*d - a*e)*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)))]
    @test_int [(d + e*x)^2/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, -(b*d - a*e)^2/(4*b^3*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (2*e*(b*d - a*e))/(3*b^3*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - e^2/(2*b^3*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [(d + e*x)^1/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 2, -(e/(3*b^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))) - (b*d - a*e)/(4*b^2*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))]
    @test_int [(d + e*x)^0/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 1, -(1/(4*b*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)))]
    @test_int [1/((d + e*x)^1*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)), x, 3, e^3/((b*d - a*e)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - 1/(4*(b*d - a*e)*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + e/(3*(b*d - a*e)^2*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - e^2/(2*(b*d - a*e)^3*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (e^4*(a + b*x)*log(a + b*x))/((b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (e^4*(a + b*x)*log(d + e*x))/((b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [1/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)), x, 3, (4*b*e^3)/((b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - b/(4*(b*d - a*e)^2*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (2*b*e)/(3*(b*d - a*e)^3*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (3*b*e^2)/(2*(b*d - a*e)^4*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (e^4*(a + b*x))/((b*d - a*e)^5*(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (5*b*e^4*(a + b*x)*log(a + b*x))/((b*d - a*e)^6*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (5*b*e^4*(a + b*x)*log(d + e*x))/((b*d - a*e)^6*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [1/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)), x, 3, (10*b^2*e^3)/((b*d - a*e)^6*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - b^2/(4*(b*d - a*e)^3*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (b^2*e)/((b*d - a*e)^4*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (3*b^2*e^2)/((b*d - a*e)^5*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (e^4*(a + b*x))/(2*(b*d - a*e)^5*(d + e*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (5*b*e^4*(a + b*x))/((b*d - a*e)^6*(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (15*b^2*e^4*(a + b*x)*log(a + b*x))/((b*d - a*e)^7*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (15*b^2*e^4*(a + b*x)*log(d + e*x))/((b*d - a*e)^7*sqrt(a^2 + 2*a*b*x + b^2*x^2))]

    @test_int [(d + e*x)*(9 + 12*x + 4*x^2)^(5/2), x, 2, ((2*d - 3*e)*(3 + 2*x)*(9 + 12*x + 4*x^2)^(5/2))/24 + (e*(9 + 12*x + 4*x^2)^(7/2))/28]
    @test_int [(d + e*x)*(9 + 12*x + 4*x^2)^(3/2), x, 2, ((2*d - 3*e)*(3 + 2*x)*(9 + 12*x + 4*x^2)^(3/2))/16 + (e*(9 + 12*x + 4*x^2)^(5/2))/20]
    @test_int [(d + e*x)*(9 + 12*x + 4*x^2)^(1/2), x, 2, ((2*d - 3*e)*(3 + 2*x)*sqrt(9 + 12*x + 4*x^2))/8 + (e*(9 + 12*x + 4*x^2)^(3/2))/12]
    @test_int [(d + e*x)/(9 + 12*x + 4*x^2)^(1/2), x, 3, (e*sqrt(9 + 12*x + 4*x^2))/4 + ((2*d - 3*e)*(3 + 2*x)*log(3 + 2*x))/(4*sqrt(9 + 12*x + 4*x^2))]
    @test_int [(d + e*x)/(9 + 12*x + 4*x^2)^(3/2), x, 2, -(e/(4*sqrt(9 + 12*x + 4*x^2))) - (2*d - 3*e)/(8*(3 + 2*x)*sqrt(9 + 12*x + 4*x^2))]
    @test_int [(d + e*x)/(9 + 12*x + 4*x^2)^(5/2), x, 2, -(e/(12*(9 + 12*x + 4*x^2)^(3/2))) - (2*d - 3*e)/(16*(3 + 2*x)*(9 + 12*x + 4*x^2)^(3/2))]
    @test_int [(d + e*x)/(9 + 12*x + 4*x^2)^(7/2), x, 2, -(e/(20*(9 + 12*x + 4*x^2)^(5/2))) - (2*d - 3*e)/(24*(3 + 2*x)*(9 + 12*x + 4*x^2)^(5/2))]

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

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

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

    @test_int [(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^2, x, 3, (2*(b*d - a*e)^4*(d + e*x)^(9/2))/(9*e^5) - (8*b*(b*d - a*e)^3*(d + e*x)^(11/2))/(11*e^5) + (12*b^2*(b*d - a*e)^2*(d + e*x)^(13/2))/(13*e^5) - (8*b^3*(b*d - a*e)*(d + e*x)^(15/2))/(15*e^5) + (2*b^4*(d + e*x)^(17/2))/(17*e^5)]
    @test_int [(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^2, x, 3, (2*(b*d - a*e)^4*(d + e*x)^(7/2))/(7*e^5) - (8*b*(b*d - a*e)^3*(d + e*x)^(9/2))/(9*e^5) + (12*b^2*(b*d - a*e)^2*(d + e*x)^(11/2))/(11*e^5) - (8*b^3*(b*d - a*e)*(d + e*x)^(13/2))/(13*e^5) + (2*b^4*(d + e*x)^(15/2))/(15*e^5)]
    @test_int [(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^2, x, 3, (2*(b*d - a*e)^4*(d + e*x)^(5/2))/(5*e^5) - (8*b*(b*d - a*e)^3*(d + e*x)^(7/2))/(7*e^5) + (4*b^2*(b*d - a*e)^2*(d + e*x)^(9/2))/(3*e^5) - (8*b^3*(b*d - a*e)*(d + e*x)^(11/2))/(11*e^5) + (2*b^4*(d + e*x)^(13/2))/(13*e^5)]
    @test_int [sqrt(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^2, x, 3, (2*(b*d - a*e)^4*(d + e*x)^(3/2))/(3*e^5) - (8*b*(b*d - a*e)^3*(d + e*x)^(5/2))/(5*e^5) + (12*b^2*(b*d - a*e)^2*(d + e*x)^(7/2))/(7*e^5) - (8*b^3*(b*d - a*e)*(d + e*x)^(9/2))/(9*e^5) + (2*b^4*(d + e*x)^(11/2))/(11*e^5)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^2/sqrt(d + e*x), x, 3, (2*(b*d - a*e)^4*sqrt(d + e*x))/e^5 - (8*b*(b*d - a*e)^3*(d + e*x)^(3/2))/(3*e^5) + (12*b^2*(b*d - a*e)^2*(d + e*x)^(5/2))/(5*e^5) - (8*b^3*(b*d - a*e)*(d + e*x)^(7/2))/(7*e^5) + (2*b^4*(d + e*x)^(9/2))/(9*e^5)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^(3/2), x, 3, (-2*(b*d - a*e)^4)/(e^5*sqrt(d + e*x)) - (8*b*(b*d - a*e)^3*sqrt(d + e*x))/e^5 + (4*b^2*(b*d - a*e)^2*(d + e*x)^(3/2))/e^5 - (8*b^3*(b*d - a*e)*(d + e*x)^(5/2))/(5*e^5) + (2*b^4*(d + e*x)^(7/2))/(7*e^5)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^(5/2), x, 3, (-2*(b*d - a*e)^4)/(3*e^5*(d + e*x)^(3/2)) + (8*b*(b*d - a*e)^3)/(e^5*sqrt(d + e*x)) + (12*b^2*(b*d - a*e)^2*sqrt(d + e*x))/e^5 - (8*b^3*(b*d - a*e)*(d + e*x)^(3/2))/(3*e^5) + (2*b^4*(d + e*x)^(5/2))/(5*e^5)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^2/(d + e*x)^(7/2), x, 3, (-2*(b*d - a*e)^4)/(5*e^5*(d + e*x)^(5/2)) + (8*b*(b*d - a*e)^3)/(3*e^5*(d + e*x)^(3/2)) - (12*b^2*(b*d - a*e)^2)/(e^5*sqrt(d + e*x)) - (8*b^3*(b*d - a*e)*sqrt(d + e*x))/e^5 + (2*b^4*(d + e*x)^(3/2))/(3*e^5)]

    @test_int [(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, (2*(b*d - a*e)^6*(d + e*x)^(9/2))/(9*e^7) - (12*b*(b*d - a*e)^5*(d + e*x)^(11/2))/(11*e^7) + (30*b^2*(b*d - a*e)^4*(d + e*x)^(13/2))/(13*e^7) - (8*b^3*(b*d - a*e)^3*(d + e*x)^(15/2))/(3*e^7) + (30*b^4*(b*d - a*e)^2*(d + e*x)^(17/2))/(17*e^7) - (12*b^5*(b*d - a*e)*(d + e*x)^(19/2))/(19*e^7) + (2*b^6*(d + e*x)^(21/2))/(21*e^7)]
    @test_int [(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, (2*(b*d - a*e)^6*(d + e*x)^(7/2))/(7*e^7) - (4*b*(b*d - a*e)^5*(d + e*x)^(9/2))/(3*e^7) + (30*b^2*(b*d - a*e)^4*(d + e*x)^(11/2))/(11*e^7) - (40*b^3*(b*d - a*e)^3*(d + e*x)^(13/2))/(13*e^7) + (2*b^4*(b*d - a*e)^2*(d + e*x)^(15/2))/e^7 - (12*b^5*(b*d - a*e)*(d + e*x)^(17/2))/(17*e^7) + (2*b^6*(d + e*x)^(19/2))/(19*e^7)]
    @test_int [(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, (2*(b*d - a*e)^6*(d + e*x)^(5/2))/(5*e^7) - (12*b*(b*d - a*e)^5*(d + e*x)^(7/2))/(7*e^7) + (10*b^2*(b*d - a*e)^4*(d + e*x)^(9/2))/(3*e^7) - (40*b^3*(b*d - a*e)^3*(d + e*x)^(11/2))/(11*e^7) + (30*b^4*(b*d - a*e)^2*(d + e*x)^(13/2))/(13*e^7) - (4*b^5*(b*d - a*e)*(d + e*x)^(15/2))/(5*e^7) + (2*b^6*(d + e*x)^(17/2))/(17*e^7)]
    @test_int [sqrt(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, (2*(b*d - a*e)^6*(d + e*x)^(3/2))/(3*e^7) - (12*b*(b*d - a*e)^5*(d + e*x)^(5/2))/(5*e^7) + (30*b^2*(b*d - a*e)^4*(d + e*x)^(7/2))/(7*e^7) - (40*b^3*(b*d - a*e)^3*(d + e*x)^(9/2))/(9*e^7) + (30*b^4*(b*d - a*e)^2*(d + e*x)^(11/2))/(11*e^7) - (12*b^5*(b*d - a*e)*(d + e*x)^(13/2))/(13*e^7) + (2*b^6*(d + e*x)^(15/2))/(15*e^7)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/sqrt(d + e*x), x, 3, (2*(b*d - a*e)^6*sqrt(d + e*x))/e^7 - (4*b*(b*d - a*e)^5*(d + e*x)^(3/2))/e^7 + (6*b^2*(b*d - a*e)^4*(d + e*x)^(5/2))/e^7 - (40*b^3*(b*d - a*e)^3*(d + e*x)^(7/2))/(7*e^7) + (10*b^4*(b*d - a*e)^2*(d + e*x)^(9/2))/(3*e^7) - (12*b^5*(b*d - a*e)*(d + e*x)^(11/2))/(11*e^7) + (2*b^6*(d + e*x)^(13/2))/(13*e^7)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^(3/2), x, 3, (-2*(b*d - a*e)^6)/(e^7*sqrt(d + e*x)) - (12*b*(b*d - a*e)^5*sqrt(d + e*x))/e^7 + (10*b^2*(b*d - a*e)^4*(d + e*x)^(3/2))/e^7 - (8*b^3*(b*d - a*e)^3*(d + e*x)^(5/2))/e^7 + (30*b^4*(b*d - a*e)^2*(d + e*x)^(7/2))/(7*e^7) - (4*b^5*(b*d - a*e)*(d + e*x)^(9/2))/(3*e^7) + (2*b^6*(d + e*x)^(11/2))/(11*e^7)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^(5/2), x, 3, (-2*(b*d - a*e)^6)/(3*e^7*(d + e*x)^(3/2)) + (12*b*(b*d - a*e)^5)/(e^7*sqrt(d + e*x)) + (30*b^2*(b*d - a*e)^4*sqrt(d + e*x))/e^7 - (40*b^3*(b*d - a*e)^3*(d + e*x)^(3/2))/(3*e^7) + (6*b^4*(b*d - a*e)^2*(d + e*x)^(5/2))/e^7 - (12*b^5*(b*d - a*e)*(d + e*x)^(7/2))/(7*e^7) + (2*b^6*(d + e*x)^(9/2))/(9*e^7)]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^(7/2), x, 3, (-2*(b*d - a*e)^6)/(5*e^7*(d + e*x)^(5/2)) + (4*b*(b*d - a*e)^5)/(e^7*(d + e*x)^(3/2)) - (30*b^2*(b*d - a*e)^4)/(e^7*sqrt(d + e*x)) - (40*b^3*(b*d - a*e)^3*sqrt(d + e*x))/e^7 + (10*b^4*(b*d - a*e)^2*(d + e*x)^(3/2))/e^7 - (12*b^5*(b*d - a*e)*(d + e*x)^(5/2))/(5*e^7) + (2*b^6*(d + e*x)^(7/2))/(7*e^7)]

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

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

    @test_int [(d + e*x)^(11/2)/(a^2 + 2*a*b*x + b^2*x^2)^2, x, 9, (231*e^3*(b*d - a*e)^2*sqrt(d + e*x))/(8*b^6) + (77*e^3*(b*d - a*e)*(d + e*x)^(3/2))/(8*b^5) + (231*e^3*(d + e*x)^(5/2))/(40*b^4) - (33*e^2*(d + e*x)^(7/2))/(8*b^3*(a + b*x)) - (11*e*(d + e*x)^(9/2))/(12*b^2*(a + b*x)^2) - (d + e*x)^(11/2)/(3*b*(a + b*x)^3) - (231*e^3*(b*d - a*e)^(5/2)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(8*b^(13/2))]
    @test_int [(d + e*x)^(9/2)/(a^2 + 2*a*b*x + b^2*x^2)^2, x, 8, (105*e^3*(b*d - a*e)*sqrt(d + e*x))/(8*b^5) + (35*e^3*(d + e*x)^(3/2))/(8*b^4) - (21*e^2*(d + e*x)^(5/2))/(8*b^3*(a + b*x)) - (3*e*(d + e*x)^(7/2))/(4*b^2*(a + b*x)^2) - (d + e*x)^(9/2)/(3*b*(a + b*x)^3) - (105*e^3*(b*d - a*e)^(3/2)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(8*b^(11/2))]
    @test_int [(d + e*x)^(7/2)/(a^2 + 2*a*b*x + b^2*x^2)^2, x, 7, (35*e^3*sqrt(d + e*x))/(8*b^4) - (35*e^2*(d + e*x)^(3/2))/(24*b^3*(a + b*x)) - (7*e*(d + e*x)^(5/2))/(12*b^2*(a + b*x)^2) - (d + e*x)^(7/2)/(3*b*(a + b*x)^3) - (35*e^3*sqrt(b*d - a*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(8*b^(9/2))]
    @test_int [(d + e*x)^(5/2)/(a^2 + 2*a*b*x + b^2*x^2)^2, x, 6, -((5*e^2*sqrt(d + e*x))/(8*b^3*(a + b*x))) - (5*e*(d + e*x)^(3/2))/(12*b^2*(a + b*x)^2) - (d + e*x)^(5/2)/(3*b*(a + b*x)^3) - (5*e^3*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(8*b^(7/2)*sqrt(b*d - a*e))]
    @test_int [(d + e*x)^(3/2)/(a^2 + 2*a*b*x + b^2*x^2)^2, x, 6, -((e*sqrt(d + e*x))/(4*b^2*(a + b*x)^2)) - (e^2*sqrt(d + e*x))/(8*b^2*(b*d - a*e)*(a + b*x)) - (d + e*x)^(3/2)/(3*b*(a + b*x)^3) + (e^3*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(8*b^(5/2)*(b*d - a*e)^(3/2))]
    @test_int [(d + e*x)^(1/2)/(a^2 + 2*a*b*x + b^2*x^2)^2, x, 6, -(sqrt(d + e*x)/(3*b*(a + b*x)^3)) - (e*sqrt(d + e*x))/(12*b*(b*d - a*e)*(a + b*x)^2) + (e^2*sqrt(d + e*x))/(8*b*(b*d - a*e)^2*(a + b*x)) - (e^3*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(8*b^(3/2)*(b*d - a*e)^(5/2))]
    @test_int [1/((d + e*x)^(1/2)*(a^2 + 2*a*b*x + b^2*x^2)^2), x, 6, -(sqrt(d + e*x)/(3*(b*d - a*e)*(a + b*x)^3)) + (5*e*sqrt(d + e*x))/(12*(b*d - a*e)^2*(a + b*x)^2) - (5*e^2*sqrt(d + e*x))/(8*(b*d - a*e)^3*(a + b*x)) + (5*e^3*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(8*sqrt(b)*(b*d - a*e)^(7/2))]
    @test_int [1/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^2), x, 7, -((35*e^3)/(8*(b*d - a*e)^4*sqrt(d + e*x))) - 1/(3*(b*d - a*e)*(a + b*x)^3*sqrt(d + e*x)) + (7*e)/(12*(b*d - a*e)^2*(a + b*x)^2*sqrt(d + e*x)) - (35*e^2)/(24*(b*d - a*e)^3*(a + b*x)*sqrt(d + e*x)) + (35*sqrt(b)*e^3*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(8*(b*d - a*e)^(9/2))]
    @test_int [1/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^2), x, 8, -((35*e^3)/(8*(b*d - a*e)^4*(d + e*x)^(3/2))) - 1/(3*(b*d - a*e)*(a + b*x)^3*(d + e*x)^(3/2)) + (3*e)/(4*(b*d - a*e)^2*(a + b*x)^2*(d + e*x)^(3/2)) - (21*e^2)/(8*(b*d - a*e)^3*(a + b*x)*(d + e*x)^(3/2)) - (105*b*e^3)/(8*(b*d - a*e)^5*sqrt(d + e*x)) + (105*b^(3/2)*e^3*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(8*(b*d - a*e)^(11/2))]
    @test_int [1/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^2), x, 9, -((231*e^3)/(40*(b*d - a*e)^4*(d + e*x)^(5/2))) - 1/(3*(b*d - a*e)*(a + b*x)^3*(d + e*x)^(5/2)) + (11*e)/(12*(b*d - a*e)^2*(a + b*x)^2*(d + e*x)^(5/2)) - (33*e^2)/(8*(b*d - a*e)^3*(a + b*x)*(d + e*x)^(5/2)) - (77*b*e^3)/(8*(b*d - a*e)^5*(d + e*x)^(3/2)) - (231*b^2*e^3)/(8*(b*d - a*e)^6*sqrt(d + e*x)) + (231*b^(5/2)*e^3*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(8*(b*d - a*e)^(13/2))]

    @test_int [(d + e*x)^(15/2)/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 11, (9009*e^5*(b*d - a*e)^2*sqrt(d + e*x))/(128*b^8) + (3003*e^5*(b*d - a*e)*(d + e*x)^(3/2))/(128*b^7) + (9009*e^5*(d + e*x)^(5/2))/(640*b^6) - (1287*e^4*(d + e*x)^(7/2))/(128*b^5*(a + b*x)) - (143*e^3*(d + e*x)^(9/2))/(64*b^4*(a + b*x)^2) - (13*e^2*(d + e*x)^(11/2))/(16*b^3*(a + b*x)^3) - (3*e*(d + e*x)^(13/2))/(8*b^2*(a + b*x)^4) - (d + e*x)^(15/2)/(5*b*(a + b*x)^5) - (9009*e^5*(b*d - a*e)^(5/2)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(128*b^(17/2))]
    @test_int [(d + e*x)^(13/2)/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 10, (3003*e^5*(b*d - a*e)*sqrt(d + e*x))/(128*b^7) + (1001*e^5*(d + e*x)^(3/2))/(128*b^6) - (3003*e^4*(d + e*x)^(5/2))/(640*b^5*(a + b*x)) - (429*e^3*(d + e*x)^(7/2))/(320*b^4*(a + b*x)^2) - (143*e^2*(d + e*x)^(9/2))/(240*b^3*(a + b*x)^3) - (13*e*(d + e*x)^(11/2))/(40*b^2*(a + b*x)^4) - (d + e*x)^(13/2)/(5*b*(a + b*x)^5) - (3003*e^5*(b*d - a*e)^(3/2)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(128*b^(15/2))]
    @test_int [(d + e*x)^(11/2)/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 9, (693*e^5*sqrt(d + e*x))/(128*b^6) - (231*e^4*(d + e*x)^(3/2))/(128*b^5*(a + b*x)) - (231*e^3*(d + e*x)^(5/2))/(320*b^4*(a + b*x)^2) - (33*e^2*(d + e*x)^(7/2))/(80*b^3*(a + b*x)^3) - (11*e*(d + e*x)^(9/2))/(40*b^2*(a + b*x)^4) - (d + e*x)^(11/2)/(5*b*(a + b*x)^5) - (693*e^5*sqrt(b*d - a*e)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(128*b^(13/2))]
    @test_int [(d + e*x)^(9/2)/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 8, -((63*e^4*sqrt(d + e*x))/(128*b^5*(a + b*x))) - (21*e^3*(d + e*x)^(3/2))/(64*b^4*(a + b*x)^2) - (21*e^2*(d + e*x)^(5/2))/(80*b^3*(a + b*x)^3) - (9*e*(d + e*x)^(7/2))/(40*b^2*(a + b*x)^4) - (d + e*x)^(9/2)/(5*b*(a + b*x)^5) - (63*e^5*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(128*b^(11/2)*sqrt(b*d - a*e))]
    @test_int [(d + e*x)^(7/2)/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 8, -((7*e^3*sqrt(d + e*x))/(64*b^4*(a + b*x)^2)) - (7*e^4*sqrt(d + e*x))/(128*b^4*(b*d - a*e)*(a + b*x)) - (7*e^2*(d + e*x)^(3/2))/(48*b^3*(a + b*x)^3) - (7*e*(d + e*x)^(5/2))/(40*b^2*(a + b*x)^4) - (d + e*x)^(7/2)/(5*b*(a + b*x)^5) + (7*e^5*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(128*b^(9/2)*(b*d - a*e)^(3/2))]
    @test_int [(d + e*x)^(5/2)/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 8, -((e^2*sqrt(d + e*x))/(16*b^3*(a + b*x)^3)) - (e^3*sqrt(d + e*x))/(64*b^3*(b*d - a*e)*(a + b*x)^2) + (3*e^4*sqrt(d + e*x))/(128*b^3*(b*d - a*e)^2*(a + b*x)) - (e*(d + e*x)^(3/2))/(8*b^2*(a + b*x)^4) - (d + e*x)^(5/2)/(5*b*(a + b*x)^5) - (3*e^5*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(128*b^(7/2)*(b*d - a*e)^(5/2))]
    @test_int [(d + e*x)^(3/2)/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 8, -((3*e*sqrt(d + e*x))/(40*b^2*(a + b*x)^4)) - (e^2*sqrt(d + e*x))/(80*b^2*(b*d - a*e)*(a + b*x)^3) + (e^3*sqrt(d + e*x))/(64*b^2*(b*d - a*e)^2*(a + b*x)^2) - (3*e^4*sqrt(d + e*x))/(128*b^2*(b*d - a*e)^3*(a + b*x)) - (d + e*x)^(3/2)/(5*b*(a + b*x)^5) + (3*e^5*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(128*b^(5/2)*(b*d - a*e)^(7/2))]
    @test_int [(d + e*x)^(1/2)/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 8, -(sqrt(d + e*x)/(5*b*(a + b*x)^5)) - (e*sqrt(d + e*x))/(40*b*(b*d - a*e)*(a + b*x)^4) + (7*e^2*sqrt(d + e*x))/(240*b*(b*d - a*e)^2*(a + b*x)^3) - (7*e^3*sqrt(d + e*x))/(192*b*(b*d - a*e)^3*(a + b*x)^2) + (7*e^4*sqrt(d + e*x))/(128*b*(b*d - a*e)^4*(a + b*x)) - (7*e^5*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(128*b^(3/2)*(b*d - a*e)^(9/2))]
    @test_int [1/((d + e*x)^(1/2)*(a^2 + 2*a*b*x + b^2*x^2)^3), x, 8, -(sqrt(d + e*x)/(5*(b*d - a*e)*(a + b*x)^5)) + (9*e*sqrt(d + e*x))/(40*(b*d - a*e)^2*(a + b*x)^4) - (21*e^2*sqrt(d + e*x))/(80*(b*d - a*e)^3*(a + b*x)^3) + (21*e^3*sqrt(d + e*x))/(64*(b*d - a*e)^4*(a + b*x)^2) - (63*e^4*sqrt(d + e*x))/(128*(b*d - a*e)^5*(a + b*x)) + (63*e^5*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(128*sqrt(b)*(b*d - a*e)^(11/2))]
    @test_int [1/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^3), x, 9, -((693*e^5)/(128*(b*d - a*e)^6*sqrt(d + e*x))) - 1/(5*(b*d - a*e)*(a + b*x)^5*sqrt(d + e*x)) + (11*e)/(40*(b*d - a*e)^2*(a + b*x)^4*sqrt(d + e*x)) - (33*e^2)/(80*(b*d - a*e)^3*(a + b*x)^3*sqrt(d + e*x)) + (231*e^3)/(320*(b*d - a*e)^4*(a + b*x)^2*sqrt(d + e*x)) - (231*e^4)/(128*(b*d - a*e)^5*(a + b*x)*sqrt(d + e*x)) + (693*sqrt(b)*e^5*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(128*(b*d - a*e)^(13/2))]
    @test_int [1/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^3), x, 10, -((1001*e^5)/(128*(b*d - a*e)^6*(d + e*x)^(3/2))) - 1/(5*(b*d - a*e)*(a + b*x)^5*(d + e*x)^(3/2)) + (13*e)/(40*(b*d - a*e)^2*(a + b*x)^4*(d + e*x)^(3/2)) - (143*e^2)/(240*(b*d - a*e)^3*(a + b*x)^3*(d + e*x)^(3/2)) + (429*e^3)/(320*(b*d - a*e)^4*(a + b*x)^2*(d + e*x)^(3/2)) - (3003*e^4)/(640*(b*d - a*e)^5*(a + b*x)*(d + e*x)^(3/2)) - (3003*b*e^5)/(128*(b*d - a*e)^7*sqrt(d + e*x)) + (3003*b^(3/2)*e^5*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(128*(b*d - a*e)^(15/2))]
    @test_int [1/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^3), x, 11, -((9009*e^5)/(640*(b*d - a*e)^6*(d + e*x)^(5/2))) - 1/(5*(b*d - a*e)*(a + b*x)^5*(d + e*x)^(5/2)) + (3*e)/(8*(b*d - a*e)^2*(a + b*x)^4*(d + e*x)^(5/2)) - (13*e^2)/(16*(b*d - a*e)^3*(a + b*x)^3*(d + e*x)^(5/2)) + (143*e^3)/(64*(b*d - a*e)^4*(a + b*x)^2*(d + e*x)^(5/2)) - (1287*e^4)/(128*(b*d - a*e)^5*(a + b*x)*(d + e*x)^(5/2)) - (3003*b*e^5)/(128*(b*d - a*e)^7*(d + e*x)^(3/2)) - (9009*b^2*e^5)/(128*(b*d - a*e)^8*sqrt(d + e*x)) + (9009*b^(5/2)*e^5*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(128*(b*d - a*e)^(17/2))]

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

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

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

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

    @test_int [(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, (-2*(b*d - a*e)^5*(d + e*x)^(7/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*e^6*(a + b*x)) + (10*b*(b*d - a*e)^4*(d + e*x)^(9/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*e^6*(a + b*x)) - (20*b^2*(b*d - a*e)^3*(d + e*x)^(11/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(11*e^6*(a + b*x)) + (20*b^3*(b*d - a*e)^2*(d + e*x)^(13/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(13*e^6*(a + b*x)) - (2*b^4*(b*d - a*e)*(d + e*x)^(15/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x)) + (2*b^5*(d + e*x)^(17/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(17*e^6*(a + b*x))]
    @test_int [(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, (-2*(b*d - a*e)^5*(d + e*x)^(5/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*e^6*(a + b*x)) + (10*b*(b*d - a*e)^4*(d + e*x)^(7/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*e^6*(a + b*x)) - (20*b^2*(b*d - a*e)^3*(d + e*x)^(9/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*e^6*(a + b*x)) + (20*b^3*(b*d - a*e)^2*(d + e*x)^(11/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(11*e^6*(a + b*x)) - (10*b^4*(b*d - a*e)*(d + e*x)^(13/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(13*e^6*(a + b*x)) + (2*b^5*(d + e*x)^(15/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(15*e^6*(a + b*x))]
    @test_int [sqrt(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, (-2*(b*d - a*e)^5*(d + e*x)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x)) + (2*b*(b*d - a*e)^4*(d + e*x)^(5/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)) - (20*b^2*(b*d - a*e)^3*(d + e*x)^(7/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*e^6*(a + b*x)) + (20*b^3*(b*d - a*e)^2*(d + e*x)^(9/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*e^6*(a + b*x)) - (10*b^4*(b*d - a*e)*(d + e*x)^(11/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(11*e^6*(a + b*x)) + (2*b^5*(d + e*x)^(13/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(13*e^6*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/sqrt(d + e*x), x, 3, (-2*(b*d - a*e)^5*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)) + (10*b*(b*d - a*e)^4*(d + e*x)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x)) - (4*b^2*(b*d - a*e)^3*(d + e*x)^(5/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)) + (20*b^3*(b*d - a*e)^2*(d + e*x)^(7/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*e^6*(a + b*x)) - (10*b^4*(b*d - a*e)*(d + e*x)^(9/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*e^6*(a + b*x)) + (2*b^5*(d + e*x)^(11/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(11*e^6*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^(3/2), x, 3, (2*(b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)*sqrt(d + e*x)) + (10*b*(b*d - a*e)^4*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)) - (20*b^2*(b*d - a*e)^3*(d + e*x)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x)) + (4*b^3*(b*d - a*e)^2*(d + e*x)^(5/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)) - (10*b^4*(b*d - a*e)*(d + e*x)^(7/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*e^6*(a + b*x)) + (2*b^5*(d + e*x)^(9/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*e^6*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^(5/2), x, 3, (2*(b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x)*(d + e*x)^(3/2)) - (10*b*(b*d - a*e)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)*sqrt(d + e*x)) - (20*b^2*(b*d - a*e)^3*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)) + (20*b^3*(b*d - a*e)^2*(d + e*x)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x)) - (2*b^4*(b*d - a*e)*(d + e*x)^(5/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)) + (2*b^5*(d + e*x)^(7/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*e^6*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^(7/2), x, 3, (2*(b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*e^6*(a + b*x)*(d + e*x)^(5/2)) - (10*b*(b*d - a*e)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x)*(d + e*x)^(3/2)) + (20*b^2*(b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)*sqrt(d + e*x)) + (20*b^3*(b*d - a*e)^2*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)) - (10*b^4*(b*d - a*e)*(d + e*x)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x)) + (2*b^5*(d + e*x)^(5/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(5*e^6*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^(9/2), x, 3, (2*(b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*e^6*(a + b*x)*(d + e*x)^(7/2)) - (2*b*(b*d - a*e)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)*(d + e*x)^(5/2)) + (20*b^2*(b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x)*(d + e*x)^(3/2)) - (20*b^3*(b*d - a*e)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)*sqrt(d + e*x)) - (10*b^4*(b*d - a*e)*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)) + (2*b^5*(d + e*x)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^(11/2), x, 3, (2*(b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*e^6*(a + b*x)*(d + e*x)^(9/2)) - (10*b*(b*d - a*e)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*e^6*(a + b*x)*(d + e*x)^(7/2)) + (4*b^2*(b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)*(d + e*x)^(5/2)) - (20*b^3*(b*d - a*e)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x)*(d + e*x)^(3/2)) + (10*b^4*(b*d - a*e)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)*sqrt(d + e*x)) + (2*b^5*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^(13/2), x, 3, (2*(b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(11*e^6*(a + b*x)*(d + e*x)^(11/2)) - (10*b*(b*d - a*e)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*e^6*(a + b*x)*(d + e*x)^(9/2)) + (20*b^2*(b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*e^6*(a + b*x)*(d + e*x)^(7/2)) - (4*b^3*(b*d - a*e)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)*(d + e*x)^(5/2)) + (10*b^4*(b*d - a*e)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x)*(d + e*x)^(3/2)) - (2*b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)*sqrt(d + e*x))]
    @test_int [(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(d + e*x)^(15/2), x, 3, (2*(b*d - a*e)^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(13*e^6*(a + b*x)*(d + e*x)^(13/2)) - (10*b*(b*d - a*e)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(11*e^6*(a + b*x)*(d + e*x)^(11/2)) + (20*b^2*(b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(9*e^6*(a + b*x)*(d + e*x)^(9/2)) - (20*b^3*(b*d - a*e)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(7*e^6*(a + b*x)*(d + e*x)^(7/2)) + (2*b^4*(b*d - a*e)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(a + b*x)*(d + e*x)^(5/2)) - (2*b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(3*e^6*(a + b*x)*(d + e*x)^(3/2))]

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

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

    @test_int [(d + e*x)^(9/2)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 8, (63*e^2*(b*d - a*e)^2*(a + b*x)*sqrt(d + e*x))/(4*b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (21*e^2*(b*d - a*e)*(a + b*x)*(d + e*x)^(3/2))/(4*b^4*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (63*e^2*(a + b*x)*(d + e*x)^(5/2))/(20*b^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (9*e*(d + e*x)^(7/2))/(4*b^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (d + e*x)^(9/2)/(2*b*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (63*e^2*(b*d - a*e)^(5/2)*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(4*b^(11/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [(d + e*x)^(7/2)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 7, (35*e^2*(b*d - a*e)*(a + b*x)*sqrt(d + e*x))/(4*b^4*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (35*e^2*(a + b*x)*(d + e*x)^(3/2))/(12*b^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (7*e*(d + e*x)^(5/2))/(4*b^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (d + e*x)^(7/2)/(2*b*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (35*e^2*(b*d - a*e)^(3/2)*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(4*b^(9/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [(d + e*x)^(5/2)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 6, (15*e^2*(a + b*x)*sqrt(d + e*x))/(4*b^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (5*e*(d + e*x)^(3/2))/(4*b^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (d + e*x)^(5/2)/(2*b*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (15*e^2*sqrt(b*d - a*e)*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(4*b^(7/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [(d + e*x)^(3/2)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 5, (-3*e*sqrt(d + e*x))/(4*b^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (d + e*x)^(3/2)/(2*b*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (3*e^2*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(4*b^(5/2)*sqrt(b*d - a*e)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [sqrt(d + e*x)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 5, -(e*sqrt(d + e*x))/(4*b*(b*d - a*e)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - sqrt(d + e*x)/(2*b*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (e^2*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(4*b^(3/2)*(b*d - a*e)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [1/(sqrt(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)), x, 5, (3*e*sqrt(d + e*x))/(4*(b*d - a*e)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - sqrt(d + e*x)/(2*(b*d - a*e)*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (3*e^2*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(4*sqrt(b)*(b*d - a*e)^(5/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [1/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)), x, 6, (5*e)/(4*(b*d - a*e)^2*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - 1/(2*(b*d - a*e)*(a + b*x)*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (15*e^2*(a + b*x))/(4*(b*d - a*e)^3*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (15*sqrt(b)*e^2*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(4*(b*d - a*e)^(7/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [1/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)), x, 7, (7*e)/(4*(b*d - a*e)^2*(d + e*x)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - 1/(2*(b*d - a*e)*(a + b*x)*(d + e*x)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (35*e^2*(a + b*x))/(12*(b*d - a*e)^3*(d + e*x)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (35*b*e^2*(a + b*x))/(4*(b*d - a*e)^4*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (35*b^(3/2)*e^2*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(4*(b*d - a*e)^(9/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [1/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)), x, 8, (9*e)/(4*(b*d - a*e)^2*(d + e*x)^(5/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - 1/(2*(b*d - a*e)*(a + b*x)*(d + e*x)^(5/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (63*e^2*(a + b*x))/(20*(b*d - a*e)^3*(d + e*x)^(5/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (21*b*e^2*(a + b*x))/(4*(b*d - a*e)^4*(d + e*x)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (63*b^2*e^2*(a + b*x))/(4*(b*d - a*e)^5*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (63*b^(5/2)*e^2*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(4*(b*d - a*e)^(11/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]

    @test_int [(d + e*x)^(13/2)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 10, (3003*e^4*(b*d - a*e)^2*(a + b*x)*sqrt(d + e*x))/(64*b^7*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (1001*e^4*(b*d - a*e)*(a + b*x)*(d + e*x)^(3/2))/(64*b^6*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (3003*e^4*(a + b*x)*(d + e*x)^(5/2))/(320*b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (429*e^3*(d + e*x)^(7/2))/(64*b^4*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (143*e^2*(d + e*x)^(9/2))/(96*b^3*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (13*e*(d + e*x)^(11/2))/(24*b^2*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (d + e*x)^(13/2)/(4*b*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (3003*e^4*(b*d - a*e)^(5/2)*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(64*b^(15/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [(d + e*x)^(11/2)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 9, (1155*e^4*(b*d - a*e)*(a + b*x)*sqrt(d + e*x))/(64*b^6*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (385*e^4*(a + b*x)*(d + e*x)^(3/2))/(64*b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (231*e^3*(d + e*x)^(5/2))/(64*b^4*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (33*e^2*(d + e*x)^(7/2))/(32*b^3*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (11*e*(d + e*x)^(9/2))/(24*b^2*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (d + e*x)^(11/2)/(4*b*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (1155*e^4*(b*d - a*e)^(3/2)*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(64*b^(13/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [(d + e*x)^(9/2)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 8, (315*e^4*(a + b*x)*sqrt(d + e*x))/(64*b^5*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (105*e^3*(d + e*x)^(3/2))/(64*b^4*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (21*e^2*(d + e*x)^(5/2))/(32*b^3*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (3*e*(d + e*x)^(7/2))/(8*b^2*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (d + e*x)^(9/2)/(4*b*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (315*e^4*sqrt(b*d - a*e)*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(64*b^(11/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [(d + e*x)^(7/2)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 7, (-35*e^3*sqrt(d + e*x))/(64*b^4*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (35*e^2*(d + e*x)^(3/2))/(96*b^3*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (7*e*(d + e*x)^(5/2))/(24*b^2*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (d + e*x)^(7/2)/(4*b*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (35*e^4*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(64*b^(9/2)*sqrt(b*d - a*e)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [(d + e*x)^(5/2)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 7, (-5*e^3*sqrt(d + e*x))/(64*b^3*(b*d - a*e)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (5*e^2*sqrt(d + e*x))/(32*b^3*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (5*e*(d + e*x)^(3/2))/(24*b^2*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (d + e*x)^(5/2)/(4*b*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (5*e^4*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(64*b^(7/2)*(b*d - a*e)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [(d + e*x)^(3/2)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 7, (3*e^3*sqrt(d + e*x))/(64*b^2*(b*d - a*e)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (e*sqrt(d + e*x))/(8*b^2*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (e^2*sqrt(d + e*x))/(32*b^2*(b*d - a*e)*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (d + e*x)^(3/2)/(4*b*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (3*e^4*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(64*b^(5/2)*(b*d - a*e)^(5/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [sqrt(d + e*x)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 7, (-5*e^3*sqrt(d + e*x))/(64*b*(b*d - a*e)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - sqrt(d + e*x)/(4*b*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (e*sqrt(d + e*x))/(24*b*(b*d - a*e)*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (5*e^2*sqrt(d + e*x))/(96*b*(b*d - a*e)^2*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (5*e^4*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(64*b^(3/2)*(b*d - a*e)^(7/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [1/(sqrt(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)), x, 7, (35*e^3*sqrt(d + e*x))/(64*(b*d - a*e)^4*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - sqrt(d + e*x)/(4*(b*d - a*e)*(a + b*x)^3*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (7*e*sqrt(d + e*x))/(24*(b*d - a*e)^2*(a + b*x)^2*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (35*e^2*sqrt(d + e*x))/(96*(b*d - a*e)^3*(a + b*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (35*e^4*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(64*sqrt(b)*(b*d - a*e)^(9/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [1/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)), x, 8, (105*e^3)/(64*(b*d - a*e)^4*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - 1/(4*(b*d - a*e)*(a + b*x)^3*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (3*e)/(8*(b*d - a*e)^2*(a + b*x)^2*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (21*e^2)/(32*(b*d - a*e)^3*(a + b*x)*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (315*e^4*(a + b*x))/(64*(b*d - a*e)^5*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (315*sqrt(b)*e^4*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(64*(b*d - a*e)^(11/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [1/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)), x, 9, (231*e^3)/(64*(b*d - a*e)^4*(d + e*x)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - 1/(4*(b*d - a*e)*(a + b*x)^3*(d + e*x)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (11*e)/(24*(b*d - a*e)^2*(a + b*x)^2*(d + e*x)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (33*e^2)/(32*(b*d - a*e)^3*(a + b*x)*(d + e*x)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (385*e^4*(a + b*x))/(64*(b*d - a*e)^5*(d + e*x)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (1155*b*e^4*(a + b*x))/(64*(b*d - a*e)^6*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (1155*b^(3/2)*e^4*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(64*(b*d - a*e)^(13/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]
    @test_int [1/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)), x, 10, (429*e^3)/(64*(b*d - a*e)^4*(d + e*x)^(5/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - 1/(4*(b*d - a*e)*(a + b*x)^3*(d + e*x)^(5/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (13*e)/(24*(b*d - a*e)^2*(a + b*x)^2*(d + e*x)^(5/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (143*e^2)/(96*(b*d - a*e)^3*(a + b*x)*(d + e*x)^(5/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (3003*e^4*(a + b*x))/(320*(b*d - a*e)^5*(d + e*x)^(5/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (1001*b*e^4*(a + b*x))/(64*(b*d - a*e)^6*(d + e*x)^(3/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) + (3003*b^2*e^4*(a + b*x))/(64*(b*d - a*e)^7*sqrt(d + e*x)*sqrt(a^2 + 2*a*b*x + b^2*x^2)) - (3003*b^(5/2)*e^4*(a + b*x)*atanh((sqrt(b)*sqrt(d + e*x))/sqrt(b*d - a*e)))/(64*(b*d - a*e)^(15/2)*sqrt(a^2 + 2*a*b*x + b^2*x^2))]

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

    @test_int [(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^3, x, 3, ((b*d - a*e)^6*(d + e*x)^(1 + m))/(e^7*(1 + m)) - (6*b*(b*d - a*e)^5*(d + e*x)^(2 + m))/(e^7*(2 + m)) + (15*b^2*(b*d - a*e)^4*(d + e*x)^(3 + m))/(e^7*(3 + m)) - (20*b^3*(b*d - a*e)^3*(d + e*x)^(4 + m))/(e^7*(4 + m)) + (15*b^4*(b*d - a*e)^2*(d + e*x)^(5 + m))/(e^7*(5 + m)) - (6*b^5*(b*d - a*e)*(d + e*x)^(6 + m))/(e^7*(6 + m)) + (b^6*(d + e*x)^(7 + m))/(e^7*(7 + m))]
    @test_int [(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^2, x, 3, ((b*d - a*e)^4*(d + e*x)^(1 + m))/(e^5*(1 + m)) - (4*b*(b*d - a*e)^3*(d + e*x)^(2 + m))/(e^5*(2 + m)) + (6*b^2*(b*d - a*e)^2*(d + e*x)^(3 + m))/(e^5*(3 + m)) - (4*b^3*(b*d - a*e)*(d + e*x)^(4 + m))/(e^5*(4 + m)) + (b^4*(d + e*x)^(5 + m))/(e^5*(5 + m))]
    @test_int [(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^1, x, 3, ((b*d - a*e)^2*(d + e*x)^(1 + m))/(e^3*(1 + m)) - (2*b*(b*d - a*e)*(d + e*x)^(2 + m))/(e^3*(2 + m)) + (b^2*(d + e*x)^(3 + m))/(e^3*(3 + m))]
    @test_int [(d + e*x)^m/(a^2 + 2*a*b*x + b^2*x^2)^1, x, 2, (e*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(2, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)))/((b*d - a*e)^2*(1 + m))]
    @test_int [(d + e*x)^m/(a^2 + 2*a*b*x + b^2*x^2)^2, x, 2, (e^3*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(4, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)))/((b*d - a*e)^4*(1 + m))]
    @test_int [(d + e*x)^m/(a^2 + 2*a*b*x + b^2*x^2)^3, x, 2, (e^5*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(6, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)))/((b*d - a*e)^6*(1 + m))]

    @test_int [(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 3, -(((b*d - a*e)^5*(d + e*x)^(1 + m)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(1 + m)*(a + b*x))) + (5*b*(b*d - a*e)^4*(d + e*x)^(2 + m)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(2 + m)*(a + b*x)) - (10*b^2*(b*d - a*e)^3*(d + e*x)^(3 + m)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(3 + m)*(a + b*x)) + (10*b^3*(b*d - a*e)^2*(d + e*x)^(4 + m)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(4 + m)*(a + b*x)) - (5*b^4*(b*d - a*e)*(d + e*x)^(5 + m)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(5 + m)*(a + b*x)) + (b^5*(d + e*x)^(6 + m)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^6*(6 + m)*(a + b*x))]
    @test_int [(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 3, -(((b*d - a*e)^3*(d + e*x)^(1 + m)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^4*(1 + m)*(a + b*x))) + (3*b*(b*d - a*e)^2*(d + e*x)^(2 + m)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^4*(2 + m)*(a + b*x)) - (3*b^2*(b*d - a*e)*(d + e*x)^(3 + m)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^4*(3 + m)*(a + b*x)) + (b^3*(d + e*x)^(4 + m)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^4*(4 + m)*(a + b*x))]
    @test_int [(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^(1/2), x, 3, -(((b*d - a*e)*(d + e*x)^(1 + m)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^2*(1 + m)*(a + b*x))) + (b*(d + e*x)^(2 + m)*sqrt(a^2 + 2*a*b*x + b^2*x^2))/(e^2*(2 + m)*(a + b*x))]
    @test_int [(d + e*x)^m/(a^2 + 2*a*b*x + b^2*x^2)^(1/2), x, 2, -(((a + b*x)*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)))/((b*d - a*e)*(1 + m)*sqrt(a^2 + 2*a*b*x + b^2*x^2)))]
    @test_int [(d + e*x)^m/(a^2 + 2*a*b*x + b^2*x^2)^(3/2), x, 2, -((e^2*(a + b*x)*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(3, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)))/((b*d - a*e)^3*(1 + m)*sqrt(a^2 + 2*a*b*x + b^2*x^2)))]
    @test_int [(d + e*x)^m/(a^2 + 2*a*b*x + b^2*x^2)^(5/2), x, 2, -((e^4*(a + b*x)*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(5, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)))/((b*d - a*e)^5*(1 + m)*sqrt(a^2 + 2*a*b*x + b^2*x^2)))]

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

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

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

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

    @test_int [(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^(p + 5), x, 3, (1/(e^11*(1 + m)))*(((b*d - a*e)^10*(d + e*x)^(1 + m)*(a^2 + 2*a*b*x + b^2*x^2)^p*HypergeometricFunctions._₂F₁(1 + m, -2*(5 + p), 2 + m, (b*(d + e*x))/(b*d - a*e)))/(-((e*(a + b*x))/(b*d - a*e)))^(2*p))]

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

    @test_int [(d + e*x)*(9 + 12*x + 4*x^2)^p, x, 2, ((2*d - 3*e)*(3 + 2*x)*(9 + 12*x + 4*x^2)^p)/(4*(1 + 2*p)) + (e*(9 + 12*x + 4*x^2)^(1 + p))/(8*(1 + p))]

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

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

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

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

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

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

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

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

    @test_int [(a*c + (b*c + a*d)*x + b*d*x^2)^3/(a + b*x)^8, x, 2, -((c + d*x)^4/(4*(b*c - a*d)*(a + b*x)^4))]
    @test_int [(a*c + (b*c + a*d)*x + b*d*x^2)^3/(a + b*x)^9, x, 3, -((c + d*x)^4/(5*(b*c - a*d)*(a + b*x)^5)) + (d*(c + d*x)^4)/(20*(b*c - a*d)^2*(a + b*x)^4)]

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

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

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

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

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

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

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

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

    @test_int [(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 3, ((c*d^2 - a*e^2)^2*(d + e*x)^5)/(5*e^3) - (c*d*(c*d^2 - a*e^2)*(d + e*x)^6)/(3*e^3) + (c^2*d^2*(d + e*x)^7)/(7*e^3)]
    @test_int [(d + e*x)^1*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 3, ((c*d^2 - a*e^2)^2*(d + e*x)^4)/(4*e^3) - (2*c*d*(c*d^2 - a*e^2)*(d + e*x)^5)/(5*e^3) + (c^2*d^2*(d + e*x)^6)/(6*e^3)]
    @test_int [(d + e*x)^0*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 3, ((c*d^2 - a*e^2)^2*(d + e*x)^3)/(3*e^3) - (c*d*(c*d^2 - a*e^2)*(d + e*x)^4)/(2*e^3) + (c^2*d^2*(d + e*x)^5)/(5*e^3)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^1, x, 3, ((c*d^2 - a*e^2)*(a*e + c*d*x)^3)/(3*c^2*d^2) + (e*(a*e + c*d*x)^4)/(4*c^2*d^2)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^2, x, 2, (a*e + c*d*x)^3/(3*c*d)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^3, x, 3, -((c*d*(c*d^2 - a*e^2)*x)/e^2) + (a*e + c*d*x)^2/(2*e) + ((c*d^2 - a*e^2)^2*log(d + e*x))/e^3]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^4, x, 3, (c^2*d^2*x)/e^2 - (c*d^2 - a*e^2)^2/(e^3*(d + e*x)) - (2*c*d*(c*d^2 - a*e^2)*log(d + e*x))/e^3]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^5, x, 3, -((c*d^2 - a*e^2)^2/(2*e^3*(d + e*x)^2)) + (2*c*d*(c*d^2 - a*e^2))/(e^3*(d + e*x)) + (c^2*d^2*log(d + e*x))/e^3]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^6, x, 2, (a*e + c*d*x)^3/(3*(c*d^2 - a*e^2)*(d + e*x)^3)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^7, x, 3, -((c*d^2 - a*e^2)^2/(4*e^3*(d + e*x)^4)) + (2*c*d*(c*d^2 - a*e^2))/(3*e^3*(d + e*x)^3) - (c^2*d^2)/(2*e^3*(d + e*x)^2)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^8, x, 3, -((c*d^2 - a*e^2)^2/(5*e^3*(d + e*x)^5)) + (c*d*(c*d^2 - a*e^2))/(2*e^3*(d + e*x)^4) - (c^2*d^2)/(3*e^3*(d + e*x)^3)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2/(d + e*x)^9, x, 3, -((c*d^2 - a*e^2)^2/(6*e^3*(d + e*x)^6)) + (2*c*d*(c*d^2 - a*e^2))/(5*e^3*(d + e*x)^5) - (c^2*d^2)/(4*e^3*(d + e*x)^4)]

    @test_int [(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 3, -(((c*d^2 - a*e^2)^3*(d + e*x)^6)/(6*e^4)) + (3*c*d*(c*d^2 - a*e^2)^2*(d + e*x)^7)/(7*e^4) - (3*c^2*d^2*(c*d^2 - a*e^2)*(d + e*x)^8)/(8*e^4) + (c^3*d^3*(d + e*x)^9)/(9*e^4)]
    @test_int [(d + e*x)^1*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 3, -(((c*d^2 - a*e^2)^3*(d + e*x)^5)/(5*e^4)) + (c*d*(c*d^2 - a*e^2)^2*(d + e*x)^6)/(2*e^4) - (3*c^2*d^2*(c*d^2 - a*e^2)*(d + e*x)^7)/(7*e^4) + (c^3*d^3*(d + e*x)^8)/(8*e^4)]
    @test_int [(d + e*x)^0*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 3, -(((c*d^2 - a*e^2)^3*(d + e*x)^4)/(4*e^4)) + (3*c*d*(c*d^2 - a*e^2)^2*(d + e*x)^5)/(5*e^4) - (c^2*d^2*(c*d^2 - a*e^2)*(d + e*x)^6)/(2*e^4) + (c^3*d^3*(d + e*x)^7)/(7*e^4)]

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

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

    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^8, x, 2, (a*e + c*d*x)^4/(4*(c*d^2 - a*e^2)*(d + e*x)^4)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^9, x, 3, (a*e + c*d*x)^4/(5*(c*d^2 - a*e^2)*(d + e*x)^5) + (c*d*(a*e + c*d*x)^4)/(20*(c*d^2 - a*e^2)^2*(d + e*x)^4)]

    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^10, x, 3, (c*d^2 - a*e^2)^3/(6*e^4*(d + e*x)^6) - (3*c*d*(c*d^2 - a*e^2)^2)/(5*e^4*(d + e*x)^5) + (3*c^2*d^2*(c*d^2 - a*e^2))/(4*e^4*(d + e*x)^4) - (c^3*d^3)/(3*e^4*(d + e*x)^3)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^11, x, 3, (c*d^2 - a*e^2)^3/(7*e^4*(d + e*x)^7) - (c*d*(c*d^2 - a*e^2)^2)/(2*e^4*(d + e*x)^6) + (3*c^2*d^2*(c*d^2 - a*e^2))/(5*e^4*(d + e*x)^5) - (c^3*d^3)/(4*e^4*(d + e*x)^4)]

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

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

    @test_int [(d + e*x)^8/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 3, (15*e^2*(c*d^2 - a*e^2)^4*x)/(c^6*d^6) - (c*d^2 - a*e^2)^6/(c^7*d^7*(a*e + c*d*x)) + (10*e^3*(c*d^2 - a*e^2)^3*(a*e + c*d*x)^2)/(c^7*d^7) + (5*e^4*(c*d^2 - a*e^2)^2*(a*e + c*d*x)^3)/(c^7*d^7) + (3*e^5*(c*d^2 - a*e^2)*(a*e + c*d*x)^4)/(2*c^7*d^7) + (e^6*(a*e + c*d*x)^5)/(5*c^7*d^7) + (6*e*(c*d^2 - a*e^2)^5*log(a*e + c*d*x))/(c^7*d^7)]
    @test_int [(d + e*x)^7/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 3, (10*e^2*(c*d^2 - a*e^2)^3*x)/(c^5*d^5) - (c*d^2 - a*e^2)^5/(c^6*d^6*(a*e + c*d*x)) + (5*e^3*(c*d^2 - a*e^2)^2*(a*e + c*d*x)^2)/(c^6*d^6) + (5*e^4*(c*d^2 - a*e^2)*(a*e + c*d*x)^3)/(3*c^6*d^6) + (e^5*(a*e + c*d*x)^4)/(4*c^6*d^6) + (5*e*(c*d^2 - a*e^2)^4*log(a*e + c*d*x))/(c^6*d^6)]
    @test_int [(d + e*x)^6/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 3, (e^2*(6*c^2*d^4 - 8*a*c*d^2*e^2 + 3*a^2*e^4)*x)/(c^4*d^4) + (e^3*(2*c*d^2 - a*e^2)*x^2)/(c^3*d^3) + (e^4*x^3)/(3*c^2*d^2) - (c*d^2 - a*e^2)^4/(c^5*d^5*(a*e + c*d*x)) + (4*e*(c*d^2 - a*e^2)^3*log(a*e + c*d*x))/(c^5*d^5)]
    @test_int [(d + e*x)^5/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 3, (e^2*(3*c*d^2 - 2*a*e^2)*x)/(c^3*d^3) + (e^3*x^2)/(2*c^2*d^2) - (c*d^2 - a*e^2)^3/(c^4*d^4*(a*e + c*d*x)) + (3*e*(c*d^2 - a*e^2)^2*log(a*e + c*d*x))/(c^4*d^4)]
    @test_int [(d + e*x)^4/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 3, (e^2*x)/(c^2*d^2) - (c*d^2 - a*e^2)^2/(c^3*d^3*(a*e + c*d*x)) + (2*e*(c*d^2 - a*e^2)*log(a*e + c*d*x))/(c^3*d^3)]
    @test_int [(d + e*x)^3/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 3, -((c*d^2 - a*e^2)/(c^2*d^2*(a*e + c*d*x))) + (e*log(a*e + c*d*x))/(c^2*d^2)]
    @test_int [(d + e*x)^2/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 2, -(1/(c*d*(a*e + c*d*x)))]
    @test_int [(d + e*x)^1/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 3, -(1/((c*d^2 - a*e^2)*(a*e + c*d*x))) - (e*log(a*e + c*d*x))/(c*d^2 - a*e^2)^2 + (e*log(d + e*x))/(c*d^2 - a*e^2)^2]
    @test_int [(d + e*x)^0/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 4, -((c*d^2 + a*e^2 + 2*c*d*e*x)/((c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))) - (2*c*d*e*log(a*e + c*d*x))/(c*d^2 - a*e^2)^3 + (2*c*d*e*log(d + e*x))/(c*d^2 - a*e^2)^3]
    @test_int [1/((d + e*x)^1*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2), x, 3, -((c^2*d^2)/((c*d^2 - a*e^2)^3*(a*e + c*d*x))) - e/(2*(c*d^2 - a*e^2)^2*(d + e*x)^2) - (2*c*d*e)/((c*d^2 - a*e^2)^3*(d + e*x)) - (3*c^2*d^2*e*log(a*e + c*d*x))/(c*d^2 - a*e^2)^4 + (3*c^2*d^2*e*log(d + e*x))/(c*d^2 - a*e^2)^4]
    @test_int [1/((d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2), x, 3, -((c^3*d^3)/((c*d^2 - a*e^2)^4*(a*e + c*d*x))) - e/(3*(c*d^2 - a*e^2)^2*(d + e*x)^3) - (c*d*e)/((c*d^2 - a*e^2)^3*(d + e*x)^2) - (3*c^2*d^2*e)/((c*d^2 - a*e^2)^4*(d + e*x)) - (4*c^3*d^3*e*log(a*e + c*d*x))/(c*d^2 - a*e^2)^5 + (4*c^3*d^3*e*log(d + e*x))/(c*d^2 - a*e^2)^5]

    @test_int [(d + e*x)^9/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 3, (20*e^3*(c*d^2 - a*e^2)^3*x)/(c^6*d^6) - (c*d^2 - a*e^2)^6/(2*c^7*d^7*(a*e + c*d*x)^2) - (6*e*(c*d^2 - a*e^2)^5)/(c^7*d^7*(a*e + c*d*x)) + (15*e^4*(c*d^2 - a*e^2)^2*(a*e + c*d*x)^2)/(2*c^7*d^7) + (2*e^5*(c*d^2 - a*e^2)*(a*e + c*d*x)^3)/(c^7*d^7) + (e^6*(a*e + c*d*x)^4)/(4*c^7*d^7) + (15*e^2*(c*d^2 - a*e^2)^4*log(a*e + c*d*x))/(c^7*d^7)]
    @test_int [(d + e*x)^8/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 3, (e^3*(10*c^2*d^4 - 15*a*c*d^2*e^2 + 6*a^2*e^4)*x)/(c^5*d^5) + (e^4*(5*c*d^2 - 3*a*e^2)*x^2)/(2*c^4*d^4) + (e^5*x^3)/(3*c^3*d^3) - (c*d^2 - a*e^2)^5/(2*c^6*d^6*(a*e + c*d*x)^2) - (5*e*(c*d^2 - a*e^2)^4)/(c^6*d^6*(a*e + c*d*x)) + (10*e^2*(c*d^2 - a*e^2)^3*log(a*e + c*d*x))/(c^6*d^6)]
    @test_int [(d + e*x)^7/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 3, (e^3*(4*c*d^2 - 3*a*e^2)*x)/(c^4*d^4) + (e^4*x^2)/(2*c^3*d^3) - (c*d^2 - a*e^2)^4/(2*c^5*d^5*(a*e + c*d*x)^2) - (4*e*(c*d^2 - a*e^2)^3)/(c^5*d^5*(a*e + c*d*x)) + (6*e^2*(c*d^2 - a*e^2)^2*log(a*e + c*d*x))/(c^5*d^5)]
    @test_int [(d + e*x)^6/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 3, (e^3*x)/(c^3*d^3) - (c*d^2 - a*e^2)^3/(2*c^4*d^4*(a*e + c*d*x)^2) - (3*e*(c*d^2 - a*e^2)^2)/(c^4*d^4*(a*e + c*d*x)) + (3*e^2*(c*d^2 - a*e^2)*log(a*e + c*d*x))/(c^4*d^4)]
    @test_int [(d + e*x)^5/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 3, -((c*d^2 - a*e^2)^2/(2*c^3*d^3*(a*e + c*d*x)^2)) - (2*e*(c*d^2 - a*e^2))/(c^3*d^3*(a*e + c*d*x)) + (e^2*log(a*e + c*d*x))/(c^3*d^3)]
    @test_int [(d + e*x)^4/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 2, -((d + e*x)^2/(2*(c*d^2 - a*e^2)*(a*e + c*d*x)^2))]
    @test_int [(d + e*x)^3/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 2, -(1/(2*c*d*(a*e + c*d*x)^2))]
    @test_int [(d + e*x)^2/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 3, -(1/(2*(c*d^2 - a*e^2)*(a*e + c*d*x)^2)) + e/((c*d^2 - a*e^2)^2*(a*e + c*d*x)) + (e^2*log(a*e + c*d*x))/(c*d^2 - a*e^2)^3 - (e^2*log(d + e*x))/(c*d^2 - a*e^2)^3]
    @test_int [(d + e*x)^1/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 3, -((c*d)/(2*(c*d^2 - a*e^2)^2*(a*e + c*d*x)^2)) + (2*c*d*e)/((c*d^2 - a*e^2)^3*(a*e + c*d*x)) + e^2/((c*d^2 - a*e^2)^3*(d + e*x)) + (3*c*d*e^2*log(a*e + c*d*x))/(c*d^2 - a*e^2)^4 - (3*c*d*e^2*log(d + e*x))/(c*d^2 - a*e^2)^4]
    @test_int [(d + e*x)^0/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 5, -((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2)) + (3*c*d*e*(c*d^2 + a*e^2 + 2*c*d*e*x))/((c*d^2 - a*e^2)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (6*c^2*d^2*e^2*log(a*e + c*d*x))/(c*d^2 - a*e^2)^5 - (6*c^2*d^2*e^2*log(d + e*x))/(c*d^2 - a*e^2)^5]
    @test_int [1/((d + e*x)^1*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3), x, 3, -((c^3*d^3)/(2*(c*d^2 - a*e^2)^4*(a*e + c*d*x)^2)) + (4*c^3*d^3*e)/((c*d^2 - a*e^2)^5*(a*e + c*d*x)) + e^2/(3*(c*d^2 - a*e^2)^3*(d + e*x)^3) + (3*c*d*e^2)/(2*(c*d^2 - a*e^2)^4*(d + e*x)^2) + (6*c^2*d^2*e^2)/((c*d^2 - a*e^2)^5*(d + e*x)) + (10*c^3*d^3*e^2*log(a*e + c*d*x))/(c*d^2 - a*e^2)^6 - (10*c^3*d^3*e^2*log(d + e*x))/(c*d^2 - a*e^2)^6]

    @test_int [(d + e*x)^10/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4, x, 3, (e^4*(15*c^2*d^4 - 24*a*c*d^2*e^2 + 10*a^2*e^4)*x)/(c^6*d^6) + (e^5*(3*c*d^2 - 2*a*e^2)*x^2)/(c^5*d^5) + (e^6*x^3)/(3*c^4*d^4) - (c*d^2 - a*e^2)^6/(3*c^7*d^7*(a*e + c*d*x)^3) - (3*e*(c*d^2 - a*e^2)^5)/(c^7*d^7*(a*e + c*d*x)^2) - (15*e^2*(c*d^2 - a*e^2)^4)/(c^7*d^7*(a*e + c*d*x)) + (20*e^3*(c*d^2 - a*e^2)^3*log(a*e + c*d*x))/(c^7*d^7)]
    @test_int [(d + e*x)^9/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4, x, 3, (e^4*(5*c*d^2 - 4*a*e^2)*x)/(c^5*d^5) + (e^5*x^2)/(2*c^4*d^4) - (c*d^2 - a*e^2)^5/(3*c^6*d^6*(a*e + c*d*x)^3) - (5*e*(c*d^2 - a*e^2)^4)/(2*c^6*d^6*(a*e + c*d*x)^2) - (10*e^2*(c*d^2 - a*e^2)^3)/(c^6*d^6*(a*e + c*d*x)) + (10*e^3*(c*d^2 - a*e^2)^2*log(a*e + c*d*x))/(c^6*d^6)]
    @test_int [(d + e*x)^8/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4, x, 3, (e^4*x)/(c^4*d^4) - (c*d^2 - a*e^2)^4/(3*c^5*d^5*(a*e + c*d*x)^3) - (2*e*(c*d^2 - a*e^2)^3)/(c^5*d^5*(a*e + c*d*x)^2) - (6*e^2*(c*d^2 - a*e^2)^2)/(c^5*d^5*(a*e + c*d*x)) + (4*e^3*(c*d^2 - a*e^2)*log(a*e + c*d*x))/(c^5*d^5)]
    @test_int [(d + e*x)^7/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4, x, 3, -((c*d^2 - a*e^2)^3/(3*c^4*d^4*(a*e + c*d*x)^3)) - (3*e*(c*d^2 - a*e^2)^2)/(2*c^4*d^4*(a*e + c*d*x)^2) - (3*e^2*(c*d^2 - a*e^2))/(c^4*d^4*(a*e + c*d*x)) + (e^3*log(a*e + c*d*x))/(c^4*d^4)]
    @test_int [(d + e*x)^6/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4, x, 2, -((d + e*x)^3/(3*(c*d^2 - a*e^2)*(a*e + c*d*x)^3))]
    @test_int [(d + e*x)^5/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4, x, 3, -((c*d^2 - a*e^2)/(3*c^2*d^2*(a*e + c*d*x)^3)) - e/(2*c^2*d^2*(a*e + c*d*x)^2)]
    @test_int [(d + e*x)^4/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4, x, 2, -(1/(3*c*d*(a*e + c*d*x)^3))]
    @test_int [(d + e*x)^3/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4, x, 3, -(1/(3*(c*d^2 - a*e^2)*(a*e + c*d*x)^3)) + e/(2*(c*d^2 - a*e^2)^2*(a*e + c*d*x)^2) - e^2/((c*d^2 - a*e^2)^3*(a*e + c*d*x)) - (e^3*log(a*e + c*d*x))/(c*d^2 - a*e^2)^4 + (e^3*log(d + e*x))/(c*d^2 - a*e^2)^4]
    @test_int [(d + e*x)^2/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4, x, 3, -((c*d)/(3*(c*d^2 - a*e^2)^2*(a*e + c*d*x)^3)) + (c*d*e)/((c*d^2 - a*e^2)^3*(a*e + c*d*x)^2) - (3*c*d*e^2)/((c*d^2 - a*e^2)^4*(a*e + c*d*x)) - e^3/((c*d^2 - a*e^2)^4*(d + e*x)) - (4*c*d*e^3*log(a*e + c*d*x))/(c*d^2 - a*e^2)^5 + (4*c*d*e^3*log(d + e*x))/(c*d^2 - a*e^2)^5]
    @test_int [(d + e*x)^1/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4, x, 3, -((c^2*d^2)/(3*(c*d^2 - a*e^2)^3*(a*e + c*d*x)^3)) + (3*c^2*d^2*e)/(2*(c*d^2 - a*e^2)^4*(a*e + c*d*x)^2) - (6*c^2*d^2*e^2)/((c*d^2 - a*e^2)^5*(a*e + c*d*x)) - e^3/(2*(c*d^2 - a*e^2)^4*(d + e*x)^2) - (4*c*d*e^3)/((c*d^2 - a*e^2)^5*(d + e*x)) - (10*c^2*d^2*e^3*log(a*e + c*d*x))/(c*d^2 - a*e^2)^6 + (10*c^2*d^2*e^3*log(d + e*x))/(c*d^2 - a*e^2)^6]
    @test_int [(d + e*x)^0/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^4, x, 6, -((c*d^2 + a*e^2 + 2*c*d*e*x)/(3*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3)) + (5*c*d*e*(c*d^2 + a*e^2 + 2*c*d*e*x))/(3*(c*d^2 - a*e^2)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2) - (10*c^2*d^2*e^2*(c*d^2 + a*e^2 + 2*c*d*e*x))/((c*d^2 - a*e^2)^6*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) - (20*c^3*d^3*e^3*log(a*e + c*d*x))/(c*d^2 - a*e^2)^7 + (20*c^3*d^3*e^3*log(d + e*x))/(c*d^2 - a*e^2)^7]

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

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

    @test_int [(d + e*x)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2), x, 7, (21*(c*d^2 - a*e^2)^4*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(512*c^5*d^5*e) + (7*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(64*c^4*d^4) + (21*(c*d^2 - a*e^2)^2*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(160*c^3*d^3) + (3*(c*d^2 - a*e^2)*(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(20*c^2*d^2) + ((d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(6*c*d) - (21*(c*d^2 - a*e^2)^6*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(1024*c^(11/2)*d^(11/2)*e^(3/2))]
    @test_int [(d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2), x, 6, (7*(c*d^2 - a*e^2)^3*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(128*c^4*d^4*e) + (7*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(48*c^3*d^3) + (7*(c*d^2 - a*e^2)*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(40*c^2*d^2) + ((d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(5*c*d) - (7*(c*d^2 - a*e^2)^5*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(256*c^(9/2)*d^(9/2)*e^(3/2))]
    @test_int [(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2), x, 5, (5*(c*d^2 - a*e^2)^2*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(64*c^3*d^3*e) + (5*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(24*c^2*d^2) + ((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(4*c*d) - (5*(c*d^2 - a*e^2)^4*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(128*c^(7/2)*d^(7/2)*e^(3/2))]
    @test_int [(d + e*x)^1*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2), x, 4, ((c*d^2 - a*e^2)*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(8*c^2*d^2*e) + (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(3*c*d) - ((c*d^2 - a*e^2)^3*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(16*c^(5/2)*d^(5/2)*e^(3/2))]
    @test_int [(d + e*x)^0*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2), x, 3, ((c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(4*c*d*e) - ((c*d^2 - a*e^2)^2*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(8*c^(3/2)*d^(3/2)*e^(3/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)/(d + e*x)^1, x, 3, sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/e - ((c*d^2 - a*e^2)*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(2*sqrt(c)*sqrt(d)*e^(3/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)/(d + e*x)^2, x, 3, -((2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(e*(d + e*x))) + (sqrt(c)*sqrt(d)*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/e^(3/2)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)/(d + e*x)^3, x, 1, (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*(c*d^2 - a*e^2)*(d + e*x)^3)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)/(d + e*x)^4, x, 2, (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(5*(c*d^2 - a*e^2)*(d + e*x)^4) + (4*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(15*(c*d^2 - a*e^2)^2*(d + e*x)^3)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)/(d + e*x)^5, x, 3, (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(7*(c*d^2 - a*e^2)*(d + e*x)^5) + (8*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(35*(c*d^2 - a*e^2)^2*(d + e*x)^4) + (16*c^2*d^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(105*(c*d^2 - a*e^2)^3*(d + e*x)^3)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)/(d + e*x)^6, x, 4, (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(9*(c*d^2 - a*e^2)*(d + e*x)^6) + (4*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(21*(c*d^2 - a*e^2)^2*(d + e*x)^5) + (16*c^2*d^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(105*(c*d^2 - a*e^2)^3*(d + e*x)^4) + (32*c^3*d^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(315*(c*d^2 - a*e^2)^4*(d + e*x)^3)]

    @test_int [(d + e*x)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 8, -((99*(c*d^2 - a*e^2)^6*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(16384*c^6*d^6*e^2)) + (33*(c*d^2 - a*e^2)^4*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(2048*c^5*d^5*e) + (33*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(640*c^4*d^4) + (33*(c*d^2 - a*e^2)^2*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(448*c^3*d^3) + (11*(c*d^2 - a*e^2)*(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(112*c^2*d^2) + ((d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(8*c*d) + (99*(c*d^2 - a*e^2)^8*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(32768*c^(13/2)*d^(13/2)*e^(5/2))]
    @test_int [(d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 7, -((9*(c*d^2 - a*e^2)^5*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(1024*c^5*d^5*e^2)) + (3*(c*d^2 - a*e^2)^3*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(128*c^4*d^4*e) + (3*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(40*c^3*d^3) + (3*(c*d^2 - a*e^2)*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(28*c^2*d^2) + ((d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(7*c*d) + (9*(c*d^2 - a*e^2)^7*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(2048*c^(11/2)*d^(11/2)*e^(5/2))]
    @test_int [(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 6, -((7*(c*d^2 - a*e^2)^4*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(512*c^4*d^4*e^2)) + (7*(c*d^2 - a*e^2)^2*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(192*c^3*d^3*e) + (7*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(60*c^2*d^2) + ((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(6*c*d) + (7*(c*d^2 - a*e^2)^6*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(1024*c^(9/2)*d^(9/2)*e^(5/2))]
    @test_int [(d + e*x)^1*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 5, -((3*(c*d^2 - a*e^2)^3*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(128*c^3*d^3*e^2)) + ((c*d^2 - a*e^2)*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(16*c^2*d^2*e) + (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(5*c*d) + (3*(c*d^2 - a*e^2)^5*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(256*c^(7/2)*d^(7/2)*e^(5/2))]
    @test_int [(d + e*x)^0*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 4, -((3*(c*d^2 - a*e^2)^2*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(64*c^2*d^2*e^2)) + ((c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(8*c*d*e) + (3*(c*d^2 - a*e^2)^4*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(128*c^(5/2)*d^(5/2)*e^(5/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^1, x, 4, (1/8)*(a/(c*d) - d/e^2)*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2) + (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(3*e) + ((c*d^2 - a*e^2)^3*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(16*c^(3/2)*d^(3/2)*e^(5/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^2, x, 4, (3/4)*(a - (c*d^2)/e^2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2) + (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(2*e*(d + e*x)) + (3*(c*d^2 - a*e^2)^2*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(8*sqrt(c)*sqrt(d)*e^(5/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^3, x, 4, (3*c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/e^2 - (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(e*(d + e*x)^2) - (3*sqrt(c)*sqrt(d)*(c*d^2 - a*e^2)*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(2*e^(5/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^4, x, 4, -((2*c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(e^2*(d + e*x))) - (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*e*(d + e*x)^3) + (c^(3/2)*d^(3/2)*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/e^(5/2)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^5, x, 1, (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(5*(c*d^2 - a*e^2)*(d + e*x)^5)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^6, x, 2, (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(7*(c*d^2 - a*e^2)*(d + e*x)^6) + (4*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(35*(c*d^2 - a*e^2)^2*(d + e*x)^5)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^7, x, 3, (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(9*(c*d^2 - a*e^2)*(d + e*x)^7) + (8*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(63*(c*d^2 - a*e^2)^2*(d + e*x)^6) + (16*c^2*d^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(315*(c*d^2 - a*e^2)^3*(d + e*x)^5)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^8, x, 4, (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(11*(c*d^2 - a*e^2)*(d + e*x)^8) + (4*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(33*(c*d^2 - a*e^2)^2*(d + e*x)^7) + (16*c^2*d^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(231*(c*d^2 - a*e^2)^3*(d + e*x)^6) + (32*c^3*d^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(1155*(c*d^2 - a*e^2)^4*(d + e*x)^5)]

    @test_int [(d + e*x)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 9, (143*(c*d^2 - a*e^2)^8*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(131072*c^7*d^7*e^3) - (143*(c*d^2 - a*e^2)^6*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(49152*c^6*d^6*e^2) + (143*(c*d^2 - a*e^2)^4*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(15360*c^5*d^5*e) + (143*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(4480*c^4*d^4) + (143*(c*d^2 - a*e^2)^2*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(2880*c^3*d^3) + (13*(c*d^2 - a*e^2)*(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(180*c^2*d^2) + ((d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(10*c*d) - (143*(c*d^2 - a*e^2)^10*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(262144*c^(15/2)*d^(15/2)*e^(7/2))]
    @test_int [(d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 8, (55*(c*d^2 - a*e^2)^7*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(32768*c^6*d^6*e^3) - (55*(c*d^2 - a*e^2)^5*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(12288*c^5*d^5*e^2) + (11*(c*d^2 - a*e^2)^3*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(768*c^4*d^4*e) + (11*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(224*c^3*d^3) + (11*(c*d^2 - a*e^2)*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(144*c^2*d^2) + ((d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(9*c*d) - (55*(c*d^2 - a*e^2)^9*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(65536*c^(13/2)*d^(13/2)*e^(7/2))]
    @test_int [(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 7, (45*(c*d^2 - a*e^2)^6*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(16384*c^5*d^5*e^3) - (15*(c*d^2 - a*e^2)^4*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(2048*c^4*d^4*e^2) + (3*(c*d^2 - a*e^2)^2*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(128*c^3*d^3*e) + (9*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(112*c^2*d^2) + ((d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(8*c*d) - (45*(c*d^2 - a*e^2)^8*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(32768*c^(11/2)*d^(11/2)*e^(7/2))]
    @test_int [(d + e*x)^1*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 6, (5*(c*d^2 - a*e^2)^5*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(1024*c^4*d^4*e^3) - (5*(c*d^2 - a*e^2)^3*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(384*c^3*d^3*e^2) + ((c*d^2 - a*e^2)*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(24*c^2*d^2*e) + (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2)/(7*c*d) - (5*(c*d^2 - a*e^2)^7*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(2048*c^(9/2)*d^(9/2)*e^(7/2))]
    @test_int [(d + e*x)^0*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 5, (5*(c*d^2 - a*e^2)^4*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(512*c^3*d^3*e^3) - (5*(c*d^2 - a*e^2)^2*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(192*c^2*d^2*e^2) + ((c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(12*c*d*e) - (5*(c*d^2 - a*e^2)^6*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(1024*c^(7/2)*d^(7/2)*e^(7/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^1, x, 5, (3*(c*d^2 - a*e^2)^3*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(128*c^2*d^2*e^3) + (1/16)*(a/(c*d) - d/e^2)*(c*d^2 + a*e^2 + 2*c*d*e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2) + (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(5*e) - (3*(c*d^2 - a*e^2)^5*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(256*c^(5/2)*d^(5/2)*e^(7/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^2, x, 6, (5*(c*d^2 - a*e^2)^2*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(64*c*d*e^3) + (5/24)*(a - (c*d^2)/e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2) + ((a*e + c*d*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(4*e) - (5*(c*d^2 - a*e^2)^4*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(128*c^(3/2)*d^(3/2)*e^(7/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^3, x, 5, (5*(c*d^2 - a*e^2)*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(8*e^3) - (5*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*e^2) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(e*(d + e*x)^2) - (5*(c*d^2 - a*e^2)^3*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(16*sqrt(c)*sqrt(d)*e^(7/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^4, x, 5, (15*c*d*(a - (c*d^2)/e^2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(4*e) + (5*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(2*e^2*(d + e*x)) - (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(e*(d + e*x)^3) + (15*sqrt(c)*sqrt(d)*(c*d^2 - a*e^2)^2*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(8*e^(7/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^5, x, 5, (5*c^2*d^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/e^3 - (10*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*e^2*(d + e*x)^2) - (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(3*e*(d + e*x)^4) - (5*c^(3/2)*d^(3/2)*(c*d^2 - a*e^2)*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(2*e^(7/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^6, x, 5, -((2*c^2*d^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(e^3*(d + e*x))) - (2*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*e^2*(d + e*x)^3) - (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(5*e*(d + e*x)^5) + (c^(5/2)*d^(5/2)*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/e^(7/2)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^7, x, 1, (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(7*(c*d^2 - a*e^2)*(d + e*x)^7)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^8, x, 2, (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(9*(c*d^2 - a*e^2)*(d + e*x)^8) + (4*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(63*(c*d^2 - a*e^2)^2*(d + e*x)^7)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^9, x, 3, (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(11*(c*d^2 - a*e^2)*(d + e*x)^9) + (8*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(99*(c*d^2 - a*e^2)^2*(d + e*x)^8) + (16*c^2*d^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(693*(c*d^2 - a*e^2)^3*(d + e*x)^7)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^10, x, 4, (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(13*(c*d^2 - a*e^2)*(d + e*x)^10) + (12*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(143*(c*d^2 - a*e^2)^2*(d + e*x)^9) + (16*c^2*d^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(429*(c*d^2 - a*e^2)^3*(d + e*x)^8) + (32*c^3*d^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(3003*(c*d^2 - a*e^2)^4*(d + e*x)^7)]

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

    @test_int [(d + e*x)^3/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2), x, 5, (5*(c*d^2 - a*e^2)^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(8*c^3*d^3) + (5*(c*d^2 - a*e^2)*(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(12*c^2*d^2) + ((d + e*x)^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(3*c*d) + (5*(c*d^2 - a*e^2)^3*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(16*c^(7/2)*d^(7/2)*sqrt(e))]
    @test_int [(d + e*x)^2/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2), x, 4, (3*(c*d^2 - a*e^2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(4*c^2*d^2) + ((d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(2*c*d) + (3*(c*d^2 - a*e^2)^2*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(8*c^(5/2)*d^(5/2)*sqrt(e))]
    @test_int [(d + e*x)^1/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2), x, 3, sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(c*d) + ((c*d^2 - a*e^2)*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(2*c^(3/2)*d^(3/2)*sqrt(e))]
    @test_int [(d + e*x)^0/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2), x, 2, atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)))/(sqrt(c)*sqrt(d)*sqrt(e))]
    @test_int [1/((d + e*x)^1*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)), x, 1, (2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/((c*d^2 - a*e^2)*(d + e*x))]
    @test_int [1/((d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)), x, 2, (2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(3*(c*d^2 - a*e^2)*(d + e*x)^2) + (4*c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(3*(c*d^2 - a*e^2)^2*(d + e*x))]
    @test_int [1/((d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)), x, 3, (2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(5*(c*d^2 - a*e^2)*(d + e*x)^3) + (8*c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(15*(c*d^2 - a*e^2)^2*(d + e*x)^2) + (16*c^2*d^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(15*(c*d^2 - a*e^2)^3*(d + e*x))]
    @test_int [1/((d + e*x)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)), x, 4, (2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(7*(c*d^2 - a*e^2)*(d + e*x)^4) + (12*c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(35*(c*d^2 - a*e^2)^2*(d + e*x)^3) + (16*c^2*d^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(35*(c*d^2 - a*e^2)^3*(d + e*x)^2) + (32*c^3*d^3*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(35*(c*d^2 - a*e^2)^4*(d + e*x))]

    @test_int [(d + e*x)^5/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 6, -((2*(d + e*x)^4)/(c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))) + (35*e*(c*d^2 - a*e^2)^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(8*c^4*d^4) + (35*e*(c*d^2 - a*e^2)*(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(12*c^3*d^3) + (7*e*(d + e*x)^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(3*c^2*d^2) + (35*sqrt(e)*(c*d^2 - a*e^2)^3*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(16*c^(9/2)*d^(9/2))]
    @test_int [(d + e*x)^4/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 5, -((2*(d + e*x)^3)/(c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))) + (15*e*(c*d^2 - a*e^2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(4*c^3*d^3) + (5*e*(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(2*c^2*d^2) + (15*sqrt(e)*(c*d^2 - a*e^2)^2*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(8*c^(7/2)*d^(7/2))]
    @test_int [(d + e*x)^3/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 4, -((2*(d + e*x)^2)/(c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))) + (3*e*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(c^2*d^2) + (3*sqrt(e)*(c*d^2 - a*e^2)*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(2*c^(5/2)*d^(5/2))]
    @test_int [(d + e*x)^2/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 3, -((2*(d + e*x))/(c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))) + (sqrt(e)*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(c^(3/2)*d^(3/2))]
    @test_int [(d + e*x)^1/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 1, -((2*(d + e*x))/((c*d^2 - a*e^2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)))]
    @test_int [(d + e*x)^0/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 1, -((2*(c*d^2 + a*e^2 + 2*c*d*e*x))/((c*d^2 - a*e^2)^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)))]
    @test_int [1/((d + e*x)^1*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)), x, 2, 2/(3*(c*d^2 - a*e^2)*(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) - (8*c*d*(c*d^2 + a*e^2 + 2*c*d*e*x))/(3*(c*d^2 - a*e^2)^3*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))]
    @test_int [1/((d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)), x, 3, 2/(5*(c*d^2 - a*e^2)*(d + e*x)^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (4*c*d)/(5*(c*d^2 - a*e^2)^2*(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) - (16*c^2*d^2*(c*d^2 + a*e^2 + 2*c*d*e*x))/(5*(c*d^2 - a*e^2)^4*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))]
    @test_int [1/((d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)), x, 4, 2/(7*(c*d^2 - a*e^2)*(d + e*x)^3*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (16*c*d)/(35*(c*d^2 - a*e^2)^2*(d + e*x)^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (32*c^2*d^2)/(35*(c*d^2 - a*e^2)^3*(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) - (128*c^3*d^3*(c*d^2 + a*e^2 + 2*c*d*e*x))/(35*(c*d^2 - a*e^2)^5*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))]
    @test_int [1/((d + e*x)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)), x, 5, 2/(9*(c*d^2 - a*e^2)*(d + e*x)^4*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (20*c*d)/(63*(c*d^2 - a*e^2)^2*(d + e*x)^3*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (32*c^2*d^2)/(63*(c*d^2 - a*e^2)^3*(d + e*x)^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (64*c^3*d^3)/(63*(c*d^2 - a*e^2)^4*(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) - (256*c^4*d^4*(c*d^2 + a*e^2 + 2*c*d*e*x))/(63*(c*d^2 - a*e^2)^6*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))]

    @test_int [(d + e*x)^6/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 6, -((2*(d + e*x)^5)/(3*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))) - (14*e*(d + e*x)^3)/(3*c^2*d^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (35*e^2*(c*d^2 - a*e^2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(4*c^4*d^4) + (35*e^2*(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(6*c^3*d^3) + (35*e^(3/2)*(c*d^2 - a*e^2)^2*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(8*c^(9/2)*d^(9/2))]
    @test_int [(d + e*x)^5/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 5, -((2*(d + e*x)^4)/(3*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))) - (10*e*(d + e*x)^2)/(3*c^2*d^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (5*e^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(c^3*d^3) + (5*e^(3/2)*(c*d^2 - a*e^2)*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(2*c^(7/2)*d^(7/2))]
    @test_int [(d + e*x)^4/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 4, -((2*(d + e*x)^3)/(3*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))) - (2*e*(d + e*x))/(c^2*d^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (e^(3/2)*atanh((c*d^2 + a*e^2 + 2*c*d*e*x)/(2*sqrt(c)*sqrt(d)*sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))))/(c^(5/2)*d^(5/2))]
    @test_int [(d + e*x)^3/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 1, -((2*(d + e*x)^3)/(3*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)))]
    @test_int [(d + e*x)^2/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 2, -((2*(d + e*x))/(3*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))) + (2*e*(c*d^2 + a*e^2 + 2*c*d*e*x))/(3*c*d*(c*d^2 - a*e^2)^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))]
    @test_int [(d + e*x)^1/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 2, -((2*(d + e*x))/(3*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))) + (8*e*(c*d^2 + a*e^2 + 2*c*d*e*x))/(3*(c*d^2 - a*e^2)^3*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))]
    @test_int [(d + e*x)^0/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 2, -((2*(c*d^2 + a*e^2 + 2*c*d*e*x))/(3*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))) + (16*c*d*e*(c*d^2 + a*e^2 + 2*c*d*e*x))/(3*(c*d^2 - a*e^2)^4*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))]
    @test_int [1/((d + e*x)^1*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)), x, 3, 2/(5*(c*d^2 - a*e^2)*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (16*c*d*(c*d^2 + a*e^2 + 2*c*d*e*x))/(15*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (128*c^2*d^2*e*(c*d^2 + a*e^2 + 2*c*d*e*x))/(15*(c*d^2 - a*e^2)^5*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))]
    @test_int [1/((d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)), x, 4, 2/(7*(c*d^2 - a*e^2)*(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (4*c*d)/(7*(c*d^2 - a*e^2)^2*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (32*c^2*d^2*(c*d^2 + a*e^2 + 2*c*d*e*x))/(21*(c*d^2 - a*e^2)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (256*c^3*d^3*e*(c*d^2 + a*e^2 + 2*c*d*e*x))/(21*(c*d^2 - a*e^2)^6*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))]
    @test_int [1/((d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)), x, 5, 2/(9*(c*d^2 - a*e^2)*(d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (8*c*d)/(21*(c*d^2 - a*e^2)^2*(d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (16*c^2*d^2)/(21*(c*d^2 - a*e^2)^3*(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (128*c^3*d^3*(c*d^2 + a*e^2 + 2*c*d*e*x))/(63*(c*d^2 - a*e^2)^5*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (1024*c^4*d^4*e*(c*d^2 + a*e^2 + 2*c*d*e*x))/(63*(c*d^2 - a*e^2)^7*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))]

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

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

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

    #= [(d + e*x)^3/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/3), x, 0, 0]
    @test_int [(d + e*x)^2/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/3), x, 0, 0] =#
    @test_int [(d + e*x)^1/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/3), x, 5, (3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(2/3))/(4*c*d) + (3*(c*d^2 - a*e^2)*sqrt((c*d^2 + a*e^2 + 2*c*d*e*x)^2)*sqrt((a*e^2 + c*d*(d + 2*e*x))^2))/(2*2^(1/3)*c^(5/3)*d^(5/3)*e^(2/3)*(c*d^2 + a*e^2 + 2*c*d*e*x)*((1 + sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))) - (3*3^(1/4)*sqrt(2 - sqrt(3))*(c*d^2 - a*e^2)^(5/3)*sqrt((c*d^2 + a*e^2 + 2*c*d*e*x)^2)*((c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))*sqrt(((c*d^2 - a*e^2)^(4/3) - 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*(c*d^2 - a*e^2)^(2/3)*((a*e + c*d*x)*(d + e*x))^(1/3) + 2*2^(1/3)*c^(2/3)*d^(2/3)*e^(2/3)*((a*e + c*d*x)*(d + e*x))^(2/3))/((1 + sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))^2)*Elliptic.E(asin(((1 - sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))/((1 + sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))), -7 - 4*sqrt(3)))/(4*2^(1/3)*c^(5/3)*d^(5/3)*e^(2/3)*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(((c*d^2 - a*e^2)^(2/3)*((c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3)))/((1 + sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))^2)*sqrt((a*e^2 + c*d*(d + 2*e*x))^2)) + (3^(3/4)*(c*d^2 - a*e^2)^(5/3)*sqrt((c*d^2 + a*e^2 + 2*c*d*e*x)^2)*((c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))*sqrt(((c*d^2 - a*e^2)^(4/3) - 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*(c*d^2 - a*e^2)^(2/3)*((a*e + c*d*x)*(d + e*x))^(1/3) + 2*2^(1/3)*c^(2/3)*d^(2/3)*e^(2/3)*((a*e + c*d*x)*(d + e*x))^(2/3))/((1 + sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))/((1 + sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))), -7 - 4*sqrt(3)))/(2^(5/6)*c^(5/3)*d^(5/3)*e^(2/3)*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(((c*d^2 - a*e^2)^(2/3)*((c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3)))/((1 + sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))^2)*sqrt((a*e^2 + c*d*(d + 2*e*x))^2))]
    @test_int [(d + e*x)^0/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/3), x, 4, (3*sqrt((c*d^2 + a*e^2 + 2*c*d*e*x)^2)*sqrt((a*e^2 + c*d*(d + 2*e*x))^2))/(2^(1/3)*c^(2/3)*d^(2/3)*e^(2/3)*(c*d^2 + a*e^2 + 2*c*d*e*x)*((1 + sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))) - (3*3^(1/4)*sqrt(2 - sqrt(3))*(c*d^2 - a*e^2)^(2/3)*sqrt((c*d^2 + a*e^2 + 2*c*d*e*x)^2)*((c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))*sqrt(((c*d^2 - a*e^2)^(4/3) - 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*(c*d^2 - a*e^2)^(2/3)*((a*e + c*d*x)*(d + e*x))^(1/3) + 2*2^(1/3)*c^(2/3)*d^(2/3)*e^(2/3)*((a*e + c*d*x)*(d + e*x))^(2/3))/((1 + sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))^2)*Elliptic.E(asin(((1 - sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))/((1 + sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))), -7 - 4*sqrt(3)))/(2*2^(1/3)*c^(2/3)*d^(2/3)*e^(2/3)*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(((c*d^2 - a*e^2)^(2/3)*((c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3)))/((1 + sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))^2)*sqrt((a*e^2 + c*d*(d + 2*e*x))^2)) + (2^(1/6)*3^(3/4)*(c*d^2 - a*e^2)^(2/3)*sqrt((c*d^2 + a*e^2 + 2*c*d*e*x)^2)*((c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))*sqrt(((c*d^2 - a*e^2)^(4/3) - 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*(c*d^2 - a*e^2)^(2/3)*((a*e + c*d*x)*(d + e*x))^(1/3) + 2*2^(1/3)*c^(2/3)*d^(2/3)*e^(2/3)*((a*e + c*d*x)*(d + e*x))^(2/3))/((1 + sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))/((1 + sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))), -7 - 4*sqrt(3)))/(c^(2/3)*d^(2/3)*e^(2/3)*(c*d^2 + a*e^2 + 2*c*d*e*x)*sqrt(((c*d^2 - a*e^2)^(2/3)*((c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3)))/((1 + sqrt(3))*(c*d^2 - a*e^2)^(2/3) + 2^(2/3)*c^(1/3)*d^(1/3)*e^(1/3)*((a*e + c*d*x)*(d + e*x))^(1/3))^2)*sqrt((a*e^2 + c*d*(d + 2*e*x))^2))]
    #= [1/((d + e*x)^1*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/3)), x, 0, 0]
    @test_int [1/((d + e*x)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/3)), x, 0, 0]
    @test_int [1/((d + e*x)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/3)), x, 0, 0]
    @test_int [1/((d + e*x)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/3)), x, 0, 0] =#

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

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

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

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

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

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

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

    @test_int [(d + e*x)^(13/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 8, (9*e*(c*d^2 - a*e^2)^3*sqrt(d + e*x))/(c^5*d^5) + (3*e*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2))/(c^4*d^4) + (9*e*(c*d^2 - a*e^2)*(d + e*x)^(5/2))/(5*c^3*d^3) + (9*e*(d + e*x)^(7/2))/(7*c^2*d^2) - (d + e*x)^(9/2)/(c*d*(a*e + c*d*x)) - (9*e*(c*d^2 - a*e^2)^(7/2)*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(c^(11/2)*d^(11/2))]
    @test_int [(d + e*x)^(11/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 7, (7*e*(c*d^2 - a*e^2)^2*sqrt(d + e*x))/(c^4*d^4) + (7*e*(c*d^2 - a*e^2)*(d + e*x)^(3/2))/(3*c^3*d^3) + (7*e*(d + e*x)^(5/2))/(5*c^2*d^2) - (d + e*x)^(7/2)/(c*d*(a*e + c*d*x)) - (7*e*(c*d^2 - a*e^2)^(5/2)*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(c^(9/2)*d^(9/2))]
    @test_int [(d + e*x)^(9/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 6, (5*e*(c*d^2 - a*e^2)*sqrt(d + e*x))/(c^3*d^3) + (5*e*(d + e*x)^(3/2))/(3*c^2*d^2) - (d + e*x)^(5/2)/(c*d*(a*e + c*d*x)) - (5*e*(c*d^2 - a*e^2)^(3/2)*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(c^(7/2)*d^(7/2))]
    @test_int [(d + e*x)^(7/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 5, (3*e*sqrt(d + e*x))/(c^2*d^2) - (d + e*x)^(3/2)/(c*d*(a*e + c*d*x)) - (3*e*sqrt(c*d^2 - a*e^2)*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(c^(5/2)*d^(5/2))]
    @test_int [(d + e*x)^(5/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 4, -(sqrt(d + e*x)/(c*d*(a*e + c*d*x))) - (e*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(c^(3/2)*d^(3/2)*sqrt(c*d^2 - a*e^2))]
    @test_int [(d + e*x)^(3/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 4, -(sqrt(d + e*x)/((c*d^2 - a*e^2)*(a*e + c*d*x))) + (e*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(sqrt(c)*sqrt(d)*(c*d^2 - a*e^2)^(3/2))]
    @test_int [(d + e*x)^(1/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2, x, 5, -((3*e)/((c*d^2 - a*e^2)^2*sqrt(d + e*x))) - 1/((c*d^2 - a*e^2)*(a*e + c*d*x)*sqrt(d + e*x)) + (3*sqrt(c)*sqrt(d)*e*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(c*d^2 - a*e^2)^(5/2)]
    @test_int [1/((d + e*x)^(1/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2), x, 6, -((5*e)/(3*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2))) - 1/((c*d^2 - a*e^2)*(a*e + c*d*x)*(d + e*x)^(3/2)) - (5*c*d*e)/((c*d^2 - a*e^2)^3*sqrt(d + e*x)) + (5*c^(3/2)*d^(3/2)*e*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(c*d^2 - a*e^2)^(7/2)]
    @test_int [1/((d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^2), x, 7, -((7*e)/(5*(c*d^2 - a*e^2)^2*(d + e*x)^(5/2))) - 1/((c*d^2 - a*e^2)*(a*e + c*d*x)*(d + e*x)^(5/2)) - (7*c*d*e)/(3*(c*d^2 - a*e^2)^3*(d + e*x)^(3/2)) - (7*c^2*d^2*e)/((c*d^2 - a*e^2)^4*sqrt(d + e*x)) + (7*c^(5/2)*d^(5/2)*e*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(c*d^2 - a*e^2)^(9/2)]

    @test_int [(d + e*x)^(15/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 8, (63*e^2*(c*d^2 - a*e^2)^2*sqrt(d + e*x))/(4*c^5*d^5) + (21*e^2*(c*d^2 - a*e^2)*(d + e*x)^(3/2))/(4*c^4*d^4) + (63*e^2*(d + e*x)^(5/2))/(20*c^3*d^3) - (9*e*(d + e*x)^(7/2))/(4*c^2*d^2*(a*e + c*d*x)) - (d + e*x)^(9/2)/(2*c*d*(a*e + c*d*x)^2) - (63*e^2*(c*d^2 - a*e^2)^(5/2)*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(4*c^(11/2)*d^(11/2))]
    @test_int [(d + e*x)^(13/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 7, (35*e^2*(c*d^2 - a*e^2)*sqrt(d + e*x))/(4*c^4*d^4) + (35*e^2*(d + e*x)^(3/2))/(12*c^3*d^3) - (7*e*(d + e*x)^(5/2))/(4*c^2*d^2*(a*e + c*d*x)) - (d + e*x)^(7/2)/(2*c*d*(a*e + c*d*x)^2) - (35*e^2*(c*d^2 - a*e^2)^(3/2)*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(4*c^(9/2)*d^(9/2))]
    @test_int [(d + e*x)^(11/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 6, (15*e^2*sqrt(d + e*x))/(4*c^3*d^3) - (5*e*(d + e*x)^(3/2))/(4*c^2*d^2*(a*e + c*d*x)) - (d + e*x)^(5/2)/(2*c*d*(a*e + c*d*x)^2) - (15*e^2*sqrt(c*d^2 - a*e^2)*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(4*c^(7/2)*d^(7/2))]
    @test_int [(d + e*x)^(9/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 5, -((3*e*sqrt(d + e*x))/(4*c^2*d^2*(a*e + c*d*x))) - (d + e*x)^(3/2)/(2*c*d*(a*e + c*d*x)^2) - (3*e^2*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(4*c^(5/2)*d^(5/2)*sqrt(c*d^2 - a*e^2))]
    @test_int [(d + e*x)^(7/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 5, -(sqrt(d + e*x)/(2*c*d*(a*e + c*d*x)^2)) - (e*sqrt(d + e*x))/(4*c*d*(c*d^2 - a*e^2)*(a*e + c*d*x)) + (e^2*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(4*c^(3/2)*d^(3/2)*(c*d^2 - a*e^2)^(3/2))]
    @test_int [(d + e*x)^(5/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 5, -(sqrt(d + e*x)/(2*(c*d^2 - a*e^2)*(a*e + c*d*x)^2)) + (3*e*sqrt(d + e*x))/(4*(c*d^2 - a*e^2)^2*(a*e + c*d*x)) - (3*e^2*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(4*sqrt(c)*sqrt(d)*(c*d^2 - a*e^2)^(5/2))]
    @test_int [(d + e*x)^(3/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 6, (15*e^2)/(4*(c*d^2 - a*e^2)^3*sqrt(d + e*x)) - 1/(2*(c*d^2 - a*e^2)*(a*e + c*d*x)^2*sqrt(d + e*x)) + (5*e)/(4*(c*d^2 - a*e^2)^2*(a*e + c*d*x)*sqrt(d + e*x)) - (15*sqrt(c)*sqrt(d)*e^2*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(4*(c*d^2 - a*e^2)^(7/2))]
    @test_int [(d + e*x)^(1/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3, x, 7, (35*e^2)/(12*(c*d^2 - a*e^2)^3*(d + e*x)^(3/2)) - 1/(2*(c*d^2 - a*e^2)*(a*e + c*d*x)^2*(d + e*x)^(3/2)) + (7*e)/(4*(c*d^2 - a*e^2)^2*(a*e + c*d*x)*(d + e*x)^(3/2)) + (35*c*d*e^2)/(4*(c*d^2 - a*e^2)^4*sqrt(d + e*x)) - (35*c^(3/2)*d^(3/2)*e^2*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(4*(c*d^2 - a*e^2)^(9/2))]
    @test_int [1/((d + e*x)^(1/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3), x, 8, (63*e^2)/(20*(c*d^2 - a*e^2)^3*(d + e*x)^(5/2)) - 1/(2*(c*d^2 - a*e^2)*(a*e + c*d*x)^2*(d + e*x)^(5/2)) + (9*e)/(4*(c*d^2 - a*e^2)^2*(a*e + c*d*x)*(d + e*x)^(5/2)) + (21*c*d*e^2)/(4*(c*d^2 - a*e^2)^4*(d + e*x)^(3/2)) + (63*c^2*d^2*e^2)/(4*(c*d^2 - a*e^2)^5*sqrt(d + e*x)) - (63*c^(5/2)*d^(5/2)*e^2*atanh((sqrt(c)*sqrt(d)*sqrt(d + e*x))/sqrt(c*d^2 - a*e^2)))/(4*(c*d^2 - a*e^2)^(11/2))]

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

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

    @test_int [(d + e*x)^(7/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2), x, 5, (256*(c*d^2 - a*e^2)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3465*c^5*d^5*(d + e*x)^(3/2)) + (128*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(1155*c^4*d^4*sqrt(d + e*x)) + (32*(c*d^2 - a*e^2)^2*sqrt(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(231*c^3*d^3) + (16*(c*d^2 - a*e^2)*(d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(99*c^2*d^2) + (2*(d + e*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(11*c*d)]
    @test_int [(d + e*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2), x, 4, (32*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(315*c^4*d^4*(d + e*x)^(3/2)) + (16*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(105*c^3*d^3*sqrt(d + e*x)) + (4*(c*d^2 - a*e^2)*sqrt(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(21*c^2*d^2) + (2*(d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(9*c*d)]
    @test_int [(d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2), x, 3, (16*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(105*c^3*d^3*(d + e*x)^(3/2)) + (8*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(35*c^2*d^2*sqrt(d + e*x)) + (2*sqrt(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(7*c*d)]
    @test_int [(d + e*x)^(1/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2), x, 2, (4*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(15*c^2*d^2*(d + e*x)^(3/2)) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(5*c*d*sqrt(d + e*x))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)/(d + e*x)^(1/2), x, 1, (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*c*d*(d + e*x)^(3/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)/(d + e*x)^(3/2), x, 3, (2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(e*sqrt(d + e*x)) - (2*sqrt(c*d^2 - a*e^2)*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/e^(3/2)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)/(d + e*x)^(5/2), x, 3, -(sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(e*(d + e*x)^(3/2))) + (c*d*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(e^(3/2)*sqrt(c*d^2 - a*e^2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)/(d + e*x)^(7/2), x, 4, -(sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(2*e*(d + e*x)^(5/2))) + (c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(4*e*(c*d^2 - a*e^2)*(d + e*x)^(3/2)) + (c^2*d^2*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(4*e^(3/2)*(c*d^2 - a*e^2)^(3/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)/(d + e*x)^(9/2), x, 5, -(sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(3*e*(d + e*x)^(7/2))) + (c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(12*e*(c*d^2 - a*e^2)*(d + e*x)^(5/2)) + (c^2*d^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(8*e*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2)) + (c^3*d^3*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(8*e^(3/2)*(c*d^2 - a*e^2)^(5/2))]

    @test_int [(d + e*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 5, (256*(c*d^2 - a*e^2)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(15015*c^5*d^5*(d + e*x)^(5/2)) + (128*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(3003*c^4*d^4*(d + e*x)^(3/2)) + (32*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(429*c^3*d^3*sqrt(d + e*x)) + (16*(c*d^2 - a*e^2)*sqrt(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(143*c^2*d^2) + (2*(d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(13*c*d)]
    @test_int [(d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 4, (32*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(1155*c^4*d^4*(d + e*x)^(5/2)) + (16*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(231*c^3*d^3*(d + e*x)^(3/2)) + (4*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(33*c^2*d^2*sqrt(d + e*x)) + (2*sqrt(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(11*c*d)]
    @test_int [(d + e*x)^(1/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 3, (16*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(315*c^3*d^3*(d + e*x)^(5/2)) + (8*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(63*c^2*d^2*(d + e*x)^(3/2)) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(9*c*d*sqrt(d + e*x))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^(1/2), x, 2, (4*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(35*c^2*d^2*(d + e*x)^(5/2)) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(7*c*d*(d + e*x)^(3/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^(3/2), x, 1, (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(5*c*d*(d + e*x)^(5/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^(5/2), x, 4, (2*(a - (c*d^2)/e^2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/sqrt(d + e*x) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*e*(d + e*x)^(3/2)) + (2*(c*d^2 - a*e^2)^(3/2)*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/e^(5/2)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^(7/2), x, 4, (3*c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(e^2*sqrt(d + e*x)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(e*(d + e*x)^(5/2)) - (3*c*d*sqrt(c*d^2 - a*e^2)*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/e^(5/2)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^(9/2), x, 4, -((3*c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(4*e^2*(d + e*x)^(3/2))) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(2*e*(d + e*x)^(7/2)) + (3*c^2*d^2*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(4*e^(5/2)*sqrt(c*d^2 - a*e^2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^(11/2), x, 5, -((c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(4*e^2*(d + e*x)^(5/2))) + (c^2*d^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(8*e^2*(c*d^2 - a*e^2)*(d + e*x)^(3/2)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(3*e*(d + e*x)^(9/2)) + (c^3*d^3*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(8*e^(5/2)*(c*d^2 - a*e^2)^(3/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(d + e*x)^(13/2), x, 6, -((c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(8*e^2*(d + e*x)^(7/2))) + (c^2*d^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(32*e^2*(c*d^2 - a*e^2)*(d + e*x)^(5/2)) + (3*c^3*d^3*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(64*e^2*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)/(4*e*(d + e*x)^(11/2)) + (3*c^4*d^4*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(64*e^(5/2)*(c*d^2 - a*e^2)^(5/2))]

    @test_int [(d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 5, (256*(c*d^2 - a*e^2)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(45045*c^5*d^5*(d + e*x)^(7/2)) + (128*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(6435*c^4*d^4*(d + e*x)^(5/2)) + (32*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(715*c^3*d^3*(d + e*x)^(3/2)) + (16*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(195*c^2*d^2*sqrt(d + e*x)) + (2*sqrt(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(15*c*d)]
    @test_int [(d + e*x)^(1/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 4, (32*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(3003*c^4*d^4*(d + e*x)^(7/2)) + (16*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(429*c^3*d^3*(d + e*x)^(5/2)) + (12*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(143*c^2*d^2*(d + e*x)^(3/2)) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(13*c*d*sqrt(d + e*x))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^(1/2), x, 3, (16*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(693*c^3*d^3*(d + e*x)^(7/2)) + (8*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(99*c^2*d^2*(d + e*x)^(5/2)) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(11*c*d*(d + e*x)^(3/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^(3/2), x, 2, (4*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(63*c^2*d^2*(d + e*x)^(7/2)) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(9*c*d*(d + e*x)^(5/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^(5/2), x, 1, (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(7/2))/(7*c*d*(d + e*x)^(7/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^(7/2), x, 5, (2*(c*d^2 - a*e^2)^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(e^3*sqrt(d + e*x)) + (2*(a - (c*d^2)/e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*(d + e*x)^(3/2)) + (2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2))/(5*e*(d + e*x)^(5/2)) - (2*(c*d^2 - a*e^2)^(5/2)*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/e^(7/2)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^(9/2), x, 5, (5*c*d*(a - (c*d^2)/e^2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(e*sqrt(d + e*x)) + (5*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(3*e^2*(d + e*x)^(3/2)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(e*(d + e*x)^(7/2)) + (5*c*d*(c*d^2 - a*e^2)^(3/2)*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/e^(7/2)]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^(11/2), x, 5, (15*c^2*d^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(4*e^3*sqrt(d + e*x)) - (5*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(4*e^2*(d + e*x)^(5/2)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(2*e*(d + e*x)^(9/2)) - (15*c^2*d^2*sqrt(c*d^2 - a*e^2)*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(4*e^(7/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^(13/2), x, 5, -((5*c^2*d^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(8*e^3*(d + e*x)^(3/2))) - (5*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(12*e^2*(d + e*x)^(7/2)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(3*e*(d + e*x)^(11/2)) + (5*c^3*d^3*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(8*e^(7/2)*sqrt(c*d^2 - a*e^2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^(15/2), x, 6, -((5*c^2*d^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(32*e^3*(d + e*x)^(5/2))) + (5*c^3*d^3*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(64*e^3*(c*d^2 - a*e^2)*(d + e*x)^(3/2)) - (5*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(24*e^2*(d + e*x)^(9/2)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(4*e*(d + e*x)^(13/2)) + (5*c^4*d^4*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(64*e^(7/2)*(c*d^2 - a*e^2)^(3/2))]
    @test_int [(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(d + e*x)^(17/2), x, 7, -((c^2*d^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(16*e^3*(d + e*x)^(7/2))) + (c^3*d^3*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(64*e^3*(c*d^2 - a*e^2)*(d + e*x)^(5/2)) + (3*c^4*d^4*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(128*e^3*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2)) - (c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))/(8*e^2*(d + e*x)^(11/2)) - (a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)/(5*e*(d + e*x)^(15/2)) + (3*c^5*d^5*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(128*e^(7/2)*(c*d^2 - a*e^2)^(5/2))]

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

    @test_int [(d + e*x)^(7/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2), x, 4, (32*(c*d^2 - a*e^2)^3*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(35*c^4*d^4*sqrt(d + e*x)) + (16*(c*d^2 - a*e^2)^2*sqrt(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(35*c^3*d^3) + (12*(c*d^2 - a*e^2)*(d + e*x)^(3/2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(35*c^2*d^2) + (2*(d + e*x)^(5/2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(7*c*d)]
    @test_int [(d + e*x)^(5/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2), x, 3, (16*(c*d^2 - a*e^2)^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(15*c^3*d^3*sqrt(d + e*x)) + (8*(c*d^2 - a*e^2)*sqrt(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(15*c^2*d^2) + (2*(d + e*x)^(3/2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(5*c*d)]
    @test_int [(d + e*x)^(3/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2), x, 2, (4*(c*d^2 - a*e^2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(3*c^2*d^2*sqrt(d + e*x)) + (2*sqrt(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(3*c*d)]
    @test_int [(d + e*x)^(1/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2), x, 1, (2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(c*d*sqrt(d + e*x))]
    @test_int [1/((d + e*x)^(1/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)), x, 2, (2*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(sqrt(e)*sqrt(c*d^2 - a*e^2))]
    @test_int [1/((d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)), x, 3, sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/((c*d^2 - a*e^2)*(d + e*x)^(3/2)) + (c*d*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(sqrt(e)*(c*d^2 - a*e^2)^(3/2))]
    @test_int [1/((d + e*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)), x, 4, sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(2*(c*d^2 - a*e^2)*(d + e*x)^(5/2)) + (3*c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(4*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2)) + (3*c^2*d^2*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(4*sqrt(e)*(c*d^2 - a*e^2)^(5/2))]
    @test_int [1/((d + e*x)^(7/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(1/2)), x, 5, sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)/(3*(c*d^2 - a*e^2)*(d + e*x)^(7/2)) + (5*c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(12*(c*d^2 - a*e^2)^2*(d + e*x)^(5/2)) + (5*c^2*d^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(8*(c*d^2 - a*e^2)^3*(d + e*x)^(3/2)) + (5*c^3*d^3*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(8*sqrt(e)*(c*d^2 - a*e^2)^(7/2))]

    @test_int [(d + e*x)^(7/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 3, -((16*(c*d^2 - a*e^2)^2*sqrt(d + e*x))/(3*c^3*d^3*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))) + (8*(c*d^2 - a*e^2)*(d + e*x)^(3/2))/(3*c^2*d^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (2*(d + e*x)^(5/2))/(3*c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))]
    @test_int [(d + e*x)^(5/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 2, -((4*(c*d^2 - a*e^2)*sqrt(d + e*x))/(c^2*d^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))) + (2*(d + e*x)^(3/2))/(c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))]
    @test_int [(d + e*x)^(3/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 1, -((2*sqrt(d + e*x))/(c*d*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)))]
    @test_int [(d + e*x)^(1/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2), x, 3, -((2*sqrt(d + e*x))/((c*d^2 - a*e^2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))) - (2*sqrt(e)*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(c*d^2 - a*e^2)^(3/2)]
    @test_int [1/((d + e*x)^(1/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)), x, 4, 1/((c*d^2 - a*e^2)*sqrt(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) - (3*c*d*sqrt(d + e*x))/((c*d^2 - a*e^2)^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) - (3*c*d*sqrt(e)*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(c*d^2 - a*e^2)^(5/2)]
    @test_int [1/((d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)), x, 5, 1/(2*(c*d^2 - a*e^2)*(d + e*x)^(3/2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (5*c*d)/(4*(c*d^2 - a*e^2)^2*sqrt(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) - (15*c^2*d^2*sqrt(d + e*x))/(4*(c*d^2 - a*e^2)^3*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) - (15*c^2*d^2*sqrt(e)*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(4*(c*d^2 - a*e^2)^(7/2))]
    @test_int [1/((d + e*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)), x, 6, 1/(3*(c*d^2 - a*e^2)*(d + e*x)^(5/2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (7*c*d)/(12*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (35*c^2*d^2)/(24*(c*d^2 - a*e^2)^3*sqrt(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) - (35*c^3*d^3*sqrt(d + e*x))/(8*(c*d^2 - a*e^2)^4*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) - (35*c^3*d^3*sqrt(e)*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(8*(c*d^2 - a*e^2)^(9/2))]
    @test_int [1/((d + e*x)^(7/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)), x, 7, 1/(4*(c*d^2 - a*e^2)*(d + e*x)^(7/2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (3*c*d)/(8*(c*d^2 - a*e^2)^2*(d + e*x)^(5/2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (21*c^2*d^2)/(32*(c*d^2 - a*e^2)^3*(d + e*x)^(3/2)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (105*c^3*d^3)/(64*(c*d^2 - a*e^2)^4*sqrt(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) - (315*c^4*d^4*sqrt(d + e*x))/(64*(c*d^2 - a*e^2)^5*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) - (315*c^4*d^4*sqrt(e)*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(64*(c*d^2 - a*e^2)^(11/2))]

    @test_int [(d + e*x)^(7/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 2, (4*(c*d^2 - a*e^2)*(d + e*x)^(3/2))/(3*c^2*d^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (2*(d + e*x)^(5/2))/(c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))]
    @test_int [(d + e*x)^(5/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 1, -((2*(d + e*x)^(3/2))/(3*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)))]
    @test_int [(d + e*x)^(3/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 5, -((2*sqrt(d + e*x))/(3*c*d*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))) - (2*e)/(3*c*d*(c*d^2 - a*e^2)*sqrt(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (2*e*sqrt(d + e*x))/((c*d^2 - a*e^2)^2*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (2*e^(3/2)*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(c*d^2 - a*e^2)^(5/2)]
    @test_int [(d + e*x)^(1/2)/(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2), x, 5, -((2*sqrt(d + e*x))/(3*(c*d^2 - a*e^2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2))) - (5*e)/(3*(c*d^2 - a*e^2)^2*sqrt(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (5*c*d*e*sqrt(d + e*x))/((c*d^2 - a*e^2)^3*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (5*c*d*e^(3/2)*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(c*d^2 - a*e^2)^(7/2)]
    @test_int [1/((d + e*x)^(1/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)), x, 6, 1/(2*(c*d^2 - a*e^2)*sqrt(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (7*c*d*sqrt(d + e*x))/(6*(c*d^2 - a*e^2)^2*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (35*c*d*e)/(12*(c*d^2 - a*e^2)^3*sqrt(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (35*c^2*d^2*e*sqrt(d + e*x))/(4*(c*d^2 - a*e^2)^4*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (35*c^2*d^2*e^(3/2)*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(4*(c*d^2 - a*e^2)^(9/2))]
    @test_int [1/((d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)), x, 7, 1/(3*(c*d^2 - a*e^2)*(d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (3*c*d)/(4*(c*d^2 - a*e^2)^2*sqrt(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (7*c^2*d^2*sqrt(d + e*x))/(4*(c*d^2 - a*e^2)^3*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (35*c^2*d^2*e)/(8*(c*d^2 - a*e^2)^4*sqrt(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (105*c^3*d^3*e*sqrt(d + e*x))/(8*(c*d^2 - a*e^2)^5*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (105*c^3*d^3*e^(3/2)*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(8*(c*d^2 - a*e^2)^(11/2))]
    @test_int [1/((d + e*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)), x, 8, 1/(4*(c*d^2 - a*e^2)*(d + e*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (11*c*d)/(24*(c*d^2 - a*e^2)^2*(d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (33*c^2*d^2)/(32*(c*d^2 - a*e^2)^3*sqrt(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (77*c^3*d^3*sqrt(d + e*x))/(32*(c*d^2 - a*e^2)^4*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (385*c^3*d^3*e)/(64*(c*d^2 - a*e^2)^5*sqrt(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (1155*c^4*d^4*e*sqrt(d + e*x))/(64*(c*d^2 - a*e^2)^6*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (1155*c^4*d^4*e^(3/2)*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(64*(c*d^2 - a*e^2)^(13/2))]
    @test_int [1/((d + e*x)^(7/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(5/2)), x, 9, 1/(5*(c*d^2 - a*e^2)*(d + e*x)^(7/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (13*c*d)/(40*(c*d^2 - a*e^2)^2*(d + e*x)^(5/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (143*c^2*d^2)/(240*(c*d^2 - a*e^2)^3*(d + e*x)^(3/2)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) + (429*c^3*d^3)/(320*(c*d^2 - a*e^2)^4*sqrt(d + e*x)*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (1001*c^4*d^4*sqrt(d + e*x))/(320*(c*d^2 - a*e^2)^5*(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^(3/2)) - (1001*c^4*d^4*e)/(128*(c*d^2 - a*e^2)^6*sqrt(d + e*x)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (3003*c^5*d^5*e*sqrt(d + e*x))/(128*(c*d^2 - a*e^2)^7*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)) + (3003*c^5*d^5*e^(3/2)*atan((sqrt(e)*sqrt(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2))/(sqrt(c*d^2 - a*e^2)*sqrt(d + e*x))))/(128*(c*d^2 - a*e^2)^(15/2))]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    @test_int [(d + e*x)^4*(a + b*x + c*x^2)^4, x, 2, ((c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^5)/(5*e^9) - (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^6)/(3*e^9) + (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^7)/(7*e^9) - ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^8)/(2*e^9) + (1/(9*e^9))*((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^9) - (2*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^10)/(5*e^9) + (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^11)/(11*e^9) - (c^3*(2*c*d - b*e)*(d + e*x)^12)/(3*e^9) + (c^4*(d + e*x)^13)/(13*e^9)]
    @test_int [(d + e*x)^3*(a + b*x + c*x^2)^4, x, 2, ((c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^4)/(4*e^9) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^5)/(5*e^9) + ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^6)/(3*e^9) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^7)/(7*e^9) + (1/(8*e^9))*((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^8) - (4*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^9)/(9*e^9) + (c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^10)/(5*e^9) - (4*c^3*(2*c*d - b*e)*(d + e*x)^11)/(11*e^9) + (c^4*(d + e*x)^12)/(12*e^9)]
    @test_int [(d + e*x)^2*(a + b*x + c*x^2)^4, x, 2, ((c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^3)/(3*e^9) - ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^4)/e^9 + (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^5)/(5*e^9) - (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^6)/(3*e^9) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^7)/(7*e^9) - (c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^8)/(2*e^9) + (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^9)/(9*e^9) - (2*c^3*(2*c*d - b*e)*(d + e*x)^10)/(5*e^9) + (c^4*(d + e*x)^11)/(11*e^9)]

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

    @test_int [(a + b*x + c*x^2)^4/(d + e*x), x, 2, -((4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*x)/e^8) + ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^2)/e^9 - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^3)/(3*e^9) + (1/(4*e^9))*((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^4) - (4*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^5)/(5*e^9) + (c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^6)/(3*e^9) - (4*c^3*(2*c*d - b*e)*(d + e*x)^7)/(7*e^9) + (c^4*(d + e*x)^8)/(8*e^9) + ((c*d^2 - b*d*e + a*e^2)^4*log(d + e*x))/e^9]
    @test_int [(a + b*x + c*x^2)^4/(d + e*x)^2, x, 2, (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*x)/e^8 - (c*d^2 - b*d*e + a*e^2)^4/(e^9*(d + e*x)) - (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^2)/e^9 + (1/(3*e^9))*((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^3) - (c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^4)/e^9 + (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^5)/(5*e^9) - (2*c^3*(2*c*d - b*e)*(d + e*x)^6)/(3*e^9) + (c^4*(d + e*x)^7)/(7*e^9) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*log(d + e*x))/e^9]
    @test_int [(a + b*x + c*x^2)^4/(d + e*x)^3, x, 2, -((4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*x)/e^8) - (c*d^2 - b*d*e + a*e^2)^4/(2*e^9*(d + e*x)^2) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(e^9*(d + e*x)) + (1/(2*e^9))*((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^2) - (4*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^3)/(3*e^9) + (c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^4)/(2*e^9) - (4*c^3*(2*c*d - b*e)*(d + e*x)^5)/(5*e^9) + (c^4*(d + e*x)^6)/(6*e^9) + (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*log(d + e*x))/e^9]
    @test_int [(a + b*x + c*x^2)^4/(d + e*x)^4, x, 2, (1/e^8)*((35*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(4*b*d - 3*a*e) - 40*c^3*d^2*e*(2*b*d - a*e) + 6*c^2*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2))*x) - (2*c*(5*c^3*d^3 - b^3*e^3 - 2*c^2*d*e*(5*b*d - 2*a*e) + 3*b*c*e^2*(2*b*d - a*e))*x^2)/e^7 + (2*c^2*(5*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(4*b*d - a*e))*x^3)/(3*e^6) - (c^3*(c*d - b*e)*x^4)/e^5 + (c^4*x^5)/(5*e^4) - (c*d^2 - b*d*e + a*e^2)^4/(3*e^9*(d + e*x)^3) + (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(e^9*(d + e*x)^2) - (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(e^9*(d + e*x)) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*log(d + e*x))/e^9]
    @test_int [(a + b*x + c*x^2)^4/(d + e*x)^5, x, 2, -((c*(35*c^3*d^3 - 4*b^3*e^3 + 6*b*c*e^2*(5*b*d - 2*a*e) - 20*c^2*d*e*(3*b*d - a*e))*x)/e^8) + (c^2*(15*c^2*d^2 + 6*b^2*e^2 - 4*c*e*(5*b*d - a*e))*x^2)/(2*e^7) - (c^3*(5*c*d - 4*b*e)*x^3)/(3*e^6) + (c^4*x^4)/(4*e^5) - (c*d^2 - b*d*e + a*e^2)^4/(4*e^9*(d + e*x)^4) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(3*e^9*(d + e*x)^3) - ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(e^9*(d + e*x)^2) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(e^9*(d + e*x)) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*log(d + e*x))/e^9]
    @test_int [(a + b*x + c*x^2)^4/(d + e*x)^6, x, 2, (c^2*(21*c^2*d^2 + 6*b^2*e^2 - 4*c*e*(6*b*d - a*e))*x)/e^8 - (c^3*(3*c*d - 2*b*e)*x^2)/e^7 + (c^4*x^3)/(3*e^6) - (c*d^2 - b*d*e + a*e^2)^4/(5*e^9*(d + e*x)^5) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(e^9*(d + e*x)^4) - (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(3*e^9*(d + e*x)^3) + (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(e^9*(d + e*x)^2) - (1/(e^9*(d + e*x)))*(70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2)) - (4*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*log(d + e*x))/e^9]
    @test_int [(a + b*x + c*x^2)^4/(d + e*x)^7, x, 2, -((c^3*(7*c*d - 4*b*e)*x)/e^8) + (c^4*x^2)/(2*e^7) - (c*d^2 - b*d*e + a*e^2)^4/(6*e^9*(d + e*x)^6) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(5*e^9*(d + e*x)^5) - ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(2*e^9*(d + e*x)^4) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(3*e^9*(d + e*x)^3) - (1/(2*e^9*(d + e*x)^2))*(70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2)) + (4*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(e^9*(d + e*x)) + (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*log(d + e*x))/e^9]
    @test_int [(a + b*x + c*x^2)^4/(d + e*x)^8, x, 2, (c^4*x)/e^8 - (c*d^2 - b*d*e + a*e^2)^4/(7*e^9*(d + e*x)^7) + (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(3*e^9*(d + e*x)^6) - (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(5*e^9*(d + e*x)^5) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(e^9*(d + e*x)^4) - (1/(3*e^9*(d + e*x)^3))*(70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2)) + (2*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(e^9*(d + e*x)^2) - (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(e^9*(d + e*x)) - (4*c^3*(2*c*d - b*e)*log(d + e*x))/e^9]
    @test_int [(a + b*x + c*x^2)^4/(d + e*x)^9, x, 2, -((c*d^2 - b*d*e + a*e^2)^4/(8*e^9*(d + e*x)^8)) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(7*e^9*(d + e*x)^7) - ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(3*e^9*(d + e*x)^6) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(5*e^9*(d + e*x)^5) - (1/(4*e^9*(d + e*x)^4))*(70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2)) + (4*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(3*e^9*(d + e*x)^3) - (c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(e^9*(d + e*x)^2) + (4*c^3*(2*c*d - b*e))/(e^9*(d + e*x)) + (c^4*log(d + e*x))/e^9]

    @test_int [(a + b*x + c*x^2)^4/(d + e*x)^10, x, 2, -((c*d^2 - b*d*e + a*e^2)^4/(9*e^9*(d + e*x)^9)) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(2*e^9*(d + e*x)^8) - (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(7*e^9*(d + e*x)^7) + (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(3*e^9*(d + e*x)^6) - (1/(5*e^9*(d + e*x)^5))*(70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2)) + (c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(e^9*(d + e*x)^4) - (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(3*e^9*(d + e*x)^3) + (2*c^3*(2*c*d - b*e))/(e^9*(d + e*x)^2) - c^4/(e^9*(d + e*x))]
    @test_int [(a + b*x + c*x^2)^4/(d + e*x)^11, x, 2, -((c*d^2 - b*d*e + a*e^2)^4/(10*e^9*(d + e*x)^10)) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(9*e^9*(d + e*x)^9) - ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(4*e^9*(d + e*x)^8) + (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(7*e^9*(d + e*x)^7) - (1/(6*e^9*(d + e*x)^6))*(70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2)) + (4*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(5*e^9*(d + e*x)^5) - (c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(2*e^9*(d + e*x)^4) + (4*c^3*(2*c*d - b*e))/(3*e^9*(d + e*x)^3) - c^4/(2*e^9*(d + e*x)^2)]
    @test_int [(a + b*x + c*x^2)^4/(d + e*x)^12, x, 2, -((c*d^2 - b*d*e + a*e^2)^4/(11*e^9*(d + e*x)^11)) + (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(5*e^9*(d + e*x)^10) - (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(9*e^9*(d + e*x)^9) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(2*e^9*(d + e*x)^8) - (1/(7*e^9*(d + e*x)^7))*(70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2)) + (2*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(3*e^9*(d + e*x)^6) - (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(5*e^9*(d + e*x)^5) + (c^3*(2*c*d - b*e))/(e^9*(d + e*x)^4) - c^4/(3*e^9*(d + e*x)^3)]

    @test_int [x^4*(3 - 4*x + x^2)^2, x, 2, (9*x^5)/5 - 4*x^6 + (22*x^7)/7 - x^8 + x^9/9]
    @test_int [x^3*(3 - 4*x + x^2)^2, x, 2, (9*x^4)/4 - (24*x^5)/5 + (11*x^6)/3 - (8*x^7)/7 + x^8/8]
    @test_int [x^2*(3 - 4*x + x^2)^2, x, 2, 3*x^3 - 6*x^4 + (22*x^5)/5 - (4*x^6)/3 + x^7/7]
    @test_int [x^1*(3 - 4*x + x^2)^2, x, 2, (9*x^2)/2 - 8*x^3 + (11*x^4)/2 - (8*x^5)/5 + x^6/6]
    @test_int [x^0*(3 - 4*x + x^2)^2, x, 3, (-(4/3))*(3 - x)^3 - (1/5)*(3 - x)^5 + (-3 + x)^4]
    @test_int [(3 - 4*x + x^2)^2/x^1, x, 2, -24*x + 11*x^2 - (8*x^3)/3 + x^4/4 + 9*log(x)]
    @test_int [(3 - 4*x + x^2)^2/x^2, x, 2, -(9/x) + 22*x - 4*x^2 + x^3/3 - 24*log(x)]
    @test_int [(3 - 4*x + x^2)^2/x^3, x, 2, -(9/(2*x^2)) + 24/x - 8*x + x^2/2 + 22*log(x)]
    @test_int [(3 - 4*x + x^2)^2/x^4, x, 2, -(3/x^3) + 12/x^2 - 22/x + x - 8*log(x)]
    @test_int [(3 - 4*x + x^2)^2/x^5, x, 2, -(9/(4*x^4)) + 8/x^3 - 11/x^2 + 8/x + log(x)]
    @test_int [(3 - 4*x + x^2)^2/x^6, x, 2, -(9/(5*x^5)) + 6/x^4 - 22/(3*x^3) + 4/x^2 - 1/x]
    @test_int [(3 - 4*x + x^2)^2/x^7, x, 2, -(3/(2*x^6)) + 24/(5*x^5) - 11/(2*x^4) + 8/(3*x^3) - 1/(2*x^2)]

    @test_int [(2 + 2*x + x^2)/(2 + x), x, 2, x^2/2 + 2*log(2 + x)]
    @test_int [(5 + 4*x + x^2)/(-2 + x), x, 2, 6*x + x^2/2 + 17*log(2 - x)]

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

    @test_int [(1 + x + x^2)/x, x, 2, x + x^2/2 + log(x)]
    @test_int [(9 + 6*x + x^2)/x^2, x, 2, -9/x + x + 6*log(x)]
    @test_int [(1 + 2*x + x^2)/x^4, x, 2, -(1/(3*x^3)) - 1/x^2 - 1/x]

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

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

    @test_int [(d + e*x)^5/(a + b*x + c*x^2)^2, x, 7, (e^2*(12*c^3*d^3 - 3*b^3*e^3 - 10*c^2*d*e*(b*d + 3*a*e) + b*c*e^2*(10*b*d + 11*a*e))*x)/(c^3*(b^2 - 4*a*c)) + (e^3*(16*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(5*b*d + 4*a*e))*x^2)/(2*c^2*(b^2 - 4*a*c)) + (e^4*(2*c*d - b*e)*x^3)/(c*(b^2 - 4*a*c)) - ((d + e*x)^4*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + ((2*c*d - b*e)*(2*c^4*d^4 - 3*b^4*e^4 - 4*c^3*d^2*e*(b*d - 5*a*e) + 4*b^2*c*e^3*(b*d + 5*a*e) - 2*c^2*e^2*(b^2*d^2 + 10*a*b*d*e + 15*a^2*e^2))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(c^4*(b^2 - 4*a*c)^(3/2)) + (e^3*(10*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(5*b*d + a*e))*log(a + b*x + c*x^2))/(2*c^4)]
    @test_int [(d + e*x)^4/(a + b*x + c*x^2)^2, x, 7, (2*e^2*(3*c^2*d^2 + b^2*e^2 - c*e*(2*b*d + 3*a*e))*x)/(c^2*(b^2 - 4*a*c)) + (e^3*(2*c*d - b*e)*x^2)/(c*(b^2 - 4*a*c)) - ((d + e*x)^3*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + (2*(2*c^4*d^4 - b^4*e^4 - 4*c^3*d^2*e*(b*d - 3*a*e) - 6*a*c^2*e^3*(2*b*d + a*e) + 2*b^2*c*e^3*(b*d + 3*a*e))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(c^3*(b^2 - 4*a*c)^(3/2)) + (e^3*(2*c*d - b*e)*log(a + b*x + c*x^2))/c^3]
    @test_int [(d + e*x)^3/(a + b*x + c*x^2)^2, x, 6, (e^2*(2*c*d - b*e)*x)/(c*(b^2 - 4*a*c)) - ((d + e*x)^2*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + ((2*c*d - b*e)*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(c^2*(b^2 - 4*a*c)^(3/2)) + (e^3*log(a + b*x + c*x^2))/(2*c^2)]
    @test_int [(d + e*x)^2/(a + b*x + c*x^2)^2, x, 3, -(((d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2))) + (4*(c*d^2 - b*d*e + a*e^2)*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(3/2)]
    @test_int [(d + e*x)^1/(a + b*x + c*x^2)^2, x, 3, -((b*d - 2*a*e + (2*c*d - b*e)*x)/((b^2 - 4*a*c)*(a + b*x + c*x^2))) + (2*(2*c*d - b*e)*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(3/2)]
    @test_int [(d + e*x)^0/(a + b*x + c*x^2)^2, x, 3, -((b + 2*c*x)/((b^2 - 4*a*c)*(a + b*x + c*x^2))) + (4*c*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(3/2)]
    @test_int [1/((d + e*x)^1*(a + b*x + c*x^2)^2), x, 7, -((b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x)/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2))) + ((2*c*d - b*e)*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/((b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)^2) + (e^3*log(d + e*x))/(c*d^2 - b*d*e + a*e^2)^2 - (e^3*log(a + b*x + c*x^2))/(2*(c*d^2 - b*d*e + a*e^2)^2)]
    @test_int [1/((d + e*x)^2*(a + b*x + c*x^2)^2), x, 7, -((2*e*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e)))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x))) - (b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x)/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*(a + b*x + c*x^2)) + (2*(2*c^4*d^4 - b^4*e^4 - 4*c^3*d^2*e*(b*d - 3*a*e) - 6*a*c^2*e^3*(2*b*d + a*e) + 2*b^2*c*e^3*(b*d + 3*a*e))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/((b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)^3) + (2*e^3*(2*c*d - b*e)*log(d + e*x))/(c*d^2 - b*d*e + a*e^2)^3 - (e^3*(2*c*d - b*e)*log(a + b*x + c*x^2))/(c*d^2 - b*d*e + a*e^2)^3]
    @test_int [1/((d + e*x)^3*(a + b*x + c*x^2)^2), x, 7, -((e*(4*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(b*d + 2*a*e)))/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2)) - (e*(2*c*d - b*e)*(c^2*d^2 + 3*b^2*e^2 - c*e*(b*d + 11*a*e)))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)) - (b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x)/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2*(a + b*x + c*x^2)) + ((2*c*d - b*e)*(2*c^4*d^4 - 3*b^4*e^4 - 4*c^3*d^2*e*(b*d - 5*a*e) + 4*b^2*c*e^3*(b*d + 5*a*e) - 2*c^2*e^2*(b^2*d^2 + 10*a*b*d*e + 15*a^2*e^2))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/((b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)^4) + (e^3*(10*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(5*b*d + a*e))*log(d + e*x))/(c*d^2 - b*d*e + a*e^2)^4 - (e^3*(10*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(5*b*d + a*e))*log(a + b*x + c*x^2))/(2*(c*d^2 - b*d*e + a*e^2)^4)]

    @test_int [x^7/(a + b*x + c*x^2)^3, x, 8, -((3*b*(2*b^2 - 9*a*c)*(b^2 - 3*a*c)*x)/(c^4*(b^2 - 4*a*c)^2)) + (3*(2*b^4 - 13*a*b^2*c + 16*a^2*c^2)*x^2)/(2*c^3*(b^2 - 4*a*c)^2) - (b*(2*b^2 - 11*a*c)*x^3)/(c^2*(b^2 - 4*a*c)^2) + (x^6*(2*a + b*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (3*x^4*(a*(b^2 - 8*a*c) + b*(b^2 - 6*a*c)*x))/(2*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) + (3*b*(2*b^6 - 21*a*b^4*c + 70*a^2*b^2*c^2 - 70*a^3*c^3)*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(c^5*(b^2 - 4*a*c)^(5/2)) + (3*(2*b^2 - a*c)*log(a + b*x + c*x^2))/(2*c^5)]
    @test_int [x^6/(a + b*x + c*x^2)^3, x, 8, (3*(b^4 - 7*a*b^2*c + 10*a^2*c^2)*x)/(c^3*(b^2 - 4*a*c)^2) - (3*b*(b^2 - 6*a*c)*x^2)/(2*c^2*(b^2 - 4*a*c)^2) + (x^5*(2*a + b*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (x^3*(a*(b^2 - 10*a*c) + b*(b^2 - 7*a*c)*x))/(c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (3*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3)*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(c^4*(b^2 - 4*a*c)^(5/2)) - (3*b*log(a + b*x + c*x^2))/(2*c^4)]
    @test_int [(d + e*x)^5/(a + b*x + c*x^2)^3, x, 7, -((e^2*(2*c*d - b*e)*(3*c^2*d^2 - b^2*e^2 - c*e*(3*b*d - 7*a*e))*x)/(c^2*(b^2 - 4*a*c)^2)) - ((d + e*x)^4*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) - ((d + e*x)^2*(8*a*c*e*(c*d^2 + 2*a*e^2) - 6*b*c*d*(c*d^2 + 3*a*e^2) + b^2*(7*c*d^2*e - a*e^3) - (2*c*d - b*e)*(6*c^2*d^2 - b^2*e^2 - 2*c*e*(3*b*d - 5*a*e))*x))/(2*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - ((12*c^5*d^5 - b^5*e^5 + 10*a*b^3*c*e^5 - 30*a^2*b*c^2*e^5 - 10*c^4*d^3*e*(3*b*d - 4*a*e) + 20*c^3*d*e^2*(b^2*d^2 - 3*a*b*d*e + 3*a^2*e^2))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(c^3*(b^2 - 4*a*c)^(5/2)) + (e^5*log(a + b*x + c*x^2))/(2*c^3)]
    @test_int [(d + e*x)^4/(a + b*x + c*x^2)^3, x, 4, -(((d + e*x)^3*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2)) + (3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (12*(c*d^2 - b*d*e + a*e^2)^2*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(5/2)]
    @test_int [(d + e*x)^3/(a + b*x + c*x^2)^3, x, 4, -(((b + 2*c*x)*(d + e*x)^3)/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2)) + (3*(2*c*d - b*e)*(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (6*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(5/2)]
    @test_int [(d + e*x)^2/(a + b*x + c*x^2)^3, x, 4, -(((d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2)) - (2*b^2*d*e + 4*a*c*d*e - 3*b*(c*d^2 + a*e^2) - (6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*x)/((b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (2*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(5/2)]
    @test_int [(d + e*x)^1/(a + b*x + c*x^2)^3, x, 4, -((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2)) + (3*(2*c*d - b*e)*(b + 2*c*x))/(2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (6*c*(2*c*d - b*e)*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(5/2)]
    @test_int [(d + e*x)^0/(a + b*x + c*x^2)^3, x, 4, -((b + 2*c*x)/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2)) + (3*c*(b + 2*c*x))/((b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (12*c^2*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(5/2)]
    @test_int [1/((d + e*x)^1*(a + b*x + c*x^2)^3), x, 8, -((b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x)/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^2)) - (3*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(6*c^2*d^2 - 2*b^2*e^2 - c*e*(3*b*d - 8*a*e)) - 2*c*(2*c*d - b*e)*(3*c^2*d^2 - b^2*e^2 - c*e*(3*b*d - 7*a*e))*x)/(2*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)) - ((12*c^5*d^5 - b^5*e^5 + 10*a*b^3*c*e^5 - 30*a^2*b*c^2*e^5 - 10*c^4*d^3*e*(3*b*d - 4*a*e) + 20*c^3*d*e^2*(b^2*d^2 - 3*a*b*d*e + 3*a^2*e^2))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/((b^2 - 4*a*c)^(5/2)*(c*d^2 - b*d*e + a*e^2)^3) + (e^5*log(d + e*x))/(c*d^2 - b*d*e + a*e^2)^3 - (e^5*log(a + b*x + c*x^2))/(2*(c*d^2 - b*d*e + a*e^2)^3)]
    @test_int [1/(x^2*(a + b*x + c*x^2)^3), x, 8, -((3*(b^2 - 5*a*c)*(b^2 - 2*a*c))/(a^3*(b^2 - 4*a*c)^2*x)) + (b^2 - 2*a*c + b*c*x)/(2*a*(b^2 - 4*a*c)*x*(a + b*x + c*x^2)^2) + (3*b^4 - 20*a*b^2*c + 20*a^2*c^2 + 3*b*c*(b^2 - 6*a*c)*x)/(2*a^2*(b^2 - 4*a*c)^2*x*(a + b*x + c*x^2)) - (3*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3)*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(a^4*(b^2 - 4*a*c)^(5/2)) - (3*b*log(x))/a^4 + (3*b*log(a + b*x + c*x^2))/(2*a^4)]
    @test_int [1/(x^3*(a + b*x + c*x^2)^3), x, 8, -((3*(2*b^4 - 13*a*b^2*c + 16*a^2*c^2))/(2*a^3*(b^2 - 4*a*c)^2*x^2)) + (3*b*(2*b^2 - 9*a*c)*(b^2 - 3*a*c))/(a^4*(b^2 - 4*a*c)^2*x) + (b^2 - 2*a*c + b*c*x)/(2*a*(b^2 - 4*a*c)*x^2*(a + b*x + c*x^2)^2) + (4*b^4 - 25*a*b^2*c + 24*a^2*c^2 + 2*b*c*(2*b^2 - 11*a*c)*x)/(2*a^2*(b^2 - 4*a*c)^2*x^2*(a + b*x + c*x^2)) + (3*b*(2*b^6 - 21*a*b^4*c + 70*a^2*b^2*c^2 - 70*a^3*c^3)*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(a^5*(b^2 - 4*a*c)^(5/2)) + (3*(2*b^2 - a*c)*log(x))/a^5 - (3*(2*b^2 - a*c)*log(a + b*x + c*x^2))/(2*a^5)]

    @test_int [x^8/(a + b*x + c*x^2)^4, x, 9, (4*(b^6 - 11*a*b^4*c + 38*a^2*b^2*c^2 - 35*a^3*c^3)*x)/(c^4*(b^2 - 4*a*c)^3) - (2*b*(b^4 - 10*a*b^2*c + 29*a^2*c^2)*x^2)/(c^3*(b^2 - 4*a*c)^3) + (x^7*(2*a + b*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3) + (x^5*(a*(b^2 - 14*a*c) + b*(b^2 - 9*a*c)*x))/(3*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) + (x^3*(4*a*(b^4 - 9*a*b^2*c + 35*a^2*c^2) + b*(4*b^4 - 39*a*b^2*c + 122*a^2*c^2)*x))/(3*c^2*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)) - (4*(b^8 - 14*a*b^6*c + 70*a^2*b^4*c^2 - 140*a^3*b^2*c^3 + 70*a^4*c^4)*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(c^5*(b^2 - 4*a*c)^(7/2)) - (2*b*log(a + b*x + c*x^2))/c^5]
    @test_int [x^7/(a + b*x + c*x^2)^4, x, 8, -((b*(b^4 - 11*a*b^2*c + 38*a^2*c^2)*x)/(c^3*(b^2 - 4*a*c)^3)) + (x^6*(2*a + b*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3) + (x^4*(a*(b^2 - 24*a*c) + b*(b^2 - 14*a*c)*x))/(6*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) + (x^2*(3*a*(b^4 - 10*a*b^2*c + 64*a^2*c^2) + b*(3*b^4 - 32*a*b^2*c + 140*a^2*c^2)*x))/(6*c^2*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)) + (b*(b^6 - 14*a*b^4*c + 70*a^2*b^2*c^2 - 140*a^3*c^3)*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(c^4*(b^2 - 4*a*c)^(7/2)) + log(a + b*x + c*x^2)/(2*c^4)]
    @test_int [x^6/(a + b*x + c*x^2)^4, x, 5, (x^5*(2*a + b*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3) - (5*a*x^3*(2*a + b*x))/(3*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) + (10*a^2*x*(2*a + b*x))/((b^2 - 4*a*c)^3*(a + b*x + c*x^2)) + (40*a^3*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(7/2)]
    @test_int [x^5/(a + b*x + c*x^2)^4, x, 5, -((x^5*(b + 2*c*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3)) + (5*b*x^3*(2*a + b*x))/(6*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) - (5*a*b*x*(2*a + b*x))/((b^2 - 4*a*c)^3*(a + b*x + c*x^2)) - (20*a^2*b*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(7/2)]
    @test_int [(d + e*x)^4/(a + b*x + c*x^2)^4, x, 5, -(((b + 2*c*x)*(d + e*x)^4)/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3)) + ((d + e*x)^3*(5*b*c*d - 2*b^2*e - 2*a*c*e + 5*c*(2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) - (2*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)^3*(a + b*x + c*x^2)) + (8*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(7/2)]
    @test_int [(d + e*x)^3/(a + b*x + c*x^2)^4, x, 5, -(((b + 2*c*x)*(d + e*x)^3)/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3)) + ((d + e*x)^2*(10*b*c*d - 3*b^2*e - 8*a*c*e + 10*c*(2*c*d - b*e)*x))/(6*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) - (3*b^3*d*e^2 - 16*a*c*e*(5*c*d^2 + a*e^2) + 6*b*c*d*(5*c*d^2 + 13*a*e^2) - b^2*(25*c*d^2*e + 11*a*e^3) + 2*(2*c*d - b*e)*(15*c^2*d^2 + 4*b^2*e^2 - c*e*(15*b*d + a*e))*x)/(3*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)) + (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(7/2)]
    @test_int [(d + e*x)^2/(a + b*x + c*x^2)^4, x, 5, -(((d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3)) - (3*b^2*d*e + 8*a*c*d*e - 5*b*(c*d^2 + a*e^2) - 2*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*x)/(3*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) - (2*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(b + 2*c*x))/((b^2 - 4*a*c)^3*(a + b*x + c*x^2)) + (8*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(7/2)]
    @test_int [(d + e*x)^1/(a + b*x + c*x^2)^4, x, 5, -((b*d - 2*a*e + (2*c*d - b*e)*x)/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3)) + (5*(2*c*d - b*e)*(b + 2*c*x))/(6*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) - (5*c*(2*c*d - b*e)*(b + 2*c*x))/((b^2 - 4*a*c)^3*(a + b*x + c*x^2)) + (20*c^2*(2*c*d - b*e)*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(7/2)]
    @test_int [(d + e*x)^0/(a + b*x + c*x^2)^4, x, 5, -((b + 2*c*x)/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^3)) + (5*c*(b + 2*c*x))/(3*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^2) - (10*c^2*(b + 2*c*x))/((b^2 - 4*a*c)^3*(a + b*x + c*x^2)) + (40*c^3*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(7/2)]
    @test_int [1/((d + e*x)^1*(a + b*x + c*x^2)^4), x, 9, -((b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x)/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^3)) - (5*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(10*c^2*d^2 - 3*b^2*e^2 - c*e*(5*b*d - 12*a*e)) - c*(2*c*d - b*e)*(10*c^2*d^2 - 3*b^2*e^2 - 2*c*e*(5*b*d - 11*a*e))*x)/(6*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)^2) + (1/(2*(b^2 - 4*a*c)^3*(c*d^2 - b*d*e + a*e^2)^3*(a + b*x + c*x^2)))*(b^5*c*d*e^4 + 2*b^6*e^5 - 64*a^3*c^3*e^5 + b^4*c*e^3*(c*d^2 - 23*a*e^2) - 2*b^3*c^2*d*e^2*(17*c*d^2 + 5*a*e^2) - 4*b*c^3*d*(5*c^2*d^4 + 16*a*c*d^2*e^2 + 19*a^2*e^4) + 2*b^2*c^2*e*(25*c^2*d^4 + 48*a*c*d^2*e^2 + 43*a^2*e^4) - 2*c*(2*c*d - b*e)*(10*c^4*d^4 + b^4*e^4 + b^2*c*e^3*(3*b*d - 11*a*e) - 4*c^3*d^2*e*(5*b*d - 8*a*e) + c^2*e^2*(7*b^2*d^2 - 32*a*b*d*e + 38*a^2*e^2))*x) + ((40*c^7*d^7 + b^7*e^7 - 14*a*b^5*c*e^7 + 70*a^2*b^3*c^2*e^7 - 140*a^3*b*c^3*e^7 - 28*c^6*d^5*e*(5*b*d - 6*a*e) + 28*c^5*d^3*e^2*(6*b^2*d^2 - 15*a*b*d*e + 10*a^2*e^2) - 70*c^4*d*e^3*(b^3*d^3 - 4*a*b^2*d^2*e + 6*a^2*b*d*e^2 - 4*a^3*e^3))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/((b^2 - 4*a*c)^(7/2)*(c*d^2 - b*d*e + a*e^2)^4) + (e^7*log(d + e*x))/(c*d^2 - b*d*e + a*e^2)^4 - (e^7*log(a + b*x + c*x^2))/(2*(c*d^2 - b*d*e + a*e^2)^4)]
    @test_int [1/(x^2*(a + b*x + c*x^2)^4), x, 9, -((4*(b^6 - 11*a*b^4*c + 38*a^2*b^2*c^2 - 35*a^3*c^3))/(a^4*(b^2 - 4*a*c)^3*x)) + (b^2 - 2*a*c + b*c*x)/(3*a*(b^2 - 4*a*c)*x*(a + b*x + c*x^2)^3) + (2*(b^4 - 7*a*b^2*c + 7*a^2*c^2) + b*c*(2*b^2 - 13*a*c)*x)/(3*a^2*(b^2 - 4*a*c)^2*x*(a + b*x + c*x^2)^2) + (2*(3*b^6 - 32*a*b^4*c + 105*a^2*b^2*c^2 - 70*a^3*c^3 + 3*b*c*(b^4 - 10*a*b^2*c + 29*a^2*c^2)*x))/(3*a^3*(b^2 - 4*a*c)^3*x*(a + b*x + c*x^2)) - (4*(b^8 - 14*a*b^6*c + 70*a^2*b^4*c^2 - 140*a^3*b^2*c^3 + 70*a^4*c^4)*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(a^5*(b^2 - 4*a*c)^(7/2)) - (4*b*log(x))/a^5 + (2*b*log(a + b*x + c*x^2))/a^5]

    @test_int [(d + e*x)^5/(a + b*x + c*x^2)^5, x, 6, -(((b + 2*c*x)*(d + e*x)^5)/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^4)) + ((d + e*x)^4*(14*b*c*d - 5*b^2*e - 8*a*c*e + 14*c*(2*c*d - b*e)*x))/(12*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^3) + ((d + e*x)^3*(63*b^2*c*d*e + 28*a*c^2*d*e - 10*b^3*e^2 - 10*b*c*(7*c*d^2 + 3*a*e^2) - c*(140*c^2*d^2 + 27*b^2*e^2 - 4*c*e*(35*b*d - 8*a*e))*x))/(12*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)^2) + (5*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)^4*(a + b*x + c*x^2)) - (10*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(9/2)]
    @test_int [(d + e*x)^4/(a + b*x + c*x^2)^5, x, 6, -(((b + 2*c*x)*(d + e*x)^4)/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^4)) + ((d + e*x)^3*(7*b*c*d - 2*b^2*e - 6*a*c*e + 7*c*(2*c*d - b*e)*x))/(6*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^3) + ((d + e*x)^2*(28*b^2*c*d*e + 28*a*c^2*d*e - 3*b^3*e^2 - b*c*(35*c*d^2 + 23*a*e^2) - c*(70*c^2*d^2 + 13*b^2*e^2 - 2*c*e*(35*b*d - 9*a*e))*x))/(6*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)^2) - (1/(6*(b^2 - 4*a*c)^4*(a + b*x + c*x^2)))*(6*b^4*d*e^3 + 16*a*c^2*d*e*(35*c*d^2 + 16*a*e^2) + 4*b^2*c*d*e*(70*c*d^2 + 83*a*e^2) - 5*b^3*(19*c*d^2*e^2 + 5*a*e^4) - 10*b*c*(21*c^2*d^4 + 88*a*c*d^2*e^2 + 11*a^2*e^4) - (420*c^4*d^4 + 19*b^4*e^4 - 40*c^3*d^2*e*(21*b*d - 2*a*e) - 38*b^2*c*e^3*(5*b*d - a*e) + 2*c^2*e^2*(305*b^2*d^2 - 40*a*b*d*e - 18*a^2*e^2))*x) - (2*(70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(9/2)]
    @test_int [(d + e*x)^3/(a + b*x + c*x^2)^5, x, 6, -(((b + 2*c*x)*(d + e*x)^3)/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^4)) + ((d + e*x)^2*(14*b*c*d - 3*b^2*e - 16*a*c*e + 14*c*(2*c*d - b*e)*x))/(12*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^3) - (3*b^3*d*e^2 - 32*a*c*e*(7*c*d^2 + a*e^2) + 2*b*c*d*(35*c*d^2 + 99*a*e^2) - b^2*(49*c*d^2*e + 27*a*e^3) + 2*(2*c*d - b*e)*(35*c^2*d^2 + 12*b^2*e^2 - c*e*(35*b*d + 13*a*e))*x)/(12*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)^2) + (5*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(b + 2*c*x))/(2*(b^2 - 4*a*c)^4*(a + b*x + c*x^2)) - (10*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(9/2)]
    @test_int [(d + e*x)^2/(a + b*x + c*x^2)^5, x, 6, -(((d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^4)) - (4*b^2*d*e + 12*a*c*d*e - 7*b*(c*d^2 + a*e^2) - (14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*x)/(6*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^3) - (5*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(b + 2*c*x))/(12*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)^2) + (5*c*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(b + 2*c*x))/(2*(b^2 - 4*a*c)^4*(a + b*x + c*x^2)) - (10*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(9/2)]
    @test_int [(d + e*x)^1/(a + b*x + c*x^2)^5, x, 6, -((b*d - 2*a*e + (2*c*d - b*e)*x)/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^4)) + (7*(2*c*d - b*e)*(b + 2*c*x))/(12*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^3) - (35*c*(2*c*d - b*e)*(b + 2*c*x))/(12*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)^2) + (35*c^2*(2*c*d - b*e)*(b + 2*c*x))/(2*(b^2 - 4*a*c)^4*(a + b*x + c*x^2)) - (70*c^3*(2*c*d - b*e)*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(9/2)]
    @test_int [(d + e*x)^0/(a + b*x + c*x^2)^5, x, 6, -((b + 2*c*x)/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^4)) + (7*c*(b + 2*c*x))/(6*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^3) - (35*c^2*(b + 2*c*x))/(6*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)^2) + (35*c^3*(b + 2*c*x))/((b^2 - 4*a*c)^4*(a + b*x + c*x^2)) - (140*c^4*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c)))/(b^2 - 4*a*c)^(9/2)]
    @test_int [1/((d + e*x)^1*(a + b*x + c*x^2)^5), x, 10, -((b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x)/(4*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^4)) - (7*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(14*c^2*d^2 - 4*b^2*e^2 - c*e*(7*b*d - 16*a*e)) - 2*c*(2*c*d - b*e)*(7*c^2*d^2 - 2*b^2*e^2 - c*e*(7*b*d - 15*a*e))*x)/(12*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)^3) + (1/(12*(b^2 - 4*a*c)^3*(c*d^2 - b*d*e + a*e^2)^3*(a + b*x + c*x^2)^2))*(5*a*c*e*(2*c*d - b*e)^2*(7*c^2*d^2 - 2*b^2*e^2 - c*e*(7*b*d - 15*a*e)) - (b*c*d - b^2*e + 2*a*c*e)*(70*c^4*d^4 + 6*b^4*e^4 + 2*b^2*c*e^3*(5*b*d - 24*a*e) - 15*c^3*d^2*e*(7*b*d - 10*a*e) + 3*c^2*e^2*(5*b^2*d^2 - 25*a*b*d*e + 32*a^2*e^2)) - 2*c*(2*c*d - b*e)*(35*c^4*d^4 + 3*b^4*e^4 + 2*b^2*c*e^3*(5*b*d - 17*a*e) - 10*c^3*d^2*e*(7*b*d - 11*a*e) + c^2*e^2*(25*b^2*d^2 - 110*a*b*d*e + 123*a^2*e^2))*x) + (1/(2*(b^2 - 4*a*c)^4*(c*d^2 - b*d*e + a*e^2)^4*(a + b*x + c*x^2)))*(b^7*c*d*e^6 + 2*b^8*e^7 + 256*a^4*c^4*e^7 + b^6*c*e^5*(c*d^2 - 31*a*e^2) + b^5*c^2*d*e^4*(c*d^2 - 14*a*e^2) - b^4*c^2*e^3*(125*c^2*d^4 + 13*a*c*d^2*e^2 - 178*a^2*e^4) + b^3*c^3*d*e^2*(295*c^2*d^4 + 492*a*c*d^2*e^2 + 69*a^2*e^4) + 2*b*c^4*d*(35*c^3*d^6 + 145*a*c^2*d^4*e^2 + 233*a^2*c*d^2*e^4 + 187*a^3*e^6) - b^2*c^3*e*(245*c^3*d^6 + 725*a*c^2*d^4*e^2 + 699*a^2*c*d^2*e^4 + 443*a^3*e^6) + 2*c*(2*c*d - b*e)*(35*c^6*d^6 - b^6*e^6 - 5*c^5*d^4*e*(21*b*d - 29*a*e) - 3*b^4*c*e^5*(b*d - 5*a*e) - b^2*c^2*e^4*(7*b^2*d^2 - 44*a*b*d*e + 82*a^2*e^2) + c^4*d^2*e^2*(95*b^2*d^2 - 290*a*b*d*e + 233*a^2*e^2) - c^3*e^3*(15*b^3*d^3 - 101*a*b^2*d^2*e + 233*a^2*b*d*e^2 - 187*a^3*e^3))*x) - (1/((b^2 - 4*a*c)^(9/2)*(c*d^2 - e*(b*d - a*e))^5))*((140*c^9*d^9 - b^9*e^9 + 18*a*b^7*c*e^9 - 126*a^2*b^5*c^2*e^9 + 420*a^3*b^3*c^3*e^9 - 630*a^4*b*c^4*e^9 - 90*c^8*d^7*e*(7*b*d - 8*a*e) + 72*c^7*d^5*e^2*(15*b^2*d^2 - 35*a*b*d*e + 21*a^2*e^2) - 84*c^6*d^3*e^3*(10*b^3*d^3 - 36*a*b^2*d^2*e + 45*a^2*b*d*e^2 - 20*a^3*e^3) + 252*c^5*d*e^4*(b^4*d^4 - 5*a*b^3*d^3*e + 10*a^2*b^2*d^2*e^2 - 10*a^3*b*d*e^3 + 5*a^4*e^4))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c))) + (e^9*log(d + e*x))/(c*d^2 - b*d*e + a*e^2)^5 - (e^9*log(a + b*x + c*x^2))/(2*(c*d^2 - b*d*e + a*e^2)^5)]
    @test_int [1/((d + e*x)^2*(a + b*x + c*x^2)^5), x, 10, (1/((b^2 - 4*a*c)^4*(c*d^2 - b*d*e + a*e^2)^5*(d + e*x)))*(5*e*(14*c^8*d^8 - b^8*e^8 - 4*c^7*d^6*e*(14*b*d - 19*a*e) + b^6*c*e^7*(b*d + 15*a*e) + b^4*c^2*e^6*(b^2*d^2 - 16*a*b*d*e - 82*a^2*e^2) + c^6*d^4*e^2*(79*b^2*d^2 - 228*a*b*d*e + 176*a^2*e^2) - c^5*d^2*e^3*(41*b^3*d^3 - 197*a*b^2*d^2*e + 352*a^2*b*d*e^2 - 244*a^3*e^3) + b^2*c^3*e^5*(b^3*d^3 - 15*a*b^2*d^2*e + 95*a^2*b*d*e^2 + 187*a^3*e^3) + c^4*e^4*(b^4*d^4 - 14*a*b^3*d^3*e + 81*a^2*b^2*d^2*e^2 - 244*a^3*b*d*e^3 - 126*a^4*e^4))) - (b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x)/(4*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*(a + b*x + c*x^2)^4) - (8*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(14*c^2*d^2 - 5*b^2*e^2 - 6*c*e*(b*d - 3*a*e)) - c*(2*c*d - b*e)*(14*c^2*d^2 - 5*b^2*e^2 - 2*c*e*(7*b*d - 17*a*e))*x)/(12*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)*(a + b*x + c*x^2)^3) + (1/(12*(b^2 - 4*a*c)^3*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)*(a + b*x + c*x^2)^2))*(3*a*c*e*(2*c*d - b*e)^2*(14*c^2*d^2 - 5*b^2*e^2 - 2*c*e*(7*b*d - 17*a*e)) - (b*c*d - b^2*e + 2*a*c*e)*(70*c^4*d^4 + 10*b^4*e^4 - 2*c^3*d^2*e*(49*b*d - 78*a*e) + 5*b^2*c*e^3*(2*b*d - 15*a*e) + 3*c^2*e^2*(b^2*d^2 - 18*a*b*d*e + 42*a^2*e^2)) - 5*c*(2*c*d - b*e)*(14*c^4*d^4 + 2*b^4*e^4 + b^2*c*e^3*(5*b*d - 21*a*e) - 4*c^3*d^2*e*(7*b*d - 12*a*e) + 3*c^2*e^2*(3*b^2*d^2 - 16*a*b*d*e + 22*a^2*e^2))*x) - (1/(6*(b^2 - 4*a*c)^4*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)*(a + b*x + c*x^2)))*(5*(2*a*c*e*(2*c*d - b*e)^2*(14*c^4*d^4 + 2*b^4*e^4 + b^2*c*e^3*(5*b*d - 21*a*e) - 4*c^3*d^2*e*(7*b*d - 12*a*e) + 3*c^2*e^2*(3*b^2*d^2 - 16*a*b*d*e + 22*a^2*e^2)) - (b*c*d - b^2*e + 2*a*c*e)*(42*c^6*d^6 - 3*b^6*e^6 - 2*c^5*d^4*e*(49*b*d - 65*a*e) - 2*b^4*c*e^5*(b*d - 17*a*e) + b^2*c^2*e^4*(b^2*d^2 + 16*a*b*d*e - 123*a^2*e^2) + c^4*d^2*e^2*(55*b^2*d^2 - 164*a*b*d*e + 150*a^2*e^2) + 6*c^3*e^3*(b^3*d^3 - 4*a*b^2*d^2*e - 3*a^2*b*d*e^2 + 21*a^3*e^3)) - 3*c*(2*c*d - b*e)*(14*c^6*d^6 - b^6*e^6 - 2*c^5*d^4*e*(21*b*d - 31*a*e) - 2*b^4*c*e^5*(b*d - 7*a*e) - b^2*c^2*e^4*(3*b^2*d^2 - 26*a*b*d*e + 69*a^2*e^2) + c^4*d^2*e^2*(37*b^2*d^2 - 124*a*b*d*e + 114*a^2*e^2) - 2*c^3*e^3*(2*b^3*d^3 - 18*a*b^2*d^2*e + 57*a^2*b*d*e^2 - 65*a^3*e^3))*x)) - (1/((b^2 - 4*a*c)^(9/2)*(c*d^2 - e*(b*d - a*e))^6))*(5*(28*c^10*d^10 + b^10*e^10 - 20*c^9*d^8*e*(7*b*d - 9*a*e) - 252*a^4*c^5*e^9*(5*b*d + a*e) + 210*a^3*b^2*c^4*e^9*(4*b*d + 3*a*e) - 84*a^2*b^4*c^3*e^9*(3*b*d + 5*a*e) + 18*a*b^6*c^2*e^9*(2*b*d + 7*a*e) - 2*b^8*c*e^9*(b*d + 9*a*e) + 18*c^8*d^6*e^2*(15*b^2*d^2 - 40*a*b*d*e + 28*a^2*e^2) - 24*c^7*d^4*e^3*(10*b^3*d^3 - 42*a*b^2*d^2*e + 63*a^2*b*d*e^2 - 35*a^3*e^3) + 84*c^6*d^2*e^4*(b^4*d^4 - 6*a*b^3*d^3*e + 15*a^2*b^2*d^2*e^2 - 20*a^3*b*d*e^3 + 15*a^4*e^4))*atanh((b + 2*c*x)/sqrt(b^2 - 4*a*c))) + (5*e^9*(2*c*d - b*e)*log(d + e*x))/(c*d^2 - b*d*e + a*e^2)^6 - (5*e^9*(2*c*d - b*e)*log(a + b*x + c*x^2))/(2*(c*d^2 - b*d*e + a*e^2)^6)]

    @test_int [1/((1 + 2*x)^1*(2 + 3*x + 5*x^2)^3), x, 8, (37 + 20*x)/(434*(2 + 3*x + 5*x^2)^2) + (2*(2609 + 2290*x))/(47089*(2 + 3*x + 5*x^2)) + (125624*atan((3 + 10*x)/sqrt(31)))/(329623*sqrt(31)) + (32/343)*log(1 + 2*x) - (16/343)*log(2 + 3*x + 5*x^2)]
    @test_int [1/((1 + 2*x)^2*(2 + 3*x + 5*x^2)^3), x, 8, -(51516/(329623*(1 + 2*x))) + (37 + 20*x)/(434*(1 + 2*x)*(2 + 3*x + 5*x^2)^2) + (6427 + 5820*x)/(47089*(1 + 2*x)*(2 + 3*x + 5*x^2)) - (1065012*atan((3 + 10*x)/sqrt(31)))/(2307361*sqrt(31)) + (384*log(1 + 2*x))/2401 - (192*log(2 + 3*x + 5*x^2))/2401]

    @test_int [1/((1 + 2*x)^1*(2 + 3*x + 5*x^2)^4), x, 9, (37 + 20*x)/(651*(2 + 3*x + 5*x^2)^3) + (4*(1983 + 1805*x))/(141267*(2 + 3*x + 5*x^2)^2) + (4*(180133 + 203230*x))/(10218313*(2 + 3*x + 5*x^2)) + (19007376*atan((3 + 10*x)/sqrt(31)))/(71528191*sqrt(31)) + (128*log(1 + 2*x))/2401 - (64*log(2 + 3*x + 5*x^2))/2401]
    @test_int [1/((1 + 2*x)^2*(2 + 3*x + 5*x^2)^4), x, 9, -(6802312/(71528191*(1 + 2*x))) + (37 + 20*x)/(651*(1 + 2*x)*(2 + 3*x + 5*x^2)^3) + (3047 + 2820*x)/(47089*(1 + 2*x)*(2 + 3*x + 5*x^2)^2) + (2*(504757 + 603620*x))/(10218313*(1 + 2*x)*(2 + 3*x + 5*x^2)) - (116056984*atan((3 + 10*x)/sqrt(31)))/(500697337*sqrt(31)) + (2048*log(1 + 2*x))/16807 - (1024*log(2 + 3*x + 5*x^2))/16807]

    @test_int [(7 - 3*x)/(-5 + 2*x + x^2), x, 3, (-(1/6))*(9 - 5*sqrt(6))*log(1 - sqrt(6) + x) - (1/6)*(9 + 5*sqrt(6))*log(1 + sqrt(6) + x)]
    @test_int [1/((-1 + x)*(1 + x + x^2)), x, 6, -(atan((1 + 2*x)/sqrt(3))/sqrt(3)) + (1/3)*log(1 - x) - (1/6)*log(1 + x + x^2)]

    @test_int [(2*((a/b)^(1/n) - x*cos(((-1 + 2*k)*pi)/n)))/((a/b)^(2/n) + x^2 - 2*(a/b)^(1/n)*x*cos(((-1 + 2*k)*pi)/n)), x, 5, (-cos((pi - 2*k*pi)/n))*log((a/b)^(2/n) + x^2 - 2*(a/b)^(1/n)*x*cos((pi - 2*k*pi)/n)) + 2*atan(((x - (a/b)^(1/n)*cos((pi - 2*k*pi)/n))*csc((pi - 2*k*pi)/n))/(a/b)^n^(-1))*sin((pi - 2*k*pi)/n)]

    @test_int [x^4/(2 + 13*x + 15*x^2), x, 5, (139*x)/3375 - (13*x^2)/450 + x^3/45 - (16/567)*log(2 + 3*x) + log(1 + 5*x)/4375]
    @test_int [x^3/(2 + 13*x + 15*x^2), x, 5, -((13*x)/225) + x^2/30 + (8/189)*log(2 + 3*x) - (1/875)*log(1 + 5*x)]
    @test_int [x^2/(2 + 13*x + 15*x^2), x, 4, x/15 - (4/63)*log(2 + 3*x) + (1/175)*log(1 + 5*x)]
    @test_int [x^1/(2 + 13*x + 15*x^2), x, 3, (2/21)*log(2 + 3*x) - (1/35)*log(1 + 5*x)]
    @test_int [x^0/(2 + 13*x + 15*x^2), x, 3, (-(1/7))*log(2 + 3*x) + (1/7)*log(1 + 5*x)]
    @test_int [1/(x^1*(2 + 13*x + 15*x^2)), x, 5, log(x)/2 + (3/14)*log(2 + 3*x) - (5/7)*log(1 + 5*x)]
    @test_int [1/(x^2*(2 + 13*x + 15*x^2)), x, 3, -(1/(2*x)) - (13*log(x))/4 - (9/28)*log(2 + 3*x) + (25/7)*log(1 + 5*x)]
    @test_int [1/(x^3*(2 + 13*x + 15*x^2)), x, 3, -(1/(4*x^2)) + 13/(4*x) + (139*log(x))/8 + (27/56)*log(2 + 3*x) - (125/7)*log(1 + 5*x)]
    @test_int [1/(x^4*(2 + 13*x + 15*x^2)), x, 3, -(1/(6*x^3)) + 13/(8*x^2) - 139/(8*x) - (1417*log(x))/16 - (81/112)*log(2 + 3*x) + (625/7)*log(1 + 5*x)]

    @test_int [x^5/(2*x + 13*x^2 + 15*x^3), x, 6, (139*x)/3375 - (13*x^2)/450 + x^3/45 - (16/567)*log(2 + 3*x) + log(1 + 5*x)/4375]
    @test_int [x^4/(2*x + 13*x^2 + 15*x^3), x, 6, -((13*x)/225) + x^2/30 + (8/189)*log(2 + 3*x) - (1/875)*log(1 + 5*x)]
    @test_int [x^3/(2*x + 13*x^2 + 15*x^3), x, 5, x/15 - (4/63)*log(2 + 3*x) + (1/175)*log(1 + 5*x)]
    @test_int [x^2/(2*x + 13*x^2 + 15*x^3), x, 4, (2/21)*log(2 + 3*x) - (1/35)*log(1 + 5*x)]
    @test_int [x/(2*x + 13*x^2 + 15*x^3), x, 4, (-(1/7))*log(2 + 3*x) + (1/7)*log(1 + 5*x)]
    @test_int [1/(2*x + 13*x^2 + 15*x^3), x, 6, log(x)/2 + (3/14)*log(2 + 3*x) - (5/7)*log(1 + 5*x)]
    @test_int [1/(x*(2*x + 13*x^2 + 15*x^3)), x, 4, -(1/(2*x)) - (13*log(x))/4 - (9/28)*log(2 + 3*x) + (25/7)*log(1 + 5*x)]
    @test_int [1/(x^2*(2*x + 13*x^2 + 15*x^3)), x, 4, -(1/(4*x^2)) + 13/(4*x) + (139*log(x))/8 + (27/56)*log(2 + 3*x) - (125/7)*log(1 + 5*x)]
    @test_int [1/(x^3*(2*x + 13*x^2 + 15*x^3)), x, 4, -(1/(6*x^3)) + 13/(8*x^2) - 139/(8*x) - (1417*log(x))/16 - (81/112)*log(2 + 3*x) + (625/7)*log(1 + 5*x)]

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

    @test_int [x^2/(1 + x + x^2), x, 5, x - atan((1 + 2*x)/sqrt(3))/sqrt(3) - log(1 + x + x^2)/2]
    @test_int [x^2/(2 - 3*x + x^2), x, 4, x - log(1 - x) + 4*log(2 - x)]
    @test_int [x^2/(-6 + x + x^2), x, 4, x + (4/5)*log(2 - x) - (9/5)*log(3 + x)]
    @test_int [x^2/(2 + 2*x + x^2)^2, x, 3, (2 + 2*x + x^2)^(-1) + atan(1 + x), -((x*(2 + x))/(2*(2 + 2*x + x^2))) + atan(1 + x)]

    @test_int [x^3/(2 - 3*x + x^2), x, 5, 3*x + x^2/2 - log(1 - x) + 8*log(2 - x)]
    @test_int [x^3/(1 + 2*x + x^2), x, 3, -2*x + x^2/2 + 1/(1 + x) + 3*log(1 + x)]
    @test_int [x^3/(1 - 2*x + x^2), x, 3, 1/(1 - x) + 2*x + x^2/2 + 3*log(1 - x)]

    @test_int [x^4/(4 + 4*x + x^2), x, 3, 12*x - 2*x^2 + x^3/3 - 16/(2 + x) - 32*log(2 + x)]

    @test_int [1/(x*(1 + x + x^2)), x, 6, -(atan((1 + 2*x)/sqrt(3))/sqrt(3)) + log(x) - log(1 + x + x^2)/2]

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

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

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

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

    @test_int [(d + e*x)^(5/2)*(a + b*x + c*x^2)^3, x, 2, (2*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(7/2))/(7*e^7) - (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(9/2))/(3*e^7) + (6*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(11/2))/(11*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(13/2))/(13*e^7) + (2*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(15/2))/(5*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(17/2))/(17*e^7) + (2*c^3*(d + e*x)^(19/2))/(19*e^7)]
    @test_int [(d + e*x)^(3/2)*(a + b*x + c*x^2)^3, x, 2, (2*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(5/2))/(5*e^7) - (6*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(7/2))/(7*e^7) + (2*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(9/2))/(3*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(11/2))/(11*e^7) + (6*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(13/2))/(13*e^7) - (2*c^2*(2*c*d - b*e)*(d + e*x)^(15/2))/(5*e^7) + (2*c^3*(d + e*x)^(17/2))/(17*e^7)]
    @test_int [sqrt(d + e*x)*(a + b*x + c*x^2)^3, x, 2, (2*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(3/2))/(3*e^7) - (6*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(5/2))/(5*e^7) + (6*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(7/2))/(7*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(9/2))/(9*e^7) + (6*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(11/2))/(11*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(13/2))/(13*e^7) + (2*c^3*(d + e*x)^(15/2))/(15*e^7)]
    @test_int [(a + b*x + c*x^2)^3/sqrt(d + e*x), x, 2, (2*(c*d^2 - b*d*e + a*e^2)^3*sqrt(d + e*x))/e^7 - (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(3/2))/e^7 + (6*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(5/2))/(5*e^7) - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(7/2))/(7*e^7) + (2*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(9/2))/(3*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(11/2))/(11*e^7) + (2*c^3*(d + e*x)^(13/2))/(13*e^7)]
    @test_int [(a + b*x + c*x^2)^3/(d + e*x)^(3/2), x, 2, -((2*(c*d^2 - b*d*e + a*e^2)^3)/(e^7*sqrt(d + e*x))) - (6*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*sqrt(d + e*x))/e^7 + (2*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(3/2))/e^7 - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(5/2))/(5*e^7) + (6*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(7/2))/(7*e^7) - (2*c^2*(2*c*d - b*e)*(d + e*x)^(9/2))/(3*e^7) + (2*c^3*(d + e*x)^(11/2))/(11*e^7)]
    @test_int [(a + b*x + c*x^2)^3/(d + e*x)^(5/2), x, 2, -((2*(c*d^2 - b*d*e + a*e^2)^3)/(3*e^7*(d + e*x)^(3/2))) + (6*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(e^7*sqrt(d + e*x)) + (6*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*sqrt(d + e*x))/e^7 - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(3/2))/(3*e^7) + (6*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(5/2))/(5*e^7) - (6*c^2*(2*c*d - b*e)*(d + e*x)^(7/2))/(7*e^7) + (2*c^3*(d + e*x)^(9/2))/(9*e^7)]
    @test_int [(a + b*x + c*x^2)^3/(d + e*x)^(7/2), x, 2, -((2*(c*d^2 - b*d*e + a*e^2)^3)/(5*e^7*(d + e*x)^(5/2))) + (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(e^7*(d + e*x)^(3/2)) - (6*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(e^7*sqrt(d + e*x)) - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*sqrt(d + e*x))/e^7 + (2*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(3/2))/e^7 - (6*c^2*(2*c*d - b*e)*(d + e*x)^(5/2))/(5*e^7) + (2*c^3*(d + e*x)^(7/2))/(7*e^7)]

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

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

    @test_int [(d + e*x)^(7/2)/(a + b*x + c*x^2)^2, x, 7, (e*(2*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(b*d + 5*a*e))*sqrt(d + e*x))/(c^2*(b^2 - 4*a*c)) + (e*(2*c*d - b*e)*(d + e*x)^(3/2))/(c*(b^2 - 4*a*c)) - ((d + e*x)^(5/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + ((8*c^4*d^4 - 3*b^3*(b - sqrt(b^2 - 4*a*c))*e^4 - 2*c^3*d^2*e*(8*b*d - sqrt(b^2 - 4*a*c)*d - 18*a*e) + b*c*e^3*(5*b^2*d - 5*b*sqrt(b^2 - 4*a*c)*d + 19*a*b*e - 13*a*sqrt(b^2 - 4*a*c)*e) + c^2*e^2*(3*b^2*d^2 + 2*a*e*(13*sqrt(b^2 - 4*a*c)*d - 10*a*e) - 3*b*d*(sqrt(b^2 - 4*a*c)*d + 12*a*e)))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)))/(sqrt(2)*c^(5/2)*(b^2 - 4*a*c)^(3/2)*sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)) - ((8*c^4*d^4 - 3*b^3*(b + sqrt(b^2 - 4*a*c))*e^4 - 2*c^3*d^2*e*(8*b*d + sqrt(b^2 - 4*a*c)*d - 18*a*e) + b*c*e^3*(5*b^2*d + 5*b*sqrt(b^2 - 4*a*c)*d + 19*a*b*e + 13*a*sqrt(b^2 - 4*a*c)*e) + c^2*e^2*(3*b^2*d^2 + 3*b*d*(sqrt(b^2 - 4*a*c)*d - 12*a*e) - 2*a*e*(13*sqrt(b^2 - 4*a*c)*d + 10*a*e)))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(sqrt(2)*c^(5/2)*(b^2 - 4*a*c)^(3/2)*sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))]
    @test_int [(d + e*x)^(5/2)/(a + b*x + c*x^2)^2, x, 6, (e*(2*c*d - b*e)*sqrt(d + e*x))/(c*(b^2 - 4*a*c)) - ((d + e*x)^(3/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + ((8*c^3*d^3 + b^2*(b - sqrt(b^2 - 4*a*c))*e^3 - 2*c^2*d*e*(6*b*d - sqrt(b^2 - 4*a*c)*d - 8*a*e) + 2*c*e^2*(b^2*d + 3*a*sqrt(b^2 - 4*a*c)*e - b*(sqrt(b^2 - 4*a*c)*d + 4*a*e)))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)))/(sqrt(2)*c^(3/2)*(b^2 - 4*a*c)^(3/2)*sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)) - ((8*c^3*d^3 + b^2*(b + sqrt(b^2 - 4*a*c))*e^3 - 2*c^2*d*e*(6*b*d + sqrt(b^2 - 4*a*c)*d - 8*a*e) + 2*c*e^2*(b^2*d + b*sqrt(b^2 - 4*a*c)*d - 4*a*b*e - 3*a*sqrt(b^2 - 4*a*c)*e))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(sqrt(2)*c^(3/2)*(b^2 - 4*a*c)^(3/2)*sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))]
    @test_int [(d + e*x)^(3/2)/(a + b*x + c*x^2)^2, x, 5, -((sqrt(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2))) + ((8*c^2*d^2 + b*(b - sqrt(b^2 - 4*a*c))*e^2 - 2*c*e*(4*b*d - sqrt(b^2 - 4*a*c)*d - 2*a*e))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)))/(sqrt(2)*sqrt(c)*(b^2 - 4*a*c)^(3/2)*sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)) - ((8*c^2*d^2 + b*(b + sqrt(b^2 - 4*a*c))*e^2 - 2*c*e*(4*b*d + sqrt(b^2 - 4*a*c)*d - 2*a*e))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(sqrt(2)*sqrt(c)*(b^2 - 4*a*c)^(3/2)*sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))]
    @test_int [(d + e*x)^(1/2)/(a + b*x + c*x^2)^2, x, 5, -(((b + 2*c*x)*sqrt(d + e*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2))) + (sqrt(2)*sqrt(c)*(4*c*d - (2*b - sqrt(b^2 - 4*a*c))*e)*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)))/((b^2 - 4*a*c)^(3/2)*sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)) - (sqrt(2)*sqrt(c)*(4*c*d - (2*b + sqrt(b^2 - 4*a*c))*e)*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/((b^2 - 4*a*c)^(3/2)*sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))]
    @test_int [1/((d + e*x)^(1/2)*(a + b*x + c*x^2)^2), x, 5, -((sqrt(d + e*x)*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2))) + (sqrt(c)*(8*c^2*d^2 - b*(b + sqrt(b^2 - 4*a*c))*e^2 - 2*c*e*(4*b*d - sqrt(b^2 - 4*a*c)*d - 6*a*e))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)))/(sqrt(2)*(b^2 - 4*a*c)^(3/2)*sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*(c*d^2 - b*d*e + a*e^2)) - (sqrt(c)*(8*c^2*d^2 - b*(b - sqrt(b^2 - 4*a*c))*e^2 - 2*c*e*(4*b*d + sqrt(b^2 - 4*a*c)*d - 6*a*e))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(sqrt(2)*(b^2 - 4*a*c)^(3/2)*sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*(c*d^2 - b*d*e + a*e^2))]
    @test_int [1/((d + e*x)^(3/2)*(a + b*x + c*x^2)^2), x, 6, -((e*(2*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(b*d + 5*a*e)))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*sqrt(d + e*x))) - (b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x)/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*sqrt(d + e*x)*(a + b*x + c*x^2)) + (sqrt(c)*(8*c^3*d^3 + 3*b^2*(b + sqrt(b^2 - 4*a*c))*e^3 - 2*c^2*d*e*(6*b*d - sqrt(b^2 - 4*a*c)*d - 16*a*e) - 2*c*e^2*(b^2*d + b*sqrt(b^2 - 4*a*c)*d + 8*a*b*e + 5*a*sqrt(b^2 - 4*a*c)*e))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)))/(sqrt(2)*(b^2 - 4*a*c)^(3/2)*sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*(c*d^2 - b*d*e + a*e^2)^2) - (sqrt(c)*(8*c^3*d^3 + 3*b^2*(b - sqrt(b^2 - 4*a*c))*e^3 - 2*c^2*d*e*(6*b*d + sqrt(b^2 - 4*a*c)*d - 16*a*e) - 2*c*e^2*(b^2*d - b*sqrt(b^2 - 4*a*c)*d + 8*a*b*e - 5*a*sqrt(b^2 - 4*a*c)*e))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(sqrt(2)*(b^2 - 4*a*c)^(3/2)*sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*(c*d^2 - b*d*e + a*e^2)^2)]
    @test_int [1/(x^(5/2)*(a + b*x + c*x^2)^2), x, 7, -((5*b^2 - 14*a*c)/(3*a^2*(b^2 - 4*a*c)*x^(3/2))) + (b*(5*b^2 - 19*a*c))/(a^3*(b^2 - 4*a*c)*sqrt(x)) + (b^2 - 2*a*c + b*c*x)/(a*(b^2 - 4*a*c)*x^(3/2)*(a + b*x + c*x^2)) + (sqrt(c)*(5*b^4 - 29*a*b^2*c + 28*a^2*c^2 + b*(5*b^2 - 19*a*c)*sqrt(b^2 - 4*a*c))*atan((sqrt(2)*sqrt(c)*sqrt(x))/sqrt(b - sqrt(b^2 - 4*a*c))))/(sqrt(2)*a^3*(b^2 - 4*a*c)^(3/2)*sqrt(b - sqrt(b^2 - 4*a*c))) - (sqrt(c)*(5*b^4 - 29*a*b^2*c + 28*a^2*c^2 - b*(5*b^2 - 19*a*c)*sqrt(b^2 - 4*a*c))*atan((sqrt(2)*sqrt(c)*sqrt(x))/sqrt(b + sqrt(b^2 - 4*a*c))))/(sqrt(2)*a^3*(b^2 - 4*a*c)^(3/2)*sqrt(b + sqrt(b^2 - 4*a*c)))]

    @test_int [(d + e*x)^(7/2)/(a + b*x + c*x^2)^3, x, 6, -(((d + e*x)^(5/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2)) + (sqrt(d + e*x)*(12*b*c*d*(c*d^2 + 3*a*e^2) - 4*a*c*e*(7*c*d^2 + 5*a*e^2) - b^2*(11*c*d^2*e + a*e^3) + (2*c*d - b*e)*(12*c^2*d^2 + b^2*e^2 - 4*c*e*(3*b*d - 2*a*e))*x))/(4*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - ((96*c^4*d^4 - b^3*(b - sqrt(b^2 - 4*a*c))*e^4 - 8*c^3*d^2*e*(24*b*d - 3*sqrt(b^2 - 4*a*c)*d - 19*a*e) - 2*b*c*e^3*(5*b^2*d - 5*b*sqrt(b^2 - 4*a*c)*d - 9*a*b*e + 8*a*sqrt(b^2 - 4*a*c)*e) + 2*c^2*e^2*(53*b^2*d^2 + 4*a*e*(4*sqrt(b^2 - 4*a*c)*d + 5*a*e) - 2*b*d*(9*sqrt(b^2 - 4*a*c)*d + 38*a*e)))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)))/(4*sqrt(2)*c^(3/2)*(b^2 - 4*a*c)^(5/2)*sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)) + ((96*c^4*d^4 - b^3*(b + sqrt(b^2 - 4*a*c))*e^4 - 8*c^3*d^2*e*(24*b*d + 3*sqrt(b^2 - 4*a*c)*d - 19*a*e) - 2*b*c*e^3*(5*b^2*d + 5*b*sqrt(b^2 - 4*a*c)*d - 9*a*b*e - 8*a*sqrt(b^2 - 4*a*c)*e) + 2*c^2*e^2*(53*b^2*d^2 + 2*b*d*(9*sqrt(b^2 - 4*a*c)*d - 38*a*e) - 4*a*e*(4*sqrt(b^2 - 4*a*c)*d - 5*a*e)))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(4*sqrt(2)*c^(3/2)*(b^2 - 4*a*c)^(5/2)*sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))]
    @test_int [(d + e*x)^(5/2)/(a + b*x + c*x^2)^3, x, 6, -(((d + e*x)^(3/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2)) - (3*sqrt(d + e*x)*(3*b^2*d*e + 4*a*c*d*e - 4*b*(c*d^2 + a*e^2) - (8*c^2*d^2 + b^2*e^2 - 4*c*e*(2*b*d - a*e))*x))/(4*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (3*(32*c^3*d^3 - b^2*(b - sqrt(b^2 - 4*a*c))*e^3 - 8*c^2*d*e*(6*b*d - sqrt(b^2 - 4*a*c)*d - 3*a*e) + 2*c*e^2*(9*b^2*d - 4*b*sqrt(b^2 - 4*a*c)*d - 6*a*b*e + 2*a*sqrt(b^2 - 4*a*c)*e))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)))/(4*sqrt(2)*sqrt(c)*(b^2 - 4*a*c)^(5/2)*sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)) + (3*(32*c^3*d^3 - b^2*(b + sqrt(b^2 - 4*a*c))*e^3 - 8*c^2*d*e*(6*b*d + sqrt(b^2 - 4*a*c)*d - 3*a*e) + 2*c*e^2*(9*b^2*d + 4*b*sqrt(b^2 - 4*a*c)*d - 6*a*b*e - 2*a*sqrt(b^2 - 4*a*c)*e))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(4*sqrt(2)*sqrt(c)*(b^2 - 4*a*c)^(5/2)*sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))]
    @test_int [(d + e*x)^(3/2)/(a + b*x + c*x^2)^3, x, 6, -((sqrt(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2)) + (sqrt(d + e*x)*(12*b*c*d - 7*b^2*e + 4*a*c*e + 12*c*(2*c*d - b*e)*x))/(4*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (3*sqrt(c)*(16*c^2*d^2 + b*(3*b - 2*sqrt(b^2 - 4*a*c))*e^2 - 4*c*e*(4*b*d - sqrt(b^2 - 4*a*c)*d - a*e))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)))/(2*sqrt(2)*(b^2 - 4*a*c)^(5/2)*sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)) + (3*sqrt(c)*(16*c^2*d^2 + b*(3*b + 2*sqrt(b^2 - 4*a*c))*e^2 - 4*c*e*(4*b*d + sqrt(b^2 - 4*a*c)*d - a*e))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(2*sqrt(2)*(b^2 - 4*a*c)^(5/2)*sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))]
    @test_int [(d + e*x)^(1/2)/(a + b*x + c*x^2)^3, x, 6, -(((b + 2*c*x)*sqrt(d + e*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2)) - (sqrt(d + e*x)*(13*b^2*c*d*e - 4*a*c^2*d*e - b^3*e^2 - 4*b*c*(3*c*d^2 + 2*a*e^2) - c*(24*c^2*d^2 + b^2*e^2 - 4*c*e*(6*b*d - 5*a*e))*x))/(4*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)) - (sqrt(c)*(96*c^3*d^3 + b^2*(b + sqrt(b^2 - 4*a*c))*e^3 - 8*c^2*d*e*(18*b*d - 3*sqrt(b^2 - 4*a*c)*d - 13*a*e) + 2*c*e^2*(23*b^2*d + 10*a*sqrt(b^2 - 4*a*c)*e - 2*b*(6*sqrt(b^2 - 4*a*c)*d + 13*a*e)))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)))/(4*sqrt(2)*(b^2 - 4*a*c)^(5/2)*sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*(c*d^2 - b*d*e + a*e^2)) + (sqrt(c)*(96*c^3*d^3 + b^2*(b - sqrt(b^2 - 4*a*c))*e^3 - 8*c^2*d*e*(18*b*d + 3*sqrt(b^2 - 4*a*c)*d - 13*a*e) + 2*c*e^2*(23*b^2*d + 12*b*sqrt(b^2 - 4*a*c)*d - 26*a*b*e - 10*a*sqrt(b^2 - 4*a*c)*e))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(4*sqrt(2)*(b^2 - 4*a*c)^(5/2)*sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*(c*d^2 - b*d*e + a*e^2))]
    @test_int [1/((d + e*x)^(1/2)*(a + b*x + c*x^2)^3), x, 6, If(13>=8, -((sqrt(d + e*x)*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^2)) - (sqrt(d + e*x)*(5*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(12*c^2*d^2 - 3*b^2*e^2 - 7*c*e*(b*d - 2*a*e)) - 3*c*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*x))/(4*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)) - (3*sqrt(c)*(32*c^4*d^4 + b^3*(b + sqrt(b^2 - 4*a*c))*e^4 - 8*c^3*d^2*e*(8*b*d - sqrt(b^2 - 4*a*c)*d - 9*a*e) + 2*b*c*e^3*(b^2*d + b*sqrt(b^2 - 4*a*c)*d - 5*a*b*e - 4*a*sqrt(b^2 - 4*a*c)*e) + 2*c^2*e^2*(15*b^2*d^2 - 6*b*d*(sqrt(b^2 - 4*a*c)*d + 6*a*e) + 4*a*e*(2*sqrt(b^2 - 4*a*c)*d + 7*a*e)))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)))/(4*sqrt(2)*(b^2 - 4*a*c)^(5/2)*sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*(c*d^2 - b*d*e + a*e^2)^2) + (3*sqrt(c)*(32*c^4*d^4 + b^3*(b - sqrt(b^2 - 4*a*c))*e^4 - 8*c^3*d^2*e*(8*b*d + sqrt(b^2 - 4*a*c)*d - 9*a*e) + 2*c^2*e^2*(15*b^2*d^2 - 4*a*e*(2*sqrt(b^2 - 4*a*c)*d - 7*a*e) + 6*b*d*(sqrt(b^2 - 4*a*c)*d - 6*a*e)) + 2*b*c*e^3*(b^2*d + 4*a*sqrt(b^2 - 4*a*c)*e - b*(sqrt(b^2 - 4*a*c)*d + 5*a*e)))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(4*sqrt(2)*(b^2 - 4*a*c)^(5/2)*sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*(c*d^2 - e*(b*d - a*e))^2), -((sqrt(d + e*x)*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^2)) - (sqrt(d + e*x)*(5*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(12*c^2*d^2 - 3*b^2*e^2 - 7*c*e*(b*d - 2*a*e)) - 3*c*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*x))/(4*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)) - (3*sqrt(c)*(32*c^4*d^4 + b^3*(b + sqrt(b^2 - 4*a*c))*e^4 - 8*c^3*d^2*e*(8*b*d - sqrt(b^2 - 4*a*c)*d - 9*a*e) + 2*b*c*e^3*(b^2*d + b*sqrt(b^2 - 4*a*c)*d - 5*a*b*e - 4*a*sqrt(b^2 - 4*a*c)*e) + 2*c^2*e^2*(15*b^2*d^2 - 6*b*d*(sqrt(b^2 - 4*a*c)*d + 6*a*e) + 4*a*e*(2*sqrt(b^2 - 4*a*c)*d + 7*a*e)))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)))/(4*sqrt(2)*(b^2 - 4*a*c)^(5/2)*sqrt(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*(c*d^2 - b*d*e + a*e^2)^2) + (3*sqrt(c)*(32*c^4*d^4 + b^3*(b - sqrt(b^2 - 4*a*c))*e^4 - 8*c^3*d^2*e*(8*b*d + sqrt(b^2 - 4*a*c)*d - 9*a*e) + 2*c^2*e^2*(15*b^2*d^2 - 4*a*e*(2*sqrt(b^2 - 4*a*c)*d - 7*a*e) + 6*b*d*(sqrt(b^2 - 4*a*c)*d - 6*a*e)) + 2*b*c*e^3*(b^2*d + 4*a*sqrt(b^2 - 4*a*c)*e - b*(sqrt(b^2 - 4*a*c)*d + 5*a*e)))*atanh((sqrt(2)*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(4*sqrt(2)*(b^2 - 4*a*c)^(5/2)*sqrt(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*(c*d^2 - b*d*e + a*e^2)^2))]

    @test_int [(d + e*x)^(1/2)/(a + b*im*x + c*x^2), x, 10, (e*atanh((sqrt(2*c*d - im*b*e + 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e))) - 2*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - im*b*e - 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e)))))/(sqrt(c)*sqrt(2*c*d - im*b*e - 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e)))) - (e*atanh((sqrt(2*c*d - im*b*e + 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e))) + 2*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - im*b*e - 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e)))))/(sqrt(c)*sqrt(2*c*d - im*b*e - 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e)))) + (e*log(sqrt(c*d^2 - e*(im*b*d - a*e)) - sqrt(2*c*d - im*b*e + 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e)))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(2*sqrt(c)*sqrt(2*c*d - im*b*e + 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e)))) - (e*log(sqrt(c*d^2 - e*(im*b*d - a*e)) + sqrt(2*c*d - im*b*e + 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e)))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(2*sqrt(c)*sqrt(2*c*d - im*b*e + 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e))))]
    @test_int [1/((d + e*x)^(1/2)*(a + b*im*x + c*x^2)), x, 10, (e*atanh((sqrt(2*c*d - im*b*e + 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e))) - 2*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - im*b*e - 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e)))))/(sqrt(c*d^2 - e*(im*b*d - a*e))*sqrt(2*c*d - im*b*e - 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e)))) - (e*atanh((sqrt(2*c*d - im*b*e + 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e))) + 2*sqrt(c)*sqrt(d + e*x))/sqrt(2*c*d - im*b*e - 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e)))))/(sqrt(c*d^2 - e*(im*b*d - a*e))*sqrt(2*c*d - im*b*e - 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e)))) - (e*log(sqrt(c*d^2 - e*(im*b*d - a*e)) - sqrt(2*c*d - im*b*e + 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e)))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(2*sqrt(c*d^2 - e*(im*b*d - a*e))*sqrt(2*c*d - im*b*e + 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e)))) + (e*log(sqrt(c*d^2 - e*(im*b*d - a*e)) + sqrt(2*c*d - im*b*e + 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e)))*sqrt(d + e*x) + sqrt(c)*(d + e*x)))/(2*sqrt(c*d^2 - e*(im*b*d - a*e))*sqrt(2*c*d - im*b*e + 2*sqrt(c)*sqrt(c*d^2 - e*(im*b*d - a*e))))]

    #= b^2-4*a*c<0 =#
    @test_int [(1 + 2*x)^(7/2)/(2 + 3*x + 5*x^2), x, 13, (-(76/125))*sqrt(1 + 2*x) + (16/75)*(1 + 2*x)^(3/2) + (4/25)*(1 + 2*x)^(5/2) + (1/125)*sqrt((2/155)*(-168698 + 42875*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) - (1/125)*sqrt((2/155)*(-168698 + 42875*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) - (1/125)*sqrt((1/310)*(168698 + 42875*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)) + (1/125)*sqrt((1/310)*(168698 + 42875*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x))]
    @test_int [(1 + 2*x)^(5/2)/(2 + 3*x + 5*x^2), x, 12, (16/25)*sqrt(1 + 2*x) + (4/15)*(1 + 2*x)^(3/2) + (1/25)*sqrt((2/155)*(7162 + 1225*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) - (1/25)*sqrt((2/155)*(7162 + 1225*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) + (1/25)*sqrt((1/310)*(-7162 + 1225*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)) - (1/25)*sqrt((1/310)*(-7162 + 1225*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x))]
    @test_int [(1 + 2*x)^(3/2)/(2 + 3*x + 5*x^2), x, 11, (4/5)*sqrt(1 + 2*x) + (1/5)*sqrt((2/155)*(-178 + 35*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) - (1/5)*sqrt((2/155)*(-178 + 35*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) + (1/5)*sqrt((1/310)*(178 + 35*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)) - (1/5)*sqrt((1/310)*(178 + 35*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x))]
    @test_int [(1 + 2*x)^(1/2)/(2 + 3*x + 5*x^2), x, 10, (-sqrt(2/(5*(-2 + sqrt(35)))))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) + sqrt(2/(5*(-2 + sqrt(35))))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) + log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x))/sqrt(10*(2 + sqrt(35))) - log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x))/sqrt(10*(2 + sqrt(35)))]
    @test_int [1/((1 + 2*x)^(1/2)*(2 + 3*x + 5*x^2)), x, 10, (-sqrt((2/217)*(2 + sqrt(35))))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) + sqrt((2/217)*(2 + sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) - log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x))/sqrt(14*(2 + sqrt(35))) + log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x))/sqrt(14*(2 + sqrt(35)))]
    @test_int [1/((1 + 2*x)^(3/2)*(2 + 3*x + 5*x^2)), x, 11, -(4/(7*sqrt(1 + 2*x))) + (1/7)*sqrt((2/217)*(-178 + 35*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) - (1/7)*sqrt((2/217)*(-178 + 35*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) - (1/7)*sqrt((1/434)*(178 + 35*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)) + (1/7)*sqrt((1/434)*(178 + 35*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x))]
    @test_int [1/((1 + 2*x)^(5/2)*(2 + 3*x + 5*x^2)), x, 12, -(4/(21*(1 + 2*x)^(3/2))) - 16/(49*sqrt(1 + 2*x)) + (1/49)*sqrt((2/217)*(7162 + 1225*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) - (1/49)*sqrt((2/217)*(7162 + 1225*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) - (1/49)*sqrt((1/434)*(-7162 + 1225*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)) + (1/49)*sqrt((1/434)*(-7162 + 1225*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x))]

    @test_int [(1 + 2*x)^(7/2)/(2 + 3*x + 5*x^2)^2, x, 13, (604/775)*sqrt(1 + 2*x) - (8/155)*(1 + 2*x)^(3/2) - ((5 - 4*x)*(1 + 2*x)^(5/2))/(31*(2 + 3*x + 5*x^2)) + (1/775)*sqrt((2/155)*(-5682718 + 968975*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) - (1/775)*sqrt((2/155)*(-5682718 + 968975*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) + (1/775)*sqrt((1/310)*(5682718 + 968975*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)) - (1/775)*sqrt((1/310)*(5682718 + 968975*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x))]
    @test_int [(1 + 2*x)^(5/2)/(2 + 3*x + 5*x^2)^2, x, 12, (-(8/155))*sqrt(1 + 2*x) - ((5 - 4*x)*(1 + 2*x)^(3/2))/(31*(2 + 3*x + 5*x^2)) - (1/155)*sqrt((2/155)*(32678 + 10325*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) + (1/155)*sqrt((2/155)*(32678 + 10325*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) + (1/155)*sqrt((1/310)*(-32678 + 10325*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)) - (1/155)*sqrt((1/310)*(-32678 + 10325*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x))]
    @test_int [(1 + 2*x)^(3/2)/(2 + 3*x + 5*x^2)^2, x, 11, -(((5 - 4*x)*sqrt(1 + 2*x))/(31*(2 + 3*x + 5*x^2))) - (1/31)*sqrt((2/155)*(218 + 47*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) + (1/31)*sqrt((2/155)*(218 + 47*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) - (1/31)*sqrt((1/310)*(-218 + 47*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)) + (1/31)*sqrt((1/310)*(-218 + 47*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x))]
    @test_int [(1 + 2*x)^(1/2)/(2 + 3*x + 5*x^2)^2, x, 11, (sqrt(1 + 2*x)*(3 + 10*x))/(31*(2 + 3*x + 5*x^2)) - (1/31)*sqrt((2/217)*(218 + 47*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) + (1/31)*sqrt((2/217)*(218 + 47*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) + (1/31)*sqrt((1/434)*(-218 + 47*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)) - (1/31)*sqrt((1/434)*(-218 + 47*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x))]
    @test_int [1/((1 + 2*x)^(1/2)*(2 + 3*x + 5*x^2)^2), x, 11, (sqrt(1 + 2*x)*(37 + 20*x))/(217*(2 + 3*x + 5*x^2)) - (1/217)*sqrt((2/217)*(32678 + 10325*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) + (1/217)*sqrt((2/217)*(32678 + 10325*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) - (1/217)*sqrt((1/434)*(-32678 + 10325*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)) + (1/217)*sqrt((1/434)*(-32678 + 10325*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x))]
    @test_int [1/((1 + 2*x)^(3/2)*(2 + 3*x + 5*x^2)^2), x, 12, -(604/(1519*sqrt(1 + 2*x))) + (37 + 20*x)/(217*sqrt(1 + 2*x)*(2 + 3*x + 5*x^2)) + (sqrt((2/217)*(-5682718 + 968975*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))))/1519 - (sqrt((2/217)*(-5682718 + 968975*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))))/1519 - (sqrt((1/434)*(5682718 + 968975*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/1519 + (sqrt((1/434)*(5682718 + 968975*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/1519]
    @test_int [1/((1 + 2*x)^(5/2)*(2 + 3*x + 5*x^2)^2), x, 13, -(820/(4557*(1 + 2*x)^(3/2))) - 4680/(10633*sqrt(1 + 2*x)) + (37 + 20*x)/(217*(1 + 2*x)^(3/2)*(2 + 3*x + 5*x^2)) + (5*sqrt((2/217)*(12504542 + 2632525*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))))/10633 - (5*sqrt((2/217)*(12504542 + 2632525*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))))/10633 - (5*sqrt((1/434)*(-12504542 + 2632525*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/10633 + (5*sqrt((1/434)*(-12504542 + 2632525*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/10633]

    @test_int [(1 + 2*x)^(9/2)/(2 + 3*x + 5*x^2)^3, x, 13, -((1584*sqrt(1 + 2*x))/24025) - ((5 - 4*x)*(1 + 2*x)^(7/2))/(62*(2 + 3*x + 5*x^2)^2) - ((1143 - 1088*x)*(1 + 2*x)^(3/2))/(9610*(2 + 3*x + 5*x^2)) - (3*sqrt((1/310)*(250141922 + 64681225*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))))/24025 + (3*sqrt((1/310)*(250141922 + 64681225*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))))/24025 + (3*sqrt((1/310)*(-250141922 + 64681225*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/48050 - (3*sqrt((1/310)*(-250141922 + 64681225*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/48050]
    @test_int [(1 + 2*x)^(7/2)/(2 + 3*x + 5*x^2)^3, x, 12, -(((5 - 4*x)*(1 + 2*x)^(5/2))/(62*(2 + 3*x + 5*x^2)^2)) - ((957 - 592*x)*sqrt(1 + 2*x))/(9610*(2 + 3*x + 5*x^2)) - (sqrt((1/310)*(9651062 + 1806875*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))))/4805 + (sqrt((1/310)*(9651062 + 1806875*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))))/4805 - (sqrt((1/310)*(-9651062 + 1806875*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/9610 + (sqrt((1/310)*(-9651062 + 1806875*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/9610]
    @test_int [(1 + 2*x)^(5/2)/(2 + 3*x + 5*x^2)^3, x, 12, -(((5 - 4*x)*(1 + 2*x)^(3/2))/(62*(2 + 3*x + 5*x^2)^2)) + (3*sqrt(1 + 2*x)*(11 + 78*x))/(1922*(2 + 3*x + 5*x^2)) - (3/961)*sqrt((1/310)*(15082 + 2705*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) + (3/961)*sqrt((1/310)*(15082 + 2705*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) + (3*sqrt((1/310)*(-15082 + 2705*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/1922 - (3*sqrt((1/310)*(-15082 + 2705*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/1922]
    @test_int [(1 + 2*x)^(3/2)/(2 + 3*x + 5*x^2)^3, x, 12, -(((5 - 4*x)*sqrt(1 + 2*x))/(62*(2 + 3*x + 5*x^2)^2)) + (sqrt(1 + 2*x)*(67 + 120*x))/(1922*(2 + 3*x + 5*x^2)) - (3/961)*sqrt((1/434)*(15082 + 2705*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) + (3/961)*sqrt((1/434)*(15082 + 2705*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))) - (3*sqrt((1/434)*(-15082 + 2705*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/1922 + (3*sqrt((1/434)*(-15082 + 2705*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/1922]
    @test_int [(1 + 2*x)^(1/2)/(2 + 3*x + 5*x^2)^3, x, 12, (sqrt(1 + 2*x)*(3 + 10*x))/(62*(2 + 3*x + 5*x^2)^2) + (sqrt(1 + 2*x)*(599 + 1790*x))/(13454*(2 + 3*x + 5*x^2)) - (sqrt((1/434)*(9651062 + 1806875*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))))/6727 + (sqrt((1/434)*(9651062 + 1806875*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))))/6727 + (sqrt((1/434)*(-9651062 + 1806875*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/13454 - (sqrt((1/434)*(-9651062 + 1806875*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/13454]
    @test_int [1/((1 + 2*x)^(1/2)*(2 + 3*x + 5*x^2)^3), x, 12, (sqrt(1 + 2*x)*(37 + 20*x))/(434*(2 + 3*x + 5*x^2)^2) + (sqrt(1 + 2*x)*(9227 + 7920*x))/(94178*(2 + 3*x + 5*x^2)) - (3*sqrt((1/434)*(2 + sqrt(35)))*(7379 + 264*sqrt(35))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))))/47089 + (3*sqrt((1/434)*(2 + sqrt(35)))*(7379 + 264*sqrt(35))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))))/47089 - (3*sqrt((1/434)*(-250141922 + 64681225*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/94178 + (3*sqrt((1/434)*(-250141922 + 64681225*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/94178]
    @test_int [1/((1 + 2*x)^(3/2)*(2 + 3*x + 5*x^2)^3), x, 13, -(81090/(329623*sqrt(1 + 2*x))) + (37 + 20*x)/(434*sqrt(1 + 2*x)*(2 + 3*x + 5*x^2)^2) + (5*(2329 + 2080*x))/(94178*sqrt(1 + 2*x)*(2 + 3*x + 5*x^2)) - (15*sqrt((1/434)*(-2257111762 + 387427075*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) - 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))))/329623 + (15*sqrt((1/434)*(-2257111762 + 387427075*sqrt(35)))*atan((sqrt(10*(2 + sqrt(35))) + 10*sqrt(1 + 2*x))/sqrt(10*(-2 + sqrt(35)))))/329623 - (15*sqrt((1/434)*(2257111762 + 387427075*sqrt(35)))*log(sqrt(35) - sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/659246 + (15*sqrt((1/434)*(2257111762 + 387427075*sqrt(35)))*log(sqrt(35) + sqrt(10*(2 + sqrt(35)))*sqrt(1 + 2*x) + 5*(1 + 2*x)))/659246]

    @test_int [x^(9/2)/(a + b*x + c*x^2)^3, x, 7, -((3*b*(b^2 - 8*a*c)*sqrt(x))/(4*c^2*(b^2 - 4*a*c)^2)) + (x^(7/2)*(2*a + b*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (x^(3/2)*(a*(b^2 - 28*a*c) + b*(b^2 - 16*a*c)*x))/(4*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) + (3*(b^4 - 9*a*b^2*c + 28*a^2*c^2 - (b^5 - 11*a*b^3*c + 44*a^2*b*c^2)/sqrt(b^2 - 4*a*c))*atan((sqrt(2)*sqrt(c)*sqrt(x))/sqrt(b - sqrt(b^2 - 4*a*c))))/(4*sqrt(2)*c^(5/2)*(b^2 - 4*a*c)^2*sqrt(b - sqrt(b^2 - 4*a*c))) + (3*(b^4 - 9*a*b^2*c + 28*a^2*c^2 + (b^5 - 11*a*b^3*c + 44*a^2*b*c^2)/sqrt(b^2 - 4*a*c))*atan((sqrt(2)*sqrt(c)*sqrt(x))/sqrt(b + sqrt(b^2 - 4*a*c))))/(4*sqrt(2)*c^(5/2)*(b^2 - 4*a*c)^2*sqrt(b + sqrt(b^2 - 4*a*c)))]
    @test_int [1/(x^(3/2)*(a + b*x + c*x^2)^3), x, 7, -((3*(5*b^2 - 12*a*c)*(b^2 - 5*a*c))/(4*a^3*(b^2 - 4*a*c)^2*sqrt(x))) + (b^2 - 2*a*c + b*c*x)/(2*a*(b^2 - 4*a*c)*sqrt(x)*(a + b*x + c*x^2)^2) + (5*b^4 - 35*a*b^2*c + 36*a^2*c^2 + b*c*(5*b^2 - 32*a*c)*x)/(4*a^2*(b^2 - 4*a*c)^2*sqrt(x)*(a + b*x + c*x^2)) - (3*sqrt(c)*(5*b^5 - 47*a*b^3*c + 124*a^2*b*c^2 + sqrt(b^2 - 4*a*c)*(5*b^4 - 37*a*b^2*c + 60*a^2*c^2))*atan((sqrt(2)*sqrt(c)*sqrt(x))/sqrt(b - sqrt(b^2 - 4*a*c))))/(4*sqrt(2)*a^3*(b^2 - 4*a*c)^(5/2)*sqrt(b - sqrt(b^2 - 4*a*c))) + (3*sqrt(c)*(5*b^5 - 47*a*b^3*c + 124*a^2*b*c^2 - 5*b^4*sqrt(b^2 - 4*a*c) + 37*a*b^2*c*sqrt(b^2 - 4*a*c) - 60*a^2*c^2*sqrt(b^2 - 4*a*c))*atan((sqrt(2)*sqrt(c)*sqrt(x))/sqrt(b + sqrt(b^2 - 4*a*c))))/(4*sqrt(2)*a^3*(b^2 - 4*a*c)^(5/2)*sqrt(b + sqrt(b^2 - 4*a*c)))]

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

    @test_int [(3 - x + x^2)/x^(1/3), x, 2, (9*x^(2/3))/2 - (3*x^(5/3))/5 + (3*x^(8/3))/8]

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

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

    @test_int [(d + e*x)^3*sqrt(a + b*x + c*x^2), x, 5, ((2*c*d - b*e)*(16*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(4*b*d + 3*a*e))*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(128*c^4) + (e*(d + e*x)^2*(a + b*x + c*x^2)^(3/2))/(5*c) + (e*(192*c^2*d^2 + 35*b^2*e^2 - 2*c*e*(75*b*d + 16*a*e) + 42*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(240*c^3) - ((b^2 - 4*a*c)*(2*c*d - b*e)*(16*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(4*b*d + 3*a*e))*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(256*c^(9/2))]
    @test_int [(d + e*x)^2*sqrt(a + b*x + c*x^2), x, 5, ((16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(4*b*d + a*e))*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(64*c^3) + (5*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(3/2))/(24*c^2) + (e*(d + e*x)*(a + b*x + c*x^2)^(3/2))/(4*c) - ((b^2 - 4*a*c)*(16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(4*b*d + a*e))*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(128*c^(7/2))]
    @test_int [(d + e*x)^1*sqrt(a + b*x + c*x^2), x, 4, ((2*c*d - b*e)*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(8*c^2) + (e*(a + b*x + c*x^2)^(3/2))/(3*c) - ((b^2 - 4*a*c)*(2*c*d - b*e)*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(16*c^(5/2))]
    @test_int [(d + e*x)^0*sqrt(a + b*x + c*x^2), x, 3, ((b + 2*c*x)*sqrt(a + b*x + c*x^2))/(4*c) - ((b^2 - 4*a*c)*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(8*c^(3/2))]
    @test_int [sqrt(a + b*x + c*x^2)/(d + e*x)^1, x, 6, sqrt(a + b*x + c*x^2)/e - ((2*c*d - b*e)*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(2*sqrt(c)*e^2) + (sqrt(c*d^2 - b*d*e + a*e^2)*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/e^2]
    @test_int [sqrt(a + b*x + c*x^2)/(d + e*x)^2, x, 6, -(sqrt(a + b*x + c*x^2)/(e*(d + e*x))) + (sqrt(c)*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/e^2 - ((2*c*d - b*e)*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(2*e^2*sqrt(c*d^2 - b*d*e + a*e^2))]
    @test_int [sqrt(a + b*x + c*x^2)/(d + e*x)^3, x, 3, ((b*d - 2*a*e + (2*c*d - b*e)*x)*sqrt(a + b*x + c*x^2))/(4*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) - ((b^2 - 4*a*c)*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(8*(c*d^2 - b*d*e + a*e^2)^(3/2))]
    @test_int [sqrt(a + b*x + c*x^2)/(d + e*x)^4, x, 4, ((2*c*d - b*e)*(b*d - 2*a*e + (2*c*d - b*e)*x)*sqrt(a + b*x + c*x^2))/(8*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2) - (e*(a + b*x + c*x^2)^(3/2))/(3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^3) - ((b^2 - 4*a*c)*(2*c*d - b*e)*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(16*(c*d^2 - b*d*e + a*e^2)^(5/2))]
    @test_int [sqrt(a + b*x + c*x^2)/(d + e*x)^5, x, 5, ((16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(4*b*d + a*e))*(b*d - 2*a*e + (2*c*d - b*e)*x)*sqrt(a + b*x + c*x^2))/(64*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^2) - (e*(a + b*x + c*x^2)^(3/2))/(4*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^4) - (5*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(3/2))/(24*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^3) - ((b^2 - 4*a*c)*(16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(4*b*d + a*e))*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(128*(c*d^2 - b*d*e + a*e^2)^(7/2))]
    @test_int [sqrt(a + b*x + c*x^2)/(d + e*x)^6, x, 6, ((2*c*d - b*e)*(16*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(4*b*d + 3*a*e))*(b*d - 2*a*e + (2*c*d - b*e)*x)*sqrt(a + b*x + c*x^2))/(128*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^2) - (e*(a + b*x + c*x^2)^(3/2))/(5*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^5) - (7*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(3/2))/(40*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^4) - (e*(108*c^2*d^2 + 35*b^2*e^2 - 4*c*e*(27*b*d + 8*a*e))*(a + b*x + c*x^2)^(3/2))/(240*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^3) - ((b^2 - 4*a*c)*(2*c*d - b*e)*(16*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(4*b*d + 3*a*e))*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(256*(c*d^2 - b*d*e + a*e^2)^(9/2))]

    @test_int [(d + e*x)^3*(a + b*x + c*x^2)^(3/2), x, 6, -((3*(b^2 - 4*a*c)*(2*c*d - b*e)*(8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(1024*c^5)) + ((2*c*d - b*e)*(8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(128*c^4) + (e*(d + e*x)^2*(a + b*x + c*x^2)^(5/2))/(7*c) + (e*(128*c^2*d^2 + 21*b^2*e^2 - 2*c*e*(49*b*d + 8*a*e) + 30*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(5/2))/(280*c^3) + (3*(b^2 - 4*a*c)^2*(2*c*d - b*e)*(8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(2048*c^(11/2))]
    @test_int [(d + e*x)^2*(a + b*x + c*x^2)^(3/2), x, 6, -(((b^2 - 4*a*c)*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(512*c^4)) + ((24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(192*c^3) + (7*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(5/2))/(60*c^2) + (e*(d + e*x)*(a + b*x + c*x^2)^(5/2))/(6*c) + ((b^2 - 4*a*c)^2*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(1024*c^(9/2))]
    @test_int [(d + e*x)^1*(a + b*x + c*x^2)^(3/2), x, 5, -((3*(b^2 - 4*a*c)*(2*c*d - b*e)*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(128*c^3)) + ((2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(16*c^2) + (e*(a + b*x + c*x^2)^(5/2))/(5*c) + (3*(b^2 - 4*a*c)^2*(2*c*d - b*e)*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(256*c^(7/2))]
    @test_int [(d + e*x)^0*(a + b*x + c*x^2)^(3/2), x, 4, -((3*(b^2 - 4*a*c)*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(64*c^2)) + ((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(8*c) + (3*(b^2 - 4*a*c)^2*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(128*c^(5/2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(d + e*x)^1, x, 7, ((8*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 4*a*e) - 2*c*e*(2*c*d - b*e)*x)*sqrt(a + b*x + c*x^2))/(8*c*e^3) + (a + b*x + c*x^2)^(3/2)/(3*e) - ((2*c*d - b*e)*(8*c^2*d^2 - b^2*e^2 - 4*c*e*(2*b*d - 3*a*e))*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(16*c^(3/2)*e^4) + ((c*d^2 - b*d*e + a*e^2)^(3/2)*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/e^4]
    @test_int [(a + b*x + c*x^2)^(3/2)/(d + e*x)^2, x, 7, -((3*(4*c*d - 3*b*e - 2*c*e*x)*sqrt(a + b*x + c*x^2))/(4*e^3)) - (a + b*x + c*x^2)^(3/2)/(e*(d + e*x)) + (3*(8*c^2*d^2 + b^2*e^2 - 4*c*e*(2*b*d - a*e))*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(8*sqrt(c)*e^4) - (3*(2*c*d - b*e)*sqrt(c*d^2 - b*d*e + a*e^2)*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(2*e^4)]
    @test_int [(a + b*x + c*x^2)^(3/2)/(d + e*x)^3, x, 7, (3*(4*c*d - b*e + 2*c*e*x)*sqrt(a + b*x + c*x^2))/(4*e^3*(d + e*x)) - (a + b*x + c*x^2)^(3/2)/(2*e*(d + e*x)^2) - (3*sqrt(c)*(2*c*d - b*e)*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(2*e^4) + (3*(8*c^2*d^2 + b^2*e^2 - 4*c*e*(2*b*d - a*e))*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(8*e^4*sqrt(c*d^2 - b*d*e + a*e^2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(d + e*x)^4, x, 7, -(((8*c^2*d^3 - b*e^2*(b*d - 2*a*e) - 2*c*d*e*(3*b*d - 2*a*e) + e*(12*c^2*d^2 + b^2*e^2 - 4*c*e*(3*b*d - 2*a*e))*x)*sqrt(a + b*x + c*x^2))/(8*e^3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2)) - (a + b*x + c*x^2)^(3/2)/(3*e*(d + e*x)^3) + (c^(3/2)*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/e^4 - ((2*c*d - b*e)*(8*c^2*d^2 - b^2*e^2 - 4*c*e*(2*b*d - 3*a*e))*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(16*e^4*(c*d^2 - b*d*e + a*e^2)^(3/2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(d + e*x)^5, x, 4, -((3*(b^2 - 4*a*c)*(b*d - 2*a*e + (2*c*d - b*e)*x)*sqrt(a + b*x + c*x^2))/(64*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2)) + ((b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(8*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^4) + (3*(b^2 - 4*a*c)^2*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(128*(c*d^2 - b*d*e + a*e^2)^(5/2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(d + e*x)^6, x, 5, -((3*(b^2 - 4*a*c)*(2*c*d - b*e)*(b*d - 2*a*e + (2*c*d - b*e)*x)*sqrt(a + b*x + c*x^2))/(128*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^2)) + ((2*c*d - b*e)*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(16*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^4) - (e*(a + b*x + c*x^2)^(5/2))/(5*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^5) + (3*(b^2 - 4*a*c)^2*(2*c*d - b*e)*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(256*(c*d^2 - b*d*e + a*e^2)^(7/2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(d + e*x)^7, x, 6, -(((b^2 - 4*a*c)*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*(b*d - 2*a*e + (2*c*d - b*e)*x)*sqrt(a + b*x + c*x^2))/(512*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^2)) + ((24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(192*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^4) - (e*(a + b*x + c*x^2)^(5/2))/(6*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^6) - (7*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(5/2))/(60*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^5) + ((b^2 - 4*a*c)^2*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(1024*(c*d^2 - b*d*e + a*e^2)^(9/2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(d + e*x)^8, x, 7, -((3*(b^2 - 4*a*c)*(2*c*d - b*e)*(8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*(b*d - 2*a*e + (2*c*d - b*e)*x)*sqrt(a + b*x + c*x^2))/(1024*(c*d^2 - b*d*e + a*e^2)^5*(d + e*x)^2)) + ((2*c*d - b*e)*(8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(128*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^4) - (e*(a + b*x + c*x^2)^(5/2))/(7*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^7) - (3*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(5/2))/(28*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^6) - (e*(68*c^2*d^2 + 21*b^2*e^2 - 4*c*e*(17*b*d + 4*a*e))*(a + b*x + c*x^2)^(5/2))/(280*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^5) + (3*(b^2 - 4*a*c)^2*(2*c*d - b*e)*(8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(2048*(c*d^2 - b*d*e + a*e^2)^(11/2))]

    @test_int [(d + e*x)^3*(a + b*x + c*x^2)^(5/2), x, 7, (5*(b^2 - 4*a*c)^2*(2*c*d - b*e)*(32*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(8*b*d + 3*a*e))*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(32768*c^6) - (5*(b^2 - 4*a*c)*(2*c*d - b*e)*(32*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(8*b*d + 3*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(12288*c^5) + ((2*c*d - b*e)*(32*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(8*b*d + 3*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(768*c^4) + (e*(d + e*x)^2*(a + b*x + c*x^2)^(7/2))/(9*c) + (e*(640*c^2*d^2 + 99*b^2*e^2 - 2*c*e*(243*b*d + 32*a*e) + 154*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(7/2))/(2016*c^3) - (5*(b^2 - 4*a*c)^3*(2*c*d - b*e)*(32*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(8*b*d + 3*a*e))*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(65536*c^(13/2))]
    @test_int [(d + e*x)^2*(a + b*x + c*x^2)^(5/2), x, 7, (5*(b^2 - 4*a*c)^2*(32*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(8*b*d + a*e))*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(16384*c^5) - (5*(b^2 - 4*a*c)*(32*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(8*b*d + a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(6144*c^4) + ((32*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(8*b*d + a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(384*c^3) + (9*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(7/2))/(112*c^2) + (e*(d + e*x)*(a + b*x + c*x^2)^(7/2))/(8*c) - (5*(b^2 - 4*a*c)^3*(32*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(8*b*d + a*e))*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(32768*c^(11/2))]
    @test_int [(d + e*x)^1*(a + b*x + c*x^2)^(5/2), x, 6, (5*(b^2 - 4*a*c)^2*(2*c*d - b*e)*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(1024*c^4) - (5*(b^2 - 4*a*c)*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(384*c^3) + ((2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(24*c^2) + (e*(a + b*x + c*x^2)^(7/2))/(7*c) - (5*(b^2 - 4*a*c)^3*(2*c*d - b*e)*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(2048*c^(9/2))]
    @test_int [(d + e*x)^0*(a + b*x + c*x^2)^(5/2), x, 5, (5*(b^2 - 4*a*c)^2*(b + 2*c*x)*sqrt(a + b*x + c*x^2))/(512*c^3) - (5*(b^2 - 4*a*c)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(192*c^2) + ((b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(12*c) - (5*(b^2 - 4*a*c)^3*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(1024*c^(7/2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(d + e*x)^1, x, 8, (1/(128*c^2*e^5))*((128*c^4*d^4 - 3*b^4*e^4 - 2*b^2*c*e^3*(5*b*d - 14*a*e) - 32*c^3*d^2*e*(9*b*d - 8*a*e) + 8*c^2*e^2*(22*b^2*d^2 - 39*a*b*d*e + 16*a^2*e^2) - 2*c*e*(2*c*d - b*e)*(16*c^2*d^2 - 3*b^2*e^2 - 4*c*e*(4*b*d - 7*a*e))*x)*sqrt(a + b*x + c*x^2)) + ((16*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(11*b*d - 8*a*e) - 6*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(48*c*e^3) + (a + b*x + c*x^2)^(5/2)/(5*e) - ((2*c*d - b*e)*(128*c^4*d^4 + 3*b^4*e^4 + 8*b^2*c*e^3*(2*b*d - 5*a*e) - 64*c^3*d^2*e*(4*b*d - 5*a*e) + 16*c^2*e^2*(7*b^2*d^2 - 20*a*b*d*e + 15*a^2*e^2))*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(256*c^(5/2)*e^6) + ((c*d^2 - b*d*e + a*e^2)^(5/2)*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/e^6]
    @test_int [(a + b*x + c*x^2)^(5/2)/(d + e*x)^2, x, 8, -((5*(64*c^3*d^3 - b^3*e^3 + 4*b*c*e^2*(12*b*d - 11*a*e) - 16*c^2*d*e*(7*b*d - 4*a*e) - 2*c*e*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*x)*sqrt(a + b*x + c*x^2))/(64*c*e^5)) - (5*(8*c*d - 7*b*e - 6*c*e*x)*(a + b*x + c*x^2)^(3/2))/(24*e^3) - (a + b*x + c*x^2)^(5/2)/(e*(d + e*x)) + (5*(128*c^4*d^4 - b^4*e^4 - 8*b^2*c*e^3*(2*b*d - 3*a*e) - 64*c^3*d^2*e*(4*b*d - 3*a*e) + 48*c^2*e^2*(3*b^2*d^2 - 4*a*b*d*e + a^2*e^2))*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(128*c^(3/2)*e^6) - (5*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^(3/2)*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(2*e^6)]
    @test_int [(a + b*x + c*x^2)^(5/2)/(d + e*x)^3, x, 8, (5*(16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(5*b*d - a*e) - 4*c*e*(2*c*d - b*e)*x)*sqrt(a + b*x + c*x^2))/(8*e^5) + (5*(8*c*d - 3*b*e + 2*c*e*x)*(a + b*x + c*x^2)^(3/2))/(12*e^3*(d + e*x)) - (a + b*x + c*x^2)^(5/2)/(2*e*(d + e*x)^2) - (5*(2*c*d - b*e)*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(16*sqrt(c)*e^6) + (5*sqrt(c*d^2 - b*d*e + a*e^2)*(16*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(4*b*d - a*e))*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(8*e^6)]
    @test_int [(a + b*x + c*x^2)^(5/2)/(d + e*x)^4, x, 8, -((5*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(3*b*d - a*e) + 4*c*e*(2*c*d - b*e)*x)*sqrt(a + b*x + c*x^2))/(8*e^5*(d + e*x))) + (5*(4*c*d - b*e + 2*c*e*x)*(a + b*x + c*x^2)^(3/2))/(12*e^3*(d + e*x)^2) - (a + b*x + c*x^2)^(5/2)/(3*e*(d + e*x)^3) + (5*sqrt(c)*(16*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(4*b*d - a*e))*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(8*e^6) - (5*(2*c*d - b*e)*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(16*e^6*sqrt(c*d^2 - b*d*e + a*e^2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(d + e*x)^5, x, 8, (5*(64*c^3*d^3 + b^3*e^3 + 4*b*c*e^2*(4*b*d - 5*a*e) - 16*c^2*d*e*(5*b*d - 4*a*e) + 2*c*e*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*x)*sqrt(a + b*x + c*x^2))/(64*e^5*(c*d^2 - b*d*e + a*e^2)*(d + e*x)) - (5*(16*c^2*d^3 - b*e^2*(b*d - 4*a*e) - 4*c*d*e*(3*b*d - a*e) + 3*e*(8*c^2*d^2 + b^2*e^2 - 4*c*e*(2*b*d - a*e))*x)*(a + b*x + c*x^2)^(3/2))/(96*e^3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^3) - (a + b*x + c*x^2)^(5/2)/(4*e*(d + e*x)^4) - (5*c^(3/2)*(2*c*d - b*e)*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(2*e^6) + (5*(128*c^4*d^4 - b^4*e^4 - 8*b^2*c*e^3*(2*b*d - 3*a*e) - 64*c^3*d^2*e*(4*b*d - 3*a*e) + 48*c^2*e^2*(3*b^2*d^2 - 4*a*b*d*e + a^2*e^2))*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(128*e^6*(c*d^2 - b*d*e + a*e^2)^(3/2))]

    @test_int [sqrt(-2 - 3*x + 5*x^2)/x, x, 6, sqrt(-2 - 3*x + 5*x^2) + sqrt(2)*atan((4 + 3*x)/(2*sqrt(2)*sqrt(-2 - 3*x + 5*x^2))) + (3*atanh((3 - 10*x)/(2*sqrt(5)*sqrt(-2 - 3*x + 5*x^2))))/(2*sqrt(5))]
    @test_int [sqrt(2 - x - x^2)/x^2, x, 6, -(sqrt(2 - x - x^2)/x) + asin((1/3)*(-1 - 2*x)) + atanh((4 - x)/(2*sqrt(2)*sqrt(2 - x - x^2)))/(2*sqrt(2))]

    @test_int [(1 + x)^3*sqrt(2 + 2*x + x^2), x, 2, (-(2/15))*(2 + 2*x + x^2)^(3/2) + (1/5)*(1 + x)^2*(2 + 2*x + x^2)^(3/2)]
    @test_int [(-2 + 3*x)*sqrt(8 + 12*x + 9*x^2), x, 4, (-(2/3))*(2 + 3*x)*sqrt(8 + 12*x + 9*x^2) + (1/9)*(8 + 12*x + 9*x^2)^(3/2) - (8/3)*asinh(1 + (3*x)/2)]
    @test_int [(7 - 2*x)*sqrt(9 + 16*x - 4*x^2), x, 4, (-(3/2))*(2 - x)*sqrt(9 + 16*x - 4*x^2) + (1/6)*(9 + 16*x - 4*x^2)^(3/2) - (75/4)*asin((2*(2 - x))/5)]

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

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

    @test_int [x^6/sqrt(a + b*x + c*x^2), x, 7, -((b*(77*b^2 - 156*a*c)*x^2*sqrt(a + b*x + c*x^2))/(320*c^4)) + ((99*b^2 - 100*a*c)*x^3*sqrt(a + b*x + c*x^2))/(480*c^3) - (11*b*x^4*sqrt(a + b*x + c*x^2))/(60*c^2) + (x^5*sqrt(a + b*x + c*x^2))/(6*c) - ((7*b*(165*b^4 - 680*a*b^2*c + 528*a^2*c^2) - 2*c*(385*b^4 - 1176*a*b^2*c + 400*a^2*c^2)*x)*sqrt(a + b*x + c*x^2))/(2560*c^6) + ((231*b^6 - 1260*a*b^4*c + 1680*a^2*b^2*c^2 - 320*a^3*c^3)*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(1024*c^(13/2))]
    @test_int [x^5/sqrt(a + b*x + c*x^2), x, 6, ((63*b^2 - 64*a*c)*x^2*sqrt(a + b*x + c*x^2))/(240*c^3) - (9*b*x^3*sqrt(a + b*x + c*x^2))/(40*c^2) + (x^4*sqrt(a + b*x + c*x^2))/(5*c) + ((945*b^4 - 2940*a*b^2*c + 1024*a^2*c^2 - 14*b*c*(45*b^2 - 92*a*c)*x)*sqrt(a + b*x + c*x^2))/(1920*c^5) - (b*(63*b^4 - 280*a*b^2*c + 240*a^2*c^2)*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(256*c^(11/2))]
    @test_int [(d + e*x)^4/sqrt(a + b*x + c*x^2), x, 5, (7*e*(2*c*d - b*e)*(d + e*x)^2*sqrt(a + b*x + c*x^2))/(24*c^2) + (e*(d + e*x)^3*sqrt(a + b*x + c*x^2))/(4*c) + (e*(608*c^3*d^3 - 105*b^3*e^3 + 20*b*c*e^2*(24*b*d + 11*a*e) - 8*c^2*d*e*(101*b*d + 64*a*e) + 2*c*e*(104*c^2*d^2 + 35*b^2*e^2 - 4*c*e*(26*b*d + 9*a*e))*x)*sqrt(a + b*x + c*x^2))/(192*c^4) + ((128*c^4*d^4 + 35*b^4*e^4 - 128*c^3*d^2*e*(2*b*d + 3*a*e) - 40*b^2*c*e^3*(4*b*d + 3*a*e) + 48*c^2*e^2*(6*b^2*d^2 + 8*a*b*d*e + a^2*e^2))*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(128*c^(9/2))]
    @test_int [(d + e*x)^3/sqrt(a + b*x + c*x^2), x, 4, (e*(d + e*x)^2*sqrt(a + b*x + c*x^2))/(3*c) + (e*(64*c^2*d^2 + 15*b^2*e^2 - 2*c*e*(27*b*d + 8*a*e) + 10*c*e*(2*c*d - b*e)*x)*sqrt(a + b*x + c*x^2))/(24*c^3) + ((2*c*d - b*e)*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(16*c^(7/2))]
    @test_int [(d + e*x)^2/sqrt(a + b*x + c*x^2), x, 4, (3*e*(2*c*d - b*e)*sqrt(a + b*x + c*x^2))/(4*c^2) + (e*(d + e*x)*sqrt(a + b*x + c*x^2))/(2*c) + ((8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(8*c^(5/2))]
    @test_int [(d + e*x)^1/sqrt(a + b*x + c*x^2), x, 3, (e*sqrt(a + b*x + c*x^2))/c + ((2*c*d - b*e)*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(2*c^(3/2))]
    @test_int [(d + e*x)^0/sqrt(a + b*x + c*x^2), x, 2, atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2)))/sqrt(c)]
    @test_int [1/((d + e*x)^1*sqrt(a + b*x + c*x^2)), x, 2, atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2)))/sqrt(c*d^2 - b*d*e + a*e^2)]
    @test_int [1/((d + e*x)^2*sqrt(a + b*x + c*x^2)), x, 3, -((e*sqrt(a + b*x + c*x^2))/((c*d^2 - b*d*e + a*e^2)*(d + e*x))) + ((2*c*d - b*e)*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(2*(c*d^2 - b*d*e + a*e^2)^(3/2))]
    @test_int [1/((d + e*x)^3*sqrt(a + b*x + c*x^2)), x, 4, -((e*sqrt(a + b*x + c*x^2))/(2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2)) - (3*e*(2*c*d - b*e)*sqrt(a + b*x + c*x^2))/(4*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) + ((8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(8*(c*d^2 - b*d*e + a*e^2)^(5/2))]
    @test_int [1/((d + e*x)^4*sqrt(a + b*x + c*x^2)), x, 5, -((e*sqrt(a + b*x + c*x^2))/(3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^3)) - (5*e*(2*c*d - b*e)*sqrt(a + b*x + c*x^2))/(12*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2) - (e*(44*c^2*d^2 + 15*b^2*e^2 - 4*c*e*(11*b*d + 4*a*e))*sqrt(a + b*x + c*x^2))/(24*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)) + ((2*c*d - b*e)*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(16*(c*d^2 - b*d*e + a*e^2)^(7/2))]

    @test_int [(d + e*x)^4/(a + b*x + c*x^2)^(3/2), x, 5, -((2*(d + e*x)^3*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*sqrt(a + b*x + c*x^2))) + (2*e*(2*c*d - b*e)*(d + e*x)^2*sqrt(a + b*x + c*x^2))/(c*(b^2 - 4*a*c)) + (e*(32*c^3*d^3 - 15*b^3*e^3 + 4*b*c*e^2*(12*b*d + 13*a*e) - 8*c^2*d*e*(5*b*d + 16*a*e) + 2*c*e*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*x)*sqrt(a + b*x + c*x^2))/(4*c^3*(b^2 - 4*a*c)) + (3*e^2*(16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(4*b*d + a*e))*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(8*c^(7/2))]
    @test_int [(d + e*x)^3/(a + b*x + c*x^2)^(3/2), x, 4, -((2*(d + e*x)^2*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*sqrt(a + b*x + c*x^2))) + (e*(8*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(3*b*d + 4*a*e) + 2*c*e*(2*c*d - b*e)*x)*sqrt(a + b*x + c*x^2))/(c^2*(b^2 - 4*a*c)) + (3*e^2*(2*c*d - b*e)*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(2*c^(5/2))]
    @test_int [(d + e*x)^2/(a + b*x + c*x^2)^(3/2), x, 4, -((2*(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*sqrt(a + b*x + c*x^2))) + (2*e*(2*c*d - b*e)*sqrt(a + b*x + c*x^2))/(c*(b^2 - 4*a*c)) + (e^2*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/c^(3/2)]
    @test_int [(d + e*x)^1/(a + b*x + c*x^2)^(3/2), x, 1, -((2*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*sqrt(a + b*x + c*x^2)))]
    @test_int [(d + e*x)^0/(a + b*x + c*x^2)^(3/2), x, 1, -((2*(b + 2*c*x))/((b^2 - 4*a*c)*sqrt(a + b*x + c*x^2)))]
    @test_int [1/((d + e*x)^1*(a + b*x + c*x^2)^(3/2)), x, 4, -((2*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))) + (e^2*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(c*d^2 - b*d*e + a*e^2)^(3/2)]
    @test_int [1/((d + e*x)^2*(a + b*x + c*x^2)^(3/2)), x, 4, -((2*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*sqrt(a + b*x + c*x^2))) - (e*(4*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(b*d + 2*a*e))*sqrt(a + b*x + c*x^2))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) + (3*e^2*(2*c*d - b*e)*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(2*(c*d^2 - b*d*e + a*e^2)^(5/2))]
    @test_int [1/((d + e*x)^3*(a + b*x + c*x^2)^(3/2)), x, 5, -((2*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2*sqrt(a + b*x + c*x^2))) - (e*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*sqrt(a + b*x + c*x^2))/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2) - (e*(2*c*d - b*e)*(8*c^2*d^2 + 15*b^2*e^2 - 4*c*e*(2*b*d + 13*a*e))*sqrt(a + b*x + c*x^2))/(4*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)) + (3*e^2*(16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(4*b*d + a*e))*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(8*(c*d^2 - b*d*e + a*e^2)^(7/2))]
    @test_int [1/((d + e*x)^4*(a + b*x + c*x^2)^(3/2)), x, 6, -((2*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^3*sqrt(a + b*x + c*x^2))) - (e*(12*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(3*b*d + 4*a*e))*sqrt(a + b*x + c*x^2))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^3) - (e*(2*c*d - b*e)*(24*c^2*d^2 + 35*b^2*e^2 - 4*c*e*(6*b*d + 29*a*e))*sqrt(a + b*x + c*x^2))/(12*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^2) - (e*(96*c^4*d^4 + 105*b^4*e^4 - 20*b^2*c*e^3*(19*b*d + 23*a*e) - 16*c^3*d^2*e*(12*b*d + 83*a*e) + 4*c^2*e^2*(119*b^2*d^2 + 332*a*b*d*e + 64*a^2*e^2))*sqrt(a + b*x + c*x^2))/(24*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)) + (5*e^2*(2*c*d - b*e)*(16*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(4*b*d + 3*a*e))*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(16*(c*d^2 - b*d*e + a*e^2)^(9/2))]

    @test_int [(d + e*x)^5/(a + b*x + c*x^2)^(5/2), x, 5, -((2*(d + e*x)^4*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2))) - (8*(d + e*x)^2*(8*a^2*c*e^3 - 2*b*c*d*(c*d^2 + 3*a*e^2) + b^2*(3*c*d^2*e - a*e^3) - (2*c*d - b*e)*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*x))/(3*c*(b^2 - 4*a*c)^2*sqrt(a + b*x + c*x^2)) - (e*(64*c^4*d^4 - 15*b^4*e^4 - 16*c^3*d^2*e*(7*b*d - 16*a*e) + 10*b^2*c*e^3*(3*b*d + 10*a*e) + 8*c^2*e^2*(b^2*d^2 - 25*a*b*d*e - 16*a^2*e^2) + 2*c*e*(2*c*d - b*e)*(8*c^2*d^2 - 5*b^2*e^2 - 4*c*e*(2*b*d - 7*a*e))*x)*sqrt(a + b*x + c*x^2))/(3*c^3*(b^2 - 4*a*c)^2) + (5*e^4*(2*c*d - b*e)*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/(2*c^(7/2))]
    @test_int [(d + e*x)^4/(a + b*x + c*x^2)^(5/2), x, 5, -((2*(d + e*x)^3*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2))) + (4*(d + e*x)*(4*b*c*d*(c*d^2 + 3*a*e^2) - 4*a*c*e*(c*d^2 + 3*a*e^2) - b^2*(5*c*d^2*e - a*e^3) + (2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*x))/(3*c*(b^2 - 4*a*c)^2*sqrt(a + b*x + c*x^2)) - (2*e*(2*c*d - b*e)*(8*c^2*d^2 - 3*b^2*e^2 - 4*c*e*(2*b*d - 5*a*e))*sqrt(a + b*x + c*x^2))/(3*c^2*(b^2 - 4*a*c)^2) + (e^4*atanh((b + 2*c*x)/(2*sqrt(c)*sqrt(a + b*x + c*x^2))))/c^(5/2)]
    @test_int [(d + e*x)^3/(a + b*x + c*x^2)^(5/2), x, 2, -((2*(d + e*x)^2*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2))) + (16*(c*d^2 - b*d*e + a*e^2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)^2*sqrt(a + b*x + c*x^2))]
    @test_int [(d + e*x)^2/(a + b*x + c*x^2)^(5/2), x, 2, -((2*(b + 2*c*x)*(d + e*x)^2)/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2))) + (8*(2*c*d - b*e)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)^2*sqrt(a + b*x + c*x^2))]
    @test_int [(d + e*x)^1/(a + b*x + c*x^2)^(5/2), x, 2, -((2*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2))) + (8*(2*c*d - b*e)*(b + 2*c*x))/(3*(b^2 - 4*a*c)^2*sqrt(a + b*x + c*x^2))]
    @test_int [(d + e*x)^0/(a + b*x + c*x^2)^(5/2), x, 2, -((2*(b + 2*c*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2))) + (16*c*(b + 2*c*x))/(3*(b^2 - 4*a*c)^2*sqrt(a + b*x + c*x^2))]
    @test_int [1/((d + e*x)^1*(a + b*x + c*x^2)^(5/2)), x, 5, -((2*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^(3/2))) - (2*(4*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(8*c^2*d^2 - 3*b^2*e^2 - 4*c*e*(b*d - 3*a*e)) - c*(2*c*d - b*e)*(8*c^2*d^2 - 3*b^2*e^2 - 4*c*e*(2*b*d - 5*a*e))*x))/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*sqrt(a + b*x + c*x^2)) + (e^4*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(c*d^2 - b*d*e + a*e^2)^(5/2)]
    @test_int [1/((d + e*x)^2*(a + b*x + c*x^2)^(5/2)), x, 5, -((2*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*(a + b*x + c*x^2)^(3/2))) - (2*(6*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(8*c^2*d^2 - 5*b^2*e^2 - 2*c*e*(b*d - 8*a*e)) - c*(2*c*d - b*e)*(8*c^2*d^2 - 5*b^2*e^2 - 4*c*e*(2*b*d - 7*a*e))*x))/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)*sqrt(a + b*x + c*x^2)) + (e*(32*c^4*d^4 - 15*b^4*e^4 - 16*c^3*d^2*e*(4*b*d - 9*a*e) + 20*b^2*c*e^3*(b*d + 5*a*e) + 4*c^2*e^2*(3*b^2*d^2 - 36*a*b*d*e - 32*a^2*e^2))*sqrt(a + b*x + c*x^2))/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)) + (5*e^4*(2*c*d - b*e)*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(2*(c*d^2 - b*d*e + a*e^2)^(7/2))]
    @test_int [1/((d + e*x)^3*(a + b*x + c*x^2)^(5/2)), x, 6, -((2*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2*(a + b*x + c*x^2)^(3/2))) - (2*(8*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(8*c^2*d^2 - 7*b^2*e^2 + 20*a*c*e^2) - c*(2*c*d - b*e)*(8*c^2*d^2 - 7*b^2*e^2 - 4*c*e*(2*b*d - 9*a*e))*x))/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2*sqrt(a + b*x + c*x^2)) + (e*(64*c^4*d^4 - 35*b^4*e^4 - 128*c^3*d^2*e*(b*d - 3*a*e) - 48*a*c^2*e^3*(8*b*d + 5*a*e) + 8*b^2*c*e^3*(8*b*d + 27*a*e))*sqrt(a + b*x + c*x^2))/(6*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^2) + (e*(2*c*d - b*e)*(64*c^4*d^4 - 105*b^4*e^4 - 64*c^3*d^2*e*(2*b*d - 7*a*e) + 40*b^2*c*e^3*(2*b*d + 19*a*e) - 16*c^2*e^2*(b^2*d^2 + 28*a*b*d*e + 81*a^2*e^2))*sqrt(a + b*x + c*x^2))/(12*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)) + (5*e^4*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*atanh((b*d - 2*a*e + (2*c*d - b*e)*x)/(2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2))))/(8*(c*d^2 - b*d*e + a*e^2)^(9/2))]

    @test_int [(3 + x)/sqrt(5 - 4*x - x^2), x, 3, -sqrt(5 - 4*x - x^2) - asin((1/3)*(-2 - x))]
    @test_int [(5 - 4*x)/sqrt(-8 + 12*x - 4*x^2), x, 3, sqrt(-8 + 12*x - 4*x^2) + (1/2)*asin(3 - 2*x)]
    @test_int [(3 + 2*x)/sqrt(5 + 2*x + x^2), x, 3, 2*sqrt(5 + 2*x + x^2) + asinh((1 + x)/2)]
    @test_int [(-1 + x)/sqrt(3 - 4*x + x^2), x, 3, sqrt(3 - 4*x + x^2) - atanh((2 - x)/sqrt(3 - 4*x + x^2))]
    @test_int [1/((1 - x)*sqrt(-4 + 2*x + x^2)), x, 2, atan((3 - 2*x)/sqrt(-4 + 2*x + x^2))]
    @test_int [1/((-2 + x)*sqrt(3 - 4*x + x^2)), x, 2, atan(sqrt(3 - 4*x + x^2))]

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

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

    @test_int [x/sqrt(2 + 4*x + 3*x^2), x, 3, (1/3)*sqrt(2 + 4*x + 3*x^2) - (2*asinh((2 + 3*x)/sqrt(2)))/(3*sqrt(3))]
    @test_int [x/sqrt(2 + 4*x - 3*x^2), x, 3, (-(1/3))*sqrt(2 + 4*x - 3*x^2) - (2*asin((2 - 3*x)/sqrt(10)))/(3*sqrt(3))]
    @test_int [x/sqrt(2 + 5*x + 3*x^2), x, 3, (1/3)*sqrt(2 + 5*x + 3*x^2) - (5*atanh((5 + 6*x)/(2*sqrt(3)*sqrt(2 + 5*x + 3*x^2))))/(6*sqrt(3))]
    @test_int [x/sqrt(2 + 5*x - 3*x^2), x, 3, (-(1/3))*sqrt(2 + 5*x - 3*x^2) - (5*asin((1/7)*(5 - 6*x)))/(6*sqrt(3))]
    @test_int [x/sqrt(-2 + 4*x + 3*x^2), x, 3, (1/3)*sqrt(-2 + 4*x + 3*x^2) - (2*atanh((2 + 3*x)/(sqrt(3)*sqrt(-2 + 4*x + 3*x^2))))/(3*sqrt(3))]
    @test_int [x/sqrt(-2 + 4*x - 3*x^2), x, 3, (-(1/3))*sqrt(-2 + 4*x - 3*x^2) - (2*atan((2 - 3*x)/(sqrt(3)*sqrt(-2 + 4*x - 3*x^2))))/(3*sqrt(3))]
    @test_int [x/sqrt(-2 + 5*x + 3*x^2), x, 3, (1/3)*sqrt(-2 + 5*x + 3*x^2) - (5*atanh((5 + 6*x)/(2*sqrt(3)*sqrt(-2 + 5*x + 3*x^2))))/(6*sqrt(3))]
    @test_int [x/sqrt(-2 + 5*x - 3*x^2), x, 3, (-(1/3))*sqrt(-2 + 5*x - 3*x^2) - (5*asin(5 - 6*x))/(6*sqrt(3))]

    @test_int [1/(x*sqrt(4 + 12*x + 9*x^2)), x, 4, -(((2 + 3*x)*atanh(1 + 3*x))/sqrt(4 + 12*x + 9*x^2)), ((2 + 3*x)*log(x))/(2*sqrt(4 + 12*x + 9*x^2)) - ((2 + 3*x)*log(2 + 3*x))/(2*sqrt(4 + 12*x + 9*x^2))]
    @test_int [1/(x*sqrt(4 - 12*x + 9*x^2)), x, 4, -(((2 - 3*x)*atanh(1 - 3*x))/sqrt(4 - 12*x + 9*x^2)), -(((2 - 3*x)*log(2 - 3*x))/(2*sqrt(4 - 12*x + 9*x^2))) + ((2 - 3*x)*log(x))/(2*sqrt(4 - 12*x + 9*x^2))]
    @test_int [1/(x*sqrt(-4 + 12*x - 9*x^2)), x, 4, -(((2 - 3*x)*atanh(1 - 3*x))/sqrt(-4 + 12*x - 9*x^2)), -(((2 - 3*x)*log(2 - 3*x))/(2*sqrt(-4 + 12*x - 9*x^2))) + ((2 - 3*x)*log(x))/(2*sqrt(-4 + 12*x - 9*x^2))]
    @test_int [1/(x*sqrt(-4 - 12*x - 9*x^2)), x, 4, -(((2 + 3*x)*atanh(1 + 3*x))/sqrt(-4 - 12*x - 9*x^2)), ((2 + 3*x)*log(x))/(2*sqrt(-4 - 12*x - 9*x^2)) - ((2 + 3*x)*log(2 + 3*x))/(2*sqrt(-4 - 12*x - 9*x^2))]

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

    @test_int [x*sqrt(3 - 2*x - x^2), x, 4, (-(1/2))*(1 + x)*sqrt(3 - 2*x - x^2) - (1/3)*(3 - 2*x - x^2)^(3/2) + 2*asin((1/2)*(-1 - x))]
    @test_int [x*sqrt(8 + 2*x - x^2), x, 4, (-(1/2))*(1 - x)*sqrt(8 + 2*x - x^2) - (1/3)*(8 + 2*x - x^2)^(3/2) - (9/2)*asin((1 - x)/3)]
    @test_int [x*sqrt(4 + 2*x + x^2), x, 4, (-(1/2))*(1 + x)*sqrt(4 + 2*x + x^2) + (1/3)*(4 + 2*x + x^2)^(3/2) - (3/2)*asinh((1 + x)/sqrt(3))]

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

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

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

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

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

    @test_int [(d*x)^(5/2)*sqrt(a + b*x + c*x^2), x, 8, -((4*(8*b^4 - 36*a*b^2*c + 21*a^2*c^2)*d^3*x*sqrt(a + b*x + c*x^2))/(315*c^(7/2)*sqrt(d*x)*(sqrt(a) + sqrt(c)*x))) + (2*d^2*sqrt(d*x)*(b*(8*b^2 + 3*a*c) + 3*c*(8*b^2 - 7*a*c)*x)*sqrt(a + b*x + c*x^2))/(315*c^3) - (4*b*d^2*sqrt(d*x)*(a + b*x + c*x^2)^(3/2))/(21*c^2) + (2*d*(d*x)^(3/2)*(a + b*x + c*x^2)^(3/2))/(9*c) + (4*a^(1/4)*(8*b^4 - 36*a*b^2*c + 21*a^2*c^2)*d^3*sqrt(x)*(sqrt(a) + sqrt(c)*x)*sqrt((a + b*x + c*x^2)/(sqrt(a) + sqrt(c)*x)^2)*Elliptic.E(2*atan((c^(1/4)*sqrt(x))/a^(1/4)), (1/4)*(2 - b/(sqrt(a)*sqrt(c)))))/(315*c^(15/4)*sqrt(d*x)*sqrt(a + b*x + c*x^2)) - (a^(1/4)*(16*b^4 - 72*a*b^2*c + 42*a^2*c^2 + sqrt(a)*b*sqrt(c)*(8*b^2 - 27*a*c))*d^3*sqrt(x)*(sqrt(a) + sqrt(c)*x)*sqrt((a + b*x + c*x^2)/(sqrt(a) + sqrt(c)*x)^2)*Elliptic.F(2*atan((c^(1/4)*sqrt(x))/a^(1/4)), (1/4)*(2 - b/(sqrt(a)*sqrt(c)))))/(315*c^(15/4)*sqrt(d*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(d + e*x)^(3/2)*sqrt(a + b*x + c*x^2), x, 7, (2*sqrt(d + e*x)*(3*c^2*d^2 - 4*b^2*e^2 + c*e*(9*b*d - 5*a*e) + 12*c*e*(2*c*d - b*e)*x)*sqrt(a + b*x + c*x^2))/(105*c^2*e) + (2*e*sqrt(d + e*x)*(a + b*x + c*x^2)^(3/2))/(7*c) - (sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*(3*c^2*d^2 + 8*b^2*e^2 - c*e*(3*b*d + 29*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(105*c^3*e^2*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (4*sqrt(2)*sqrt(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(3*c^2*d^2 + 2*b^2*e^2 - c*e*(3*b*d + 5*a*e))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(105*c^3*e^2*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(d + e*x)^(1/2)*sqrt(a + b*x + c*x^2), x, 7, (-2*(2*c*d - b*e)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))/(15*c*e) + (2*(d + e*x)^(3/2)*sqrt(a + b*x + c*x^2))/(5*e) - (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(15*c^2*e^2*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(15*c^2*e^2*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [sqrt(a + b*x + c*x^2)/(d + e*x)^(1/2), x, 6, (2*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))/(3*e) - (sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*c*e^2*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (4*sqrt(2)*sqrt(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*c*e^2*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [sqrt(a + b*x + c*x^2)/(d + e*x)^(3/2), x, 6, (-2*sqrt(a + b*x + c*x^2))/(e*sqrt(d + e*x)) + (2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(e^2*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(c*e^2*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [sqrt(a + b*x + c*x^2)/(d + e*x)^(5/2), x, 7, (-2*sqrt(a + b*x + c*x^2))/(3*e*(d + e*x)^(3/2)) + (2*(2*c*d - b*e)*sqrt(a + b*x + c*x^2))/(3*e*(c*d^2 - b*d*e + a*e^2)*sqrt(d + e*x)) - (sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*e^2*(c*d^2 - b*d*e + a*e^2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*e^2*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [sqrt(a + b*x + c*x^2)/(d + e*x)^(7/2), x, 8, (-2*sqrt(a + b*x + c*x^2))/(5*e*(d + e*x)^(5/2)) + (2*(2*c*d - b*e)*sqrt(a + b*x + c*x^2))/(15*e*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2)) + (4*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*sqrt(a + b*x + c*x^2))/(15*e*(c*d^2 - b*d*e + a*e^2)^2*sqrt(d + e*x)) - (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(15*e^2*(c*d^2 - b*d*e + a*e^2)^2*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(15*e^2*(c*d^2 - b*d*e + a*e^2)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]

    @test_int [(d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2), x, 8, (2*sqrt(d + e*x)*(8*c^4*d^4 + 8*b^4*e^4 - c^3*d^2*e*(19*b*d - 42*a*e) - b^2*c*e^3*(19*b*d + 21*a*e) + 3*c^2*e^2*(2*b^2*d^2 + 17*a*b*d*e - 10*a^2*e^2) - 3*c*e*(2*c*d - b*e)*(c^2*d^2 + 8*b^2*e^2 - c*e*(b*d + 31*a*e))*x)*sqrt(a + b*x + c*x^2))/(1155*c^3*e^3) + (2*sqrt(d + e*x)*(c^2*d^2 - 6*b^2*e^2 + c*e*(13*b*d - 3*a*e) + 14*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(231*c^2*e) + (2*e*sqrt(d + e*x)*(a + b*x + c*x^2)^(5/2))/(11*c) - (8*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*(c^2*d^2 - 2*b^2*e^2 - c*e*(b*d - 9*a*e))*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(1155*c^4*e^4*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(16*c^4*d^4 - 8*b^4*e^4 - 4*c^3*d^2*e*(8*b*d - 21*a*e) + b^2*c*e^3*(13*b*d + 51*a*e) + 3*c^2*e^2*(b^2*d^2 - 28*a*b*d*e - 20*a^2*e^2))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(1155*c^4*e^4*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(d + e*x)^(1/2)*(a + b*x + c*x^2)^(3/2), x, 8, (2*sqrt(d + e*x)*(8*c^3*d^3 - 4*b^3*e^3 - 3*c^2*d*e*(5*b*d - 8*a*e) + 3*b*c*e^2*(b*d + 3*a*e) - 6*c*e*(c^2*d^2 + 2*b^2*e^2 - c*e*(b*d + 7*a*e))*x)*sqrt(a + b*x + c*x^2))/(315*c^2*e^3) - (2*(2*c*d - b*e)*sqrt(d + e*x)*(a + b*x + c*x^2)^(3/2))/(21*c*e) + (2*(d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2))/(9*e) - (sqrt(2)*sqrt(b^2 - 4*a*c)*(16*c^4*d^4 - 8*b^4*e^4 - 4*c^3*d^2*e*(8*b*d - 15*a*e) + b^2*c*e^3*(7*b*d + 57*a*e) + 3*c^2*e^2*(3*b^2*d^2 - 20*a*b*d*e - 28*a^2*e^2))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(315*c^3*e^4*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (8*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(315*c^3*e^4*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(d + e*x)^(1/2), x, 7, (2*sqrt(d + e*x)*(8*c^2*d^2 + b^2*e^2 - c*e*(11*b*d - 10*a*e) - 3*c*e*(2*c*d - b*e)*x)*sqrt(a + b*x + c*x^2))/(35*c*e^3) + (2*sqrt(d + e*x)*(a + b*x + c*x^2)^(3/2))/(7*e) - (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), -((2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))))/(35*c^2*e^4*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(16*c^2*d^2 - b^2*e^2 - 4*c*e*(4*b*d - 5*a*e))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), -((2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))))/(35*c^2*e^4*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(d + e*x)^(3/2), x, 7, (-2*sqrt(d + e*x)*(8*c*d - 7*b*e - 6*c*e*x)*sqrt(a + b*x + c*x^2))/(5*e^3) - (2*(a + b*x + c*x^2)^(3/2))/(e*sqrt(d + e*x)) + (sqrt(2)*sqrt(b^2 - 4*a*c)*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(5*c*e^4*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (16*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(5*c*e^4*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(d + e*x)^(5/2), x, 7, (2*(8*c*d - 3*b*e + 2*c*e*x)*sqrt(a + b*x + c*x^2))/(3*e^3*sqrt(d + e*x)) - (2*(a + b*x + c*x^2)^(3/2))/(3*e*(d + e*x)^(3/2)) - (8*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*e^4*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(16*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(4*b*d - a*e))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*c*e^4*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(d + e*x)^(7/2), x, 7, -((2*(8*c^2*d^3 + a*b*e^3 - c*d*e*(7*b*d - 4*a*e) + e*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*x)*sqrt(a + b*x + c*x^2))/(5*e^3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2))) - (2*(a + b*x + c*x^2)^(3/2))/(5*e*(d + e*x)^(5/2)) + (sqrt(2)*sqrt(b^2 - 4*a*c)*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), -((2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))))/(5*e^4*(c*d^2 - b*d*e + a*e^2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (16*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), -((2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))))/(5*e^4*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(3/2)/(d + e*x)^(9/2), x, 8, (4*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*sqrt(a + b*x + c*x^2))/(35*e^3*(c*d^2 - b*d*e + a*e^2)^2*sqrt(d + e*x)) - (2*(8*c^2*d^3 - c*d*e*(5*b*d - 4*a*e) - b*e^2*(2*b*d - 3*a*e) + e*(14*c^2*d^2 + b^2*e^2 - 2*c*e*(7*b*d - 5*a*e))*x)*sqrt(a + b*x + c*x^2))/(35*e^3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(5/2)) - (2*(a + b*x + c*x^2)^(3/2))/(7*e*(d + e*x)^(7/2)) - (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), -((2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))))/(35*e^4*(c*d^2 - b*d*e + a*e^2)^2*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(16*c^2*d^2 - b^2*e^2 - 4*c*e*(4*b*d - 5*a*e))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), -((2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))))/(35*e^4*(c*d^2 - b*d*e + a*e^2)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]

    @test_int [(d*x)^(1/2)*(a + b*x + c*x^2)^(5/2), x, 9, -((4*(24*b^6 - 268*a*b^4*c + 951*a^2*b^2*c^2 - 924*a^3*c^3)*d*x*sqrt(a + b*x + c*x^2))/(9009*c^(7/2)*sqrt(d*x)*(sqrt(a) + sqrt(c)*x))) + (2*sqrt(d*x)*(b*(24*b^4 - 151*a*b^2*c + 108*a^2*c^2) + 3*c*(24*b^4 - 181*a*b^2*c + 308*a^2*c^2)*x)*sqrt(a + b*x + c*x^2))/(9009*c^3) - (10*sqrt(d*x)*(3*b*(6*b^2 - 19*a*c) + 14*c*(3*b^2 - 11*a*c)*x)*(a + b*x + c*x^2)^(3/2))/(9009*c^2) + (10*b*sqrt(d*x)*(a + b*x + c*x^2)^(5/2))/(143*c) + (2*(d*x)^(3/2)*(a + b*x + c*x^2)^(5/2))/(13*d) + (4*a^(1/4)*(24*b^6 - 268*a*b^4*c + 951*a^2*b^2*c^2 - 924*a^3*c^3)*d*sqrt(x)*(sqrt(a) + sqrt(c)*x)*sqrt((a + b*x + c*x^2)/(sqrt(a) + sqrt(c)*x)^2)*Elliptic.E(2*atan((c^(1/4)*sqrt(x))/a^(1/4)), (1/4)*(2 - b/(sqrt(a)*sqrt(c)))))/(9009*c^(15/4)*sqrt(d*x)*sqrt(a + b*x + c*x^2)) - (a^(1/4)*(sqrt(a)*b*sqrt(c)*(24*b^4 - 241*a*b^2*c + 708*a^2*c^2) + 2*(24*b^6 - 268*a*b^4*c + 951*a^2*b^2*c^2 - 924*a^3*c^3))*d*sqrt(x)*(sqrt(a) + sqrt(c)*x)*sqrt((a + b*x + c*x^2)/(sqrt(a) + sqrt(c)*x)^2)*Elliptic.F(2*atan((c^(1/4)*sqrt(x))/a^(1/4)), (1/4)*(2 - b/(sqrt(a)*sqrt(c)))))/(9009*c^(15/4)*sqrt(d*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(d + e*x)^(1/2), x, 8, (2*sqrt(d + e*x)*(128*c^4*d^4 - 4*b^4*e^4 - 4*c^3*d^2*e*(76*b*d - 69*a*e) - b^2*c*e^3*(7*b*d - 27*a*e) + 3*c^2*e^2*(65*b^2*d^2 - 124*a*b*d*e + 60*a^2*e^2) - 12*c*e*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*x)*sqrt(a + b*x + c*x^2))/(693*c^2*e^5) + (10*sqrt(d + e*x)*(16*c^2*d^2 + 3*b^2*e^2 - c*e*(23*b*d - 18*a*e) - 7*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(693*c*e^3) + (2*sqrt(d + e*x)*(a + b*x + c*x^2)^(5/2))/(11*e) - (sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*(128*c^4*d^4 + 8*b^4*e^4 + b^2*c*e^3*(29*b*d - 93*a*e) - 4*c^3*d^2*e*(64*b*d - 93*a*e) + 3*c^2*e^2*(33*b^2*d^2 - 124*a*b*d*e + 124*a^2*e^2))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(693*c^3*e^6*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (4*sqrt(2)*sqrt(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(128*c^4*d^4 + 2*b^4*e^4 - 4*c^3*d^2*e*(64*b*d - 69*a*e) + b^2*c*e^3*(5*b*d - 21*a*e) + 3*c^2*e^2*(41*b^2*d^2 - 92*a*b*d*e + 60*a^2*e^2))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(693*c^3*e^6*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(d + e*x)^(3/2), x, 8, (-2*sqrt(d + e*x)*(128*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(37*b*d - 36*a*e) - 12*c^2*d*e*(20*b*d - 11*a*e) - 3*c*e*(32*c^2*d^2 + b^2*e^2 - 4*c*e*(8*b*d - 7*a*e))*x)*sqrt(a + b*x + c*x^2))/(63*c*e^5) - (10*sqrt(d + e*x)*(16*c*d - 15*b*e - 14*c*e*x)*(a + b*x + c*x^2)^(3/2))/(63*e^3) - (2*(a + b*x + c*x^2)^(5/2))/(e*sqrt(d + e*x)) + (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(128*c^4*d^4 - b^4*e^4 - 4*c^3*d^2*e*(64*b*d - 57*a*e) - b^2*c*e^3*(7*b*d - 15*a*e) + 3*c^2*e^2*(45*b^2*d^2 - 76*a*b*d*e + 28*a^2*e^2))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(63*c^2*e^6*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(128*c^2*d^2 - b^2*e^2 - 4*c*e*(32*b*d - 33*a*e))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(63*c^2*e^6*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(d + e*x)^(5/2), x, 8, (2*sqrt(d + e*x)*(128*c^2*d^2 + 51*b^2*e^2 - 4*c*e*(44*b*d - 5*a*e) - 48*c*e*(2*c*d - b*e)*x)*sqrt(a + b*x + c*x^2))/(21*e^5) + (10*(16*c*d - 7*b*e + 2*c*e*x)*(a + b*x + c*x^2)^(3/2))/(21*e^3*sqrt(d + e*x)) - (2*(a + b*x + c*x^2)^(5/2))/(3*e*(d + e*x)^(3/2)) - (sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*(128*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(32*b*d - 29*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(21*c*e^6*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (4*sqrt(2)*sqrt(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(128*c^2*d^2 + 27*b^2*e^2 - 4*c*e*(32*b*d - 5*a*e))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(21*c*e^6*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(d + e*x)^(7/2), x, 8, (-2*(128*c^2*d^2 + 15*b^2*e^2 - 4*c*e*(28*b*d - 9*a*e) + 16*c*e*(2*c*d - b*e)*x)*sqrt(a + b*x + c*x^2))/(15*e^5*sqrt(d + e*x)) + (2*(16*c*d - 5*b*e + 6*c*e*x)*(a + b*x + c*x^2)^(3/2))/(15*e^3*(d + e*x)^(3/2)) - (2*(a + b*x + c*x^2)^(5/2))/(5*e*(d + e*x)^(5/2)) + (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(128*c^2*d^2 + 23*b^2*e^2 - 4*c*e*(32*b*d - 9*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(15*e^6*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*(128*c^2*d^2 + 15*b^2*e^2 - 4*c*e*(32*b*d - 17*a*e))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(15*c*e^6*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(d + e*x)^(9/2), x, 8, (2*c*(128*c^2*d^3 - 4*c*d*e*(44*b*d - 29*a*e) + 3*b*e^2*(17*b*d - 16*a*e) + e*(32*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(8*b*d - 5*a*e))*x)*sqrt(a + b*x + c*x^2))/(21*e^5*(c*d^2 - b*d*e + a*e^2)*sqrt(d + e*x)) - (2*(16*c^2*d^3 + 3*a*b*e^3 - c*d*e*(13*b*d - 4*a*e) + e*(22*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(11*b*d - 5*a*e))*x)*(a + b*x + c*x^2)^(3/2))/(21*e^3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(5/2)) - (2*(a + b*x + c*x^2)^(5/2))/(7*e*(d + e*x)^(7/2)) - (sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*(128*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(32*b*d - 29*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), -((2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))))/(21*e^6*(c*d^2 - b*d*e + a*e^2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (4*sqrt(2)*sqrt(b^2 - 4*a*c)*(128*c^2*d^2 + 27*b^2*e^2 - 4*c*e*(32*b*d - 5*a*e))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), -((2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))))/(21*e^6*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(a + b*x + c*x^2)^(5/2)/(d + e*x)^(11/2), x, 8, -((2*(128*c^4*d^5 - 2*a*b^3*e^5 - 4*c^3*d^3*e*(60*b*d - 49*a*e) - b*c*e^3*(b^2*d^2 + 9*a*b*d*e - 24*a^2*e^2) + 3*c^2*d*e^2*(37*b^2*d^2 - 52*a*b*d*e + 12*a^2*e^2) + e*(160*c^4*d^4 - 2*b^4*e^4 - 4*c^3*d^2*e*(80*b*d - 69*a*e) - b^2*c*e^3*(11*b*d - 27*a*e) + 3*c^2*e^2*(57*b^2*d^2 - 92*a*b*d*e + 28*a^2*e^2))*x)*sqrt(a + b*x + c*x^2))/(63*e^5*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(3/2))) - (2*(16*c^2*d^3 - b*e^2*(2*b*d - 5*a*e) - c*d*e*(11*b*d - 4*a*e) + e*(26*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(13*b*d - 7*a*e))*x)*(a + b*x + c*x^2)^(3/2))/(63*e^3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(7/2)) - (2*(a + b*x + c*x^2)^(5/2))/(9*e*(d + e*x)^(9/2)) + (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(128*c^4*d^4 - b^4*e^4 - 4*c^3*d^2*e*(64*b*d - 57*a*e) - b^2*c*e^3*(7*b*d - 15*a*e) + 3*c^2*e^2*(45*b^2*d^2 - 76*a*b*d*e + 28*a^2*e^2))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), -((2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))))/(63*e^6*(c*d^2 - b*d*e + a*e^2)^2*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*(128*c^2*d^2 - b^2*e^2 - 4*c*e*(32*b*d - 33*a*e))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), -((2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))))/(63*e^6*(c*d^2 - b*d*e + a*e^2)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]

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

    @test_int [(d + e*x)^(7/2)/sqrt(a + b*x + c*x^2), x, 8, (2*e*(71*c^2*d^2 + 24*b^2*e^2 - c*e*(71*b*d + 25*a*e))*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))/(105*c^3) + (12*e*(2*c*d - b*e)*(d + e*x)^(3/2)*sqrt(a + b*x + c*x^2))/(35*c^2) + (2*e*(d + e*x)^(5/2)*sqrt(a + b*x + c*x^2))/(7*c) + (8*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*(11*c^2*d^2 + 6*b^2*e^2 - c*e*(11*b*d + 13*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(105*c^4*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(71*c^2*d^2 + 24*b^2*e^2 - c*e*(71*b*d + 25*a*e))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(105*c^4*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(d + e*x)^(5/2)/sqrt(a + b*x + c*x^2), x, 7, (8*e*(2*c*d - b*e)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))/(15*c^2) + (2*e*(d + e*x)^(3/2)*sqrt(a + b*x + c*x^2))/(5*c) + (sqrt(2)*sqrt(b^2 - 4*a*c)*(23*c^2*d^2 + 8*b^2*e^2 - c*e*(23*b*d + 9*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(15*c^3*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (8*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(15*c^3*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(d + e*x)^(3/2)/sqrt(a + b*x + c*x^2), x, 6, (2*e*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))/(3*c) + (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*c^2*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*c^2*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(d + e*x)^(1/2)/sqrt(a + b*x + c*x^2), x, 2, (sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(c*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2))]
    @test_int [1/((d + e*x)^(1/2)*sqrt(a + b*x + c*x^2)), x, 2, (2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(c*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [1/((d + e*x)^(3/2)*sqrt(a + b*x + c*x^2)), x, 4, (-2*e*sqrt(a + b*x + c*x^2))/((c*d^2 - b*d*e + a*e^2)*sqrt(d + e*x)) + (sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/((c*d^2 - b*d*e + a*e^2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2))]
    @test_int [1/((d + e*x)^(5/2)*sqrt(a + b*x + c*x^2)), x, 7, (-2*e*sqrt(a + b*x + c*x^2))/(3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2)) - (4*e*(2*c*d - b*e)*sqrt(a + b*x + c*x^2))/(3*(c*d^2 - b*d*e + a*e^2)^2*sqrt(d + e*x)) + (2*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*(c*d^2 - b*d*e + a*e^2)^2*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*(c*d^2 - b*d*e + a*e^2)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [1/((d + e*x)^(7/2)*sqrt(a + b*x + c*x^2)), x, 8, (-2*e*sqrt(a + b*x + c*x^2))/(5*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(5/2)) - (8*e*(2*c*d - b*e)*sqrt(a + b*x + c*x^2))/(15*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(3/2)) - (2*e*(23*c^2*d^2 + 8*b^2*e^2 - c*e*(23*b*d + 9*a*e))*sqrt(a + b*x + c*x^2))/(15*(c*d^2 - b*d*e + a*e^2)^3*sqrt(d + e*x)) + (sqrt(2)*sqrt(b^2 - 4*a*c)*(23*c^2*d^2 + 8*b^2*e^2 - c*e*(23*b*d + 9*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(15*(c*d^2 - b*d*e + a*e^2)^3*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (8*sqrt(2)*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(15*(c*d^2 - b*d*e + a*e^2)^2*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]

    @test_int [(d + e*x)^(7/2)/(a + b*x + c*x^2)^(3/2), x, 8, (-2*(d + e*x)^(5/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*sqrt(a + b*x + c*x^2)) + (4*e*(3*c^2*d^2 + 2*b^2*e^2 - c*e*(3*b*d + 5*a*e))*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))/(3*c^2*(b^2 - 4*a*c)) + (2*e*(2*c*d - b*e)*(d + e*x)^(3/2)*sqrt(a + b*x + c*x^2))/(c*(b^2 - 4*a*c)) + (sqrt(2)*(2*c*d - b*e)*(3*c^2*d^2 + 8*b^2*e^2 - c*e*(3*b*d + 29*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*c^3*sqrt(b^2 - 4*a*c)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (4*sqrt(2)*(c*d^2 - b*d*e + a*e^2)*(3*c^2*d^2 + 2*b^2*e^2 - c*e*(3*b*d + 5*a*e))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*c^3*sqrt(b^2 - 4*a*c)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(d + e*x)^(5/2)/(a + b*x + c*x^2)^(3/2), x, 7, (-2*(d + e*x)^(3/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*sqrt(a + b*x + c*x^2)) + (2*e*(2*c*d - b*e)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))/(c*(b^2 - 4*a*c)) + (2*sqrt(2)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(c^2*sqrt(b^2 - 4*a*c)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (2*sqrt(2)*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(c^2*sqrt(b^2 - 4*a*c)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(d + e*x)^(3/2)/(a + b*x + c*x^2)^(3/2), x, 6, -((2*sqrt(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*sqrt(a + b*x + c*x^2))) + (sqrt(2)*(2*c*d - b*e)*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), -((2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))))/(c*sqrt(b^2 - 4*a*c)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (4*sqrt(2)*(c*d^2 - b*d*e + a*e^2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), -((2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))))/(c*sqrt(b^2 - 4*a*c)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(d + e*x)^(1/2)/(a + b*x + c*x^2)^(3/2), x, 6, (-2*(b + 2*c*x)*sqrt(d + e*x))/((b^2 - 4*a*c)*sqrt(a + b*x + c*x^2)) + (2*sqrt(2)*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(sqrt(b^2 - 4*a*c)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (2*sqrt(2)*(2*c*d - b*e)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(c*sqrt(b^2 - 4*a*c)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [1/((d + e*x)^(1/2)*(a + b*x + c*x^2)^(3/2)), x, 6, (-2*sqrt(d + e*x)*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2)) + (sqrt(2)*(2*c*d - b*e)*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(sqrt(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (4*sqrt(2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(sqrt(b^2 - 4*a*c)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [1/((d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2)), x, 7, (-2*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2)) - (4*e*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*sqrt(a + b*x + c*x^2))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*sqrt(d + e*x)) + (2*sqrt(2)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(sqrt(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (2*sqrt(2)*(2*c*d - b*e)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(sqrt(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [1/((d + e*x)^(5/2)*(a + b*x + c*x^2)^(3/2)), x, 8, (-2*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2)*sqrt(a + b*x + c*x^2)) - (4*e*(3*c^2*d^2 + 2*b^2*e^2 - c*e*(3*b*d + 5*a*e))*sqrt(a + b*x + c*x^2))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(3/2)) - (2*e*(2*c*d - b*e)*(3*c^2*d^2 + 8*b^2*e^2 - c*e*(3*b*d + 29*a*e))*sqrt(a + b*x + c*x^2))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^3*sqrt(d + e*x)) + (sqrt(2)*(2*c*d - b*e)*(3*c^2*d^2 + 8*b^2*e^2 - c*e*(3*b*d + 29*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*sqrt(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^3*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) - (4*sqrt(2)*(3*c^2*d^2 + 2*b^2*e^2 - c*e*(3*b*d + 5*a*e))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*sqrt(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]

    @test_int [(d + e*x)^(7/2)/(a + b*x + c*x^2)^(5/2), x, 7, -((2*(d + e*x)^(5/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2))) + (2*sqrt(d + e*x)*(8*b*c*d*(c*d^2 + 3*a*e^2) - 4*a*c*e*(3*c*d^2 + 5*a*e^2) - b^2*(9*c*d^2*e - a*e^3) + (2*c*d - b*e)*(8*c^2*d^2 - b^2*e^2 - 4*c*e*(2*b*d - 3*a*e))*x))/(3*c*(b^2 - 4*a*c)^2*sqrt(a + b*x + c*x^2)) - (2*sqrt(2)*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), -((2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))))/(3*c^2*(b^2 - 4*a*c)^(3/2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (2*sqrt(2)*(c*d^2 - b*d*e + a*e^2)*(16*c^2*d^2 - b^2*e^2 - 4*c*e*(4*b*d - 5*a*e))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), -((2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))))/(3*c^2*(b^2 - 4*a*c)^(3/2)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(d + e*x)^(5/2)/(a + b*x + c*x^2)^(5/2), x, 7, (-2*(d + e*x)^(3/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) - (2*sqrt(d + e*x)*(7*b^2*d*e + 4*a*c*d*e - 8*b*(c*d^2 + a*e^2) - (16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*x))/(3*(b^2 - 4*a*c)^2*sqrt(a + b*x + c*x^2)) - (sqrt(2)*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*c*(b^2 - 4*a*c)^(3/2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (16*sqrt(2)*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*c*(b^2 - 4*a*c)^(3/2)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(d + e*x)^(3/2)/(a + b*x + c*x^2)^(5/2), x, 7, (-2*sqrt(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) + (2*sqrt(d + e*x)*(8*b*c*d - 5*b^2*e + 4*a*c*e + 8*c*(2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)^2*sqrt(a + b*x + c*x^2)) - (8*sqrt(2)*(2*c*d - b*e)*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*(b^2 - 4*a*c)^(3/2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (2*sqrt(2)*(16*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(4*b*d - a*e))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*c*(b^2 - 4*a*c)^(3/2)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [(d + e*x)^(1/2)/(a + b*x + c*x^2)^(5/2), x, 7, (-2*(b + 2*c*x)*sqrt(d + e*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) - (2*sqrt(d + e*x)*(9*b^2*c*d*e - 4*a*c^2*d*e - b^3*e^2 - 4*b*c*(2*c*d^2 + a*e^2) - c*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*x))/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)*sqrt(a + b*x + c*x^2)) - (sqrt(2)*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*(b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (16*sqrt(2)*(2*c*d - b*e)*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*(b^2 - 4*a*c)^(3/2)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [1/((d + e*x)^(1/2)*(a + b*x + c*x^2)^(5/2)), x, 7, (-2*sqrt(d + e*x)*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^(3/2)) - (2*sqrt(d + e*x)*(3*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(8*c^2*d^2 - 2*b^2*e^2 - 5*c*e*(b*d - 2*a*e)) - 2*c*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*x))/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*sqrt(a + b*x + c*x^2)) - (2*sqrt(2)*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*(b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)^2*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (2*sqrt(2)*(16*c^2*d^2 - b^2*e^2 - 4*c*e*(4*b*d - 5*a*e))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*(b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]
    @test_int [1/((d + e*x)^(3/2)*(a + b*x + c*x^2)^(5/2)), x, 8, (-2*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*sqrt(d + e*x)*(a + b*x + c*x^2)^(3/2)) - (2*(5*a*c*e*(2*c*d - b*e)^2 - (b*c*d - b^2*e + 2*a*c*e)*(8*c^2*d^2 - 4*b^2*e^2 - c*e*(3*b*d - 14*a*e)) - 4*c*(2*c*d - b*e)*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*x))/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*sqrt(d + e*x)*sqrt(a + b*x + c*x^2)) + (2*e*(16*c^4*d^4 - 8*b^4*e^4 - 4*c^3*d^2*e*(8*b*d - 15*a*e) + b^2*c*e^3*(7*b*d + 57*a*e) + 3*c^2*e^2*(3*b^2*d^2 - 20*a*b*d*e - 28*a^2*e^2))*sqrt(a + b*x + c*x^2))/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^3*sqrt(d + e*x)) - (sqrt(2)*(16*c^4*d^4 - 8*b^4*e^4 - 4*c^3*d^2*e*(8*b*d - 15*a*e) + b^2*c*e^3*(7*b*d + 57*a*e) + 3*c^2*e^2*(3*b^2*d^2 - 20*a*b*d*e - 28*a^2*e^2))*sqrt(d + e*x)*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.E(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*(b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)^3*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(a + b*x + c*x^2)) + (8*sqrt(2)*(2*c*d - b*e)*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*sqrt((c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))*sqrt(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))*Elliptic.F(asin(sqrt((b + sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c))/sqrt(2)), (-2*sqrt(b^2 - 4*a*c)*e)/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(3*(b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)^2*sqrt(d + e*x)*sqrt(a + b*x + c*x^2))]

    @test_int [sqrt(3 + 5*x)/sqrt(2 + 5*x - 12*x^2), x, 2, (-(1/3))*sqrt(19)*Elliptic.E(asin((2*sqrt(2 - 3*x))/sqrt(11)), 55/76)]

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

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

    @test_int [(d + e*x)^2*(a + b*x + c*x^2)^(4/3), x, 6, -((3*(b^2 - 4*a*c)*(17*c^2*d^2 + 5*b^2*e^2 - c*e*(17*b*d + 3*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/3))/(935*c^4)) + (3*(17*c^2*d^2 + 5*b^2*e^2 - c*e*(17*b*d + 3*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(4/3))/(374*c^3) + (15*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(7/3))/(119*c^2) + (3*e*(d + e*x)*(a + b*x + c*x^2)^(7/3))/(17*c) + (2^(1/3)*3^(3/4)*sqrt(2 + sqrt(3))*(b^2 - 4*a*c)^2*(17*c^2*d^2 + 5*b^2*e^2 - c*e*(17*b*d + 3*a*e))*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*sqrt(((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))), -7 - 4*sqrt(3)))/(935*c^(13/3)*(b + 2*c*x)*sqrt(((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2))]
    @test_int [(d + e*x)^1*(a + b*x + c*x^2)^(4/3), x, 5, -((3*(b^2 - 4*a*c)*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/3))/(110*c^3)) + (3*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(4/3))/(44*c^2) + (3*e*(a + b*x + c*x^2)^(7/3))/(14*c) + (3^(3/4)*sqrt(2 + sqrt(3))*(b^2 - 4*a*c)^2*(2*c*d - b*e)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*sqrt(((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))), -7 - 4*sqrt(3)))/(55*2^(2/3)*c^(10/3)*(b + 2*c*x)*sqrt(((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2))]
    @test_int [(d + e*x)^0*(a + b*x + c*x^2)^(4/3), x, 4, -((3*(b^2 - 4*a*c)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/3))/(55*c^2)) + (3*(b + 2*c*x)*(a + b*x + c*x^2)^(4/3))/(22*c) + (2^(1/3)*3^(3/4)*sqrt(2 + sqrt(3))*(b^2 - 4*a*c)^2*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*sqrt(((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))), -7 - 4*sqrt(3)))/(55*c^(7/3)*(b + 2*c*x)*sqrt(((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2))]
    @test_int [(a + b*x + c*x^2)^(4/3)/(d + e*x)^1, x, 2, (3*(a + b*x + c*x^2)^(4/3)*AppellF1(-(8/3), -(4/3), -(4/3), -(5/3), (2*c*d - (b - sqrt(b^2 - 4*a*c))*e)/(2*c*(d + e*x)), (2*d - ((b + sqrt(b^2 - 4*a*c))*e)/c)/(2*(d + e*x))))/(2^(1/3)*e*((e*(b - sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^(4/3)*((e*(b + sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^(4/3))]
    @test_int [(a + b*x + c*x^2)^(4/3)/(d + e*x)^2, x, 2, (12*2^(2/3)*(a + b*x + c*x^2)^(4/3)*AppellF1(-(5/3), -(4/3), -(4/3), -(2/3), (2*c*d - (b - sqrt(b^2 - 4*a*c))*e)/(2*c*(d + e*x)), (2*d - ((b + sqrt(b^2 - 4*a*c))*e)/c)/(2*(d + e*x))))/(5*e*((e*(b - sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^(4/3)*((e*(b + sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^(4/3)*(d + e*x))]
    @test_int [(a + b*x + c*x^2)^(4/3)/(d + e*x)^3, x, 2, (6*2^(2/3)*(a + b*x + c*x^2)^(4/3)*AppellF1(-(2/3), -(4/3), -(4/3), 1/3, (2*c*d - (b - sqrt(b^2 - 4*a*c))*e)/(2*c*(d + e*x)), (2*d - ((b + sqrt(b^2 - 4*a*c))*e)/c)/(2*(d + e*x))))/(e*((e*(b - sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^(4/3)*((e*(b + sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^(4/3)*(d + e*x)^2)]

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

    @test_int [(d + e*x)^3/(a + b*x + c*x^2)^(7/3), x, 6, -((3*(d + e*x)^2*(b*d - 2*a*e + (2*c*d - b*e)*x))/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(4/3))) + (3*(10*b*c*d*(c*d^2 + 3*a*e^2) - 8*a*c*e*(2*c*d^2 + 3*a*e^2) - b^2*(11*c*d^2*e - a*e^3) + (2*c*d - b*e)*(10*c^2*d^2 - b^2*e^2 - 2*c*e*(5*b*d - 7*a*e))*x))/(4*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(1/3)) - (3*(2*c*d - b*e)*(5*c^2*d^2 - b^2*e^2 - c*e*(5*b*d - 9*a*e))*(b + 2*c*x))/(2*2^(1/3)*c^(5/3)*(b^2 - 4*a*c)^2*((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))) + (3*3^(1/4)*sqrt(2 - sqrt(3))*(2*c*d - b*e)*(5*c^2*d^2 - b^2*e^2 - c*e*(5*b*d - 9*a*e))*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*sqrt(((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2)*Elliptic.E(asin(((1 - sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))), -7 - 4*sqrt(3)))/(4*2^(1/3)*c^(5/3)*(b^2 - 4*a*c)^(5/3)*(b + 2*c*x)*sqrt(((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2)) - (3^(3/4)*(2*c*d - b*e)*(5*c^2*d^2 - b^2*e^2 - c*e*(5*b*d - 9*a*e))*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*sqrt(((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))), -7 - 4*sqrt(3)))/(2^(5/6)*c^(5/3)*(b^2 - 4*a*c)^(5/3)*(b + 2*c*x)*sqrt(((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2))]
    @test_int [(d + e*x)^2/(a + b*x + c*x^2)^(7/3), x, 6, -((3*(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(4/3))) - (3*(4*b^2*d*e + 4*a*c*d*e - 5*b*(c*d^2 + a*e^2) - (10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*x))/(2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(1/3)) - (3*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(b + 2*c*x))/(2*2^(1/3)*c^(2/3)*(b^2 - 4*a*c)^2*((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))) + (3*3^(1/4)*sqrt(2 - sqrt(3))*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*sqrt(((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2)*Elliptic.E(asin(((1 - sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))), -7 - 4*sqrt(3)))/(4*2^(1/3)*c^(2/3)*(b^2 - 4*a*c)^(5/3)*(b + 2*c*x)*sqrt(((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2)) - (3^(3/4)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*sqrt(((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))), -7 - 4*sqrt(3)))/(2^(5/6)*c^(2/3)*(b^2 - 4*a*c)^(5/3)*(b + 2*c*x)*sqrt(((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2))]
    @test_int [(d + e*x)^1/(a + b*x + c*x^2)^(7/3), x, 6, -((3*(b*d - 2*a*e + (2*c*d - b*e)*x))/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(4/3))) + (15*(2*c*d - b*e)*(b + 2*c*x))/(4*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(1/3)) - (15*c^(1/3)*(2*c*d - b*e)*(b + 2*c*x))/(2*2^(1/3)*(b^2 - 4*a*c)^2*((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))) + (15*3^(1/4)*sqrt(2 - sqrt(3))*c^(1/3)*(2*c*d - b*e)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*sqrt(((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2)*Elliptic.E(asin(((1 - sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))), -7 - 4*sqrt(3)))/(4*2^(1/3)*(b^2 - 4*a*c)^(5/3)*(b + 2*c*x)*sqrt(((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2)) - (5*3^(3/4)*c^(1/3)*(2*c*d - b*e)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*sqrt(((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))), -7 - 4*sqrt(3)))/(2^(5/6)*(b^2 - 4*a*c)^(5/3)*(b + 2*c*x)*sqrt(((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2))]
    @test_int [(d + e*x)^0/(a + b*x + c*x^2)^(7/3), x, 6, -((3*(b + 2*c*x))/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(4/3))) + (15*c*(b + 2*c*x))/(2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(1/3)) - (15*c^(4/3)*(b + 2*c*x))/(2^(1/3)*(b^2 - 4*a*c)^2*((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))) + (15*3^(1/4)*sqrt(2 - sqrt(3))*c^(4/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*sqrt(((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2)*Elliptic.E(asin(((1 - sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))), -7 - 4*sqrt(3)))/(2*2^(1/3)*(b^2 - 4*a*c)^(5/3)*(b + 2*c*x)*sqrt(((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2)) - (5*2^(1/6)*3^(3/4)*c^(4/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))*sqrt(((b^2 - 4*a*c)^(2/3) - 2^(2/3)*c^(1/3)*(b^2 - 4*a*c)^(1/3)*(a + b*x + c*x^2)^(1/3) + 2*2^(1/3)*c^(2/3)*(a + b*x + c*x^2)^(2/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2)*Elliptic.F(asin(((1 - sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))), -7 - 4*sqrt(3)))/((b^2 - 4*a*c)^(5/3)*(b + 2*c*x)*sqrt(((b^2 - 4*a*c)^(1/3)*((b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3)))/((1 + sqrt(3))*(b^2 - 4*a*c)^(1/3) + 2^(2/3)*c^(1/3)*(a + b*x + c*x^2)^(1/3))^2))]
    @test_int [1/((d + e*x)^1*(a + b*x + c*x^2)^(7/3)), x, 2, -((3*((e*(b - sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^(7/3)*((e*(b + sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^(7/3)*AppellF1(14/3, 7/3, 7/3, 17/3, (2*c*d - (b - sqrt(b^2 - 4*a*c))*e)/(2*c*(d + e*x)), (2*d - ((b + sqrt(b^2 - 4*a*c))*e)/c)/(2*(d + e*x))))/(224*2^(2/3)*e*(a + b*x + c*x^2)^(7/3)))]
    @test_int [1/((d + e*x)^2*(a + b*x + c*x^2)^(7/3)), x, 2, -((3*((e*(b - sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^(7/3)*((e*(b + sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^(7/3)*AppellF1(17/3, 7/3, 7/3, 20/3, (2*c*d - (b - sqrt(b^2 - 4*a*c))*e)/(2*c*(d + e*x)), (2*d - ((b + sqrt(b^2 - 4*a*c))*e)/c)/(2*(d + e*x))))/(272*2^(2/3)*e*(d + e*x)*(a + b*x + c*x^2)^(7/3)))]
    @test_int [1/((d + e*x)^3*(a + b*x + c*x^2)^(7/3)), x, 2, -((3*((e*(b - sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^(7/3)*((e*(b + sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^(7/3)*AppellF1(20/3, 7/3, 7/3, 23/3, (2*c*d - (b - sqrt(b^2 - 4*a*c))*e)/(2*c*(d + e*x)), (2*d - ((b + sqrt(b^2 - 4*a*c))*e)/c)/(2*(d + e*x))))/(320*2^(2/3)*e*(d + e*x)^2*(a + b*x + c*x^2)^(7/3)))]

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

    @test_int [(2 + 3*x)^3/(52 - 54*x + 27*x^2)^(1/3), x, 7, (1/30)*(2 + 3*x)^2*(52 - 54*x + 27*x^2)^(2/3) + (1/7)*(27 + 8*x)*(52 - 54*x + 27*x^2)^(2/3) + (9000*5^(1/3)*(1 - x))/(7*(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))) - (25*5^(5/6)*sqrt((1/2)*(2 + sqrt(3)))*(30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*sqrt((900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)*Elliptic.E(asin((30*(1 + sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(189*3^(1/4)*(1 - x)*sqrt(-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2))) + (50*5^(5/6)*(30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*sqrt((900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)*Elliptic.F(asin((30*(1 + sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(189*3^(3/4)*(1 - x)*sqrt(-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)))]
    @test_int [(2 + 3*x)^2/(52 - 54*x + 27*x^2)^(1/3), x, 8, (25/42)*(52 - 54*x + 27*x^2)^(2/3) + (1/21)*(2 + 3*x)*(52 - 54*x + 27*x^2)^(2/3) + (2700*5^(1/3)*(1 - x))/(7*(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))) - (5*5^(5/6)*sqrt((1/2)*(2 + sqrt(3)))*(30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*sqrt((900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)*Elliptic.E(asin((30*(1 + sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(126*3^(1/4)*(1 - x)*sqrt(-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2))) + (5*5^(5/6)*(30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*sqrt((900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)*Elliptic.F(asin((30*(1 + sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(63*3^(3/4)*(1 - x)*sqrt(-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)))]
    @test_int [(2 + 3*x)^1/(52 - 54*x + 27*x^2)^(1/3), x, 6, (1/12)*(52 - 54*x + 27*x^2)^(2/3) + (90*5^(1/3)*(1 - x))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3)) - (5^(5/6)*sqrt((1/2)*(2 + sqrt(3)))*(30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*sqrt((900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)*Elliptic.E(asin((30*(1 + sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(108*3^(1/4)*(1 - x)*sqrt(-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2))) + (5^(5/6)*(30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*sqrt((900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)*Elliptic.F(asin((30*(1 + sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(54*3^(3/4)*(1 - x)*sqrt(-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)))]
    @test_int [1/((2 + 3*x)^1*(52 - 54*x + 27*x^2)^(1/3)), x, 1, -(atan(1/sqrt(3) + (2^(2/3)*(8 - 3*x))/(sqrt(3)*5^(1/3)*(52 - 54*x + 27*x^2)^(1/3)))/(3*sqrt(3)*10^(2/3))) - log(2 + 3*x)/(6*10^(2/3)) + log(216 - 81*x - 27*10^(1/3)*(52 - 54*x + 27*x^2)^(1/3))/(6*10^(2/3))]
    @test_int [1/((2 + 3*x)^2*(52 - 54*x + 27*x^2)^(1/3)), x, 8, -((52 - 54*x + 27*x^2)^(2/3)/(300*(2 + 3*x))) + (9*(1 - x))/(10*5^(2/3)*(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))) - atan(1/sqrt(3) + (2^(2/3)*(8 - 3*x))/(sqrt(3)*5^(1/3)*(52 - 54*x + 27*x^2)^(1/3)))/(30*sqrt(3)*10^(2/3)) - (sqrt((1/2)*(2 + sqrt(3)))*(30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*sqrt((900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)*Elliptic.E(asin((30*(1 + sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(10800*3^(1/4)*5^(1/6)*(1 - x)*sqrt(-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2))) + ((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*sqrt((900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)*Elliptic.F(asin((30*(1 + sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(5400*3^(3/4)*5^(1/6)*(1 - x)*sqrt(-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2))) - log(2 + 3*x)/(60*10^(2/3)) + log(216 - 81*x - 27*10^(1/3)*(52 - 54*x + 27*x^2)^(1/3))/(60*10^(2/3))]
    @test_int [1/((2 + 3*x)^3*(52 - 54*x + 27*x^2)^(1/3)), x, 9, -((52 - 54*x + 27*x^2)^(2/3)/(600*(2 + 3*x)^2)) - (52 - 54*x + 27*x^2)^(2/3)/(1500*(2 + 3*x)) + (9*(1 - x))/(50*5^(2/3)*(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))) - atan(1/sqrt(3) + (2^(2/3)*(8 - 3*x))/(sqrt(3)*5^(1/3)*(52 - 54*x + 27*x^2)^(1/3)))/(300*sqrt(3)*10^(2/3)) - (sqrt((1/2)*(2 + sqrt(3)))*(30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*sqrt((900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)*Elliptic.E(asin((30*(1 + sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(54000*3^(1/4)*5^(1/6)*(1 - x)*sqrt(-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2))) + ((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))*sqrt((900 + 30*10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3) + 10^(2/3)*(2700 + (-54 + 54*x)^2)^(2/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2)*Elliptic.F(asin((30*(1 + sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(27000*3^(3/4)*5^(1/6)*(1 - x)*sqrt(-((30 - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))/(30*(1 - sqrt(3)) - 10^(1/3)*(2700 + (-54 + 54*x)^2)^(1/3))^2))) - log(2 + 3*x)/(600*10^(2/3)) + log(216 - 81*x - 27*10^(1/3)*(52 - 54*x + 27*x^2)^(1/3))/(600*10^(2/3))]

    @test_int [(2 + 3*x)^3/(28 + 54*x + 27*x^2)^(1/3), x, 7, (1/30)*(2 + 3*x)^2*(28 + 54*x + 27*x^2)^(2/3) - (1/35)*(1 + 8*x)*(28 + 54*x + 27*x^2)^(2/3) + (72*(1 + x))/(7*(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))) - (sqrt(2*(2 + sqrt(3)))*(6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*sqrt((1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)*Elliptic.E(asin((6*(1 + sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(63*3^(1/4)*(1 + x)*sqrt(-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2))) + (4*(6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*sqrt((1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)*Elliptic.F(asin((6*(1 + sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(63*3^(3/4)*(1 + x)*sqrt(-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)))]
    @test_int [(2 + 3*x)^2/(28 + 54*x + 27*x^2)^(1/3), x, 7, (-(5/42))*(28 + 54*x + 27*x^2)^(2/3) + (1/21)*(2 + 3*x)*(28 + 54*x + 27*x^2)^(2/3) - (108*(1 + x))/(7*(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))) + (sqrt(2 + sqrt(3))*(6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*sqrt((1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)*Elliptic.E(asin((6*(1 + sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(21*sqrt(2)*3^(1/4)*(1 + x)*sqrt(-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2))) - (2*(6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*sqrt((1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)*Elliptic.F(asin((6*(1 + sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(21*3^(3/4)*(1 + x)*sqrt(-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)))]
    @test_int [(2 + 3*x)^1/(28 + 54*x + 27*x^2)^(1/3), x, 6, (1/12)*(28 + 54*x + 27*x^2)^(2/3) + (18*(1 + x))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3)) - (sqrt(2 + sqrt(3))*(6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*sqrt((1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)*Elliptic.E(asin((6*(1 + sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(18*sqrt(2)*3^(1/4)*(1 + x)*sqrt(-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2))) + ((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*sqrt((1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)*Elliptic.F(asin((6*(1 + sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(9*3^(3/4)*(1 + x)*sqrt(-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)))]
    @test_int [1/((2 + 3*x)^1*(28 + 54*x + 27*x^2)^(1/3)), x, 1, -(atan(1/sqrt(3) + (2^(2/3)*(4 + 3*x))/(sqrt(3)*(28 + 54*x + 27*x^2)^(1/3)))/(3*2^(2/3)*sqrt(3))) - log(2 + 3*x)/(6*2^(2/3)) + log(-108 - 81*x + 27*2^(1/3)*(28 + 54*x + 27*x^2)^(1/3))/(6*2^(2/3))]
    @test_int [1/((2 + 3*x)^2*(28 + 54*x + 27*x^2)^(1/3)), x, 9, -((28 + 54*x + 27*x^2)^(2/3)/(12*(2 + 3*x))) - (9*(1 + x))/(2*(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))) + atan(1/sqrt(3) + (2^(2/3)*(4 + 3*x))/(sqrt(3)*(28 + 54*x + 27*x^2)^(1/3)))/(6*2^(2/3)*sqrt(3)) + (sqrt(2 + sqrt(3))*(6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*sqrt((1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)*Elliptic.E(asin((6*(1 + sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(72*sqrt(2)*3^(1/4)*(1 + x)*sqrt(-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2))) - ((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*sqrt((1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)*Elliptic.F(asin((6*(1 + sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(36*3^(3/4)*(1 + x)*sqrt(-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2))) + log(2 + 3*x)/(12*2^(2/3)) - log(-108 - 81*x + 27*2^(1/3)*(28 + 54*x + 27*x^2)^(1/3))/(12*2^(2/3))]
    @test_int [1/((2 + 3*x)^3*(28 + 54*x + 27*x^2)^(1/3)), x, 9, -((28 + 54*x + 27*x^2)^(2/3)/(24*(2 + 3*x)^2)) + (28 + 54*x + 27*x^2)^(2/3)/(12*(2 + 3*x)) + (9*(1 + x))/(2*(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))) - atan(1/sqrt(3) + (2^(2/3)*(4 + 3*x))/(sqrt(3)*(28 + 54*x + 27*x^2)^(1/3)))/(12*2^(2/3)*sqrt(3)) - (sqrt(2 + sqrt(3))*(6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*sqrt((1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)*Elliptic.E(asin((6*(1 + sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(72*sqrt(2)*3^(1/4)*(1 + x)*sqrt(-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2))) + ((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))*sqrt((1 + (28 + 54*x + 27*x^2)^(1/3) + (28 + 54*x + 27*x^2)^(2/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2)*Elliptic.F(asin((6*(1 + sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))), -7 + 4*sqrt(3)))/(36*3^(3/4)*(1 + x)*sqrt(-((6 - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))/(6*(1 - sqrt(3)) - 2^(1/3)*(108 + (54 + 54*x)^2)^(1/3))^2))) - log(2 + 3*x)/(24*2^(2/3)) + log(-108 - 81*x + 27*2^(1/3)*(28 + 54*x + 27*x^2)^(1/3))/(24*2^(2/3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(d+e*x)^m*(a+b*x+c*x^2)^(p/3)*when*c^2*d^2-b*c*d*e-2*b^2*e^2+9*a*c*e^2=0=#

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

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

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

    @test_int [(d + e*x)^3*(a + b*x + c*x^2)^(1/4), x, 5, ((2*c*d - b*e)*(28*c^2*d^2 + 13*b^2*e^2 - 4*c*e*(7*b*d + 6*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(168*c^4) + (2*e*(d + e*x)^2*(a + b*x + c*x^2)^(5/4))/(9*c) + (e*(616*c^2*d^2 + 117*b^2*e^2 - 2*c*e*(243*b*d + 56*a*e) + 130*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(5/4))/(630*c^3) - ((b^2 - 4*a*c)^(5/4)*(2*c*d - b*e)*(28*c^2*d^2 + 13*b^2*e^2 - 4*c*e*(7*b*d + 6*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(336*sqrt(2)*c^(17/4)*(b + 2*c*x))]
    @test_int [(d + e*x)^2*(a + b*x + c*x^2)^(1/4), x, 5, ((28*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(7*b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(84*c^3) + (9*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(5/4))/(35*c^2) + (2*e*(d + e*x)*(a + b*x + c*x^2)^(5/4))/(7*c) - ((b^2 - 4*a*c)^(5/4)*(28*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(7*b*d + 2*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(168*sqrt(2)*c^(13/4)*(b + 2*c*x))]
    @test_int [(d + e*x)^1*(a + b*x + c*x^2)^(1/4), x, 4, ((2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(6*c^2) + (2*e*(a + b*x + c*x^2)^(5/4))/(5*c) - ((b^2 - 4*a*c)^(5/4)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(12*sqrt(2)*c^(9/4)*(b + 2*c*x))]
    @test_int [(d + e*x)^0*(a + b*x + c*x^2)^(1/4), x, 3, ((b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(3*c) - ((b^2 - 4*a*c)^(5/4)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(6*sqrt(2)*c^(5/4)*(b + 2*c*x))]
    @test_int [(a + b*x + c*x^2)^(1/4)/(d + e*x)^1, x, 19, (2*(a + b*x + c*x^2)^(1/4))/e - ((-b^2 + 4*a*c)^(3/4)*(c*d^2 - b*d*e + a*e^2)^(1/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*atan(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(c^(3/4)*e^(3/2)*(a + b*x + c*x^2)^(3/4)) - ((-b^2 + 4*a*c)^(3/4)*(c*d^2 - b*d*e + a*e^2)^(1/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*atanh(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(c^(3/4)*e^(3/2)*(a + b*x + c*x^2)^(3/4)) - ((b^2 - 4*a*c)^(1/4)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(sqrt(2)*c^(1/4)*e^2*(b + 2*c*x)) - ((b^2 - 4*a*c)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*Elliptic.Pi(-((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2))), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(sqrt(2)*c*e^2*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4)) - ((b^2 - 4*a*c)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*Elliptic.Pi((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2)), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(sqrt(2)*c*e^2*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))]
    @test_int [(a + b*x + c*x^2)^(1/4)/(d + e*x)^2, x, 19, -((a + b*x + c*x^2)^(1/4)/(e*(d + e*x))) + ((-b^2 + 4*a*c)^(3/4)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*atan(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(4*c^(3/4)*e^(3/2)*(c*d^2 - b*d*e + a*e^2)^(3/4)*(a + b*x + c*x^2)^(3/4)) + ((-b^2 + 4*a*c)^(3/4)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*atanh(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(4*c^(3/4)*e^(3/2)*(c*d^2 - b*d*e + a*e^2)^(3/4)*(a + b*x + c*x^2)^(3/4)) + (c^(3/4)*(b^2 - 4*a*c)^(1/4)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(sqrt(2)*e^2*(b + 2*c*x)) + ((b^2 - 4*a*c)*(2*c*d - b*e)^2*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*Elliptic.Pi(-((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2))), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(4*sqrt(2)*c*e^2*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4)) + ((b^2 - 4*a*c)*(2*c*d - b*e)^2*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*Elliptic.Pi((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2)), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(4*sqrt(2)*c*e^2*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))]

    @test_int [(d + e*x)^3*(a + b*x + c*x^2)^(3/4), x, 7, ((2*c*d - b*e)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))/(120*c^4) + (2*e*(d + e*x)^2*(a + b*x + c*x^2)^(7/4))/(11*c) + (e*(312*c^2*d^2 + 55*b^2*e^2 - 2*c*e*(121*b*d + 24*a*e) + 70*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(7/4))/(462*c^3) - (sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(80*c^(9/2)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) + ((b^2 - 4*a*c)^(7/4)*(2*c*d - b*e)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(80*sqrt(2)*c^(19/4)*(b + 2*c*x)) - ((b^2 - 4*a*c)^(7/4)*(2*c*d - b*e)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(160*sqrt(2)*c^(19/4)*(b + 2*c*x))]
    @test_int [(d + e*x)^2*(a + b*x + c*x^2)^(3/4), x, 7, ((36*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(9*b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))/(180*c^3) + (11*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(7/4))/(63*c^2) + (2*e*(d + e*x)*(a + b*x + c*x^2)^(7/4))/(9*c) - (sqrt(b^2 - 4*a*c)*(36*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(9*b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(120*c^(7/2)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) + ((b^2 - 4*a*c)^(7/4)*(36*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(9*b*d + 2*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(120*sqrt(2)*c^(15/4)*(b + 2*c*x)) - ((b^2 - 4*a*c)^(7/4)*(36*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(9*b*d + 2*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(240*sqrt(2)*c^(15/4)*(b + 2*c*x))]
    @test_int [(d + e*x)^1*(a + b*x + c*x^2)^(3/4), x, 6, ((2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))/(10*c^2) + (2*e*(a + b*x + c*x^2)^(7/4))/(7*c) - (3*sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(20*c^(5/2)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) + (3*(b^2 - 4*a*c)^(7/4)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(20*sqrt(2)*c^(11/4)*(b + 2*c*x)) - (3*(b^2 - 4*a*c)^(7/4)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(40*sqrt(2)*c^(11/4)*(b + 2*c*x))]
    @test_int [(d + e*x)^0*(a + b*x + c*x^2)^(3/4), x, 5, ((b + 2*c*x)*(a + b*x + c*x^2)^(3/4))/(5*c) - (3*sqrt(b^2 - 4*a*c)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(10*c^(3/2)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) + (3*(b^2 - 4*a*c)^(7/4)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(10*sqrt(2)*c^(7/4)*(b + 2*c*x)) - (3*(b^2 - 4*a*c)^(7/4)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(20*sqrt(2)*c^(7/4)*(b + 2*c*x))]
    @test_int [(a + b*x + c*x^2)^(3/4)/(d + e*x)^1, x, 20, (2*(a + b*x + c*x^2)^(3/4))/(3*e) - ((2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(sqrt(c)*sqrt(b^2 - 4*a*c)*e^2*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) + ((-b^2 + 4*a*c)^(1/4)*(c*d^2 - b*d*e + a*e^2)^(3/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*atan(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(c^(1/4)*e^(5/2)*(a + b*x + c*x^2)^(1/4)) - ((-b^2 + 4*a*c)^(1/4)*(c*d^2 - b*d*e + a*e^2)^(3/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*atanh(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(c^(1/4)*e^(5/2)*(a + b*x + c*x^2)^(1/4)) + ((b^2 - 4*a*c)^(3/4)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(sqrt(2)*c^(3/4)*e^2*(b + 2*c*x)) - ((b^2 - 4*a*c)^(3/4)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(2*sqrt(2)*c^(3/4)*e^2*(b + 2*c*x)) - (sqrt(-b^2 + 4*a*c)*(2*c*d - b*e)*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*Elliptic.Pi(-((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2))), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(sqrt(2)*sqrt(c)*e^3*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4)) + (sqrt(-b^2 + 4*a*c)*(2*c*d - b*e)*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*Elliptic.Pi((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2)), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(sqrt(2)*sqrt(c)*e^3*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))]
    @test_int [(a + b*x + c*x^2)^(3/4)/(d + e*x)^2, x, 20, -((a + b*x + c*x^2)^(3/4)/(e*(d + e*x))) + (3*sqrt(c)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(sqrt(b^2 - 4*a*c)*e^2*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) - (3*(-b^2 + 4*a*c)^(1/4)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*atan(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(4*c^(1/4)*e^(5/2)*(c*d^2 - b*d*e + a*e^2)^(1/4)*(a + b*x + c*x^2)^(1/4)) + (3*(-b^2 + 4*a*c)^(1/4)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*atanh(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(4*c^(1/4)*e^(5/2)*(c*d^2 - b*d*e + a*e^2)^(1/4)*(a + b*x + c*x^2)^(1/4)) - (3*c^(1/4)*(b^2 - 4*a*c)^(3/4)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(sqrt(2)*e^2*(b + 2*c*x)) + (3*c^(1/4)*(b^2 - 4*a*c)^(3/4)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(2*sqrt(2)*e^2*(b + 2*c*x)) + (3*sqrt(-b^2 + 4*a*c)*(2*c*d - b*e)^2*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*Elliptic.Pi(-((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2))), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(4*sqrt(2)*sqrt(c)*e^3*sqrt(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4)) - (3*sqrt(-b^2 + 4*a*c)*(2*c*d - b*e)^2*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*Elliptic.Pi((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2)), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(4*sqrt(2)*sqrt(c)*e^3*sqrt(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))]

    @test_int [(d + e*x)^3*(a + b*x + c*x^2)^(5/4), x, 6, -((5*(b^2 - 4*a*c)*(2*c*d - b*e)*(44*c^2*d^2 + 17*b^2*e^2 - 4*c*e*(11*b*d + 6*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(7392*c^5)) + ((2*c*d - b*e)*(44*c^2*d^2 + 17*b^2*e^2 - 4*c*e*(11*b*d + 6*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(5/4))/(616*c^4) + (2*e*(d + e*x)^2*(a + b*x + c*x^2)^(9/4))/(13*c) + (e*(1320*c^2*d^2 + 221*b^2*e^2 - 2*c*e*(507*b*d + 88*a*e) + 306*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(9/4))/(2574*c^3) + (5*(b^2 - 4*a*c)^(9/4)*(2*c*d - b*e)*(44*c^2*d^2 + 17*b^2*e^2 - 4*c*e*(11*b*d + 6*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(14784*sqrt(2)*c^(21/4)*(b + 2*c*x))]
    @test_int [(d + e*x)^2*(a + b*x + c*x^2)^(5/4), x, 6, -((5*(b^2 - 4*a*c)*(44*c^2*d^2 + 13*b^2*e^2 - 4*c*e*(11*b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(3696*c^4)) + ((44*c^2*d^2 + 13*b^2*e^2 - 4*c*e*(11*b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(5/4))/(308*c^3) + (13*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(9/4))/(99*c^2) + (2*e*(d + e*x)*(a + b*x + c*x^2)^(9/4))/(11*c) + (5*(b^2 - 4*a*c)^(9/4)*(44*c^2*d^2 + 13*b^2*e^2 - 4*c*e*(11*b*d + 2*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(7392*sqrt(2)*c^(17/4)*(b + 2*c*x))]
    @test_int [(d + e*x)^1*(a + b*x + c*x^2)^(5/4), x, 5, -((5*(b^2 - 4*a*c)*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(168*c^3)) + ((2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(5/4))/(14*c^2) + (2*e*(a + b*x + c*x^2)^(9/4))/(9*c) + (1/(336*sqrt(2)*c^(13/4)*(b + 2*c*x)))*(5*(b^2 - 4*a*c)^(9/4)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))]
    @test_int [(d + e*x)^0*(a + b*x + c*x^2)^(5/4), x, 4, -((5*(b^2 - 4*a*c)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(84*c^2)) + ((b + 2*c*x)*(a + b*x + c*x^2)^(5/4))/(7*c) + (5*(b^2 - 4*a*c)^(9/4)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(168*sqrt(2)*c^(9/4)*(b + 2*c*x))]
    @test_int [(a + b*x + c*x^2)^(5/4)/(d + e*x)^1, x, 20, ((12*c^2*d^2 + b^2*e^2 - 2*c*e*(7*b*d - 6*a*e) - 2*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(1/4))/(6*c*e^3) + (2*(a + b*x + c*x^2)^(5/4))/(5*e) - ((-b^2 + 4*a*c)^(3/4)*(c*d^2 - b*d*e + a*e^2)^(5/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*atan(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(c^(3/4)*e^(7/2)*(a + b*x + c*x^2)^(3/4)) - ((-b^2 + 4*a*c)^(3/4)*(c*d^2 - b*d*e + a*e^2)^(5/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*atanh(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(c^(3/4)*e^(7/2)*(a + b*x + c*x^2)^(3/4)) - ((b^2 - 4*a*c)^(1/4)*(2*c*d - b*e)*(12*c^2*d^2 - b^2*e^2 - 4*c*e*(3*b*d - 4*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(12*sqrt(2)*c^(5/4)*e^4*(b + 2*c*x)) - ((b^2 - 4*a*c)*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*Elliptic.Pi(-((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2))), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(sqrt(2)*c*e^4*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4)) - ((b^2 - 4*a*c)*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*Elliptic.Pi((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2)), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(sqrt(2)*c*e^4*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))]
    @test_int [(a + b*x + c*x^2)^(5/4)/(d + e*x)^2, x, 20, -((5*(3*c*d - 2*b*e - c*e*x)*(a + b*x + c*x^2)^(1/4))/(3*e^3)) - (a + b*x + c*x^2)^(5/4)/(e*(d + e*x)) + (5*(-b^2 + 4*a*c)^(3/4)*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^(1/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*atan(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(4*c^(3/4)*e^(7/2)*(a + b*x + c*x^2)^(3/4)) + (5*(-b^2 + 4*a*c)^(3/4)*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^(1/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*atanh(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(4*c^(3/4)*e^(7/2)*(a + b*x + c*x^2)^(3/4)) + (5*(b^2 - 4*a*c)^(1/4)*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(6*sqrt(2)*c^(1/4)*e^4*(b + 2*c*x)) + (5*(b^2 - 4*a*c)*(2*c*d - b*e)^2*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*Elliptic.Pi(-((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2))), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(4*sqrt(2)*c*e^4*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4)) + (5*(b^2 - 4*a*c)*(2*c*d - b*e)^2*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*Elliptic.Pi((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2)), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(4*sqrt(2)*c*e^4*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))]

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

    @test_int [(d + e*x)^3/(a + b*x + c*x^2)^(1/4), x, 6, (2*e*(d + e*x)^2*(a + b*x + c*x^2)^(3/4))/(7*c) + (e*(360*c^2*d^2 + 77*b^2*e^2 - 2*c*e*(147*b*d + 40*a*e) + 66*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/4))/(210*c^3) + ((2*c*d - b*e)*(20*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(5*b*d + 6*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(20*c^(7/2)*sqrt(b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) - ((b^2 - 4*a*c)^(3/4)*(2*c*d - b*e)*(20*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(5*b*d + 6*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(20*sqrt(2)*c^(15/4)*(b + 2*c*x)) + ((b^2 - 4*a*c)^(3/4)*(2*c*d - b*e)*(20*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(5*b*d + 6*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(40*sqrt(2)*c^(15/4)*(b + 2*c*x))]
    @test_int [(d + e*x)^2/(a + b*x + c*x^2)^(1/4), x, 6, (7*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(3/4))/(15*c^2) + (2*e*(d + e*x)*(a + b*x + c*x^2)^(3/4))/(5*c) + ((20*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(5*b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(10*c^(5/2)*sqrt(b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) - ((b^2 - 4*a*c)^(3/4)*(20*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(5*b*d + 2*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(10*sqrt(2)*c^(11/4)*(b + 2*c*x)) + ((b^2 - 4*a*c)^(3/4)*(20*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(5*b*d + 2*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(20*sqrt(2)*c^(11/4)*(b + 2*c*x))]
    @test_int [(d + e*x)^1/(a + b*x + c*x^2)^(1/4), x, 5, (2*e*(a + b*x + c*x^2)^(3/4))/(3*c) + ((2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(c^(3/2)*sqrt(b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) - ((b^2 - 4*a*c)^(3/4)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(sqrt(2)*c^(7/4)*(b + 2*c*x)) + ((b^2 - 4*a*c)^(3/4)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(2*sqrt(2)*c^(7/4)*(b + 2*c*x))]
    @test_int [(d + e*x)^0/(a + b*x + c*x^2)^(1/4), x, 4, (2*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(sqrt(c)*sqrt(b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) - (sqrt(2)*(b^2 - 4*a*c)^(3/4)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(c^(3/4)*(b + 2*c*x)) + ((b^2 - 4*a*c)^(3/4)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(sqrt(2)*c^(3/4)*(b + 2*c*x))]
    @test_int [1/((d + e*x)^1*(a + b*x + c*x^2)^(1/4)), x, 14, ((-b^2 + 4*a*c)^(1/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*atan(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(c^(1/4)*sqrt(e)*(c*d^2 - b*d*e + a*e^2)^(1/4)*(a + b*x + c*x^2)^(1/4)) - ((-b^2 + 4*a*c)^(1/4)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*atanh(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(c^(1/4)*sqrt(e)*(c*d^2 - b*d*e + a*e^2)^(1/4)*(a + b*x + c*x^2)^(1/4)) - (sqrt(-b^2 + 4*a*c)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*Elliptic.Pi(-((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2))), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(sqrt(2)*sqrt(c)*e*sqrt(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4)) + (sqrt(-b^2 + 4*a*c)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*Elliptic.Pi((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2)), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(sqrt(2)*sqrt(c)*e*sqrt(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))]
    @test_int [1/((d + e*x)^2*(a + b*x + c*x^2)^(1/4)), x, 20, -((e*(a + b*x + c*x^2)^(3/4))/((c*d^2 - b*d*e + a*e^2)*(d + e*x))) + (sqrt(c)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(sqrt(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) + ((-b^2 + 4*a*c)^(1/4)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*atan(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(4*c^(1/4)*sqrt(e)*(c*d^2 - b*d*e + a*e^2)^(5/4)*(a + b*x + c*x^2)^(1/4)) - ((-b^2 + 4*a*c)^(1/4)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*atanh(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(4*c^(1/4)*sqrt(e)*(c*d^2 - b*d*e + a*e^2)^(5/4)*(a + b*x + c*x^2)^(1/4)) - (c^(1/4)*(b^2 - 4*a*c)^(3/4)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(sqrt(2)*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)) + (c^(1/4)*(b^2 - 4*a*c)^(3/4)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(2*sqrt(2)*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)) - (sqrt(-b^2 + 4*a*c)*(2*c*d - b*e)^2*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*Elliptic.Pi(-((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2))), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(4*sqrt(2)*sqrt(c)*e*(c*d^2 - b*d*e + a*e^2)^(3/2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4)) + (sqrt(-b^2 + 4*a*c)*(2*c*d - b*e)^2*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*Elliptic.Pi((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2)), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(4*sqrt(2)*sqrt(c)*e*(c*d^2 - b*d*e + a*e^2)^(3/2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))]
    @test_int [1/((d + e*x)^3*(a + b*x + c*x^2)^(1/4)), x, 21, -((e*(a + b*x + c*x^2)^(3/4))/(2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2)) - (5*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(3/4))/(8*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) + (5*sqrt(c)*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(8*sqrt(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) + ((-b^2 + 4*a*c)^(1/4)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*atan(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(32*c^(1/4)*sqrt(e)*(c*d^2 - b*d*e + a*e^2)^(9/4)*(a + b*x + c*x^2)^(1/4)) - ((-b^2 + 4*a*c)^(1/4)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*atanh(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(32*c^(1/4)*sqrt(e)*(c*d^2 - b*d*e + a*e^2)^(9/4)*(a + b*x + c*x^2)^(1/4)) - (5*c^(1/4)*(b^2 - 4*a*c)^(3/4)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(8*sqrt(2)*(c*d^2 - b*d*e + a*e^2)^2*(b + 2*c*x)) + (5*c^(1/4)*(b^2 - 4*a*c)^(3/4)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(16*sqrt(2)*(c*d^2 - b*d*e + a*e^2)^2*(b + 2*c*x)) - (sqrt(-b^2 + 4*a*c)*(2*c*d - b*e)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*Elliptic.Pi(-((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2))), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(32*sqrt(2)*sqrt(c)*e*(c*d^2 - b*d*e + a*e^2)^(5/2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4)) + (sqrt(-b^2 + 4*a*c)*(2*c*d - b*e)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*Elliptic.Pi((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2)), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(32*sqrt(2)*sqrt(c)*e*(c*d^2 - b*d*e + a*e^2)^(5/2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))]

    @test_int [(d + e*x)^3/(a + b*x + c*x^2)^(3/4), x, 4, (2*e*(d + e*x)^2*(a + b*x + c*x^2)^(1/4))/(5*c) + (e*(56*c^2*d^2 + 15*b^2*e^2 - 2*c*e*(25*b*d + 8*a*e) + 6*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(1/4))/(10*c^3) + ((b^2 - 4*a*c)^(1/4)*(2*c*d - b*e)*(4*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(b*d + 2*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(4*sqrt(2)*c^(13/4)*(b + 2*c*x))]
    @test_int [(d + e*x)^2/(a + b*x + c*x^2)^(3/4), x, 4, (5*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(1/4))/(3*c^2) + (2*e*(d + e*x)*(a + b*x + c*x^2)^(1/4))/(3*c) + ((b^2 - 4*a*c)^(1/4)*(12*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + 2*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(6*sqrt(2)*c^(9/4)*(b + 2*c*x))]
    @test_int [(d + e*x)^1/(a + b*x + c*x^2)^(3/4), x, 3, (2*e*(a + b*x + c*x^2)^(1/4))/c + ((b^2 - 4*a*c)^(1/4)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(sqrt(2)*c^(5/4)*(b + 2*c*x))]
    @test_int [(d + e*x)^0/(a + b*x + c*x^2)^(3/4), x, 2, (sqrt(2)*(b^2 - 4*a*c)^(1/4)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(c^(1/4)*(b + 2*c*x))]
    @test_int [1/((d + e*x)^1*(a + b*x + c*x^2)^(3/4)), x, 15, -(((-b^2 + 4*a*c)^(3/4)*sqrt(e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*atan(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(c^(3/4)*(c*d^2 - b*d*e + a*e^2)^(3/4)*(a + b*x + c*x^2)^(3/4))) - ((-b^2 + 4*a*c)^(3/4)*sqrt(e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*atanh(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(c^(3/4)*(c*d^2 - b*d*e + a*e^2)^(3/4)*(a + b*x + c*x^2)^(3/4)) - ((b^2 - 4*a*c)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*Elliptic.Pi(-((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2))), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(sqrt(2)*c*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4)) - ((b^2 - 4*a*c)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*Elliptic.Pi((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2)), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(sqrt(2)*c*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))]
    @test_int [1/((d + e*x)^2*(a + b*x + c*x^2)^(3/4)), x, 19, -((e*(a + b*x + c*x^2)^(1/4))/((c*d^2 - b*d*e + a*e^2)*(d + e*x))) - (3*(-b^2 + 4*a*c)^(3/4)*sqrt(e)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*atan(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(4*c^(3/4)*(c*d^2 - b*d*e + a*e^2)^(7/4)*(a + b*x + c*x^2)^(3/4)) - (3*(-b^2 + 4*a*c)^(3/4)*sqrt(e)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*atanh(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(4*c^(3/4)*(c*d^2 - b*d*e + a*e^2)^(7/4)*(a + b*x + c*x^2)^(3/4)) - (c^(3/4)*(b^2 - 4*a*c)^(1/4)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(sqrt(2)*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)) - (3*(b^2 - 4*a*c)*(2*c*d - b*e)^2*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*Elliptic.Pi(-((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2))), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(4*sqrt(2)*c*(c*d^2 - b*d*e + a*e^2)^2*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4)) - (3*(b^2 - 4*a*c)*(2*c*d - b*e)^2*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*Elliptic.Pi((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2)), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(4*sqrt(2)*c*(c*d^2 - b*d*e + a*e^2)^2*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))]
    @test_int [1/((d + e*x)^3*(a + b*x + c*x^2)^(3/4)), x, 20, -((e*(a + b*x + c*x^2)^(1/4))/(2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2)) - (7*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(1/4))/(8*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) - (3*(-b^2 + 4*a*c)^(3/4)*sqrt(e)*(20*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(5*b*d + 2*a*e))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*atan(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(32*c^(3/4)*(c*d^2 - b*d*e + a*e^2)^(11/4)*(a + b*x + c*x^2)^(3/4)) - (3*(-b^2 + 4*a*c)^(3/4)*sqrt(e)*(20*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(5*b*d + 2*a*e))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*atanh(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(32*c^(3/4)*(c*d^2 - b*d*e + a*e^2)^(11/4)*(a + b*x + c*x^2)^(3/4)) - (7*c^(3/4)*(b^2 - 4*a*c)^(1/4)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(8*sqrt(2)*(c*d^2 - b*d*e + a*e^2)^2*(b + 2*c*x)) - (3*(b^2 - 4*a*c)*(2*c*d - b*e)*(20*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(5*b*d + 2*a*e))*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*Elliptic.Pi(-((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2))), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(32*sqrt(2)*c*(c*d^2 - b*d*e + a*e^2)^3*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4)) - (3*(b^2 - 4*a*c)*(2*c*d - b*e)*(20*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(5*b*d + 2*a*e))*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(3/4)*Elliptic.Pi((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2)), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(32*sqrt(2)*c*(c*d^2 - b*d*e + a*e^2)^3*(b + 2*c*x)*(a + b*x + c*x^2)^(3/4))]

    @test_int [(d + e*x)^3/(a + b*x + c*x^2)^(5/4), x, 6, -((4*(d + e*x)^2*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)^(1/4))) + (2*e*(24*c^2*d^2 + 7*b^2*e^2 - 2*c*e*(9*b*d + 8*a*e) + 6*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/4))/(3*c^2*(b^2 - 4*a*c)) + ((2*c*d - b*e)*(4*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(b*d + 6*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(c^(5/2)*(b^2 - 4*a*c)^(3/2)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) - ((2*c*d - b*e)*(4*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(b*d + 6*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(sqrt(2)*c^(11/4)*(b^2 - 4*a*c)^(1/4)*(b + 2*c*x)) + ((2*c*d - b*e)*(4*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(b*d + 6*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(2*sqrt(2)*c^(11/4)*(b^2 - 4*a*c)^(1/4)*(b + 2*c*x))]
    @test_int [(d + e*x)^2/(a + b*x + c*x^2)^(5/4), x, 6, -((4*(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)^(1/4))) + (4*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(3/4))/(c*(b^2 - 4*a*c)) + (2*(4*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(b*d + 2*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(c^(3/2)*(b^2 - 4*a*c)^(3/2)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) - (sqrt(2)*(4*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(b*d + 2*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(c^(7/4)*(b^2 - 4*a*c)^(1/4)*(b + 2*c*x)) + ((4*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(b*d + 2*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(sqrt(2)*c^(7/4)*(b^2 - 4*a*c)^(1/4)*(b + 2*c*x))]
    @test_int [(d + e*x)^1/(a + b*x + c*x^2)^(5/4), x, 5, -((4*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)^(1/4))) + (4*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/(sqrt(c)*(b^2 - 4*a*c)^(3/2)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) - (2*sqrt(2)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(c^(3/4)*(b^2 - 4*a*c)^(1/4)*(b + 2*c*x)) + (sqrt(2)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(c^(3/4)*(b^2 - 4*a*c)^(1/4)*(b + 2*c*x))]
    @test_int [(d + e*x)^0/(a + b*x + c*x^2)^(5/4), x, 5, -((4*(b + 2*c*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)^(1/4))) + (8*sqrt(c)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/((b^2 - 4*a*c)^(3/2)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) - (4*sqrt(2)*c^(1/4)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/((b^2 - 4*a*c)^(1/4)*(b + 2*c*x)) + (2*sqrt(2)*c^(1/4)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/((b^2 - 4*a*c)^(1/4)*(b + 2*c*x))]
    @test_int [1/((d + e*x)^1*(a + b*x + c*x^2)^(5/4)), x, 20, -((4*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^(1/4))) + (4*sqrt(c)*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/((b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) + ((-b^2 + 4*a*c)^(1/4)*e^(3/2)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*atan(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(5/4)*(a + b*x + c*x^2)^(1/4)) - ((-b^2 + 4*a*c)^(1/4)*e^(3/2)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*atanh(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(5/4)*(a + b*x + c*x^2)^(1/4)) - (2*sqrt(2)*c^(1/4)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/((b^2 - 4*a*c)^(1/4)*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)) + (sqrt(2)*c^(1/4)*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/((b^2 - 4*a*c)^(1/4)*(c*d^2 - b*d*e + a*e^2)*(b + 2*c*x)) - (sqrt(-b^2 + 4*a*c)*e*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*Elliptic.Pi(-((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2))), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(sqrt(2)*sqrt(c)*(c*d^2 - b*d*e + a*e^2)^(3/2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4)) + (sqrt(-b^2 + 4*a*c)*e*(2*c*d - b*e)*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*Elliptic.Pi((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2)), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(sqrt(2)*sqrt(c)*(c*d^2 - b*d*e + a*e^2)^(3/2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))]
    @test_int [1/((d + e*x)^2*(a + b*x + c*x^2)^(5/4)), x, 21, -((4*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*(a + b*x + c*x^2)^(1/4))) - (e*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*(a + b*x + c*x^2)^(3/4))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) + (sqrt(c)*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))/((b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)^2*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))) + (5*(-b^2 + 4*a*c)^(1/4)*e^(3/2)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*atan(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(4*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(9/4)*(a + b*x + c*x^2)^(1/4)) - (5*(-b^2 + 4*a*c)^(1/4)*e^(3/2)*(2*c*d - b*e)*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*atanh(((-b^2 + 4*a*c)^(1/4)*sqrt(e)*(1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4))/(sqrt(2)*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(1/4))))/(4*c^(1/4)*(c*d^2 - b*d*e + a*e^2)^(9/4)*(a + b*x + c*x^2)^(1/4)) - (c^(1/4)*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.E(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(sqrt(2)*(b^2 - 4*a*c)^(1/4)*(c*d^2 - b*d*e + a*e^2)^2*(b + 2*c*x)) + (c^(1/4)*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*sqrt((b + 2*c*x)^2/((b^2 - 4*a*c)*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))^2))*(1 + (2*sqrt(c)*sqrt(a + b*x + c*x^2))/sqrt(b^2 - 4*a*c))*Elliptic.F(2*atan((sqrt(2)*c^(1/4)*(a + b*x + c*x^2)^(1/4))/(b^2 - 4*a*c)^(1/4)), 1/2))/(2*sqrt(2)*(b^2 - 4*a*c)^(1/4)*(c*d^2 - b*d*e + a*e^2)^2*(b + 2*c*x)) - (5*sqrt(-b^2 + 4*a*c)*e*(2*c*d - b*e)^2*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*Elliptic.Pi(-((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2))), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(4*sqrt(2)*sqrt(c)*(c*d^2 - b*d*e + a*e^2)^(5/2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4)) + (5*sqrt(-b^2 + 4*a*c)*e*(2*c*d - b*e)^2*sqrt((b + 2*c*x)^2/(b^2 - 4*a*c))*(-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c)))^(1/4)*Elliptic.Pi((sqrt(-b^2 + 4*a*c)*e)/(2*sqrt(c)*sqrt(c*d^2 - b*d*e + a*e^2)), asin((1 - (b + 2*c*x)^2/(b^2 - 4*a*c))^(1/4)), -1))/(4*sqrt(2)*sqrt(c)*(c*d^2 - b*d*e + a*e^2)^(5/2)*(b + 2*c*x)*(a + b*x + c*x^2)^(1/4))]

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

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

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

    @test_int [(d + e*x)^m*(a + b*x + c*x^2)^4, x, 2, ((c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^(1 + m))/(e^9*(1 + m)) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(2 + m))/(e^9*(2 + m)) + (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(3 + m))/(e^9*(3 + m)) - (4*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(4 + m))/(e^9*(4 + m)) + (1/(e^9*(5 + m)))*((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^(5 + m)) - (4*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(6 + m))/(e^9*(6 + m)) + (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(7 + m))/(e^9*(7 + m)) - (4*c^3*(2*c*d - b*e)*(d + e*x)^(8 + m))/(e^9*(8 + m)) + (c^4*(d + e*x)^(9 + m))/(e^9*(9 + m))]
    @test_int [(d + e*x)^m*(a + b*x + c*x^2)^3, x, 2, ((c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(1 + m))/(e^7*(1 + m)) - (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(2 + m))/(e^7*(2 + m)) + (3*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(3 + m))/(e^7*(3 + m)) - ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(4 + m))/(e^7*(4 + m)) + (3*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(5 + m))/(e^7*(5 + m)) - (3*c^2*(2*c*d - b*e)*(d + e*x)^(6 + m))/(e^7*(6 + m)) + (c^3*(d + e*x)^(7 + m))/(e^7*(7 + m))]
    @test_int [(d + e*x)^m*(a + b*x + c*x^2)^2, x, 2, ((c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(1 + m))/(e^5*(1 + m)) - (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(2 + m))/(e^5*(2 + m)) + ((6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^(3 + m))/(e^5*(3 + m)) - (2*c*(2*c*d - b*e)*(d + e*x)^(4 + m))/(e^5*(4 + m)) + (c^2*(d + e*x)^(5 + m))/(e^5*(5 + m))]
    @test_int [(d + e*x)^m*(a + b*x + c*x^2)^1, x, 2, ((c*d^2 - b*d*e + a*e^2)*(d + e*x)^(1 + m))/(e^3*(1 + m)) - ((2*c*d - b*e)*(d + e*x)^(2 + m))/(e^3*(2 + m)) + (c*(d + e*x)^(3 + m))/(e^3*(3 + m))]
    @test_int [(d + e*x)^m/(a + b*x + c*x^2)^1, x, 4, -((2*c*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (2*c*(d + e*x))/(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)))/(sqrt(b^2 - 4*a*c)*(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*(1 + m))) + (2*c*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (2*c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/(sqrt(b^2 - 4*a*c)*(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*(1 + m))]
    @test_int [(d + e*x)^m/(a + b*x + c*x^2)^2, x, 5, -(((d + e*x)^(1 + m)*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2))) + (c*(4*c^2*d^2 + b*(b + sqrt(b^2 - 4*a*c))*e^2*m - 2*c*e*(2*b*d - 2*a*e*(1 - m) + sqrt(b^2 - 4*a*c)*d*m))*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (2*c*(d + e*x))/(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)))/((b^2 - 4*a*c)^(3/2)*(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*(c*d^2 - b*d*e + a*e^2)*(1 + m)) - (c*(e*(2*c*d - b*e)*m + (4*c^2*d^2 - 4*c*e*(b*d - a*e*(1 - m)) + b^2*e^2*m)/sqrt(b^2 - 4*a*c))*(d + e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, 1 + m, 2 + m, (2*c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/((b^2 - 4*a*c)*(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*(c*d^2 - b*d*e + a*e^2)*(1 + m))]

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

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

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

    @test_int [(a + b*x + c*x^2)^p*(d + e*x)^3, x, 3, If(13>=8, (e*(d + e*x)^2*(a + b*x + c*x^2)^(1 + p))/(2*c*(2 + p)) - (e*(b*e*(2*c*d - b*e)*(2 + p)*(3 + p) - 2*c*(3 + 2*p)*(c*d^2*(5 + 2*p) - e*(a*e + b*d*(2 + p))) - 2*c*e*(2*c*d - b*e)*(1 + p)*(3 + p)*x)*(a + b*x + c*x^2)^(1 + p))/(4*c^3*(1 + p)*(2 + p)*(3 + 2*p)) - (2^(-1 + p)*(2*c*d - b*e)*(b^2*e^2*(3 + p) + 2*c^2*d^2*(3 + 2*p) - 2*c*e*(3*a*e + b*d*(3 + 2*p)))*(-((b - sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c)))^(-1 - p)*(a + b*x + c*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(-p, 1 + p, 2 + p, (b + sqrt(b^2 - 4*a*c) + 2*c*x)/(2*sqrt(b^2 - 4*a*c))))/(c^3*sqrt(b^2 - 4*a*c)*(1 + p)*(3 + 2*p)), (e*(d + e*x)^2*(a + b*x + c*x^2)^(1 + p))/(2*c*(2 + p)) - (e*(b*e*(2*c*d - b*e)*(2 + p)*(3 + p) - 2*c*(3 + 2*p)*(c*d^2*(5 + 2*p) - e*(a*e + b*d*(2 + p))) - 2*c*e*(2*c*d - b*e)*(1 + p)*(3 + p)*x)*(a + b*x + c*x^2)^(1 + p))/(4*c^3*(2 + p)*(3 + 5*p + 2*p^2)) - (2^(-1 + p)*(2*c*d - b*e)*(b^2*e^2*(3 + p) + 2*c^2*d^2*(3 + 2*p) - 2*c*e*(3*a*e + b*d*(3 + 2*p)))*(-((b - sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c)))^(-1 - p)*(a + b*x + c*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(-p, 1 + p, 2 + p, (b + sqrt(b^2 - 4*a*c) + 2*c*x)/(2*sqrt(b^2 - 4*a*c))))/(c^3*sqrt(b^2 - 4*a*c)*(1 + p)*(3 + 2*p)))]
    @test_int [(a + b*x + c*x^2)^p*(d + e*x)^2, x, 3, (e*(2*c*d - b*e)*(2 + p)*(a + b*x + c*x^2)^(1 + p))/(2*c^2*(1 + p)*(3 + 2*p)) + (e*(d + e*x)*(a + b*x + c*x^2)^(1 + p))/(c*(3 + 2*p)) - (2^p*(b^2*e^2*(2 + p) + 2*c^2*d^2*(3 + 2*p) - 2*c*e*(a*e + b*d*(3 + 2*p)))*(-((b - sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c)))^(-1 - p)*(a + b*x + c*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(-p, 1 + p, 2 + p, (b + sqrt(b^2 - 4*a*c) + 2*c*x)/(2*sqrt(b^2 - 4*a*c))))/(c^2*sqrt(b^2 - 4*a*c)*(1 + p)*(3 + 2*p))]
    @test_int [(a + b*x + c*x^2)^p*(d + e*x)^1, x, 2, (e*(a + b*x + c*x^2)^(1 + p))/(2*c*(1 + p)) - (2^p*(2*c*d - b*e)*(-((b - sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c)))^(-1 - p)*(a + b*x + c*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(-p, 1 + p, 2 + p, (b + sqrt(b^2 - 4*a*c) + 2*c*x)/(2*sqrt(b^2 - 4*a*c))))/(c*sqrt(b^2 - 4*a*c)*(1 + p))]
    @test_int [(a + b*x + c*x^2)^p*(d + e*x)^0, x, 1, -((2^(1 + p)*(-((b - sqrt(b^2 - 4*a*c) + 2*c*x)/sqrt(b^2 - 4*a*c)))^(-1 - p)*(a + b*x + c*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(-p, 1 + p, 2 + p, (b + sqrt(b^2 - 4*a*c) + 2*c*x)/(2*sqrt(b^2 - 4*a*c))))/(sqrt(b^2 - 4*a*c)*(1 + p)))]
    @test_int [(a + b*x + c*x^2)^p/(d + e*x)^1, x, 2, (2^(-1 + 2*p)*(a + b*x + c*x^2)^p*AppellF1(-2*p, -p, -p, 1 - 2*p, (2*c*d - (b - sqrt(b^2 - 4*a*c))*e)/(2*c*(d + e*x)), (2*d - ((b + sqrt(b^2 - 4*a*c))*e)/c)/(2*(d + e*x))))/(((e*(b - sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^p*((e*(b + sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^p*(e*p))]
    @test_int [(a + b*x + c*x^2)^p/(d + e*x)^2, x, 2, -((4^p*(a + b*x + c*x^2)^p*AppellF1(1 - 2*p, -p, -p, 2*(1 - p), (2*c*d - (b - sqrt(b^2 - 4*a*c))*e)/(2*c*(d + e*x)), (2*d - ((b + sqrt(b^2 - 4*a*c))*e)/c)/(2*(d + e*x))))/(((e*(b - sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^p*((e*(b + sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^p*(e*(1 - 2*p)*(d + e*x))))]
    @test_int [(a + b*x + c*x^2)^p/(d + e*x)^3, x, 2, -((2^(-1 + 2*p)*(a + b*x + c*x^2)^p*AppellF1(2*(1 - p), -p, -p, 3 - 2*p, (2*c*d - (b - sqrt(b^2 - 4*a*c))*e)/(2*c*(d + e*x)), (2*d - ((b + sqrt(b^2 - 4*a*c))*e)/c)/(2*(d + e*x))))/(((e*(b - sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^p*((e*(b + sqrt(b^2 - 4*a*c) + 2*c*x))/(c*(d + e*x)))^p*(e*(1 - p)*(d + e*x)^2)))]

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

    @test_int [(a + b*x + c*x^2)^p/(d + e*x)^(2*p + 0), x, 2, ((d + e*x)^(1 - 2*p)*(a + b*x + c*x^2)^p*AppellF1(1 - 2*p, -p, -p, 2 - 2*p, (2*c*(d + e*x))/(2*c*d - (b - sqrt(b^2 - 4*a*c))*e), (2*c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/((1 - (2*c*(d + e*x))/(2*c*d - (b - sqrt(b^2 - 4*a*c))*e))^p*(1 - (2*c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))^p*(e*(1 - 2*p)))]
    @test_int [(a + b*x + c*x^2)^p/(d + e*x)^(2*p + 1), x, 2, -(((a + b*x + c*x^2)^p*AppellF1(-2*p, -p, -p, 1 - 2*p, (2*c*(d + e*x))/(2*c*d - (b - sqrt(b^2 - 4*a*c))*e), (2*c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e)))/((d + e*x)^(2*p)*(1 - (2*c*(d + e*x))/(2*c*d - (b - sqrt(b^2 - 4*a*c))*e))^p*(1 - (2*c*(d + e*x))/(2*c*d - (b + sqrt(b^2 - 4*a*c))*e))^p*(2*e*p)))]
    @test_int [(a + b*x + c*x^2)^p/(d + e*x)^(2*p + 2), x, 1, ((b - sqrt(b^2 - 4*a*c) + 2*c*x)*(d + e*x)^(-1 - 2*p)*(a + b*x + c*x^2)^p*HypergeometricFunctions._₂F₁(-1 - 2*p, -p, -2*p, -((4*c*sqrt(b^2 - 4*a*c)*(d + e*x))/((2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*(b - sqrt(b^2 - 4*a*c) + 2*c*x)))))/((((2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*(b + sqrt(b^2 - 4*a*c) + 2*c*x))/((2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*(b - sqrt(b^2 - 4*a*c) + 2*c*x)))^p*((2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*(1 + 2*p)))]
    @test_int [(a + b*x + c*x^2)^p/(d + e*x)^(2*p + 3), x, 2, -((e*(a + b*x + c*x^2)^(1 + p))/((d + e*x)^(2*(1 + p))*(2*(c*d^2 - b*d*e + a*e^2)*(1 + p)))) + ((2*c*d - b*e)*(b - sqrt(b^2 - 4*a*c) + 2*c*x)*(d + e*x)^(-1 - 2*p)*(a + b*x + c*x^2)^p*HypergeometricFunctions._₂F₁(-1 - 2*p, -p, -2*p, -((4*c*sqrt(b^2 - 4*a*c)*(d + e*x))/((2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*(b - sqrt(b^2 - 4*a*c) + 2*c*x)))))/((((2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*(b + sqrt(b^2 - 4*a*c) + 2*c*x))/((2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*(b - sqrt(b^2 - 4*a*c) + 2*c*x)))^p*(2*(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*(c*d^2 - b*d*e + a*e^2)*(1 + 2*p)))]
    @test_int [(a + b*x + c*x^2)^p/(d + e*x)^(2*p + 4), x, 3, -((e*(d + e*x)^(-3 - 2*p)*(a + b*x + c*x^2)^(1 + p))/((c*d^2 - b*d*e + a*e^2)*(3 + 2*p))) - (e*(2*c*d - b*e)*(2 + p)*(a + b*x + c*x^2)^(1 + p))/((d + e*x)^(2*(1 + p))*(2*(c*d^2 - b*d*e + a*e^2)^2*(1 + p)*(3 + 2*p))) + ((b^2*e^2*(2 + p) + 2*c^2*d^2*(3 + 2*p) - 2*c*e*(a*e + b*d*(3 + 2*p)))*(b - sqrt(b^2 - 4*a*c) + 2*c*x)*(d + e*x)^(-1 - 2*p)*(a + b*x + c*x^2)^p*HypergeometricFunctions._₂F₁(-1 - 2*p, -p, -2*p, -((4*c*sqrt(b^2 - 4*a*c)*(d + e*x))/((2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*(b - sqrt(b^2 - 4*a*c) + 2*c*x)))))/((((2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*(b + sqrt(b^2 - 4*a*c) + 2*c*x))/((2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*(b - sqrt(b^2 - 4*a*c) + 2*c*x)))^p*(2*(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*(c*d^2 - b*d*e + a*e^2)^2*(1 + 2*p)*(3 + 2*p)))]
    @test_int [(a + b*x + c*x^2)^p/(d + e*x)^(2*p + 5), x, 4, -((e*(2*c*d - b*e)*(3 + p)*(d + e*x)^(-3 - 2*p)*(a + b*x + c*x^2)^(1 + p))/(2*(c*d^2 - b*d*e + a*e^2)^2*(2 + p)*(3 + 2*p))) - (e*(b^2*e^2*(6 + 5*p + p^2) + 2*c^2*d^2*(9 + 8*p + 2*p^2) - 2*c*e*(a*e*(3 + 2*p) + b*d*(9 + 8*p + 2*p^2)))*(a + b*x + c*x^2)^(1 + p))/((d + e*x)^(2*(1 + p))*(4*(c*d^2 - b*d*e + a*e^2)^3*(1 + p)*(2 + p)*(3 + 2*p))) - (e*(a + b*x + c*x^2)^(1 + p))/((d + e*x)^(2*(2 + p))*(2*(c*d^2 - b*d*e + a*e^2)*(2 + p))) + ((2*c*d - b*e)*(b^2*e^2*(3 + p) + 2*c^2*d^2*(3 + 2*p) - 2*c*e*(3*a*e + b*d*(3 + 2*p)))*(b - sqrt(b^2 - 4*a*c) + 2*c*x)*(d + e*x)^(-1 - 2*p)*(a + b*x + c*x^2)^p*HypergeometricFunctions._₂F₁(-1 - 2*p, -p, -2*p, -((4*c*sqrt(b^2 - 4*a*c)*(d + e*x))/((2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*(b - sqrt(b^2 - 4*a*c) + 2*c*x)))))/(((2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*(b + sqrt(b^2 - 4*a*c) + 2*c*x))/((2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*(b - sqrt(b^2 - 4*a*c) + 2*c*x)))^p/(4*(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*(c*d^2 - b*d*e + a*e^2)^3*(1 + 2*p)*(3 + 2*p))]
    @test_int [(a + b*x + c*x^2)^p/(d + e*x)^(2*p + 6), x, 5, -((e*(d + e*x)^(-5 - 2*p)*(a + b*x + c*x^2)^(1 + p))/((c*d^2 - b*d*e + a*e^2)*(5 + 2*p))) - (e*(b^2*e^2*(12 + 7*p + p^2) + 2*c^2*d^2*(18 + 11*p + 2*p^2) - 2*c*e*(3*a*e*(2 + p) + b*d*(18 + 11*p + 2*p^2)))*(d + e*x)^(-3 - 2*p)*(a + b*x + c*x^2)^(1 + p))/(2*(c*d^2 - b*d*e + a*e^2)^3*(2 + p)*(3 + 2*p)*(5 + 2*p)) - (e*(2*c*d - b*e)*(3 + p)*(b^2*e^2*(8 + 6*p + p^2) + 2*c^2*d^2*(8 + 7*p + 2*p^2) - 2*c*e*(a*e*(8 + 5*p) + b*d*(8 + 7*p + 2*p^2)))*(a + b*x + c*x^2)^(1 + p))/((d + e*x)^(2*(1 + p))*(4*(c*d^2 - b*d*e + a*e^2)^4*(1 + p)*(2 + p)*(3 + 2*p)*(5 + 2*p))) - (e*(2*c*d - b*e)*(4 + p)*(a + b*x + c*x^2)^(1 + p))/((d + e*x)^(2*(2 + p))*(2*(c*d^2 - b*d*e + a*e^2)^2*(2 + p)*(5 + 2*p))) + ((b^4*e^4*(12 + 7*p + p^2) + 4*c^4*d^4*(15 + 16*p + 4*p^2) - 8*c^3*d^2*e*(5 + 2*p)*(3*a*e + b*d*(3 + 2*p)) - 4*b^2*c*e^3*(3 + p)*(3*a*e + b*d*(5 + 2*p)) + 12*c^2*e^2*(a^2*e^2 + 2*a*b*d*e*(5 + 2*p) + b^2*d^2*(10 + 9*p + 2*p^2)))*(b - sqrt(b^2 - 4*a*c) + 2*c*x)*(d + e*x)^(-1 - 2*p)*(a + b*x + c*x^2)^p*HypergeometricFunctions._₂F₁(-1 - 2*p, -p, -2*p, -((4*c*sqrt(b^2 - 4*a*c)*(d + e*x))/((2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*(b - sqrt(b^2 - 4*a*c) + 2*c*x)))))/(((2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*(b + sqrt(b^2 - 4*a*c) + 2*c*x))/((2*c*d - (b + sqrt(b^2 - 4*a*c))*e)*(b - sqrt(b^2 - 4*a*c) + 2*c*x)))^p/(4*(2*c*d - (b - sqrt(b^2 - 4*a*c))*e)*(c*d^2 - b*d*e + a*e^2)^4*(1 + 2*p)*(3 + 2*p)*(5 + 2*p))]

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

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

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

    @test_int [1/((b*e - c*e*x)^(1/3)*(b^2 + b*c*x + c^2*x^2)^(1/3)), x, 2, -(((b^3*e - c^3*e*x^3)^(1/3)*atan((1 - (2*c*e^(1/3)*x)/(b^3*e - c^3*e*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*c*e^(1/3)*(b*e - c*e*x)^(1/3)*(b^2 + b*c*x + c^2*x^2)^(1/3))) + ((b^3*e - c^3*e*x^3)^(1/3)*log(c*e^(1/3)*x + (b^3*e - c^3*e*x^3)^(1/3)))/(2*c*e^(1/3)*(b*e - c*e*x)^(1/3)*(b^2 + b*c*x + c^2*x^2)^(1/3))]
    @test_int [1/((b*e - c*e*x)^(2/3)*(b^2 + b*c*x + c^2*x^2)^(2/3)), x, 3, (x*(1 - (c^3*x^3)/b^3)^(2/3)*HypergeometricFunctions._₂F₁(1/3, 2/3, 4/3, (c^3*x^3)/b^3))/((b*e - c*e*x)^(2/3)*(b^2 + b*c*x + c^2*x^2)^(2/3))]
    @test_int [(b*e - c*e*x)^p*(b^2 + b*c*x + c^2*x^2)^p, x, 3, (x*(b*e - c*e*x)^p*(b^2 + b*c*x + c^2*x^2)^p*HypergeometricFunctions._₂F₁(1/3, -p, 4/3, (c^3*x^3)/b^3))/(1 - (c^3*x^3)/b^3)^p]
    end

max_stars_repo_path: test/1 Algebraic functions/1.2 Trinomial products/1.2.1 Quadratic/1.2.1.2 (d+e x)^m (a+b x+c x^2)^p.jl