text:
@testset "3.4 u (a+b log(c (d+e x^m)^n))^p" begin
    (a, b, c, d, e, f, g, h, m, n, p, q, x, ) = @variables a b c d e f g h m n p q x

    #= ::Package:: =#

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

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^q*log(c*(d+e*x^m)^n)=#

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

    @test_int [x^4*log(c*(a + b*x^2)^p), x, 4, -((2*a^2*p*x)/(5*b^2)) + (2*a*p*x^3)/(15*b) - (2*p*x^5)/25 + (2*a^(5/2)*p*atan((sqrt(b)*x)/sqrt(a)))/(5*b^(5/2)) + (1/5)*x^5*log(c*(a + b*x^2)^p)]
    @test_int [x^3*log(c*(a + b*x^2)^p), x, 4, (a*p*x^2)/(4*b) - (p*x^4)/8 - (a^2*p*log(a + b*x^2))/(4*b^2) + (1/4)*x^4*log(c*(a + b*x^2)^p)]
    @test_int [x^2*log(c*(a + b*x^2)^p), x, 4, (2*a*p*x)/(3*b) - (2*p*x^3)/9 - (2*a^(3/2)*p*atan((sqrt(b)*x)/sqrt(a)))/(3*b^(3/2)) + (1/3)*x^3*log(c*(a + b*x^2)^p)]
    @test_int [x^1*log(c*(a + b*x^2)^p), x, 3, -((p*x^2)/2) + ((a + b*x^2)*log(c*(a + b*x^2)^p))/(2*b)]
    @test_int [x^0*log(c*(a + b*x^2)^p), x, 3, -2*p*x + (2*sqrt(a)*p*atan((sqrt(b)*x)/sqrt(a)))/sqrt(b) + x*log(c*(a + b*x^2)^p)]
    @test_int [log(c*(a + b*x^2)^p)/x^1, x, 3, (1/2)*log(-((b*x^2)/a))*log(c*(a + b*x^2)^p) + (1/2)*p*PolyLog(2, 1 + (b*x^2)/a)]
    @test_int [log(c*(a + b*x^2)^p)/x^2, x, 2, (2*sqrt(b)*p*atan((sqrt(b)*x)/sqrt(a)))/sqrt(a) - log(c*(a + b*x^2)^p)/x]
    @test_int [log(c*(a + b*x^2)^p)/x^3, x, 5, (b*p*log(x))/a - ((a + b*x^2)*log(c*(a + b*x^2)^p))/(2*a*x^2), (b*p*log(x))/a - (b*p*log(a + b*x^2))/(2*a) - log(c*(a + b*x^2)^p)/(2*x^2)]
    @test_int [log(c*(a + b*x^2)^p)/x^4, x, 3, -((2*b*p)/(3*a*x)) - (2*b^(3/2)*p*atan((sqrt(b)*x)/sqrt(a)))/(3*a^(3/2)) - log(c*(a + b*x^2)^p)/(3*x^3)]
    @test_int [log(c*(a + b*x^2)^p)/x^5, x, 4, -((b*p)/(4*a*x^2)) - (b^2*p*log(x))/(2*a^2) + (b^2*p*log(a + b*x^2))/(4*a^2) - log(c*(a + b*x^2)^p)/(4*x^4)]
    @test_int [log(c*(a + b*x^2)^p)/x^6, x, 4, -((2*b*p)/(15*a*x^3)) + (2*b^2*p)/(5*a^2*x) + (2*b^(5/2)*p*atan((sqrt(b)*x)/sqrt(a)))/(5*a^(5/2)) - log(c*(a + b*x^2)^p)/(5*x^5)]
    @test_int [log(c*(a + b*x^2)^p)/x^7, x, 4, -((b*p)/(12*a*x^4)) + (b^2*p)/(6*a^2*x^2) + (b^3*p*log(x))/(3*a^3) - (b^3*p*log(a + b*x^2))/(6*a^3) - log(c*(a + b*x^2)^p)/(6*x^6)]

    @test_int [x^5*log(c*(a + b*x^3)^p), x, 4, (a*p*x^3)/(6*b) - (p*x^6)/12 - (a^2*p*log(a + b*x^3))/(6*b^2) + (1/6)*x^6*log(c*(a + b*x^3)^p)]
    @test_int [x^4*log(c*(a + b*x^3)^p), x, 9, (3*a*p*x^2)/(10*b) - (3*p*x^5)/25 + (sqrt(3)*a^(5/3)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(5*b^(5/3)) + (a^(5/3)*p*log(a^(1/3) + b^(1/3)*x))/(5*b^(5/3)) - (a^(5/3)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(10*b^(5/3)) + (1/5)*x^5*log(c*(a + b*x^3)^p)]
    @test_int [x^3*log(c*(a + b*x^3)^p), x, 9, (3*a*p*x)/(4*b) - (3*p*x^4)/16 + (sqrt(3)*a^(4/3)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(4*b^(4/3)) - (a^(4/3)*p*log(a^(1/3) + b^(1/3)*x))/(4*b^(4/3)) + (a^(4/3)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(8*b^(4/3)) + (1/4)*x^4*log(c*(a + b*x^3)^p)]
    @test_int [x^2*log(c*(a + b*x^3)^p), x, 3, -((p*x^3)/3) + ((a + b*x^3)*log(c*(a + b*x^3)^p))/(3*b)]
    @test_int [x^1*log(c*(a + b*x^3)^p), x, 8, -((3*p*x^2)/4) - (sqrt(3)*a^(2/3)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(2*b^(2/3)) - (a^(2/3)*p*log(a^(1/3) + b^(1/3)*x))/(2*b^(2/3)) + (a^(2/3)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(4*b^(2/3)) + (1/2)*x^2*log(c*(a + b*x^3)^p)]
    @test_int [x^0*log(c*(a + b*x^3)^p), x, 8, -3*p*x - (sqrt(3)*a^(1/3)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/b^(1/3) + (a^(1/3)*p*log(a^(1/3) + b^(1/3)*x))/b^(1/3) - (a^(1/3)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(2*b^(1/3)) + x*log(c*(a + b*x^3)^p)]
    @test_int [log(c*(a + b*x^3)^p)/x^1, x, 3, (1/3)*log(-((b*x^3)/a))*log(c*(a + b*x^3)^p) + (1/3)*p*PolyLog(2, 1 + (b*x^3)/a)]
    @test_int [log(c*(a + b*x^3)^p)/x^2, x, 7, -((sqrt(3)*b^(1/3)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/a^(1/3)) - (b^(1/3)*p*log(a^(1/3) + b^(1/3)*x))/a^(1/3) + (b^(1/3)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(2*a^(1/3)) - log(c*(a + b*x^3)^p)/x]
    @test_int [log(c*(a + b*x^3)^p)/x^3, x, 7, -((sqrt(3)*b^(2/3)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(2*a^(2/3))) + (b^(2/3)*p*log(a^(1/3) + b^(1/3)*x))/(2*a^(2/3)) - (b^(2/3)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(4*a^(2/3)) - log(c*(a + b*x^3)^p)/(2*x^2)]
    @test_int [log(c*(a + b*x^3)^p)/x^4, x, 5, (b*p*log(x))/a - (b*p*log(a + b*x^3))/(3*a) - log(c*(a + b*x^3)^p)/(3*x^3)]
    @test_int [log(c*(a + b*x^3)^p)/x^5, x, 8, -((3*b*p)/(4*a*x)) + (sqrt(3)*b^(4/3)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(4*a^(4/3)) + (b^(4/3)*p*log(a^(1/3) + b^(1/3)*x))/(4*a^(4/3)) - (b^(4/3)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(8*a^(4/3)) - log(c*(a + b*x^3)^p)/(4*x^4)]
    @test_int [log(c*(a + b*x^3)^p)/x^6, x, 8, -((3*b*p)/(10*a*x^2)) + (sqrt(3)*b^(5/3)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(5*a^(5/3)) - (b^(5/3)*p*log(a^(1/3) + b^(1/3)*x))/(5*a^(5/3)) + (b^(5/3)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(10*a^(5/3)) - log(c*(a + b*x^3)^p)/(5*x^5)]
    @test_int [log(c*(a + b*x^3)^p)/x^7, x, 4, -((b*p)/(6*a*x^3)) - (b^2*p*log(x))/(2*a^2) + (b^2*p*log(a + b*x^3))/(6*a^2) - log(c*(a + b*x^3)^p)/(6*x^6)]

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

    @test_int [x^4*log(c*(a + b/x)^p), x, 4, -((b^4*p*x)/(5*a^4)) + (b^3*p*x^2)/(10*a^3) - (b^2*p*x^3)/(15*a^2) + (b*p*x^4)/(20*a) + (1/5)*x^5*log(c*(a + b/x)^p) + (b^5*p*log(b + a*x))/(5*a^5)]
    @test_int [x^3*log(c*(a + b/x)^p), x, 4, (b^3*p*x)/(4*a^3) - (b^2*p*x^2)/(8*a^2) + (b*p*x^3)/(12*a) + (1/4)*x^4*log(c*(a + b/x)^p) - (b^4*p*log(b + a*x))/(4*a^4)]
    @test_int [x^2*log(c*(a + b/x)^p), x, 4, -((b^2*p*x)/(3*a^2)) + (b*p*x^2)/(6*a) + (1/3)*x^3*log(c*(a + b/x)^p) + (b^3*p*log(b + a*x))/(3*a^3)]
    @test_int [x^1*log(c*(a + b/x)^p), x, 4, (b*p*x)/(2*a) + (1/2)*x^2*log(c*(a + b/x)^p) - (b^2*p*log(b + a*x))/(2*a^2)]
    @test_int [x^0*log(c*(a + b/x)^p), x, 3, x*log(c*(a + b/x)^p) + (b*p*log(b + a*x))/a]
    @test_int [log(c*(a + b/x)^p)/x^1, x, 3, (-log(c*(a + b/x)^p))*log(-(b/(a*x))) - p*PolyLog(2, 1 + b/(a*x))]
    @test_int [log(c*(a + b/x)^p)/x^2, x, 3, p/x - ((a + b/x)*log(c*(a + b/x)^p))/b]
    @test_int [log(c*(a + b/x)^p)/x^3, x, 4, p/(4*x^2) - (a*p)/(2*b*x) + (a^2*p*log(a + b/x))/(2*b^2) - log(c*(a + b/x)^p)/(2*x^2)]
    @test_int [log(c*(a + b/x)^p)/x^4, x, 4, p/(9*x^3) - (a*p)/(6*b*x^2) + (a^2*p)/(3*b^2*x) - (a^3*p*log(a + b/x))/(3*b^3) - log(c*(a + b/x)^p)/(3*x^3)]
    @test_int [log(c*(a + b/x)^p)/x^5, x, 4, p/(16*x^4) - (a*p)/(12*b*x^3) + (a^2*p)/(8*b^2*x^2) - (a^3*p)/(4*b^3*x) + (a^4*p*log(a + b/x))/(4*b^4) - log(c*(a + b/x)^p)/(4*x^4)]

    @test_int [x^4*log(c*(a + b/x^2)^p), x, 5, -((2*b^2*p*x)/(5*a^2)) + (2*b*p*x^3)/(15*a) + (2*b^(5/2)*p*atan((sqrt(a)*x)/sqrt(b)))/(5*a^(5/2)) + (1/5)*x^5*log(c*(a + b/x^2)^p)]
    @test_int [x^3*log(c*(a + b/x^2)^p), x, 5, (b*p*x^2)/(4*a) + (1/4)*x^4*log(c*(a + b/x^2)^p) - (b^2*p*log(b + a*x^2))/(4*a^2)]
    @test_int [x^2*log(c*(a + b/x^2)^p), x, 4, (2*b*p*x)/(3*a) - (2*b^(3/2)*p*atan((sqrt(a)*x)/sqrt(b)))/(3*a^(3/2)) + (1/3)*x^3*log(c*(a + b/x^2)^p)]
    @test_int [x^1*log(c*(a + b/x^2)^p), x, 3, (1/2)*x^2*log(c*(a + b/x^2)^p) + (b*p*log(b + a*x^2))/(2*a)]
    @test_int [x^0*log(c*(a + b/x^2)^p), x, 3, (2*sqrt(b)*p*atan((sqrt(a)*x)/sqrt(b)))/sqrt(a) + x*log(c*(a + b/x^2)^p)]
    @test_int [log(c*(a + b/x^2)^p)/x^1, x, 3, (-(1/2))*log(c*(a + b/x^2)^p)*log(-(b/(a*x^2))) - (1/2)*p*PolyLog(2, 1 + b/(a*x^2))]
    @test_int [log(c*(a + b/x^2)^p)/x^2, x, 4, (2*p)/x + (2*sqrt(a)*p*atan((sqrt(a)*x)/sqrt(b)))/sqrt(b) - log(c*(a + b/x^2)^p)/x]
    @test_int [log(c*(a + b/x^2)^p)/x^3, x, 3, p/(2*x^2) - ((a + b/x^2)*log(c*(a + b/x^2)^p))/(2*b)]
    @test_int [log(c*(a + b/x^2)^p)/x^4, x, 5, (2*p)/(9*x^3) - (2*a*p)/(3*b*x) - (2*a^(3/2)*p*atan((sqrt(a)*x)/sqrt(b)))/(3*b^(3/2)) - log(c*(a + b/x^2)^p)/(3*x^3)]

    @test_int [log(1 + b/x)/x, x, 1, PolyLog(2, -b/x)]

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

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

    @test_int [x^3*log(c*(a + b*sqrt(x))^p), x, 4, (a^7*p*sqrt(x))/(4*b^7) - (a^6*p*x)/(8*b^6) + (a^5*p*x^(3/2))/(12*b^5) - (a^4*p*x^2)/(16*b^4) + (a^3*p*x^(5/2))/(20*b^3) - (a^2*p*x^3)/(24*b^2) + (a*p*x^(7/2))/(28*b) - (p*x^4)/32 - (a^8*p*log(a + b*sqrt(x)))/(4*b^8) + (1/4)*x^4*log(c*(a + b*sqrt(x))^p)]
    @test_int [x^2*log(c*(a + b*sqrt(x))^p), x, 4, (a^5*p*sqrt(x))/(3*b^5) - (a^4*p*x)/(6*b^4) + (a^3*p*x^(3/2))/(9*b^3) - (a^2*p*x^2)/(12*b^2) + (a*p*x^(5/2))/(15*b) - (p*x^3)/18 - (a^6*p*log(a + b*sqrt(x)))/(3*b^6) + (1/3)*x^3*log(c*(a + b*sqrt(x))^p)]
    @test_int [x^1*log(c*(a + b*sqrt(x))^p), x, 4, (a^3*p*sqrt(x))/(2*b^3) - (a^2*p*x)/(4*b^2) + (a*p*x^(3/2))/(6*b) - (p*x^2)/8 - (a^4*p*log(a + b*sqrt(x)))/(2*b^4) + (1/2)*x^2*log(c*(a + b*sqrt(x))^p)]
    @test_int [x^0*log(c*(a + b*sqrt(x))^p), x, 4, (a*p*sqrt(x))/b - (p*x)/2 - (a^2*p*log(a + b*sqrt(x)))/b^2 + x*log(c*(a + b*sqrt(x))^p)]
    @test_int [log(c*(a + b*sqrt(x))^p)/x^1, x, 3, 2*log(c*(a + b*sqrt(x))^p)*log(-((b*sqrt(x))/a)) + 2*p*PolyLog(2, 1 + (b*sqrt(x))/a)]
    @test_int [log(c*(a + b*sqrt(x))^p)/x^2, x, 4, -((b*p)/(a*sqrt(x))) + (b^2*p*log(a + b*sqrt(x)))/a^2 - log(c*(a + b*sqrt(x))^p)/x - (b^2*p*log(x))/(2*a^2)]
    @test_int [log(c*(a + b*sqrt(x))^p)/x^3, x, 4, -((b*p)/(6*a*x^(3/2))) + (b^2*p)/(4*a^2*x) - (b^3*p)/(2*a^3*sqrt(x)) + (b^4*p*log(a + b*sqrt(x)))/(2*a^4) - log(c*(a + b*sqrt(x))^p)/(2*x^2) - (b^4*p*log(x))/(4*a^4)]
    @test_int [log(c*(a + b*sqrt(x))^p)/x^4, x, 4, -((b*p)/(15*a*x^(5/2))) + (b^2*p)/(12*a^2*x^2) - (b^3*p)/(9*a^3*x^(3/2)) + (b^4*p)/(6*a^4*x) - (b^5*p)/(3*a^5*sqrt(x)) + (b^6*p*log(a + b*sqrt(x)))/(3*a^6) - log(c*(a + b*sqrt(x))^p)/(3*x^3) - (b^6*p*log(x))/(6*a^6)]

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

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

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

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

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f*x)^q*log(c*(d+e*x^m)^n)*when*q*symbolic=#

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

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f*x)^q*log(c*(d+e*x^m)^n)*when*m*symbolic=#

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

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

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

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

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

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

    @test_int [x^5*log(c*(a + b*x^2)^p)^2, x, 8, (a^2*p^2*x^2)/b^2 - (a*p^2*(a + b*x^2)^2)/(4*b^3) + (p^2*(a + b*x^2)^3)/(27*b^3) - (a^3*p^2*log(a + b*x^2)^2)/(6*b^3) - (a^2*p*(a + b*x^2)*log(c*(a + b*x^2)^p))/b^3 + (a*p*(a + b*x^2)^2*log(c*(a + b*x^2)^p))/(2*b^3) - (p*(a + b*x^2)^3*log(c*(a + b*x^2)^p))/(9*b^3) + (a^3*p*log(a + b*x^2)*log(c*(a + b*x^2)^p))/(3*b^3) + (1/6)*x^6*log(c*(a + b*x^2)^p)^2]
    @test_int [x^3*log(c*(a + b*x^2)^p)^2, x, 9, -((a*p^2*x^2)/b) + (p^2*(a + b*x^2)^2)/(8*b^2) + (a*p*(a + b*x^2)*log(c*(a + b*x^2)^p))/b^2 - (p*(a + b*x^2)^2*log(c*(a + b*x^2)^p))/(4*b^2) - (a*(a + b*x^2)*log(c*(a + b*x^2)^p)^2)/(2*b^2) + ((a + b*x^2)^2*log(c*(a + b*x^2)^p)^2)/(4*b^2)]
    @test_int [x^1*log(c*(a + b*x^2)^p)^2, x, 4, p^2*x^2 - (p*(a + b*x^2)*log(c*(a + b*x^2)^p))/b + ((a + b*x^2)*log(c*(a + b*x^2)^p)^2)/(2*b)]
    @test_int [log(c*(a + b*x^2)^p)^2/x^1, x, 5, (1/2)*log(-((b*x^2)/a))*log(c*(a + b*x^2)^p)^2 + p*log(c*(a + b*x^2)^p)*PolyLog(2, 1 + (b*x^2)/a) - p^2*PolyLog(3, 1 + (b*x^2)/a)]
    @test_int [log(c*(a + b*x^2)^p)^2/x^3, x, 4, (b*p*log(-((b*x^2)/a))*log(c*(a + b*x^2)^p))/a - ((a + b*x^2)*log(c*(a + b*x^2)^p)^2)/(2*a*x^2) + (b*p^2*PolyLog(2, 1 + (b*x^2)/a))/a]
    @test_int [log(c*(a + b*x^2)^p)^2/x^5, x, 8, (b^2*p^2*log(x))/a^2 - (b*p*(a + b*x^2)*log(c*(a + b*x^2)^p))/(2*a^2*x^2) - log(c*(a + b*x^2)^p)^2/(4*x^4) - (b^2*p*log(c*(a + b*x^2)^p)*log(1 - a/(a + b*x^2)))/(2*a^2) + (b^2*p^2*PolyLog(2, a/(a + b*x^2)))/(2*a^2)]
    @test_int [log(c*(a + b*x^2)^p)^2/x^7, x, 12, -((b^2*p^2)/(6*a^2*x^2)) - (b^3*p^2*log(x))/a^3 + (b^3*p^2*log(a + b*x^2))/(6*a^3) - (b*p*log(c*(a + b*x^2)^p))/(6*a*x^4) + (b^2*p*(a + b*x^2)*log(c*(a + b*x^2)^p))/(3*a^3*x^2) - log(c*(a + b*x^2)^p)^2/(6*x^6) + (b^3*p*log(c*(a + b*x^2)^p)*log(1 - a/(a + b*x^2)))/(3*a^3) - (b^3*p^2*PolyLog(2, a/(a + b*x^2)))/(3*a^3)]

    @test_int [x^4*log(c*(a + b*x^2)^p)^2, x, 20, (184*a^2*p^2*x)/(75*b^2) - (64*a*p^2*x^3)/(225*b) + (8*p^2*x^5)/125 - (184*a^(5/2)*p^2*atan((sqrt(b)*x)/sqrt(a)))/(75*b^(5/2)) + (4*im*a^(5/2)*p^2*atan((sqrt(b)*x)/sqrt(a))^2)/(5*b^(5/2)) + (8*a^(5/2)*p^2*atan((sqrt(b)*x)/sqrt(a))*log((2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/(5*b^(5/2)) - (4*a^2*p*x*log(c*(a + b*x^2)^p))/(5*b^2) + (4*a*p*x^3*log(c*(a + b*x^2)^p))/(15*b) - (4/25)*p*x^5*log(c*(a + b*x^2)^p) + (4*a^(5/2)*p*atan((sqrt(b)*x)/sqrt(a))*log(c*(a + b*x^2)^p))/(5*b^(5/2)) + (1/5)*x^5*log(c*(a + b*x^2)^p)^2 + (4*im*a^(5/2)*p^2*PolyLog(2, 1 - (2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/(5*b^(5/2))]
    @test_int [x^2*log(c*(a + b*x^2)^p)^2, x, 16, -((32*a*p^2*x)/(9*b)) + (8*p^2*x^3)/27 + (32*a^(3/2)*p^2*atan((sqrt(b)*x)/sqrt(a)))/(9*b^(3/2)) - (4*im*a^(3/2)*p^2*atan((sqrt(b)*x)/sqrt(a))^2)/(3*b^(3/2)) - (8*a^(3/2)*p^2*atan((sqrt(b)*x)/sqrt(a))*log((2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/(3*b^(3/2)) + (4*a*p*x*log(c*(a + b*x^2)^p))/(3*b) - (4/9)*p*x^3*log(c*(a + b*x^2)^p) - (4*a^(3/2)*p*atan((sqrt(b)*x)/sqrt(a))*log(c*(a + b*x^2)^p))/(3*b^(3/2)) + (1/3)*x^3*log(c*(a + b*x^2)^p)^2 - (4*im*a^(3/2)*p^2*PolyLog(2, 1 - (2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/(3*b^(3/2))]
    @test_int [x^0*log(c*(a + b*x^2)^p)^2, x, 12, 8*p^2*x - (8*sqrt(a)*p^2*atan((sqrt(b)*x)/sqrt(a)))/sqrt(b) + (4*im*sqrt(a)*p^2*atan((sqrt(b)*x)/sqrt(a))^2)/sqrt(b) + (8*sqrt(a)*p^2*atan((sqrt(b)*x)/sqrt(a))*log((2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/sqrt(b) - 4*p*x*log(c*(a + b*x^2)^p) + (4*sqrt(a)*p*atan((sqrt(b)*x)/sqrt(a))*log(c*(a + b*x^2)^p))/sqrt(b) + x*log(c*(a + b*x^2)^p)^2 + (4*im*sqrt(a)*p^2*PolyLog(2, 1 - (2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/sqrt(b)]
    @test_int [log(c*(a + b*x^2)^p)^2/x^2, x, 7, (4*im*sqrt(b)*p^2*atan((sqrt(b)*x)/sqrt(a))^2)/sqrt(a) + (8*sqrt(b)*p^2*atan((sqrt(b)*x)/sqrt(a))*log((2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/sqrt(a) + (4*sqrt(b)*p*atan((sqrt(b)*x)/sqrt(a))*log(c*(a + b*x^2)^p))/sqrt(a) - log(c*(a + b*x^2)^p)^2/x + (4*im*sqrt(b)*p^2*PolyLog(2, 1 - (2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/sqrt(a)]
    @test_int [log(c*(a + b*x^2)^p)^2/x^4, x, 11, (8*b^(3/2)*p^2*atan((sqrt(b)*x)/sqrt(a)))/(3*a^(3/2)) - (4*im*b^(3/2)*p^2*atan((sqrt(b)*x)/sqrt(a))^2)/(3*a^(3/2)) - (8*b^(3/2)*p^2*atan((sqrt(b)*x)/sqrt(a))*log((2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/(3*a^(3/2)) - (4*b*p*log(c*(a + b*x^2)^p))/(3*a*x) - (4*b^(3/2)*p*atan((sqrt(b)*x)/sqrt(a))*log(c*(a + b*x^2)^p))/(3*a^(3/2)) - log(c*(a + b*x^2)^p)^2/(3*x^3) - (4*im*b^(3/2)*p^2*PolyLog(2, 1 - (2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/(3*a^(3/2))]
    @test_int [log(c*(a + b*x^2)^p)^2/x^6, x, 14, -((8*b^2*p^2)/(15*a^2*x)) - (32*b^(5/2)*p^2*atan((sqrt(b)*x)/sqrt(a)))/(15*a^(5/2)) + (4*im*b^(5/2)*p^2*atan((sqrt(b)*x)/sqrt(a))^2)/(5*a^(5/2)) + (8*b^(5/2)*p^2*atan((sqrt(b)*x)/sqrt(a))*log((2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/(5*a^(5/2)) - (4*b*p*log(c*(a + b*x^2)^p))/(15*a*x^3) + (4*b^2*p*log(c*(a + b*x^2)^p))/(5*a^2*x) + (4*b^(5/2)*p*atan((sqrt(b)*x)/sqrt(a))*log(c*(a + b*x^2)^p))/(5*a^(5/2)) - log(c*(a + b*x^2)^p)^2/(5*x^5) + (4*im*b^(5/2)*p^2*PolyLog(2, 1 - (2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/(5*a^(5/2))]
    @test_int [log(c*(a + b*x^2)^p)^2/x^8, x, 18, -((8*b^2*p^2)/(105*a^2*x^3)) + (64*b^3*p^2)/(105*a^3*x) + (184*b^(7/2)*p^2*atan((sqrt(b)*x)/sqrt(a)))/(105*a^(7/2)) - (4*im*b^(7/2)*p^2*atan((sqrt(b)*x)/sqrt(a))^2)/(7*a^(7/2)) - (8*b^(7/2)*p^2*atan((sqrt(b)*x)/sqrt(a))*log((2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/(7*a^(7/2)) - (4*b*p*log(c*(a + b*x^2)^p))/(35*a*x^5) + (4*b^2*p*log(c*(a + b*x^2)^p))/(21*a^2*x^3) - (4*b^3*p*log(c*(a + b*x^2)^p))/(7*a^3*x) - (4*b^(7/2)*p*atan((sqrt(b)*x)/sqrt(a))*log(c*(a + b*x^2)^p))/(7*a^(7/2)) - log(c*(a + b*x^2)^p)^2/(7*x^7) - (4*im*b^(7/2)*p^2*PolyLog(2, 1 - (2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/(7*a^(7/2))]

    @test_int [x^5*log(c*(a + b*x^2)^p)^3, x, 15, -((3*a^2*p^3*x^2)/b^2) + (3*a*p^3*(a + b*x^2)^2)/(8*b^3) - (p^3*(a + b*x^2)^3)/(27*b^3) + (3*a^2*p^2*(a + b*x^2)*log(c*(a + b*x^2)^p))/b^3 - (3*a*p^2*(a + b*x^2)^2*log(c*(a + b*x^2)^p))/(4*b^3) + (p^2*(a + b*x^2)^3*log(c*(a + b*x^2)^p))/(9*b^3) - (3*a^2*p*(a + b*x^2)*log(c*(a + b*x^2)^p)^2)/(2*b^3) + (3*a*p*(a + b*x^2)^2*log(c*(a + b*x^2)^p)^2)/(4*b^3) - (p*(a + b*x^2)^3*log(c*(a + b*x^2)^p)^2)/(6*b^3) + (a^2*(a + b*x^2)*log(c*(a + b*x^2)^p)^3)/(2*b^3) - (a*(a + b*x^2)^2*log(c*(a + b*x^2)^p)^3)/(2*b^3) + ((a + b*x^2)^3*log(c*(a + b*x^2)^p)^3)/(6*b^3)]
    @test_int [x^3*log(c*(a + b*x^2)^p)^3, x, 11, (3*a*p^3*x^2)/b - (3*p^3*(a + b*x^2)^2)/(16*b^2) - (3*a*p^2*(a + b*x^2)*log(c*(a + b*x^2)^p))/b^2 + (3*p^2*(a + b*x^2)^2*log(c*(a + b*x^2)^p))/(8*b^2) + (3*a*p*(a + b*x^2)*log(c*(a + b*x^2)^p)^2)/(2*b^2) - (3*p*(a + b*x^2)^2*log(c*(a + b*x^2)^p)^2)/(8*b^2) - (a*(a + b*x^2)*log(c*(a + b*x^2)^p)^3)/(2*b^2) + ((a + b*x^2)^2*log(c*(a + b*x^2)^p)^3)/(4*b^2)]
    @test_int [x^1*log(c*(a + b*x^2)^p)^3, x, 5, -3*p^3*x^2 + (3*p^2*(a + b*x^2)*log(c*(a + b*x^2)^p))/b - (3*p*(a + b*x^2)*log(c*(a + b*x^2)^p)^2)/(2*b) + ((a + b*x^2)*log(c*(a + b*x^2)^p)^3)/(2*b)]
    @test_int [log(c*(a + b*x^2)^p)^3/x^1, x, 6, (1/2)*log(-((b*x^2)/a))*log(c*(a + b*x^2)^p)^3 + (3/2)*p*log(c*(a + b*x^2)^p)^2*PolyLog(2, 1 + (b*x^2)/a) - 3*p^2*log(c*(a + b*x^2)^p)*PolyLog(3, 1 + (b*x^2)/a) + 3*p^3*PolyLog(4, 1 + (b*x^2)/a)]
    @test_int [log(c*(a + b*x^2)^p)^3/x^3, x, 6, (3*b*p*log(-((b*x^2)/a))*log(c*(a + b*x^2)^p)^2)/(2*a) - ((a + b*x^2)*log(c*(a + b*x^2)^p)^3)/(2*a*x^2) + (3*b*p^2*log(c*(a + b*x^2)^p)*PolyLog(2, 1 + (b*x^2)/a))/a - (3*b*p^3*PolyLog(3, 1 + (b*x^2)/a))/a]
    @test_int [log(c*(a + b*x^2)^p)^3/x^5, x, 10, (3*b^2*p^2*log(-((b*x^2)/a))*log(c*(a + b*x^2)^p))/(2*a^2) - (3*b*p*(a + b*x^2)*log(c*(a + b*x^2)^p)^2)/(4*a^2*x^2) - log(c*(a + b*x^2)^p)^3/(4*x^4) - (3*b^2*p*log(c*(a + b*x^2)^p)^2*log(1 - a/(a + b*x^2)))/(4*a^2) + (3*b^2*p^2*log(c*(a + b*x^2)^p)*PolyLog(2, a/(a + b*x^2)))/(2*a^2) + (3*b^2*p^3*PolyLog(2, 1 + (b*x^2)/a))/(2*a^2) + (3*b^2*p^3*PolyLog(3, a/(a + b*x^2)))/(2*a^2)]
    @test_int [log(c*(a + b*x^2)^p)^3/x^7, x, 17, (b^3*p^3*log(x))/a^3 - (b^2*p^2*(a + b*x^2)*log(c*(a + b*x^2)^p))/(2*a^3*x^2) - (b^3*p^2*log(-((b*x^2)/a))*log(c*(a + b*x^2)^p))/a^3 - (b*p*log(c*(a + b*x^2)^p)^2)/(4*a*x^4) + (b^2*p*(a + b*x^2)*log(c*(a + b*x^2)^p)^2)/(2*a^3*x^2) - log(c*(a + b*x^2)^p)^3/(6*x^6) - (b^3*p^2*log(c*(a + b*x^2)^p)*log(1 - a/(a + b*x^2)))/(2*a^3) + (b^3*p*log(c*(a + b*x^2)^p)^2*log(1 - a/(a + b*x^2)))/(2*a^3) + (b^3*p^3*PolyLog(2, a/(a + b*x^2)))/(2*a^3) - (b^3*p^2*log(c*(a + b*x^2)^p)*PolyLog(2, a/(a + b*x^2)))/a^3 - (b^3*p^3*PolyLog(2, 1 + (b*x^2)/a))/a^3 - (b^3*p^3*PolyLog(3, a/(a + b*x^2)))/a^3]

    @test_int [x^2*log(c*(a + b*x^2)^p)^3, x, 31, (208*a*p^3*x)/(9*b) - (16*p^3*x^3)/27 - (208*a^(3/2)*p^3*atan((sqrt(b)*x)/sqrt(a)))/(9*b^(3/2)) + (32*im*a^(3/2)*p^3*atan((sqrt(b)*x)/sqrt(a))^2)/(3*b^(3/2)) + (64*a^(3/2)*p^3*atan((sqrt(b)*x)/sqrt(a))*log((2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/(3*b^(3/2)) - (32*a*p^2*x*log(c*(a + b*x^2)^p))/(3*b) + (8/9)*p^2*x^3*log(c*(a + b*x^2)^p) + (32*a^(3/2)*p^2*atan((sqrt(b)*x)/sqrt(a))*log(c*(a + b*x^2)^p))/(3*b^(3/2)) + (2*a*p*x*log(c*(a + b*x^2)^p)^2)/b - (2/3)*p*x^3*log(c*(a + b*x^2)^p)^2 + (1/3)*x^3*log(c*(a + b*x^2)^p)^3 + (32*im*a^(3/2)*p^3*PolyLog(2, 1 - (2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/(3*b^(3/2)) - (2*a^2*p*Unintegrable(log(c*(a + b*x^2)^p)^2/(a + b*x^2), x))/b]
    @test_int [x^0*log(c*(a + b*x^2)^p)^3, x, 15, -48*p^3*x + (48*sqrt(a)*p^3*atan((sqrt(b)*x)/sqrt(a)))/sqrt(b) - (24*im*sqrt(a)*p^3*atan((sqrt(b)*x)/sqrt(a))^2)/sqrt(b) - (48*sqrt(a)*p^3*atan((sqrt(b)*x)/sqrt(a))*log((2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/sqrt(b) + 24*p^2*x*log(c*(a + b*x^2)^p) - (24*sqrt(a)*p^2*atan((sqrt(b)*x)/sqrt(a))*log(c*(a + b*x^2)^p))/sqrt(b) - 6*p*x*log(c*(a + b*x^2)^p)^2 + x*log(c*(a + b*x^2)^p)^3 - (24*im*sqrt(a)*p^3*PolyLog(2, 1 - (2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/sqrt(b) + 6*a*p*Unintegrable(log(c*(a + b*x^2)^p)^2/(a + b*x^2), x)]
    @test_int [log(c*(a + b*x^2)^p)^3/x^2, x, 1, -(log(c*(a + b*x^2)^p)^3/x) + 6*b*p*Unintegrable(log(c*(a + b*x^2)^p)^2/(a + b*x^2), x)]
    @test_int [log(c*(a + b*x^2)^p)^3/x^4, x, 10, (8*im*b^(3/2)*p^3*atan((sqrt(b)*x)/sqrt(a))^2)/a^(3/2) + (16*b^(3/2)*p^3*atan((sqrt(b)*x)/sqrt(a))*log((2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/a^(3/2) + (8*b^(3/2)*p^2*atan((sqrt(b)*x)/sqrt(a))*log(c*(a + b*x^2)^p))/a^(3/2) - (2*b*p*log(c*(a + b*x^2)^p)^2)/(a*x) - log(c*(a + b*x^2)^p)^3/(3*x^3) + (8*im*b^(3/2)*p^3*PolyLog(2, 1 - (2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/a^(3/2) - (2*b^2*p*Unintegrable(log(c*(a + b*x^2)^p)^2/(a + b*x^2), x))/a]

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

    @test_int [x^3/log(c*(a + b*x^2)^p), x, 9, -((a*(a + b*x^2)*ExpIntegralEi(log(c*(a + b*x^2)^p)/p))/((c*(a + b*x^2)^p)^p^(-1)*(2*b^2*p))) + ((a + b*x^2)^2*ExpIntegralEi((2*log(c*(a + b*x^2)^p))/p))/((c*(a + b*x^2)^p)^(2/p)*(2*b^2*p))]
    @test_int [x^1/log(c*(a + b*x^2)^p), x, 4, ((a + b*x^2)*ExpIntegralEi(log(c*(a + b*x^2)^p)/p))/(2*b*p*(c*(a + b*x^2)^p)^p^(-1))]
    @test_int [1/(x^1*log(c*(a + b*x^2)^p)), x, 0, Unintegrable(1/(x*log(c*(a + b*x^2)^p)), x)]
    @test_int [1/(x^3*log(c*(a + b*x^2)^p)), x, 0, Unintegrable(1/(x^3*log(c*(a + b*x^2)^p)), x)]

    @test_int [x^2/log(c*(a + b*x^2)^p), x, 0, Unintegrable(x^2/log(c*(a + b*x^2)^p), x)]
    @test_int [x^0/log(c*(a + b*x^2)^p), x, 0, Unintegrable(1/log(c*(a + b*x^2)^p), x)]
    @test_int [1/(x^2*log(c*(a + b*x^2)^p)), x, 0, Unintegrable(1/(x^2*log(c*(a + b*x^2)^p)), x)]

    @test_int [x^3/log(c*(a + b*x^2)^p)^2, x, 13, -((a*(a + b*x^2)*ExpIntegralEi(log(c*(a + b*x^2)^p)/p))/((c*(a + b*x^2)^p)^p^(-1)*(2*b^2*p^2))) + ((a + b*x^2)^2*ExpIntegralEi((2*log(c*(a + b*x^2)^p))/p))/((c*(a + b*x^2)^p)^(2/p)*(b^2*p^2)) - (x^2*(a + b*x^2))/(2*b*p*log(c*(a + b*x^2)^p))]
    @test_int [x^1/log(c*(a + b*x^2)^p)^2, x, 5, ((a + b*x^2)*ExpIntegralEi(log(c*(a + b*x^2)^p)/p))/((c*(a + b*x^2)^p)^p^(-1)*(2*b*p^2)) - (a + b*x^2)/(2*b*p*log(c*(a + b*x^2)^p))]
    @test_int [1/(x^1*log(c*(a + b*x^2)^p)^2), x, 0, Unintegrable(1/(x*log(c*(a + b*x^2)^p)^2), x)]
    @test_int [1/(x^3*log(c*(a + b*x^2)^p)^2), x, 0, Unintegrable(1/(x^3*log(c*(a + b*x^2)^p)^2), x)]

    @test_int [x^2/log(c*(a + b*x^2)^p)^2, x, 0, Unintegrable(x^2/log(c*(a + b*x^2)^p)^2, x)]
    @test_int [x^0/log(c*(a + b*x^2)^p)^2, x, 0, Unintegrable(1/log(c*(a + b*x^2)^p)^2, x)]
    @test_int [1/(x^2*log(c*(a + b*x^2)^p)^2), x, 0, Unintegrable(1/(x^2*log(c*(a + b*x^2)^p)^2), x)]

    @test_int [x^3/log(c*(a + b*x^2)^p)^3, x, 18, -((a*(a + b*x^2)*ExpIntegralEi(log(c*(a + b*x^2)^p)/p))/((c*(a + b*x^2)^p)^p^(-1)*(4*b^2*p^3))) + ((a + b*x^2)^2*ExpIntegralEi((2*log(c*(a + b*x^2)^p))/p))/((c*(a + b*x^2)^p)^(2/p)*(b^2*p^3)) - (x^2*(a + b*x^2))/(4*b*p*log(c*(a + b*x^2)^p)^2) - (a*(a + b*x^2))/(4*b^2*p^2*log(c*(a + b*x^2)^p)) - (x^2*(a + b*x^2))/(2*b*p^2*log(c*(a + b*x^2)^p))]
    @test_int [x^1/log(c*(a + b*x^2)^p)^3, x, 6, ((a + b*x^2)*ExpIntegralEi(log(c*(a + b*x^2)^p)/p))/((c*(a + b*x^2)^p)^p^(-1)*(4*b*p^3)) - (a + b*x^2)/(4*b*p*log(c*(a + b*x^2)^p)^2) - (a + b*x^2)/(4*b*p^2*log(c*(a + b*x^2)^p))]
    @test_int [1/(x^1*log(c*(a + b*x^2)^p)^3), x, 0, Unintegrable(1/(x*log(c*(a + b*x^2)^p)^3), x)]
    @test_int [1/(x^3*log(c*(a + b*x^2)^p)^3), x, 0, Unintegrable(1/(x^3*log(c*(a + b*x^2)^p)^3), x)]

    @test_int [x^2/log(c*(a + b*x^2)^p)^3, x, 0, Unintegrable(x^2/log(c*(a + b*x^2)^p)^3, x)]
    @test_int [x^0/log(c*(a + b*x^2)^p)^3, x, 0, Unintegrable(1/log(c*(a + b*x^2)^p)^3, x)]
    @test_int [1/(x^2*log(c*(a + b*x^2)^p)^3), x, 0, Unintegrable(1/(x^2*log(c*(a + b*x^2)^p)^3), x)]

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

    @test_int [x^3/log(c*(a + b*x^2))^2, x, 11, ExpIntegralEi(2*log(c*(a + b*x^2)))/(b^2*c^2) - (x^2*(a + b*x^2))/(2*b*log(c*(a + b*x^2))) - (a*LogIntegral(c*(a + b*x^2)))/(2*b^2*c)]
    @test_int [x^1/log(c*(a + b*x^2))^2, x, 4, -((a + b*x^2)/(2*b*log(c*(a + b*x^2)))) + LogIntegral(c*(a + b*x^2))/(2*b*c)]

    @test_int [x^3/log(c*(a + b*x^2))^3, x, 15, ExpIntegralEi(2*log(c*(a + b*x^2)))/(b^2*c^2) - (x^2*(a + b*x^2))/(4*b*log(c*(a + b*x^2))^2) - (a*(a + b*x^2))/(4*b^2*log(c*(a + b*x^2))) - (x^2*(a + b*x^2))/(2*b*log(c*(a + b*x^2))) - (a*LogIntegral(c*(a + b*x^2)))/(4*b^2*c)]
    @test_int [x^1/log(c*(a + b*x^2))^3, x, 5, -((a + b*x^2)/(4*b*log(c*(a + b*x^2))^2)) - (a + b*x^2)/(4*b*log(c*(a + b*x^2))) + LogIntegral(c*(a + b*x^2))/(4*b*c)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^q*log(c*(d+e*x^3)^n)^p =#

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

    @test_int [x^5*log(c*(d + e*x^3)^p)^2, x, 9, -((2*d*p^2*x^3)/(3*e)) + (p^2*(d + e*x^3)^2)/(12*e^2) + (2*d*p*(d + e*x^3)*log(c*(d + e*x^3)^p))/(3*e^2) - (p*(d + e*x^3)^2*log(c*(d + e*x^3)^p))/(6*e^2) - (d*(d + e*x^3)*log(c*(d + e*x^3)^p)^2)/(3*e^2) + ((d + e*x^3)^2*log(c*(d + e*x^3)^p)^2)/(6*e^2)]
    @test_int [x^2*log(c*(d + e*x^3)^p)^2, x, 4, (2*p^2*x^3)/3 - (2*p*(d + e*x^3)*log(c*(d + e*x^3)^p))/(3*e) + ((d + e*x^3)*log(c*(d + e*x^3)^p)^2)/(3*e)]
    @test_int [log(c*(d + e*x^3)^p)^2/x^1, x, 5, (1/3)*log(-((e*x^3)/d))*log(c*(d + e*x^3)^p)^2 + (2/3)*p*log(c*(d + e*x^3)^p)*PolyLog(2, 1 + (e*x^3)/d) - (2/3)*p^2*PolyLog(3, 1 + (e*x^3)/d)]
    @test_int [log(c*(d + e*x^3)^p)^2/x^4, x, 4, (2*e*p*log(-((e*x^3)/d))*log(c*(d + e*x^3)^p))/(3*d) - ((d + e*x^3)*log(c*(d + e*x^3)^p)^2)/(3*d*x^3) + (2*e*p^2*PolyLog(2, 1 + (e*x^3)/d))/(3*d)]

    @test_int [x^1*log(c*(d + e*x^3)^p)^2, x, If(13>=8, 49, 51), If(13>=8, If(13<11, (9*p^2*x^2)/4 + (3*sqrt(3)*d^(2/3)*p^2*atan((d^(1/3) - 2*e^(1/3)*x)/(sqrt(3)*d^(1/3))))/(2*e^(2/3)) + (3*d^(2/3)*p^2*log(d^(1/3) + e^(1/3)*x))/(2*e^(2/3)) + (d^(2/3)*p^2*log(d^(1/3) + e^(1/3)*x)^2)/(2*e^(2/3)) + (d^(2/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(-(((-1)^(2/3)*d^(1/3) + e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3)))))/e^(2/3) - ((-1)^(1/3)*d^(2/3)*p^2*log(((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/e^(2/3) - ((-1)^(1/3)*d^(2/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)^2)/(2*e^(2/3)) + ((-1)^(2/3)*d^(2/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/e^(2/3) + ((-1)^(2/3)*d^(2/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/e^(2/3) + ((-1)^(2/3)*d^(2/3)*p^2*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)^2)/(2*e^(2/3)) - ((-1)^(2/3)*d^(2/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(2/3) + (d^(2/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(((-1)^(1/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/e^(2/3) - ((-1)^(1/3)*d^(2/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(2/3) - (3*d^(2/3)*p^2*log(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2))/(4*e^(2/3)) - (3/2)*p*x^2*log(c*(d + e*x^3)^p) - (d^(2/3)*p*log(d^(1/3) + e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(2/3) + ((-1)^(1/3)*d^(2/3)*p*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(2/3) - ((-1)^(2/3)*d^(2/3)*p*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(2/3) + (1/2)*x^2*log(c*(d + e*x^3)^p)^2 + (d^(2/3)*p^2*PolyLog(2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(2/3) + (d^(2/3)*p^2*PolyLog(2, (2*(d^(1/3) + e^(1/3)*x))/((3 - im*sqrt(3))*d^(1/3))))/e^(2/3) - ((-1)^(1/3)*d^(2/3)*p^2*PolyLog(2, -(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(2/3) - ((-1)^(1/3)*d^(2/3)*p^2*PolyLog(2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(2/3) - ((-1)^(2/3)*d^(2/3)*p^2*PolyLog(2, ((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/e^(2/3) + ((-1)^(2/3)*d^(2/3)*p^2*PolyLog(2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))))/e^(2/3), (9*p^2*x^2)/4 + (3*sqrt(3)*d^(2/3)*p^2*atan((d^(1/3) - 2*e^(1/3)*x)/(sqrt(3)*d^(1/3))))/(2*e^(2/3)) + (3*d^(2/3)*p^2*log(d^(1/3) + e^(1/3)*x))/(2*e^(2/3)) + (d^(2/3)*p^2*log(d^(1/3) + e^(1/3)*x)^2)/(2*e^(2/3)) + (d^(2/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(-(((-1)^(2/3)*d^(1/3) + e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3)))))/e^(2/3) - ((-1)^(1/3)*d^(2/3)*p^2*log(((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/e^(2/3) - ((-1)^(1/3)*d^(2/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)^2)/(2*e^(2/3)) + ((-1)^(2/3)*d^(2/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/e^(2/3) + ((-1)^(2/3)*d^(2/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/e^(2/3) + ((-1)^(2/3)*d^(2/3)*p^2*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)^2)/(2*e^(2/3)) + (d^(2/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(((-1)^(1/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/e^(2/3) - ((-1)^(2/3)*d^(2/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))))/e^(2/3) - ((-1)^(1/3)*d^(2/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(2/3) - (3*d^(2/3)*p^2*log(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2))/(4*e^(2/3)) - (3/2)*p*x^2*log(c*(d + e*x^3)^p) - (d^(2/3)*p*log(d^(1/3) + e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(2/3) + ((-1)^(1/3)*d^(2/3)*p*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(2/3) - ((-1)^(2/3)*d^(2/3)*p*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(2/3) + (1/2)*x^2*log(c*(d + e*x^3)^p)^2 + (d^(2/3)*p^2*PolyLog(2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(2/3) - ((-1)^(2/3)*d^(2/3)*p^2*PolyLog(2, -(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(2/3) + (d^(2/3)*p^2*PolyLog(2, (2*(d^(1/3) + e^(1/3)*x))/((3 - im*sqrt(3))*d^(1/3))))/e^(2/3) - ((-1)^(1/3)*d^(2/3)*p^2*PolyLog(2, -(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(2/3) - ((-1)^(1/3)*d^(2/3)*p^2*PolyLog(2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(2/3) + ((-1)^(2/3)*d^(2/3)*p^2*PolyLog(2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(2/3)), (9*p^2*x^2)/4 + (3*sqrt(3)*d^(2/3)*p^2*atan((d^(1/3) - 2*e^(1/3)*x)/(sqrt(3)*d^(1/3))))/(2*e^(2/3)) + (3*d^(2/3)*p^2*log(d^(1/3) + e^(1/3)*x))/(2*e^(2/3)) + (d^(2/3)*p^2*log(d^(1/3) + e^(1/3)*x)^2)/(2*e^(2/3)) + (d^(2/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(-(((-1)^(2/3)*d^(1/3) + e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3)))))/e^(2/3) - ((-1)^(1/3)*d^(2/3)*p^2*log(((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/e^(2/3) - ((-1)^(1/3)*d^(2/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)^2)/(2*e^(2/3)) + ((-1)^(2/3)*d^(2/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/e^(2/3) + ((-1)^(2/3)*d^(2/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/e^(2/3) + ((-1)^(2/3)*d^(2/3)*p^2*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)^2)/(2*e^(2/3)) - ((-1)^(2/3)*d^(2/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(2/3) + (d^(2/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(((-1)^(1/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/e^(2/3) - ((-1)^(2/3)*d^(2/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))))/e^(2/3) + ((-1)^(1/3)*d^(2/3)*p^2*log(-(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(2/3) - ((-1)^(1/3)*d^(2/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(2/3) - (3*d^(2/3)*p^2*log(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2))/(4*e^(2/3)) - (3/2)*p*x^2*log(c*(d + e*x^3)^p) - (d^(2/3)*p*log(d^(1/3) + e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(2/3) + ((-1)^(1/3)*d^(2/3)*p*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(2/3) - ((-1)^(2/3)*d^(2/3)*p*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(2/3) + (1/2)*x^2*log(c*(d + e*x^3)^p)^2 + (d^(2/3)*p^2*PolyLog(2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(2/3) - ((-1)^(2/3)*d^(2/3)*p^2*PolyLog(2, -(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(2/3) + (d^(2/3)*p^2*PolyLog(2, (2*(d^(1/3) + e^(1/3)*x))/((3 - im*sqrt(3))*d^(1/3))))/e^(2/3) - ((-1)^(1/3)*d^(2/3)*p^2*PolyLog(2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(2/3) - ((-1)^(2/3)*d^(2/3)*p^2*PolyLog(2, ((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/e^(2/3) + ((-1)^(1/3)*d^(2/3)*p^2*PolyLog(2, -(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(2/3))]
    @test_int [x^0*log(c*(d + e*x^3)^p)^2, x, If(13>=8, 49, 51), If(13>=8, If(13<11, 18*p^2*x + (6*sqrt(3)*d^(1/3)*p^2*atan((d^(1/3) - 2*e^(1/3)*x)/(sqrt(3)*d^(1/3))))/e^(1/3) - (d^(1/3)*p^2*log(-d^(1/3) - e^(1/3)*x)^2)/e^(1/3) - (6*d^(1/3)*p^2*log(d^(1/3) + e^(1/3)*x))/e^(1/3) - (2*d^(1/3)*p^2*log(-d^(1/3) - e^(1/3)*x)*log(-(((-1)^(2/3)*d^(1/3) + e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3)))))/e^(1/3) - (2*(-1)^(2/3)*d^(1/3)*p^2*log(((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x))/e^(1/3) - ((-1)^(2/3)*d^(1/3)*p^2*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)^2)/e^(1/3) + (2*(-1)^(1/3)*d^(1/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x))/e^(1/3) + (2*(-1)^(1/3)*d^(1/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x))/e^(1/3) + ((-1)^(1/3)*d^(1/3)*p^2*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x)^2)/e^(1/3) - (2*(-1)^(1/3)*d^(1/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(1/3) - (2*d^(1/3)*p^2*log(-d^(1/3) - e^(1/3)*x)*log(((-1)^(1/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/e^(1/3) - (2*(-1)^(2/3)*d^(1/3)*p^2*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(1/3) + (3*d^(1/3)*p^2*log(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2))/e^(1/3) - 6*p*x*log(c*(d + e*x^3)^p) + (2*d^(1/3)*p*log(-d^(1/3) - e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(1/3) + (2*(-1)^(2/3)*d^(1/3)*p*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(1/3) - (2*(-1)^(1/3)*d^(1/3)*p*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(1/3) + x*log(c*(d + e*x^3)^p)^2 - (2*d^(1/3)*p^2*PolyLog(2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(1/3) - (2*d^(1/3)*p^2*PolyLog(2, (2*(d^(1/3) + e^(1/3)*x))/((3 - im*sqrt(3))*d^(1/3))))/e^(1/3) - (2*(-1)^(2/3)*d^(1/3)*p^2*PolyLog(2, -(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(1/3) - (2*(-1)^(2/3)*d^(1/3)*p^2*PolyLog(2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(1/3) - (2*(-1)^(1/3)*d^(1/3)*p^2*PolyLog(2, ((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/e^(1/3) + (2*(-1)^(1/3)*d^(1/3)*p^2*PolyLog(2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))))/e^(1/3), 18*p^2*x + (6*sqrt(3)*d^(1/3)*p^2*atan((d^(1/3) - 2*e^(1/3)*x)/(sqrt(3)*d^(1/3))))/e^(1/3) - (d^(1/3)*p^2*log(-d^(1/3) - e^(1/3)*x)^2)/e^(1/3) - (6*d^(1/3)*p^2*log(d^(1/3) + e^(1/3)*x))/e^(1/3) - (2*d^(1/3)*p^2*log(-d^(1/3) - e^(1/3)*x)*log(-(((-1)^(2/3)*d^(1/3) + e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3)))))/e^(1/3) - (2*(-1)^(2/3)*d^(1/3)*p^2*log(((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x))/e^(1/3) - ((-1)^(2/3)*d^(1/3)*p^2*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)^2)/e^(1/3) + (2*(-1)^(1/3)*d^(1/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x))/e^(1/3) + (2*(-1)^(1/3)*d^(1/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x))/e^(1/3) + ((-1)^(1/3)*d^(1/3)*p^2*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x)^2)/e^(1/3) - (2*d^(1/3)*p^2*log(-d^(1/3) - e^(1/3)*x)*log(((-1)^(1/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/e^(1/3) - (2*(-1)^(1/3)*d^(1/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))))/e^(1/3) - (2*(-1)^(2/3)*d^(1/3)*p^2*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(1/3) + (3*d^(1/3)*p^2*log(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2))/e^(1/3) - 6*p*x*log(c*(d + e*x^3)^p) + (2*d^(1/3)*p*log(-d^(1/3) - e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(1/3) + (2*(-1)^(2/3)*d^(1/3)*p*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(1/3) - (2*(-1)^(1/3)*d^(1/3)*p*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(1/3) + x*log(c*(d + e*x^3)^p)^2 - (2*d^(1/3)*p^2*PolyLog(2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(1/3) - (2*(-1)^(1/3)*d^(1/3)*p^2*PolyLog(2, -(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(1/3) - (2*d^(1/3)*p^2*PolyLog(2, (2*(d^(1/3) + e^(1/3)*x))/((3 - im*sqrt(3))*d^(1/3))))/e^(1/3) - (2*(-1)^(2/3)*d^(1/3)*p^2*PolyLog(2, -(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(1/3) - (2*(-1)^(2/3)*d^(1/3)*p^2*PolyLog(2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(1/3) + (2*(-1)^(1/3)*d^(1/3)*p^2*PolyLog(2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(1/3)), 18*p^2*x + (6*sqrt(3)*d^(1/3)*p^2*atan((d^(1/3) - 2*e^(1/3)*x)/(sqrt(3)*d^(1/3))))/e^(1/3) - (d^(1/3)*p^2*log(-d^(1/3) - e^(1/3)*x)^2)/e^(1/3) - (6*d^(1/3)*p^2*log(d^(1/3) + e^(1/3)*x))/e^(1/3) - (2*d^(1/3)*p^2*log(-d^(1/3) - e^(1/3)*x)*log(-(((-1)^(2/3)*d^(1/3) + e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3)))))/e^(1/3) - (2*(-1)^(2/3)*d^(1/3)*p^2*log(((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x))/e^(1/3) - ((-1)^(2/3)*d^(1/3)*p^2*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)^2)/e^(1/3) + (2*(-1)^(1/3)*d^(1/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x))/e^(1/3) + (2*(-1)^(1/3)*d^(1/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x))/e^(1/3) + ((-1)^(1/3)*d^(1/3)*p^2*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x)^2)/e^(1/3) - (2*(-1)^(1/3)*d^(1/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(1/3) - (2*d^(1/3)*p^2*log(-d^(1/3) - e^(1/3)*x)*log(((-1)^(1/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/e^(1/3) - (2*(-1)^(1/3)*d^(1/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))))/e^(1/3) + (2*(-1)^(2/3)*d^(1/3)*p^2*log(-(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(1/3) - (2*(-1)^(2/3)*d^(1/3)*p^2*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(1/3) + (3*d^(1/3)*p^2*log(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2))/e^(1/3) - 6*p*x*log(c*(d + e*x^3)^p) + (2*d^(1/3)*p*log(-d^(1/3) - e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(1/3) + (2*(-1)^(2/3)*d^(1/3)*p*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(1/3) - (2*(-1)^(1/3)*d^(1/3)*p*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/e^(1/3) + x*log(c*(d + e*x^3)^p)^2 - (2*d^(1/3)*p^2*PolyLog(2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(1/3) - (2*(-1)^(1/3)*d^(1/3)*p^2*PolyLog(2, -(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(1/3) - (2*d^(1/3)*p^2*PolyLog(2, (2*(d^(1/3) + e^(1/3)*x))/((3 - im*sqrt(3))*d^(1/3))))/e^(1/3) - (2*(-1)^(2/3)*d^(1/3)*p^2*PolyLog(2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/e^(1/3) - (2*(-1)^(1/3)*d^(1/3)*p^2*PolyLog(2, ((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/e^(1/3) + (2*(-1)^(2/3)*d^(1/3)*p^2*PolyLog(2, -(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/e^(1/3))]
    @test_int [log(c*(d + e*x^3)^p)^2/x^2, x, If(13>=8, 39, 41), If(13>=8, If(13<11, (e^(1/3)*p^2*log(d^(1/3) + e^(1/3)*x)^2)/d^(1/3) + (2*e^(1/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(-(((-1)^(2/3)*d^(1/3) + e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3)))))/d^(1/3) - (2*(-1)^(1/3)*e^(1/3)*p^2*log(((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/d^(1/3) - ((-1)^(1/3)*e^(1/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)^2)/d^(1/3) + (2*(-1)^(2/3)*e^(1/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/d^(1/3) + (2*(-1)^(2/3)*e^(1/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/d^(1/3) + ((-1)^(2/3)*e^(1/3)*p^2*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)^2)/d^(1/3) - (2*(-1)^(2/3)*e^(1/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(1/3) + (2*e^(1/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(((-1)^(1/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/d^(1/3) - (2*(-1)^(1/3)*e^(1/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(1/3) - (2*e^(1/3)*p*log(d^(1/3) + e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(1/3) + (2*(-1)^(1/3)*e^(1/3)*p*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(1/3) - (2*(-1)^(2/3)*e^(1/3)*p*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(1/3) - log(c*(d + e*x^3)^p)^2/x + (2*e^(1/3)*p^2*PolyLog(2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(1/3) + (2*e^(1/3)*p^2*PolyLog(2, (2*(d^(1/3) + e^(1/3)*x))/((3 - im*sqrt(3))*d^(1/3))))/d^(1/3) - (2*(-1)^(1/3)*e^(1/3)*p^2*PolyLog(2, -(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(1/3) - (2*(-1)^(1/3)*e^(1/3)*p^2*PolyLog(2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(1/3) - (2*(-1)^(2/3)*e^(1/3)*p^2*PolyLog(2, ((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/d^(1/3) + (2*(-1)^(2/3)*e^(1/3)*p^2*PolyLog(2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))))/d^(1/3), (e^(1/3)*p^2*log(d^(1/3) + e^(1/3)*x)^2)/d^(1/3) + (2*e^(1/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(-(((-1)^(2/3)*d^(1/3) + e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3)))))/d^(1/3) - (2*(-1)^(1/3)*e^(1/3)*p^2*log(((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/d^(1/3) - ((-1)^(1/3)*e^(1/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)^2)/d^(1/3) + (2*(-1)^(2/3)*e^(1/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/d^(1/3) + (2*(-1)^(2/3)*e^(1/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/d^(1/3) + ((-1)^(2/3)*e^(1/3)*p^2*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)^2)/d^(1/3) + (2*e^(1/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(((-1)^(1/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/d^(1/3) - (2*(-1)^(2/3)*e^(1/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))))/d^(1/3) - (2*(-1)^(1/3)*e^(1/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(1/3) - (2*e^(1/3)*p*log(d^(1/3) + e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(1/3) + (2*(-1)^(1/3)*e^(1/3)*p*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(1/3) - (2*(-1)^(2/3)*e^(1/3)*p*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(1/3) - log(c*(d + e*x^3)^p)^2/x + (2*e^(1/3)*p^2*PolyLog(2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(1/3) - (2*(-1)^(2/3)*e^(1/3)*p^2*PolyLog(2, -(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(1/3) + (2*e^(1/3)*p^2*PolyLog(2, (2*(d^(1/3) + e^(1/3)*x))/((3 - im*sqrt(3))*d^(1/3))))/d^(1/3) - (2*(-1)^(1/3)*e^(1/3)*p^2*PolyLog(2, -(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(1/3) - (2*(-1)^(1/3)*e^(1/3)*p^2*PolyLog(2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(1/3) + (2*(-1)^(2/3)*e^(1/3)*p^2*PolyLog(2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(1/3)), (e^(1/3)*p^2*log(d^(1/3) + e^(1/3)*x)^2)/d^(1/3) + (2*e^(1/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(-(((-1)^(2/3)*d^(1/3) + e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3)))))/d^(1/3) - (2*(-1)^(1/3)*e^(1/3)*p^2*log(((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/d^(1/3) - ((-1)^(1/3)*e^(1/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)^2)/d^(1/3) + (2*(-1)^(2/3)*e^(1/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/d^(1/3) + (2*(-1)^(2/3)*e^(1/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/d^(1/3) + ((-1)^(2/3)*e^(1/3)*p^2*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)^2)/d^(1/3) - (2*(-1)^(2/3)*e^(1/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(1/3) + (2*e^(1/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(((-1)^(1/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/d^(1/3) - (2*(-1)^(2/3)*e^(1/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))))/d^(1/3) + (2*(-1)^(1/3)*e^(1/3)*p^2*log(-(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(1/3) - (2*(-1)^(1/3)*e^(1/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(1/3) - (2*e^(1/3)*p*log(d^(1/3) + e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(1/3) + (2*(-1)^(1/3)*e^(1/3)*p*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(1/3) - (2*(-1)^(2/3)*e^(1/3)*p*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(1/3) - log(c*(d + e*x^3)^p)^2/x + (2*e^(1/3)*p^2*PolyLog(2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(1/3) - (2*(-1)^(2/3)*e^(1/3)*p^2*PolyLog(2, -(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(1/3) + (2*e^(1/3)*p^2*PolyLog(2, (2*(d^(1/3) + e^(1/3)*x))/((3 - im*sqrt(3))*d^(1/3))))/d^(1/3) - (2*(-1)^(1/3)*e^(1/3)*p^2*PolyLog(2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(1/3) - (2*(-1)^(2/3)*e^(1/3)*p^2*PolyLog(2, ((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/d^(1/3) + (2*(-1)^(1/3)*e^(1/3)*p^2*PolyLog(2, -(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(1/3))]
    @test_int [log(c*(d + e*x^3)^p)^2/x^3, x, If(13>=8, 39, 41), If(13>=8, If(13<11, -((e^(2/3)*p^2*log(-d^(1/3) - e^(1/3)*x)^2)/(2*d^(2/3))) - (e^(2/3)*p^2*log(-d^(1/3) - e^(1/3)*x)*log(-(((-1)^(2/3)*d^(1/3) + e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3)))))/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^2*log(((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x))/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^2*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)^2)/(2*d^(2/3)) + ((-1)^(1/3)*e^(2/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x))/d^(2/3) + ((-1)^(1/3)*e^(2/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x))/d^(2/3) + ((-1)^(1/3)*e^(2/3)*p^2*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x)^2)/(2*d^(2/3)) - ((-1)^(1/3)*e^(2/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(2/3) - (e^(2/3)*p^2*log(-d^(1/3) - e^(1/3)*x)*log(((-1)^(1/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^2*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(2/3) + (e^(2/3)*p*log(-d^(1/3) - e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(2/3) + ((-1)^(2/3)*e^(2/3)*p*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(2/3) - ((-1)^(1/3)*e^(2/3)*p*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(2/3) - log(c*(d + e*x^3)^p)^2/(2*x^2) - (e^(2/3)*p^2*PolyLog(2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(2/3) - (e^(2/3)*p^2*PolyLog(2, (2*(d^(1/3) + e^(1/3)*x))/((3 - im*sqrt(3))*d^(1/3))))/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^2*PolyLog(2, -(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^2*PolyLog(2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(2/3) - ((-1)^(1/3)*e^(2/3)*p^2*PolyLog(2, ((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/d^(2/3) + ((-1)^(1/3)*e^(2/3)*p^2*PolyLog(2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))))/d^(2/3), -((e^(2/3)*p^2*log(-d^(1/3) - e^(1/3)*x)^2)/(2*d^(2/3))) - (e^(2/3)*p^2*log(-d^(1/3) - e^(1/3)*x)*log(-(((-1)^(2/3)*d^(1/3) + e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3)))))/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^2*log(((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x))/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^2*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)^2)/(2*d^(2/3)) + ((-1)^(1/3)*e^(2/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x))/d^(2/3) + ((-1)^(1/3)*e^(2/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x))/d^(2/3) + ((-1)^(1/3)*e^(2/3)*p^2*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x)^2)/(2*d^(2/3)) - (e^(2/3)*p^2*log(-d^(1/3) - e^(1/3)*x)*log(((-1)^(1/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/d^(2/3) - ((-1)^(1/3)*e^(2/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))))/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^2*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(2/3) + (e^(2/3)*p*log(-d^(1/3) - e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(2/3) + ((-1)^(2/3)*e^(2/3)*p*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(2/3) - ((-1)^(1/3)*e^(2/3)*p*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(2/3) - log(c*(d + e*x^3)^p)^2/(2*x^2) - (e^(2/3)*p^2*PolyLog(2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(2/3) - ((-1)^(1/3)*e^(2/3)*p^2*PolyLog(2, -(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(2/3) - (e^(2/3)*p^2*PolyLog(2, (2*(d^(1/3) + e^(1/3)*x))/((3 - im*sqrt(3))*d^(1/3))))/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^2*PolyLog(2, -(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^2*PolyLog(2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(2/3) + ((-1)^(1/3)*e^(2/3)*p^2*PolyLog(2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(2/3)), -((e^(2/3)*p^2*log(-d^(1/3) - e^(1/3)*x)^2)/(2*d^(2/3))) - (e^(2/3)*p^2*log(-d^(1/3) - e^(1/3)*x)*log(-(((-1)^(2/3)*d^(1/3) + e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3)))))/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^2*log(((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x))/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^2*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)^2)/(2*d^(2/3)) + ((-1)^(1/3)*e^(2/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x))/d^(2/3) + ((-1)^(1/3)*e^(2/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x))/d^(2/3) + ((-1)^(1/3)*e^(2/3)*p^2*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x)^2)/(2*d^(2/3)) - ((-1)^(1/3)*e^(2/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(2/3) - (e^(2/3)*p^2*log(-d^(1/3) - e^(1/3)*x)*log(((-1)^(1/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/d^(2/3) - ((-1)^(1/3)*e^(2/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))))/d^(2/3) + ((-1)^(2/3)*e^(2/3)*p^2*log(-(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^2*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(2/3) + (e^(2/3)*p*log(-d^(1/3) - e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(2/3) + ((-1)^(2/3)*e^(2/3)*p*log(-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(2/3) - ((-1)^(1/3)*e^(2/3)*p*log(-d^(1/3) - (-1)^(2/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/d^(2/3) - log(c*(d + e*x^3)^p)^2/(2*x^2) - (e^(2/3)*p^2*PolyLog(2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(2/3) - ((-1)^(1/3)*e^(2/3)*p^2*PolyLog(2, -(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(2/3) - (e^(2/3)*p^2*PolyLog(2, (2*(d^(1/3) + e^(1/3)*x))/((3 - im*sqrt(3))*d^(1/3))))/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^2*PolyLog(2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/d^(2/3) - ((-1)^(1/3)*e^(2/3)*p^2*PolyLog(2, ((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/d^(2/3) + ((-1)^(2/3)*e^(2/3)*p^2*PolyLog(2, -(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/d^(2/3))]
    @test_int [log(c*(d + e*x^3)^p)^2/x^5, x, If(13>=8, 48, 50), If(13>=8, If(13<11, -((3*sqrt(3)*e^(4/3)*p^2*atan((d^(1/3) - 2*e^(1/3)*x)/(sqrt(3)*d^(1/3))))/(2*d^(4/3))) - (3*e^(4/3)*p^2*log(d^(1/3) + e^(1/3)*x))/(2*d^(4/3)) - (e^(4/3)*p^2*log(d^(1/3) + e^(1/3)*x)^2)/(4*d^(4/3)) - (e^(4/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(-(((-1)^(2/3)*d^(1/3) + e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3)))))/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^2*log(((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)^2)/(4*d^(4/3)) - ((-1)^(2/3)*e^(4/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/(2*d^(4/3)) - ((-1)^(2/3)*e^(4/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/(2*d^(4/3)) - ((-1)^(2/3)*e^(4/3)*p^2*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)^2)/(4*d^(4/3)) + ((-1)^(2/3)*e^(4/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/(2*d^(4/3)) - (e^(4/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(((-1)^(1/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/(2*d^(4/3)) + (3*e^(4/3)*p^2*log(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2))/(4*d^(4/3)) - (3*e*p*log(c*(d + e*x^3)^p))/(2*d*x) + (e^(4/3)*p*log(d^(1/3) + e^(1/3)*x)*log(c*(d + e*x^3)^p))/(2*d^(4/3)) - ((-1)^(1/3)*e^(4/3)*p*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/(2*d^(4/3)) + ((-1)^(2/3)*e^(4/3)*p*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/(2*d^(4/3)) - log(c*(d + e*x^3)^p)^2/(4*x^4) - (e^(4/3)*p^2*PolyLog(2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/(2*d^(4/3)) - (e^(4/3)*p^2*PolyLog(2, (2*(d^(1/3) + e^(1/3)*x))/((3 - im*sqrt(3))*d^(1/3))))/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^2*PolyLog(2, -(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^2*PolyLog(2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/(2*d^(4/3)) + ((-1)^(2/3)*e^(4/3)*p^2*PolyLog(2, ((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/(2*d^(4/3)) - ((-1)^(2/3)*e^(4/3)*p^2*PolyLog(2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))))/(2*d^(4/3)), -((3*sqrt(3)*e^(4/3)*p^2*atan((d^(1/3) - 2*e^(1/3)*x)/(sqrt(3)*d^(1/3))))/(2*d^(4/3))) - (3*e^(4/3)*p^2*log(d^(1/3) + e^(1/3)*x))/(2*d^(4/3)) - (e^(4/3)*p^2*log(d^(1/3) + e^(1/3)*x)^2)/(4*d^(4/3)) - (e^(4/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(-(((-1)^(2/3)*d^(1/3) + e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3)))))/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^2*log(((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)^2)/(4*d^(4/3)) - ((-1)^(2/3)*e^(4/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/(2*d^(4/3)) - ((-1)^(2/3)*e^(4/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/(2*d^(4/3)) - ((-1)^(2/3)*e^(4/3)*p^2*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)^2)/(4*d^(4/3)) - (e^(4/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(((-1)^(1/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/(2*d^(4/3)) + ((-1)^(2/3)*e^(4/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))))/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/(2*d^(4/3)) + (3*e^(4/3)*p^2*log(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2))/(4*d^(4/3)) - (3*e*p*log(c*(d + e*x^3)^p))/(2*d*x) + (e^(4/3)*p*log(d^(1/3) + e^(1/3)*x)*log(c*(d + e*x^3)^p))/(2*d^(4/3)) - ((-1)^(1/3)*e^(4/3)*p*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/(2*d^(4/3)) + ((-1)^(2/3)*e^(4/3)*p*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/(2*d^(4/3)) - log(c*(d + e*x^3)^p)^2/(4*x^4) - (e^(4/3)*p^2*PolyLog(2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/(2*d^(4/3)) + ((-1)^(2/3)*e^(4/3)*p^2*PolyLog(2, -(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/(2*d^(4/3)) - (e^(4/3)*p^2*PolyLog(2, (2*(d^(1/3) + e^(1/3)*x))/((3 - im*sqrt(3))*d^(1/3))))/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^2*PolyLog(2, -(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^2*PolyLog(2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/(2*d^(4/3)) - ((-1)^(2/3)*e^(4/3)*p^2*PolyLog(2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/(2*d^(4/3))), -((3*sqrt(3)*e^(4/3)*p^2*atan((d^(1/3) - 2*e^(1/3)*x)/(sqrt(3)*d^(1/3))))/(2*d^(4/3))) - (3*e^(4/3)*p^2*log(d^(1/3) + e^(1/3)*x))/(2*d^(4/3)) - (e^(4/3)*p^2*log(d^(1/3) + e^(1/3)*x)^2)/(4*d^(4/3)) - (e^(4/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(-(((-1)^(2/3)*d^(1/3) + e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3)))))/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^2*log(((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)^2)/(4*d^(4/3)) - ((-1)^(2/3)*e^(4/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/(2*d^(4/3)) - ((-1)^(2/3)*e^(4/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/(2*d^(4/3)) - ((-1)^(2/3)*e^(4/3)*p^2*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)^2)/(4*d^(4/3)) + ((-1)^(2/3)*e^(4/3)*p^2*log(((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3)))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/(2*d^(4/3)) - (e^(4/3)*p^2*log(d^(1/3) + e^(1/3)*x)*log(((-1)^(1/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/(2*d^(4/3)) + ((-1)^(2/3)*e^(4/3)*p^2*log(-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log((d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))))/(2*d^(4/3)) - ((-1)^(1/3)*e^(4/3)*p^2*log(-(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3))))*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^2*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/(2*d^(4/3)) + (3*e^(4/3)*p^2*log(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2))/(4*d^(4/3)) - (3*e*p*log(c*(d + e*x^3)^p))/(2*d*x) + (e^(4/3)*p*log(d^(1/3) + e^(1/3)*x)*log(c*(d + e*x^3)^p))/(2*d^(4/3)) - ((-1)^(1/3)*e^(4/3)*p*log(d^(1/3) - (-1)^(1/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/(2*d^(4/3)) + ((-1)^(2/3)*e^(4/3)*p*log(d^(1/3) + (-1)^(2/3)*e^(1/3)*x)*log(c*(d + e*x^3)^p))/(2*d^(4/3)) - log(c*(d + e*x^3)^p)^2/(4*x^4) - (e^(4/3)*p^2*PolyLog(2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/(2*d^(4/3)) + ((-1)^(2/3)*e^(4/3)*p^2*PolyLog(2, -(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/(2*d^(4/3)) - (e^(4/3)*p^2*PolyLog(2, (2*(d^(1/3) + e^(1/3)*x))/((3 - im*sqrt(3))*d^(1/3))))/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^2*PolyLog(2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))))/(2*d^(4/3)) + ((-1)^(2/3)*e^(4/3)*p^2*PolyLog(2, ((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))))/(2*d^(4/3)) - ((-1)^(1/3)*e^(4/3)*p^2*PolyLog(2, -(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))))/(2*d^(4/3)))]

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

    @test_int [x^8/log(c*(d + e*x^3)^p), x, 12, (d^2*(d + e*x^3)*ExpIntegralEi(log(c*(d + e*x^3)^p)/p))/((c*(d + e*x^3)^p)^p^(-1)*(3*e^3*p)) - (2*d*(d + e*x^3)^2*ExpIntegralEi((2*log(c*(d + e*x^3)^p))/p))/((c*(d + e*x^3)^p)^(2/p)*(3*e^3*p)) + ((d + e*x^3)^3*ExpIntegralEi((3*log(c*(d + e*x^3)^p))/p))/((c*(d + e*x^3)^p)^(3/p)*(3*e^3*p))]
    @test_int [x^5/log(c*(d + e*x^3)^p), x, 9, -(d*(d + e*x^3)*ExpIntegralEi(log(c*(d + e*x^3)^p)/p))/(3*e^2*p*(c*(d + e*x^3)^p)^p^(-1)) + ((d + e*x^3)^2*ExpIntegralEi((2*log(c*(d + e*x^3)^p))/p))/(3*e^2*p*(c*(d + e*x^3)^p)^(2/p))]
    @test_int [x^2/log(c*(d + e*x^3)^p), x, 4, ((d + e*x^3)*ExpIntegralEi(log(c*(d + e*x^3)^p)/p))/(3*e*p*(c*(d + e*x^3)^p)^p^(-1))]
    @test_int [1/(x^1*log(c*(d + e*x^3)^p)), x, 0, Unintegrable(1/(x*log(c*(d + e*x^3)^p)), x)]
    @test_int [1/(x^4*log(c*(d + e*x^3)^p)), x, 0, Unintegrable(1/(x^4*log(c*(d + e*x^3)^p)), x)]

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

    @test_int [x^8/log(c*(d + e*x^3)^p)^2, x, 21, (d^2*(d + e*x^3)*ExpIntegralEi(log(c*(d + e*x^3)^p)/p))/((c*(d + e*x^3)^p)^p^(-1)*(3*e^3*p^2)) - (4*d*(d + e*x^3)^2*ExpIntegralEi((2*log(c*(d + e*x^3)^p))/p))/((c*(d + e*x^3)^p)^(2/p)*(3*e^3*p^2)) + ((d + e*x^3)^3*ExpIntegralEi((3*log(c*(d + e*x^3)^p))/p))/((c*(d + e*x^3)^p)^(3/p)*(e^3*p^2)) - (x^6*(d + e*x^3))/(3*e*p*log(c*(d + e*x^3)^p))]
    @test_int [x^5/log(c*(d + e*x^3)^p)^2, x, 13, -(d*(d + e*x^3)*ExpIntegralEi(log(c*(d + e*x^3)^p)/p))/(3*e^2*p^2*(c*(d + e*x^3)^p)^p^(-1)) + (2*(d + e*x^3)^2*ExpIntegralEi((2*log(c*(d + e*x^3)^p))/p))/(3*e^2*p^2*(c*(d + e*x^3)^p)^(2/p)) - (x^3*(d + e*x^3))/(3*e*p*log(c*(d + e*x^3)^p))]
    @test_int [x^2/log(c*(d + e*x^3)^p)^2, x, 5, ((d + e*x^3)*ExpIntegralEi(log(c*(d + e*x^3)^p)/p))/(3*e*p^2*(c*(d + e*x^3)^p)^p^(-1)) - (d + e*x^3)/(3*e*p*log(c*(d + e*x^3)^p))]
    @test_int [1/(x^1*log(c*(d + e*x^3)^p)^2), x, 0, Unintegrable(1/(x*log(c*(d + e*x^3)^p)^2), x)]
    @test_int [1/(x^4*log(c*(d + e*x^3)^p)^2), x, 0, Unintegrable(1/(x^4*log(c*(d + e*x^3)^p)^2), x)]

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

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

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

    @test_int [(f*x)^(3*n - 1)*log(c*(d + e*x^n)^p)^2, x, 9, (2*d^2*p^2*x^(1 - 2*n)*(f*x)^(-1 + 3*n))/(e^2*n) - (d*p^2*x^(1 - 3*n)*(f*x)^(-1 + 3*n)*(d + e*x^n)^2)/(2*e^3*n) + (2*p^2*x^(1 - 3*n)*(f*x)^(-1 + 3*n)*(d + e*x^n)^3)/(27*e^3*n) - (d^3*p^2*x^(1 - 3*n)*(f*x)^(-1 + 3*n)*log(d + e*x^n)^2)/(3*e^3*n) - (2*d^2*p*x^(1 - 3*n)*(f*x)^(-1 + 3*n)*(d + e*x^n)*log(c*(d + e*x^n)^p))/(e^3*n) + (d*p*x^(1 - 3*n)*(f*x)^(-1 + 3*n)*(d + e*x^n)^2*log(c*(d + e*x^n)^p))/(e^3*n) - (2*p*x^(1 - 3*n)*(f*x)^(-1 + 3*n)*(d + e*x^n)^3*log(c*(d + e*x^n)^p))/(9*e^3*n) + (2*d^3*p*x^(1 - 3*n)*(f*x)^(-1 + 3*n)*log(d + e*x^n)*log(c*(d + e*x^n)^p))/(3*e^3*n) + (x*(f*x)^(-1 + 3*n)*log(c*(d + e*x^n)^p)^2)/(3*n)]
    @test_int [(f*x)^(2*n - 1)*log(c*(d + e*x^n)^p)^2, x, 10, -((2*d*p^2*x^(1 - n)*(f*x)^(-1 + 2*n))/(e*n)) + (p^2*x^(1 - 2*n)*(f*x)^(-1 + 2*n)*(d + e*x^n)^2)/(4*e^2*n) + (2*d*p*x^(1 - 2*n)*(f*x)^(-1 + 2*n)*(d + e*x^n)*log(c*(d + e*x^n)^p))/(e^2*n) - (p*x^(1 - 2*n)*(f*x)^(-1 + 2*n)*(d + e*x^n)^2*log(c*(d + e*x^n)^p))/(2*e^2*n) - (d*x^(1 - 2*n)*(f*x)^(-1 + 2*n)*(d + e*x^n)*log(c*(d + e*x^n)^p)^2)/(e^2*n) + (x^(1 - 2*n)*(f*x)^(-1 + 2*n)*(d + e*x^n)^2*log(c*(d + e*x^n)^p)^2)/(2*e^2*n)]
    @test_int [(f*x)^(1*n - 1)*log(c*(d + e*x^n)^p)^2, x, 5, (2*p^2*x*(f*x)^(-1 + n))/n - (2*p*x^(1 - n)*(f*x)^(-1 + n)*(d + e*x^n)*log(c*(d + e*x^n)^p))/(e*n) + (x^(1 - n)*(f*x)^(-1 + n)*(d + e*x^n)*log(c*(d + e*x^n)^p)^2)/(e*n)]
    @test_int [(f*x)^(0*n - 1)*log(c*(d + e*x^n)^p)^2, x, 6, (log(-((e*x^n)/d))*log(c*(d + e*x^n)^p)^2)/(f*n) + (2*p*log(c*(d + e*x^n)^p)*PolyLog(2, 1 + (e*x^n)/d))/(f*n) - (2*p^2*PolyLog(3, 1 + (e*x^n)/d))/(f*n)]
    @test_int [(f*x)^(-1*n - 1)*log(c*(d + e*x^n)^p)^2, x, 5, (2*e*p*x^(1 + n)*(f*x)^(-1 - n)*log(-((e*x^n)/d))*log(c*(d + e*x^n)^p))/(d*n) - (x*(f*x)^(-1 - n)*(d + e*x^n)*log(c*(d + e*x^n)^p)^2)/(d*n) + (2*e*p^2*x^(1 + n)*(f*x)^(-1 - n)*PolyLog(2, 1 + (e*x^n)/d))/(d*n)]
    @test_int [(f*x)^(-2*n - 1)*log(c*(d + e*x^n)^p)^2, x, 9, (e^2*p^2*x^(1 + 2*n)*(f*x)^(-1 - 2*n)*log(x))/d^2 - (e*p*x^(1 + n)*(f*x)^(-1 - 2*n)*(d + e*x^n)*log(c*(d + e*x^n)^p))/(d^2*n) - (x*(f*x)^(-1 - 2*n)*log(c*(d + e*x^n)^p)^2)/(2*n) - (e^2*p*x^(1 + 2*n)*(f*x)^(-1 - 2*n)*log(c*(d + e*x^n)^p)*log(1 - d/(d + e*x^n)))/(d^2*n) + (e^2*p^2*x^(1 + 2*n)*(f*x)^(-1 - 2*n)*PolyLog(2, d/(d + e*x^n)))/(d^2*n)]

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

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

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

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f+g*x)^q*log(c*(d+e*x^m)^n)=#

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

    @test_int [log(c*(a + b*x)^p)*(d + e*x)^3, x, 3, -(((b*d - a*e)^3*p*x)/(4*b^3)) - ((b*d - a*e)^2*p*(d + e*x)^2)/(8*b^2*e) - ((b*d - a*e)*p*(d + e*x)^3)/(12*b*e) - (p*(d + e*x)^4)/(16*e) - ((b*d - a*e)^4*p*log(a + b*x))/(4*b^4*e) + ((d + e*x)^4*log(c*(a + b*x)^p))/(4*e)]
    @test_int [log(c*(a + b*x)^p)*(d + e*x)^2, x, 3, -(((b*d - a*e)^2*p*x)/(3*b^2)) - ((b*d - a*e)*p*(d + e*x)^2)/(6*b*e) - (p*(d + e*x)^3)/(9*e) - ((b*d - a*e)^3*p*log(a + b*x))/(3*b^3*e) + ((d + e*x)^3*log(c*(a + b*x)^p))/(3*e)]
    @test_int [log(c*(a + b*x)^p)*(d + e*x)^1, x, 3, -(((b*d - a*e)*p*x)/(2*b)) - (p*(d + e*x)^2)/(4*e) - ((b*d - a*e)^2*p*log(a + b*x))/(2*b^2*e) + ((d + e*x)^2*log(c*(a + b*x)^p))/(2*e)]
    @test_int [log(c*(a + b*x)^p)*(d + e*x)^0, x, 2, (-p)*x + ((a + b*x)*log(c*(a + b*x)^p))/b]
    @test_int [log(c*(a + b*x)^p)/(d + e*x)^1, x, 3, (log(c*(a + b*x)^p)*log((b*(d + e*x))/(b*d - a*e)))/e + (p*PolyLog(2, -((e*(a + b*x))/(b*d - a*e))))/e]
    @test_int [log(c*(a + b*x)^p)/(d + e*x)^2, x, 4, (b*p*log(a + b*x))/(e*(b*d - a*e)) - log(c*(a + b*x)^p)/(e*(d + e*x)) - (b*p*log(d + e*x))/(e*(b*d - a*e))]
    @test_int [log(c*(a + b*x)^p)/(d + e*x)^3, x, 3, (b*p)/(2*e*(b*d - a*e)*(d + e*x)) + (b^2*p*log(a + b*x))/(2*e*(b*d - a*e)^2) - log(c*(a + b*x)^p)/(2*e*(d + e*x)^2) - (b^2*p*log(d + e*x))/(2*e*(b*d - a*e)^2)]
    @test_int [log(c*(a + b*x)^p)/(d + e*x)^4, x, 3, (b*p)/(6*e*(b*d - a*e)*(d + e*x)^2) + (b^2*p)/(3*e*(b*d - a*e)^2*(d + e*x)) + (b^3*p*log(a + b*x))/(3*e*(b*d - a*e)^3) - log(c*(a + b*x)^p)/(3*e*(d + e*x)^3) - (b^3*p*log(d + e*x))/(3*e*(b*d - a*e)^3)]

    @test_int [log(c*(a + b*x^2)^p)*(d + e*x)^3, x, 6, -((2*d*(b*d^2 - a*e^2)*p*x)/b) - (e*(6*b*d^2 - a*e^2)*p*x^2)/(4*b) - (2/3)*d*e^2*p*x^3 - (1/8)*e^3*p*x^4 + (2*sqrt(a)*d*(b*d^2 - a*e^2)*p*atan((sqrt(b)*x)/sqrt(a)))/b^(3/2) - ((b^2*d^4 - 6*a*b*d^2*e^2 + a^2*e^4)*p*log(a + b*x^2))/(4*b^2*e) + ((d + e*x)^4*log(c*(a + b*x^2)^p))/(4*e)]
    @test_int [log(c*(a + b*x^2)^p)*(d + e*x)^2, x, 6, -((2*(3*b*d^2 - a*e^2)*p*x)/(3*b)) - d*e*p*x^2 - (2/9)*e^2*p*x^3 + (2*sqrt(a)*(3*b*d^2 - a*e^2)*p*atan((sqrt(b)*x)/sqrt(a)))/(3*b^(3/2)) - (d*(b*d^2 - 3*a*e^2)*p*log(a + b*x^2))/(3*b*e) + ((d + e*x)^3*log(c*(a + b*x^2)^p))/(3*e)]
    @test_int [log(c*(a + b*x^2)^p)*(d + e*x)^1, x, 6, -2*d*p*x - (1/2)*e*p*x^2 + (2*sqrt(a)*d*p*atan((sqrt(b)*x)/sqrt(a)))/sqrt(b) - ((b*d^2 - a*e^2)*p*log(a + b*x^2))/(2*b*e) + ((d + e*x)^2*log(c*(a + b*x^2)^p))/(2*e)]
    @test_int [log(c*(a + b*x^2)^p)*(d + e*x)^0, x, 3, -2*p*x + (2*sqrt(a)*p*atan((sqrt(b)*x)/sqrt(a)))/sqrt(b) + x*log(c*(a + b*x^2)^p)]
    @test_int [log(c*(a + b*x^2)^p)/(d + e*x)^1, x, 9, -((p*log((e*(sqrt(-a) - sqrt(b)*x))/(sqrt(b)*d + sqrt(-a)*e))*log(d + e*x))/e) - (p*log(-((e*(sqrt(-a) + sqrt(b)*x))/(sqrt(b)*d - sqrt(-a)*e)))*log(d + e*x))/e + (log(d + e*x)*log(c*(a + b*x^2)^p))/e - (p*PolyLog(2, (sqrt(b)*(d + e*x))/(sqrt(b)*d - sqrt(-a)*e)))/e - (p*PolyLog(2, (sqrt(b)*(d + e*x))/(sqrt(b)*d + sqrt(-a)*e)))/e]
    @test_int [log(c*(a + b*x^2)^p)/(d + e*x)^2, x, 6, (2*sqrt(a)*sqrt(b)*p*atan((sqrt(b)*x)/sqrt(a)))/(b*d^2 + a*e^2) - (2*b*d*p*log(d + e*x))/(e*(b*d^2 + a*e^2)) + (b*d*p*log(a + b*x^2))/(e*(b*d^2 + a*e^2)) - log(c*(a + b*x^2)^p)/(e*(d + e*x))]
    @test_int [log(c*(a + b*x^2)^p)/(d + e*x)^3, x, 6, (b*d*p)/(e*(b*d^2 + a*e^2)*(d + e*x)) + (2*sqrt(a)*b^(3/2)*d*p*atan((sqrt(b)*x)/sqrt(a)))/(b*d^2 + a*e^2)^2 - (b*(b*d^2 - a*e^2)*p*log(d + e*x))/(e*(b*d^2 + a*e^2)^2) + (b*(b*d^2 - a*e^2)*p*log(a + b*x^2))/(2*e*(b*d^2 + a*e^2)^2) - log(c*(a + b*x^2)^p)/(2*e*(d + e*x)^2)]

    @test_int [log(c*(a + b*x^3)^p)*(d + e*x)^3, x, 13, -((3*(4*b*d^3 - a*e^3)*p*x)/(4*b)) - (9/4)*d^2*e*p*x^2 - d*e^2*p*x^3 - (3/16)*e^3*p*x^4 - (sqrt(3)*a^(1/3)*(4*b*d^3 + 6*a^(1/3)*b^(2/3)*d^2*e - a*e^3)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(4*b^(4/3)) + (a^(1/3)*(4*b*d^3 - 6*a^(1/3)*b^(2/3)*d^2*e - a*e^3)*p*log(a^(1/3) + b^(1/3)*x))/(4*b^(4/3)) - (a^(1/3)*(4*b*d^3 - 6*a^(1/3)*b^(2/3)*d^2*e - a*e^3)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(8*b^(4/3)) - (d*(b*d^3 - 4*a*e^3)*p*log(a + b*x^3))/(4*b*e) + ((d + e*x)^4*log(c*(a + b*x^3)^p))/(4*e)]
    @test_int [log(c*(a + b*x^3)^p)*(d + e*x)^2, x, 12, -3*d^2*p*x - (3/2)*d*e*p*x^2 - (1/3)*e^2*p*x^3 - (sqrt(3)*a^(1/3)*d*(b^(1/3)*d + a^(1/3)*e)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/b^(2/3) + (a^(1/3)*d*(b^(1/3)*d - a^(1/3)*e)*p*log(a^(1/3) + b^(1/3)*x))/b^(2/3) - (a^(1/3)*d*(b^(1/3)*d - a^(1/3)*e)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(2*b^(2/3)) - ((b*d^3 - a*e^3)*p*log(a + b*x^3))/(3*b*e) + ((d + e*x)^3*log(c*(a + b*x^3)^p))/(3*e)]
    @test_int [log(c*(a + b*x^3)^p)*(d + e*x)^1, x, 11, -3*d*p*x - (3/4)*e*p*x^2 - (sqrt(3)*a^(1/3)*(2*b^(1/3)*d + a^(1/3)*e)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(2*b^(2/3)) + (a^(1/3)*(2*b^(1/3)*d - a^(1/3)*e)*p*log(a^(1/3) + b^(1/3)*x))/(2*b^(2/3)) - (a^(1/3)*(2*b^(1/3)*d - a^(1/3)*e)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(4*b^(2/3)) - (d^2*p*log(a + b*x^3))/(2*e) + ((d + e*x)^2*log(c*(a + b*x^3)^p))/(2*e)]
    @test_int [log(c*(a + b*x^3)^p)*(d + e*x)^0, x, 8, -3*p*x - (sqrt(3)*a^(1/3)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/b^(1/3) + (a^(1/3)*p*log(a^(1/3) + b^(1/3)*x))/b^(1/3) - (a^(1/3)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(2*b^(1/3)) + x*log(c*(a + b*x^3)^p)]
    @test_int [log(c*(a + b*x^3)^p)/(d + e*x)^1, x, 12, -((p*log(-((e*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - a^(1/3)*e)))*log(d + e*x))/e) - (p*log(-((e*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))*log(d + e*x))/e - (p*log(((-1)^(1/3)*e*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e))*log(d + e*x))/e + (log(d + e*x)*log(c*(a + b*x^3)^p))/e - (p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)))/e - (p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)))/e - (p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))/e]
    @test_int [log(c*(a + b*x^3)^p)/(d + e*x)^2, x, 11, -((sqrt(3)*a^(1/3)*b^(1/3)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(b^(2/3)*d^2 + a^(1/3)*b^(1/3)*d*e + a^(2/3)*e^2)) + (a^(1/3)*b^(1/3)*(b^(1/3)*d + a^(1/3)*e)*p*log(a^(1/3) + b^(1/3)*x))/(b*d^3 - a*e^3) - (3*b*d^2*p*log(d + e*x))/(e*(b*d^3 - a*e^3)) - (a^(1/3)*b^(1/3)*(b^(1/3)*d + a^(1/3)*e)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(2*(b*d^3 - a*e^3)) + (b*d^2*p*log(a + b*x^3))/(e*(b*d^3 - a*e^3)) - log(c*(a + b*x^3)^p)/(e*(d + e*x))]
    @test_int [log(c*(a + b*x^3)^p)/(d + e*x)^3, x, 11, (3*b*d^2*p)/(2*e*(b*d^3 - a*e^3)*(d + e*x)) - (sqrt(3)*a^(1/3)*b^(2/3)*(2*b*d^3 - 3*a^(1/3)*b^(2/3)*d^2*e + a*e^3)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(2*(b*d^3 - a*e^3)^2) + (a^(1/3)*b^(2/3)*(2*b*d^3 + 3*a^(1/3)*b^(2/3)*d^2*e + a*e^3)*p*log(a^(1/3) + b^(1/3)*x))/(2*(b*d^3 - a*e^3)^2) - (3*b*d*(b*d^3 + 2*a*e^3)*p*log(d + e*x))/(2*e*(b*d^3 - a*e^3)^2) - (a^(1/3)*b^(2/3)*(2*b*d^3 + 3*a^(1/3)*b^(2/3)*d^2*e + a*e^3)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(4*(b*d^3 - a*e^3)^2) + (b*d*(b*d^3 + 2*a*e^3)*p*log(a + b*x^3))/(2*e*(b*d^3 - a*e^3)^2) - log(c*(a + b*x^3)^p)/(2*e*(d + e*x)^2)]

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

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

    @test_int [log(a + b/x)/(c + d*x), x, 8, (log(a + b/x)*log(c + d*x))/d + (log(-((d*x)/c))*log(c + d*x))/d - (log(-((d*(b + a*x))/(a*c - b*d)))*log(c + d*x))/d - PolyLog(2, (a*(c + d*x))/(a*c - b*d))/d + PolyLog(2, 1 + (d*x)/c)/d]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f+g*x)^q*log(c*(d+e*x^m)^n)*when*r*symbolic=#

    @test_int [(d + e*x)^m*log(c*(a + b*x^3)^p), x, 6, (b^(1/3)*p*(d + e*x)^(2 + m)*HypergeometricFunctions._₂F₁(1, 2 + m, 3 + m, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)))/(e*(b^(1/3)*d - a^(1/3)*e)*(1 + m)*(2 + m)) + (b^(1/3)*p*(d + e*x)^(2 + m)*HypergeometricFunctions._₂F₁(1, 2 + m, 3 + m, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)))/(e*(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)*(1 + m)*(2 + m)) + (b^(1/3)*p*(d + e*x)^(2 + m)*HypergeometricFunctions._₂F₁(1, 2 + m, 3 + m, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))/(e*(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)*(1 + m)*(2 + m)) + ((d + e*x)^(1 + m)*log(c*(a + b*x^3)^p))/(e*(1 + m))]
    @test_int [(d + e*x)^m*log(c*(a + b*x^2)^p), x, 5, (sqrt(b)*p*(d + e*x)^(2 + m)*HypergeometricFunctions._₂F₁(1, 2 + m, 3 + m, (sqrt(b)*(d + e*x))/(sqrt(b)*d - sqrt(-a)*e)))/(e*(sqrt(b)*d - sqrt(-a)*e)*(1 + m)*(2 + m)) + (sqrt(b)*p*(d + e*x)^(2 + m)*HypergeometricFunctions._₂F₁(1, 2 + m, 3 + m, (sqrt(b)*(d + e*x))/(sqrt(b)*d + sqrt(-a)*e)))/(e*(sqrt(b)*d + sqrt(-a)*e)*(1 + m)*(2 + m)) + ((d + e*x)^(1 + m)*log(c*(a + b*x^2)^p))/(e*(1 + m))]
    @test_int [(d + e*x)^m*log(c*(a + b*x^1)^p), x, 2, (b*p*(d + e*x)^(2 + m)*HypergeometricFunctions._₂F₁(1, 2 + m, 3 + m, (b*(d + e*x))/(b*d - a*e)))/(e*(b*d - a*e)*(1 + m)*(2 + m)) + ((d + e*x)^(1 + m)*log(c*(a + b*x)^p))/(e*(1 + m))]
    @test_int [(d + e*x)^m*log(c*(a + b/x^1)^p), x, 5, (a*p*(d + e*x)^(2 + m)*HypergeometricFunctions._₂F₁(1, 2 + m, 3 + m, (a*(d + e*x))/(a*d - b*e)))/(e*(a*d - b*e)*(1 + m)*(2 + m)) - (p*(d + e*x)^(2 + m)*HypergeometricFunctions._₂F₁(1, 2 + m, 3 + m, 1 + (e*x)/d))/(d*e*(2 + 3*m + m^2)) + ((d + e*x)^(1 + m)*log(c*(a + b/x)^p))/(e*(1 + m))]
    @test_int [(d + e*x)^m*log(c*(a + b/x^2)^p), x, 9, (sqrt(-a)*p*(d + e*x)^(2 + m)*HypergeometricFunctions._₂F₁(1, 2 + m, 3 + m, (sqrt(-a)*(d + e*x))/(sqrt(-a)*d - sqrt(b)*e)))/(e*(sqrt(-a)*d - sqrt(b)*e)*(1 + m)*(2 + m)) + (sqrt(-a)*p*(d + e*x)^(2 + m)*HypergeometricFunctions._₂F₁(1, 2 + m, 3 + m, (sqrt(-a)*(d + e*x))/(sqrt(-a)*d + sqrt(b)*e)))/(e*(sqrt(-a)*d + sqrt(b)*e)*(1 + m)*(2 + m)) - (2*p*(d + e*x)^(2 + m)*HypergeometricFunctions._₂F₁(1, 2 + m, 3 + m, 1 + (e*x)/d))/(d*e*(2 + 3*m + m^2)) + ((d + e*x)^(1 + m)*log(c*(a + b/x^2)^p))/(e*(1 + m))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f+g*x)^q*log(c*(d+e*x^m)^n)*when*n*symbolic=#

    @test_int [(f + g*x)^m*log(c*(d + e*x^n)^p), x, 0, Unintegrable((f + g*x)^m*log(c*(d + e*x^n)^p), x)]

    @test_int [(f + g*x)^3*log(c*(d + e*x^n)^p), x, 8, -((e*f^3*n*p*x^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + 1/n, 2 + 1/n, -((e*x^n)/d)))/(d*(1 + n))) - (3*e*f^2*g*n*p*x^(2 + n)*HypergeometricFunctions._₂F₁(1, (2 + n)/n, 2*(1 + 1/n), -((e*x^n)/d)))/(2*d*(2 + n)) - (e*f*g^2*n*p*x^(3 + n)*HypergeometricFunctions._₂F₁(1, (3 + n)/n, 2 + 3/n, -((e*x^n)/d)))/(d*(3 + n)) - (e*g^3*n*p*x^(4 + n)*HypergeometricFunctions._₂F₁(1, (4 + n)/n, 2*(1 + 2/n), -((e*x^n)/d)))/(4*d*(4 + n)) - (f^4*p*log(d + e*x^n))/(4*g) + ((f + g*x)^4*log(c*(d + e*x^n)^p))/(4*g)]
    @test_int [(f + g*x)^2*log(c*(d + e*x^n)^p), x, 7, -((e*f^2*n*p*x^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + 1/n, 2 + 1/n, -((e*x^n)/d)))/(d*(1 + n))) - (e*f*g*n*p*x^(2 + n)*HypergeometricFunctions._₂F₁(1, (2 + n)/n, 2*(1 + 1/n), -((e*x^n)/d)))/(d*(2 + n)) - (e*g^2*n*p*x^(3 + n)*HypergeometricFunctions._₂F₁(1, (3 + n)/n, 2 + 3/n, -((e*x^n)/d)))/(3*d*(3 + n)) - (f^3*p*log(d + e*x^n))/(3*g) + ((f + g*x)^3*log(c*(d + e*x^n)^p))/(3*g)]
    @test_int [(f + g*x)^1*log(c*(d + e*x^n)^p), x, 6, -((e*f*n*p*x^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + 1/n, 2 + 1/n, -((e*x^n)/d)))/(d*(1 + n))) - (e*g*n*p*x^(2 + n)*HypergeometricFunctions._₂F₁(1, (2 + n)/n, 2*(1 + 1/n), -((e*x^n)/d)))/(2*d*(2 + n)) - (f^2*p*log(d + e*x^n))/(2*g) + ((f + g*x)^2*log(c*(d + e*x^n)^p))/(2*g)]
    @test_int [(f + g*x)^0*log(c*(d + e*x^n)^p), x, 2, -((e*n*p*x^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + 1/n, 2 + 1/n, -((e*x^n)/d)))/(d*(1 + n))) + x*log(c*(d + e*x^n)^p)]
    @test_int [log(c*(d + e*x^n)^p)/(f + g*x)^1, x, 0, Unintegrable(log(c*(d + e*x^n)^p)/(f + g*x), x)]
    @test_int [log(c*(d + e*x^n)^p)/(f + g*x)^2, x, 0, Unintegrable(log(c*(d + e*x^n)^p)/(f + g*x)^2, x)]
    @test_int [log(c*(d + e*x^n)^p)/(f + g*x)^3, x, 0, Unintegrable(log(c*(d + e*x^n)^p)/(f + g*x)^3, x)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(h*x)^r*(f+g*x)^q*log(c*(d+e*x^m)^n)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^r / (f+g*x)*log(c*(d+e*x^m)^n)=#

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

    @test_int [x^3*log(c*(a + b*x)^p)/(d + e*x), x, 13, -((d^2*p*x)/e^3) - (a*d*p*x)/(2*b*e^2) - (a^2*p*x)/(3*b^2*e) + (d*p*x^2)/(4*e^2) + (a*p*x^2)/(6*b*e) - (p*x^3)/(9*e) + (a^2*d*p*log(a + b*x))/(2*b^2*e^2) + (a^3*p*log(a + b*x))/(3*b^3*e) - (d*x^2*log(c*(a + b*x)^p))/(2*e^2) + (x^3*log(c*(a + b*x)^p))/(3*e) + (d^2*(a + b*x)*log(c*(a + b*x)^p))/(b*e^3) - (d^3*log(c*(a + b*x)^p)*log((b*(d + e*x))/(b*d - a*e)))/e^4 - (d^3*p*PolyLog(2, -((e*(a + b*x))/(b*d - a*e))))/e^4]
    @test_int [x^2*log(c*(a + b*x)^p)/(d + e*x), x, 10, (d*p*x)/e^2 + (a*p*x)/(2*b*e) - (p*x^2)/(4*e) - (a^2*p*log(a + b*x))/(2*b^2*e) + (x^2*log(c*(a + b*x)^p))/(2*e) - (d*(a + b*x)*log(c*(a + b*x)^p))/(b*e^2) + (d^2*log(c*(a + b*x)^p)*log((b*(d + e*x))/(b*d - a*e)))/e^3 + (d^2*p*PolyLog(2, -((e*(a + b*x))/(b*d - a*e))))/e^3]
    @test_int [x^1*log(c*(a + b*x)^p)/(d + e*x), x, 7, -((p*x)/e) + ((a + b*x)*log(c*(a + b*x)^p))/(b*e) - (d*log(c*(a + b*x)^p)*log((b*(d + e*x))/(b*d - a*e)))/e^2 - (d*p*PolyLog(2, -((e*(a + b*x))/(b*d - a*e))))/e^2]
    @test_int [x^0*log(c*(a + b*x)^p)/(d + e*x), x, 3, (log(c*(a + b*x)^p)*log((b*(d + e*x))/(b*d - a*e)))/e + (p*PolyLog(2, -((e*(a + b*x))/(b*d - a*e))))/e]
    @test_int [log(c*(a + b*x)^p)/(x^1*(d + e*x)), x, 7, (log(-((b*x)/a))*log(c*(a + b*x)^p))/d - (log(c*(a + b*x)^p)*log((b*(d + e*x))/(b*d - a*e)))/d - (p*PolyLog(2, -((e*(a + b*x))/(b*d - a*e))))/d + (p*PolyLog(2, 1 + (b*x)/a))/d]
    @test_int [log(c*(a + b*x)^p)/(x^2*(d + e*x)), x, 11, (b*p*log(x))/(a*d) - (b*p*log(a + b*x))/(a*d) - log(c*(a + b*x)^p)/(d*x) - (e*log(-((b*x)/a))*log(c*(a + b*x)^p))/d^2 + (e*log(c*(a + b*x)^p)*log((b*(d + e*x))/(b*d - a*e)))/d^2 + (e*p*PolyLog(2, -((e*(a + b*x))/(b*d - a*e))))/d^2 - (e*p*PolyLog(2, 1 + (b*x)/a))/d^2]
    @test_int [log(c*(a + b*x)^p)/(x^3*(d + e*x)), x, 14, -((b*p)/(2*a*d*x)) - (b^2*p*log(x))/(2*a^2*d) - (b*e*p*log(x))/(a*d^2) + (b^2*p*log(a + b*x))/(2*a^2*d) + (b*e*p*log(a + b*x))/(a*d^2) - log(c*(a + b*x)^p)/(2*d*x^2) + (e*log(c*(a + b*x)^p))/(d^2*x) + (e^2*log(-((b*x)/a))*log(c*(a + b*x)^p))/d^3 - (e^2*log(c*(a + b*x)^p)*log((b*(d + e*x))/(b*d - a*e)))/d^3 - (e^2*p*PolyLog(2, -((e*(a + b*x))/(b*d - a*e))))/d^3 + (e^2*p*PolyLog(2, 1 + (b*x)/a))/d^3]

    @test_int [x^3*log(c*(a + b*x^2)^p)/(d + e*x), x, 21, -((2*d^2*p*x)/e^3) + (2*a*p*x)/(3*b*e) + (d*p*x^2)/(2*e^2) - (2*p*x^3)/(9*e) + (2*sqrt(a)*d^2*p*atan((sqrt(b)*x)/sqrt(a)))/(sqrt(b)*e^3) - (2*a^(3/2)*p*atan((sqrt(b)*x)/sqrt(a)))/(3*b^(3/2)*e) + (d^3*p*log((e*(sqrt(-a) - sqrt(b)*x))/(sqrt(b)*d + sqrt(-a)*e))*log(d + e*x))/e^4 + (d^3*p*log(-((e*(sqrt(-a) + sqrt(b)*x))/(sqrt(b)*d - sqrt(-a)*e)))*log(d + e*x))/e^4 + (d^2*x*log(c*(a + b*x^2)^p))/e^3 + (x^3*log(c*(a + b*x^2)^p))/(3*e) - (d*(a + b*x^2)*log(c*(a + b*x^2)^p))/(2*b*e^2) - (d^3*log(d + e*x)*log(c*(a + b*x^2)^p))/e^4 + (d^3*p*PolyLog(2, (sqrt(b)*(d + e*x))/(sqrt(b)*d - sqrt(-a)*e)))/e^4 + (d^3*p*PolyLog(2, (sqrt(b)*(d + e*x))/(sqrt(b)*d + sqrt(-a)*e)))/e^4]
    @test_int [x^2*log(c*(a + b*x^2)^p)/(d + e*x), x, 17, (2*d*p*x)/e^2 - (p*x^2)/(2*e) - (2*sqrt(a)*d*p*atan((sqrt(b)*x)/sqrt(a)))/(sqrt(b)*e^2) - (d^2*p*log((e*(sqrt(-a) - sqrt(b)*x))/(sqrt(b)*d + sqrt(-a)*e))*log(d + e*x))/e^3 - (d^2*p*log(-((e*(sqrt(-a) + sqrt(b)*x))/(sqrt(b)*d - sqrt(-a)*e)))*log(d + e*x))/e^3 - (d*x*log(c*(a + b*x^2)^p))/e^2 + ((a + b*x^2)*log(c*(a + b*x^2)^p))/(2*b*e) + (d^2*log(d + e*x)*log(c*(a + b*x^2)^p))/e^3 - (d^2*p*PolyLog(2, (sqrt(b)*(d + e*x))/(sqrt(b)*d - sqrt(-a)*e)))/e^3 - (d^2*p*PolyLog(2, (sqrt(b)*(d + e*x))/(sqrt(b)*d + sqrt(-a)*e)))/e^3]
    @test_int [x^1*log(c*(a + b*x^2)^p)/(d + e*x), x, 14, -((2*p*x)/e) + (2*sqrt(a)*p*atan((sqrt(b)*x)/sqrt(a)))/(sqrt(b)*e) + (d*p*log((e*(sqrt(-a) - sqrt(b)*x))/(sqrt(b)*d + sqrt(-a)*e))*log(d + e*x))/e^2 + (d*p*log(-((e*(sqrt(-a) + sqrt(b)*x))/(sqrt(b)*d - sqrt(-a)*e)))*log(d + e*x))/e^2 + (x*log(c*(a + b*x^2)^p))/e - (d*log(d + e*x)*log(c*(a + b*x^2)^p))/e^2 + (d*p*PolyLog(2, (sqrt(b)*(d + e*x))/(sqrt(b)*d - sqrt(-a)*e)))/e^2 + (d*p*PolyLog(2, (sqrt(b)*(d + e*x))/(sqrt(b)*d + sqrt(-a)*e)))/e^2]
    @test_int [x^0*log(c*(a + b*x^2)^p)/(d + e*x), x, 9, -((p*log((e*(sqrt(-a) - sqrt(b)*x))/(sqrt(b)*d + sqrt(-a)*e))*log(d + e*x))/e) - (p*log(-((e*(sqrt(-a) + sqrt(b)*x))/(sqrt(b)*d - sqrt(-a)*e)))*log(d + e*x))/e + (log(d + e*x)*log(c*(a + b*x^2)^p))/e - (p*PolyLog(2, (sqrt(b)*(d + e*x))/(sqrt(b)*d - sqrt(-a)*e)))/e - (p*PolyLog(2, (sqrt(b)*(d + e*x))/(sqrt(b)*d + sqrt(-a)*e)))/e]
    @test_int [log(c*(a + b*x^2)^p)/(x^1*(d + e*x)), x, 14, (p*log((e*(sqrt(-a) - sqrt(b)*x))/(sqrt(b)*d + sqrt(-a)*e))*log(d + e*x))/d + (p*log(-((e*(sqrt(-a) + sqrt(b)*x))/(sqrt(b)*d - sqrt(-a)*e)))*log(d + e*x))/d + (log(-((b*x^2)/a))*log(c*(a + b*x^2)^p))/(2*d) - (log(d + e*x)*log(c*(a + b*x^2)^p))/d + (p*PolyLog(2, (sqrt(b)*(d + e*x))/(sqrt(b)*d - sqrt(-a)*e)))/d + (p*PolyLog(2, (sqrt(b)*(d + e*x))/(sqrt(b)*d + sqrt(-a)*e)))/d + (p*PolyLog(2, 1 + (b*x^2)/a))/(2*d)]
    @test_int [log(c*(a + b*x^2)^p)/(x^2*(d + e*x)), x, 16, (2*sqrt(b)*p*atan((sqrt(b)*x)/sqrt(a)))/(sqrt(a)*d) - (e*p*log((e*(sqrt(-a) - sqrt(b)*x))/(sqrt(b)*d + sqrt(-a)*e))*log(d + e*x))/d^2 - (e*p*log(-((e*(sqrt(-a) + sqrt(b)*x))/(sqrt(b)*d - sqrt(-a)*e)))*log(d + e*x))/d^2 - log(c*(a + b*x^2)^p)/(d*x) - (e*log(-((b*x^2)/a))*log(c*(a + b*x^2)^p))/(2*d^2) + (e*log(d + e*x)*log(c*(a + b*x^2)^p))/d^2 - (e*p*PolyLog(2, (sqrt(b)*(d + e*x))/(sqrt(b)*d - sqrt(-a)*e)))/d^2 - (e*p*PolyLog(2, (sqrt(b)*(d + e*x))/(sqrt(b)*d + sqrt(-a)*e)))/d^2 - (e*p*PolyLog(2, 1 + (b*x^2)/a))/(2*d^2)]
    @test_int [log(c*(a + b*x^2)^p)/(x^3*(d + e*x)), x, 21, -((2*sqrt(b)*e*p*atan((sqrt(b)*x)/sqrt(a)))/(sqrt(a)*d^2)) + (b*p*log(x))/(a*d) + (e^2*p*log((e*(sqrt(-a) - sqrt(b)*x))/(sqrt(b)*d + sqrt(-a)*e))*log(d + e*x))/d^3 + (e^2*p*log(-((e*(sqrt(-a) + sqrt(b)*x))/(sqrt(b)*d - sqrt(-a)*e)))*log(d + e*x))/d^3 - (b*p*log(a + b*x^2))/(2*a*d) - log(c*(a + b*x^2)^p)/(2*d*x^2) + (e*log(c*(a + b*x^2)^p))/(d^2*x) + (e^2*log(-((b*x^2)/a))*log(c*(a + b*x^2)^p))/(2*d^3) - (e^2*log(d + e*x)*log(c*(a + b*x^2)^p))/d^3 + (e^2*p*PolyLog(2, (sqrt(b)*(d + e*x))/(sqrt(b)*d - sqrt(-a)*e)))/d^3 + (e^2*p*PolyLog(2, (sqrt(b)*(d + e*x))/(sqrt(b)*d + sqrt(-a)*e)))/d^3 + (e^2*p*PolyLog(2, 1 + (b*x^2)/a))/(2*d^3)]

    @test_int [x^3*log(c*(a + b*x^3)^p)/(d + e*x), x, 33, -((3*d^2*p*x)/e^3) + (3*d*p*x^2)/(4*e^2) - (p*x^3)/(3*e) - (sqrt(3)*a^(1/3)*d^2*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(b^(1/3)*e^3) + (sqrt(3)*a^(2/3)*d*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(2*b^(2/3)*e^2) + (a^(1/3)*d^2*p*log(a^(1/3) + b^(1/3)*x))/(b^(1/3)*e^3) + (a^(2/3)*d*p*log(a^(1/3) + b^(1/3)*x))/(2*b^(2/3)*e^2) + (d^3*p*log(-((e*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - a^(1/3)*e)))*log(d + e*x))/e^4 + (d^3*p*log(-((e*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))*log(d + e*x))/e^4 + (d^3*p*log(((-1)^(1/3)*e*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e))*log(d + e*x))/e^4 - (a^(1/3)*d^2*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(2*b^(1/3)*e^3) - (a^(2/3)*d*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(4*b^(2/3)*e^2) + (d^2*x*log(c*(a + b*x^3)^p))/e^3 - (d*x^2*log(c*(a + b*x^3)^p))/(2*e^2) + ((a + b*x^3)*log(c*(a + b*x^3)^p))/(3*b*e) - (d^3*log(d + e*x)*log(c*(a + b*x^3)^p))/e^4 + (d^3*p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)))/e^4 + (d^3*p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)))/e^4 + (d^3*p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))/e^4]
    @test_int [x^2*log(c*(a + b*x^3)^p)/(d + e*x), x, 30, (3*d*p*x)/e^2 - (3*p*x^2)/(4*e) + (sqrt(3)*a^(1/3)*d*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(b^(1/3)*e^2) - (sqrt(3)*a^(2/3)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(2*b^(2/3)*e) - (a^(1/3)*d*p*log(a^(1/3) + b^(1/3)*x))/(b^(1/3)*e^2) - (a^(2/3)*p*log(a^(1/3) + b^(1/3)*x))/(2*b^(2/3)*e) - (d^2*p*log(-((e*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - a^(1/3)*e)))*log(d + e*x))/e^3 - (d^2*p*log(-((e*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))*log(d + e*x))/e^3 - (d^2*p*log(((-1)^(1/3)*e*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e))*log(d + e*x))/e^3 + (a^(1/3)*d*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(2*b^(1/3)*e^2) + (a^(2/3)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(4*b^(2/3)*e) - (d*x*log(c*(a + b*x^3)^p))/e^2 + (x^2*log(c*(a + b*x^3)^p))/(2*e) + (d^2*log(d + e*x)*log(c*(a + b*x^3)^p))/e^3 - (d^2*p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)))/e^3 - (d^2*p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)))/e^3 - (d^2*p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))/e^3]
    @test_int [x^1*log(c*(a + b*x^3)^p)/(d + e*x), x, 22, -((3*p*x)/e) - (sqrt(3)*a^(1/3)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(b^(1/3)*e) + (a^(1/3)*p*log(a^(1/3) + b^(1/3)*x))/(b^(1/3)*e) + (d*p*log(-((e*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - a^(1/3)*e)))*log(d + e*x))/e^2 + (d*p*log(-((e*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))*log(d + e*x))/e^2 + (d*p*log(((-1)^(1/3)*e*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e))*log(d + e*x))/e^2 - (a^(1/3)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(2*b^(1/3)*e) + (x*log(c*(a + b*x^3)^p))/e - (d*log(d + e*x)*log(c*(a + b*x^3)^p))/e^2 + (d*p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)))/e^2 + (d*p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)))/e^2 + (d*p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))/e^2]
    @test_int [x^0*log(c*(a + b*x^3)^p)/(d + e*x), x, 12, -((p*log(-((e*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - a^(1/3)*e)))*log(d + e*x))/e) - (p*log(-((e*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))*log(d + e*x))/e - (p*log(((-1)^(1/3)*e*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e))*log(d + e*x))/e + (log(d + e*x)*log(c*(a + b*x^3)^p))/e - (p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)))/e - (p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)))/e - (p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))/e]
    @test_int [log(c*(a + b*x^3)^p)/(x^1*(d + e*x)), x, 17, (p*log(-((e*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - a^(1/3)*e)))*log(d + e*x))/d + (p*log(-((e*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))*log(d + e*x))/d + (p*log(((-1)^(1/3)*e*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e))*log(d + e*x))/d + (log(-((b*x^3)/a))*log(c*(a + b*x^3)^p))/(3*d) - (log(d + e*x)*log(c*(a + b*x^3)^p))/d + (p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)))/d + (p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)))/d + (p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))/d + (p*PolyLog(2, 1 + (b*x^3)/a))/(3*d)]
    @test_int [log(c*(a + b*x^3)^p)/(x^2*(d + e*x)), x, 24, -((sqrt(3)*b^(1/3)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(a^(1/3)*d)) - (b^(1/3)*p*log(a^(1/3) + b^(1/3)*x))/(a^(1/3)*d) - (e*p*log(-((e*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - a^(1/3)*e)))*log(d + e*x))/d^2 - (e*p*log(-((e*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))*log(d + e*x))/d^2 - (e*p*log(((-1)^(1/3)*e*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e))*log(d + e*x))/d^2 + (b^(1/3)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(2*a^(1/3)*d) - log(c*(a + b*x^3)^p)/(d*x) - (e*log(-((b*x^3)/a))*log(c*(a + b*x^3)^p))/(3*d^2) + (e*log(d + e*x)*log(c*(a + b*x^3)^p))/d^2 - (e*p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)))/d^2 - (e*p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)))/d^2 - (e*p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))/d^2 - (e*p*PolyLog(2, 1 + (b*x^3)/a))/(3*d^2)]
    @test_int [log(c*(a + b*x^3)^p)/(x^3*(d + e*x)), x, 31, -((sqrt(3)*b^(2/3)*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(2*a^(2/3)*d)) + (sqrt(3)*b^(1/3)*e*p*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(a^(1/3)*d^2) + (b^(2/3)*p*log(a^(1/3) + b^(1/3)*x))/(2*a^(2/3)*d) + (b^(1/3)*e*p*log(a^(1/3) + b^(1/3)*x))/(a^(1/3)*d^2) + (e^2*p*log(-((e*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - a^(1/3)*e)))*log(d + e*x))/d^3 + (e^2*p*log(-((e*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))*log(d + e*x))/d^3 + (e^2*p*log(((-1)^(1/3)*e*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e))*log(d + e*x))/d^3 - (b^(2/3)*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(4*a^(2/3)*d) - (b^(1/3)*e*p*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(2*a^(1/3)*d^2) - log(c*(a + b*x^3)^p)/(2*d*x^2) + (e*log(c*(a + b*x^3)^p))/(d^2*x) + (e^2*log(-((b*x^3)/a))*log(c*(a + b*x^3)^p))/(3*d^3) - (e^2*log(d + e*x)*log(c*(a + b*x^3)^p))/d^3 + (e^2*p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)))/d^3 + (e^2*p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)))/d^3 + (e^2*p*PolyLog(2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))/d^3 + (e^2*p*PolyLog(2, 1 + (b*x^3)/a))/(3*d^3)]

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

    @test_int [x^3*log(c*(a + b/x)^p)/(d + e*x), x, 21, -((b*d*p*x)/(2*a*e^2)) - (b^2*p*x)/(3*a^2*e) + (b*p*x^2)/(6*a*e) + (d^2*x*log(c*(a + b/x)^p))/e^3 - (d*x^2*log(c*(a + b/x)^p))/(2*e^2) + (x^3*log(c*(a + b/x)^p))/(3*e) + (b*d^2*p*log(b + a*x))/(a*e^3) + (b^2*d*p*log(b + a*x))/(2*a^2*e^2) + (b^3*p*log(b + a*x))/(3*a^3*e) - (d^3*log(c*(a + b/x)^p)*log(d + e*x))/e^4 - (d^3*p*log(-((e*x)/d))*log(d + e*x))/e^4 + (d^3*p*log(-((e*(b + a*x))/(a*d - b*e)))*log(d + e*x))/e^4 + (d^3*p*PolyLog(2, (a*(d + e*x))/(a*d - b*e)))/e^4 - (d^3*p*PolyLog(2, 1 + (e*x)/d))/e^4]
    @test_int [x^2*log(c*(a + b/x)^p)/(d + e*x), x, 17, (b*p*x)/(2*a*e) - (d*x*log(c*(a + b/x)^p))/e^2 + (x^2*log(c*(a + b/x)^p))/(2*e) - (b*d*p*log(b + a*x))/(a*e^2) - (b^2*p*log(b + a*x))/(2*a^2*e) + (d^2*log(c*(a + b/x)^p)*log(d + e*x))/e^3 + (d^2*p*log(-((e*x)/d))*log(d + e*x))/e^3 - (d^2*p*log(-((e*(b + a*x))/(a*d - b*e)))*log(d + e*x))/e^3 - (d^2*p*PolyLog(2, (a*(d + e*x))/(a*d - b*e)))/e^3 + (d^2*p*PolyLog(2, 1 + (e*x)/d))/e^3]
    @test_int [x^1*log(c*(a + b/x)^p)/(d + e*x), x, 13, (x*log(c*(a + b/x)^p))/e + (b*p*log(b + a*x))/(a*e) - (d*log(c*(a + b/x)^p)*log(d + e*x))/e^2 - (d*p*log(-((e*x)/d))*log(d + e*x))/e^2 + (d*p*log(-((e*(b + a*x))/(a*d - b*e)))*log(d + e*x))/e^2 + (d*p*PolyLog(2, (a*(d + e*x))/(a*d - b*e)))/e^2 - (d*p*PolyLog(2, 1 + (e*x)/d))/e^2]
    @test_int [x^0*log(c*(a + b/x)^p)/(d + e*x), x, 8, (log(c*(a + b/x)^p)*log(d + e*x))/e + (p*log(-((e*x)/d))*log(d + e*x))/e - (p*log(-((e*(b + a*x))/(a*d - b*e)))*log(d + e*x))/e - (p*PolyLog(2, (a*(d + e*x))/(a*d - b*e)))/e + (p*PolyLog(2, 1 + (e*x)/d))/e]
    @test_int [log(c*(a + b/x)^p)/(x^1*(d + e*x)), x, 13, -((log(c*(a + b/x)^p)*log(-(b/(a*x))))/d) - (log(c*(a + b/x)^p)*log(d + e*x))/d - (p*log(-((e*x)/d))*log(d + e*x))/d + (p*log(-((e*(b + a*x))/(a*d - b*e)))*log(d + e*x))/d - (p*PolyLog(2, 1 + b/(a*x)))/d + (p*PolyLog(2, (a*(d + e*x))/(a*d - b*e)))/d - (p*PolyLog(2, 1 + (e*x)/d))/d]
    @test_int [log(c*(a + b/x)^p)/(x^2*(d + e*x)), x, 16, p/(d*x) - ((a + b/x)*log(c*(a + b/x)^p))/(b*d) + (e*log(c*(a + b/x)^p)*log(-(b/(a*x))))/d^2 + (e*log(c*(a + b/x)^p)*log(d + e*x))/d^2 + (e*p*log(-((e*x)/d))*log(d + e*x))/d^2 - (e*p*log(-((e*(b + a*x))/(a*d - b*e)))*log(d + e*x))/d^2 + (e*p*PolyLog(2, 1 + b/(a*x)))/d^2 - (e*p*PolyLog(2, (a*(d + e*x))/(a*d - b*e)))/d^2 + (e*p*PolyLog(2, 1 + (e*x)/d))/d^2]
    @test_int [log(c*(a + b/x)^p)/(x^3*(d + e*x)), x, 20, p/(4*d*x^2) - (a*p)/(2*b*d*x) - (e*p)/(d^2*x) + (a^2*p*log(a + b/x))/(2*b^2*d) + (e*(a + b/x)*log(c*(a + b/x)^p))/(b*d^2) - log(c*(a + b/x)^p)/(2*d*x^2) - (e^2*log(c*(a + b/x)^p)*log(-(b/(a*x))))/d^3 - (e^2*log(c*(a + b/x)^p)*log(d + e*x))/d^3 - (e^2*p*log(-((e*x)/d))*log(d + e*x))/d^3 + (e^2*p*log(-((e*(b + a*x))/(a*d - b*e)))*log(d + e*x))/d^3 - (e^2*p*PolyLog(2, 1 + b/(a*x)))/d^3 + (e^2*p*PolyLog(2, (a*(d + e*x))/(a*d - b*e)))/d^3 - (e^2*p*PolyLog(2, 1 + (e*x)/d))/d^3]

    @test_int [x^3*log(c*(a + b/x^2)^p)/(d + e*x), x, 25, (2*b*p*x)/(3*a*e) + (2*sqrt(b)*d^2*p*atan((sqrt(a)*x)/sqrt(b)))/(sqrt(a)*e^3) - (2*b^(3/2)*p*atan((sqrt(a)*x)/sqrt(b)))/(3*a^(3/2)*e) + (d^2*x*log(c*(a + b/x^2)^p))/e^3 - (d*x^2*log(c*(a + b/x^2)^p))/(2*e^2) + (x^3*log(c*(a + b/x^2)^p))/(3*e) - (d^3*log(c*(a + b/x^2)^p)*log(d + e*x))/e^4 - (2*d^3*p*log(-((e*x)/d))*log(d + e*x))/e^4 + (d^3*p*log((e*(sqrt(b) - sqrt(-a)*x))/(sqrt(-a)*d + sqrt(b)*e))*log(d + e*x))/e^4 + (d^3*p*log(-((e*(sqrt(b) + sqrt(-a)*x))/(sqrt(-a)*d - sqrt(b)*e)))*log(d + e*x))/e^4 - (b*d*p*log(b + a*x^2))/(2*a*e^2) + (d^3*p*PolyLog(2, (sqrt(-a)*(d + e*x))/(sqrt(-a)*d - sqrt(b)*e)))/e^4 + (d^3*p*PolyLog(2, (sqrt(-a)*(d + e*x))/(sqrt(-a)*d + sqrt(b)*e)))/e^4 - (2*d^3*p*PolyLog(2, 1 + (e*x)/d))/e^4]
    @test_int [x^2*log(c*(a + b/x^2)^p)/(d + e*x), x, 21, -((2*sqrt(b)*d*p*atan((sqrt(a)*x)/sqrt(b)))/(sqrt(a)*e^2)) - (d*x*log(c*(a + b/x^2)^p))/e^2 + (x^2*log(c*(a + b/x^2)^p))/(2*e) + (d^2*log(c*(a + b/x^2)^p)*log(d + e*x))/e^3 + (2*d^2*p*log(-((e*x)/d))*log(d + e*x))/e^3 - (d^2*p*log((e*(sqrt(b) - sqrt(-a)*x))/(sqrt(-a)*d + sqrt(b)*e))*log(d + e*x))/e^3 - (d^2*p*log(-((e*(sqrt(b) + sqrt(-a)*x))/(sqrt(-a)*d - sqrt(b)*e)))*log(d + e*x))/e^3 + (b*p*log(b + a*x^2))/(2*a*e) - (d^2*p*PolyLog(2, (sqrt(-a)*(d + e*x))/(sqrt(-a)*d - sqrt(b)*e)))/e^3 - (d^2*p*PolyLog(2, (sqrt(-a)*(d + e*x))/(sqrt(-a)*d + sqrt(b)*e)))/e^3 + (2*d^2*p*PolyLog(2, 1 + (e*x)/d))/e^3]
    @test_int [x^1*log(c*(a + b/x^2)^p)/(d + e*x), x, 18, (2*sqrt(b)*p*atan((sqrt(a)*x)/sqrt(b)))/(sqrt(a)*e) + (x*log(c*(a + b/x^2)^p))/e - (d*log(c*(a + b/x^2)^p)*log(d + e*x))/e^2 - (2*d*p*log(-((e*x)/d))*log(d + e*x))/e^2 + (d*p*log((e*(sqrt(b) - sqrt(-a)*x))/(sqrt(-a)*d + sqrt(b)*e))*log(d + e*x))/e^2 + (d*p*log(-((e*(sqrt(b) + sqrt(-a)*x))/(sqrt(-a)*d - sqrt(b)*e)))*log(d + e*x))/e^2 + (d*p*PolyLog(2, (sqrt(-a)*(d + e*x))/(sqrt(-a)*d - sqrt(b)*e)))/e^2 + (d*p*PolyLog(2, (sqrt(-a)*(d + e*x))/(sqrt(-a)*d + sqrt(b)*e)))/e^2 - (2*d*p*PolyLog(2, 1 + (e*x)/d))/e^2]
    @test_int [x^0*log(c*(a + b/x^2)^p)/(d + e*x), x, 13, (log(c*(a + b/x^2)^p)*log(d + e*x))/e + (2*p*log(-((e*x)/d))*log(d + e*x))/e - (p*log((e*(sqrt(b) - sqrt(-a)*x))/(sqrt(-a)*d + sqrt(b)*e))*log(d + e*x))/e - (p*log(-((e*(sqrt(b) + sqrt(-a)*x))/(sqrt(-a)*d - sqrt(b)*e)))*log(d + e*x))/e - (p*PolyLog(2, (sqrt(-a)*(d + e*x))/(sqrt(-a)*d - sqrt(b)*e)))/e - (p*PolyLog(2, (sqrt(-a)*(d + e*x))/(sqrt(-a)*d + sqrt(b)*e)))/e + (2*p*PolyLog(2, 1 + (e*x)/d))/e]
    @test_int [log(c*(a + b/x^2)^p)/(x^1*(d + e*x)), x, 18, -((log(c*(a + b/x^2)^p)*log(-(b/(a*x^2))))/(2*d)) - (log(c*(a + b/x^2)^p)*log(d + e*x))/d - (2*p*log(-((e*x)/d))*log(d + e*x))/d + (p*log((e*(sqrt(b) - sqrt(-a)*x))/(sqrt(-a)*d + sqrt(b)*e))*log(d + e*x))/d + (p*log(-((e*(sqrt(b) + sqrt(-a)*x))/(sqrt(-a)*d - sqrt(b)*e)))*log(d + e*x))/d - (p*PolyLog(2, 1 + b/(a*x^2)))/(2*d) + (p*PolyLog(2, (sqrt(-a)*(d + e*x))/(sqrt(-a)*d - sqrt(b)*e)))/d + (p*PolyLog(2, (sqrt(-a)*(d + e*x))/(sqrt(-a)*d + sqrt(b)*e)))/d - (2*p*PolyLog(2, 1 + (e*x)/d))/d]
    @test_int [log(c*(a + b/x^2)^p)/(x^2*(d + e*x)), x, 22, (2*p)/(d*x) + (2*sqrt(a)*p*atan((sqrt(a)*x)/sqrt(b)))/(sqrt(b)*d) - log(c*(a + b/x^2)^p)/(d*x) + (e*log(c*(a + b/x^2)^p)*log(-(b/(a*x^2))))/(2*d^2) + (e*log(c*(a + b/x^2)^p)*log(d + e*x))/d^2 + (2*e*p*log(-((e*x)/d))*log(d + e*x))/d^2 - (e*p*log((e*(sqrt(b) - sqrt(-a)*x))/(sqrt(-a)*d + sqrt(b)*e))*log(d + e*x))/d^2 - (e*p*log(-((e*(sqrt(b) + sqrt(-a)*x))/(sqrt(-a)*d - sqrt(b)*e)))*log(d + e*x))/d^2 + (e*p*PolyLog(2, 1 + b/(a*x^2)))/(2*d^2) - (e*p*PolyLog(2, (sqrt(-a)*(d + e*x))/(sqrt(-a)*d - sqrt(b)*e)))/d^2 - (e*p*PolyLog(2, (sqrt(-a)*(d + e*x))/(sqrt(-a)*d + sqrt(b)*e)))/d^2 + (2*e*p*PolyLog(2, 1 + (e*x)/d))/d^2]
    @test_int [log(c*(a + b/x^2)^p)/(x^3*(d + e*x)), x, 25, p/(2*d*x^2) - (2*e*p)/(d^2*x) - (2*sqrt(a)*e*p*atan((sqrt(a)*x)/sqrt(b)))/(sqrt(b)*d^2) - ((a + b/x^2)*log(c*(a + b/x^2)^p))/(2*b*d) + (e*log(c*(a + b/x^2)^p))/(d^2*x) - (e^2*log(c*(a + b/x^2)^p)*log(-(b/(a*x^2))))/(2*d^3) - (e^2*log(c*(a + b/x^2)^p)*log(d + e*x))/d^3 - (2*e^2*p*log(-((e*x)/d))*log(d + e*x))/d^3 + (e^2*p*log((e*(sqrt(b) - sqrt(-a)*x))/(sqrt(-a)*d + sqrt(b)*e))*log(d + e*x))/d^3 + (e^2*p*log(-((e*(sqrt(b) + sqrt(-a)*x))/(sqrt(-a)*d - sqrt(b)*e)))*log(d + e*x))/d^3 - (e^2*p*PolyLog(2, 1 + b/(a*x^2)))/(2*d^3) + (e^2*p*PolyLog(2, (sqrt(-a)*(d + e*x))/(sqrt(-a)*d - sqrt(b)*e)))/d^3 + (e^2*p*PolyLog(2, (sqrt(-a)*(d + e*x))/(sqrt(-a)*d + sqrt(b)*e)))/d^3 - (2*e^2*p*PolyLog(2, 1 + (e*x)/d))/d^3]

    @test_int [x^3*log(c*(a + b/x^3)^p)/(d + e*x), x, 37, -((sqrt(3)*b^(1/3)*d^2*p*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(a^(1/3)*e^3)) + (sqrt(3)*b^(2/3)*d*p*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(2*a^(2/3)*e^2) + (d^2*x*log(c*(a + b/x^3)^p))/e^3 - (d*x^2*log(c*(a + b/x^3)^p))/(2*e^2) + (x^3*log(c*(a + b/x^3)^p))/(3*e) + (b^(1/3)*d^2*p*log(b^(1/3) + a^(1/3)*x))/(a^(1/3)*e^3) + (b^(2/3)*d*p*log(b^(1/3) + a^(1/3)*x))/(2*a^(2/3)*e^2) - (d^3*log(c*(a + b/x^3)^p)*log(d + e*x))/e^4 - (3*d^3*p*log(-((e*x)/d))*log(d + e*x))/e^4 + (d^3*p*log(-((e*(b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - b^(1/3)*e)))*log(d + e*x))/e^4 + (d^3*p*log(-((e*((-1)^(2/3)*b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)))*log(d + e*x))/e^4 + (d^3*p*log(((-1)^(1/3)*e*(b^(1/3) + (-1)^(2/3)*a^(1/3)*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e))*log(d + e*x))/e^4 - (b^(1/3)*d^2*p*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(2*a^(1/3)*e^3) - (b^(2/3)*d*p*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(4*a^(2/3)*e^2) + (b*p*log(b + a*x^3))/(3*a*e) + (d^3*p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)))/e^4 + (d^3*p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)))/e^4 + (d^3*p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)))/e^4 - (3*d^3*p*PolyLog(2, 1 + (e*x)/d))/e^4]
    @test_int [x^2*log(c*(a + b/x^3)^p)/(d + e*x), x, 34, (sqrt(3)*b^(1/3)*d*p*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(a^(1/3)*e^2) - (sqrt(3)*b^(2/3)*p*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(2*a^(2/3)*e) - (d*x*log(c*(a + b/x^3)^p))/e^2 + (x^2*log(c*(a + b/x^3)^p))/(2*e) - (b^(1/3)*d*p*log(b^(1/3) + a^(1/3)*x))/(a^(1/3)*e^2) - (b^(2/3)*p*log(b^(1/3) + a^(1/3)*x))/(2*a^(2/3)*e) + (d^2*log(c*(a + b/x^3)^p)*log(d + e*x))/e^3 + (3*d^2*p*log(-((e*x)/d))*log(d + e*x))/e^3 - (d^2*p*log(-((e*(b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - b^(1/3)*e)))*log(d + e*x))/e^3 - (d^2*p*log(-((e*((-1)^(2/3)*b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)))*log(d + e*x))/e^3 - (d^2*p*log(((-1)^(1/3)*e*(b^(1/3) + (-1)^(2/3)*a^(1/3)*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e))*log(d + e*x))/e^3 + (b^(1/3)*d*p*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(2*a^(1/3)*e^2) + (b^(2/3)*p*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(4*a^(2/3)*e) - (d^2*p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)))/e^3 - (d^2*p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)))/e^3 - (d^2*p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)))/e^3 + (3*d^2*p*PolyLog(2, 1 + (e*x)/d))/e^3]
    @test_int [x^1*log(c*(a + b/x^3)^p)/(d + e*x), x, 26, -((sqrt(3)*b^(1/3)*p*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(a^(1/3)*e)) + (x*log(c*(a + b/x^3)^p))/e + (b^(1/3)*p*log(b^(1/3) + a^(1/3)*x))/(a^(1/3)*e) - (d*log(c*(a + b/x^3)^p)*log(d + e*x))/e^2 - (3*d*p*log(-((e*x)/d))*log(d + e*x))/e^2 + (d*p*log(-((e*(b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - b^(1/3)*e)))*log(d + e*x))/e^2 + (d*p*log(-((e*((-1)^(2/3)*b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)))*log(d + e*x))/e^2 + (d*p*log(((-1)^(1/3)*e*(b^(1/3) + (-1)^(2/3)*a^(1/3)*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e))*log(d + e*x))/e^2 - (b^(1/3)*p*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(2*a^(1/3)*e) + (d*p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)))/e^2 + (d*p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)))/e^2 + (d*p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)))/e^2 - (3*d*p*PolyLog(2, 1 + (e*x)/d))/e^2]
    @test_int [x^0*log(c*(a + b/x^3)^p)/(d + e*x), x, 16, (log(c*(a + b/x^3)^p)*log(d + e*x))/e + (3*p*log(-((e*x)/d))*log(d + e*x))/e - (p*log(-((e*(b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - b^(1/3)*e)))*log(d + e*x))/e - (p*log(-((e*((-1)^(2/3)*b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)))*log(d + e*x))/e - (p*log(((-1)^(1/3)*e*(b^(1/3) + (-1)^(2/3)*a^(1/3)*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e))*log(d + e*x))/e - (p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)))/e - (p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)))/e - (p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)))/e + (3*p*PolyLog(2, 1 + (e*x)/d))/e]
    @test_int [log(c*(a + b/x^3)^p)/(x^1*(d + e*x)), x, 21, -((log(c*(a + b/x^3)^p)*log(-(b/(a*x^3))))/(3*d)) - (log(c*(a + b/x^3)^p)*log(d + e*x))/d - (3*p*log(-((e*x)/d))*log(d + e*x))/d + (p*log(-((e*(b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - b^(1/3)*e)))*log(d + e*x))/d + (p*log(-((e*((-1)^(2/3)*b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)))*log(d + e*x))/d + (p*log(((-1)^(1/3)*e*(b^(1/3) + (-1)^(2/3)*a^(1/3)*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e))*log(d + e*x))/d - (p*PolyLog(2, 1 + b/(a*x^3)))/(3*d) + (p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)))/d + (p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)))/d + (p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)))/d - (3*p*PolyLog(2, 1 + (e*x)/d))/d]
    @test_int [log(c*(a + b/x^3)^p)/(x^2*(d + e*x)), x, 30, (3*p)/(d*x) - (sqrt(3)*a^(1/3)*p*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(b^(1/3)*d) - log(c*(a + b/x^3)^p)/(d*x) + (e*log(c*(a + b/x^3)^p)*log(-(b/(a*x^3))))/(3*d^2) - (a^(1/3)*p*log(b^(1/3) + a^(1/3)*x))/(b^(1/3)*d) + (e*log(c*(a + b/x^3)^p)*log(d + e*x))/d^2 + (3*e*p*log(-((e*x)/d))*log(d + e*x))/d^2 - (e*p*log(-((e*(b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - b^(1/3)*e)))*log(d + e*x))/d^2 - (e*p*log(-((e*((-1)^(2/3)*b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)))*log(d + e*x))/d^2 - (e*p*log(((-1)^(1/3)*e*(b^(1/3) + (-1)^(2/3)*a^(1/3)*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e))*log(d + e*x))/d^2 + (a^(1/3)*p*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(2*b^(1/3)*d) + (e*p*PolyLog(2, 1 + b/(a*x^3)))/(3*d^2) - (e*p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)))/d^2 - (e*p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)))/d^2 - (e*p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)))/d^2 + (3*e*p*PolyLog(2, 1 + (e*x)/d))/d^2]
    @test_int [log(c*(a + b/x^3)^p)/(x^3*(d + e*x)), x, 39, (3*p)/(4*d*x^2) - (3*e*p)/(d^2*x) - (sqrt(3)*a^(2/3)*p*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(2*b^(2/3)*d) + (sqrt(3)*a^(1/3)*e*p*atan((b^(1/3) - 2*a^(1/3)*x)/(sqrt(3)*b^(1/3))))/(b^(1/3)*d^2) - log(c*(a + b/x^3)^p)/(2*d*x^2) + (e*log(c*(a + b/x^3)^p))/(d^2*x) - (e^2*log(c*(a + b/x^3)^p)*log(-(b/(a*x^3))))/(3*d^3) + (a^(2/3)*p*log(b^(1/3) + a^(1/3)*x))/(2*b^(2/3)*d) + (a^(1/3)*e*p*log(b^(1/3) + a^(1/3)*x))/(b^(1/3)*d^2) - (e^2*log(c*(a + b/x^3)^p)*log(d + e*x))/d^3 - (3*e^2*p*log(-((e*x)/d))*log(d + e*x))/d^3 + (e^2*p*log(-((e*(b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - b^(1/3)*e)))*log(d + e*x))/d^3 + (e^2*p*log(-((e*((-1)^(2/3)*b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)))*log(d + e*x))/d^3 + (e^2*p*log(((-1)^(1/3)*e*(b^(1/3) + (-1)^(2/3)*a^(1/3)*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e))*log(d + e*x))/d^3 - (a^(2/3)*p*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(4*b^(2/3)*d) - (a^(1/3)*e*p*log(b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2))/(2*b^(1/3)*d^2) - (e^2*p*PolyLog(2, 1 + b/(a*x^3)))/(3*d^3) + (e^2*p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)))/d^3 + (e^2*p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)))/d^3 + (e^2*p*PolyLog(2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)))/d^3 - (3*e^2*p*PolyLog(2, 1 + (e*x)/d))/d^3]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f+g*x^r)^q*log(c*(d+e*x^m)^n)^p=#

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

    #= ::Subsubsection:: =#
    #=q>0=#

    #= ::Subsubsection::Closed:: =#
    #=q<0=#

    @test_int [log(c*(d + e*x^3)^p)/(f + g*x^2), x, 16, (3*p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(sqrt(f)*sqrt(g)) - (p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f)*sqrt(g)*(d^(1/3) + e^(1/3)*x))/((im*e^(1/3)*sqrt(f) + d^(1/3)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(sqrt(f)*sqrt(g)) - (p*atan((sqrt(g)*x)/sqrt(f))*log(-((2*im*sqrt(f)*sqrt(g)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((e^(1/3)*sqrt(f) + (-1)^(1/6)*d^(1/3)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x)))))/(sqrt(f)*sqrt(g)) - (p*atan((sqrt(g)*x)/sqrt(f))*log((2*(-1)^(5/6)*sqrt(f)*sqrt(g)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((e^(1/3)*sqrt(f) + (-1)^(5/6)*d^(1/3)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(sqrt(f)*sqrt(g)) + (atan((sqrt(g)*x)/sqrt(f))*log(c*(d + e*x^3)^p))/(sqrt(f)*sqrt(g)) - (3*im*p*PolyLog(2, 1 - (2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(2*sqrt(f)*sqrt(g)) + (im*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*(d^(1/3) + e^(1/3)*x))/((im*e^(1/3)*sqrt(f) + d^(1/3)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*sqrt(f)*sqrt(g)) + (im*p*PolyLog(2, 1 + (2*im*sqrt(f)*sqrt(g)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((e^(1/3)*sqrt(f) + (-1)^(1/6)*d^(1/3)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*sqrt(f)*sqrt(g)) + (im*p*PolyLog(2, 1 - (2*(-1)^(5/6)*sqrt(f)*sqrt(g)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((e^(1/3)*sqrt(f) + (-1)^(5/6)*d^(1/3)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*sqrt(f)*sqrt(g))]
    @test_int [log(c*(d + e*x^2)^p)/(f + g*x^2), x, 12, (2*p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(sqrt(f)*sqrt(g)) - (p*atan((sqrt(g)*x)/sqrt(f))*log(-((2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x)))))/(sqrt(f)*sqrt(g)) - (p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(sqrt(f)*sqrt(g)) + (atan((sqrt(g)*x)/sqrt(f))*log(c*(d + e*x^2)^p))/(sqrt(f)*sqrt(g)) - (im*p*PolyLog(2, 1 - (2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(sqrt(f)*sqrt(g)) + (im*p*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*sqrt(f)*sqrt(g)) + (im*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*sqrt(f)*sqrt(g))]
    @test_int [log(c*(d + e*x^1)^p)/(f + g*x^2), x, 8, (log(c*(d + e*x)^p)*log((e*(sqrt(-f) - sqrt(g)*x))/(e*sqrt(-f) + d*sqrt(g))))/(2*sqrt(-f)*sqrt(g)) - (log(c*(d + e*x)^p)*log((e*(sqrt(-f) + sqrt(g)*x))/(e*sqrt(-f) - d*sqrt(g))))/(2*sqrt(-f)*sqrt(g)) - (p*PolyLog(2, -((sqrt(g)*(d + e*x))/(e*sqrt(-f) - d*sqrt(g)))))/(2*sqrt(-f)*sqrt(g)) + (p*PolyLog(2, (sqrt(g)*(d + e*x))/(e*sqrt(-f) + d*sqrt(g))))/(2*sqrt(-f)*sqrt(g))]
    @test_int [log(c*(d + e/x^1)^p)/(f + g*x^2), x, 12, (atan((sqrt(g)*x)/sqrt(f))*log(c*(d + e/x)^p))/(sqrt(f)*sqrt(g)) + (p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(sqrt(f)*sqrt(g)) - (p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f)*sqrt(g)*(e + d*x))/((im*d*sqrt(f) + e*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(sqrt(f)*sqrt(g)) + (im*p*PolyLog(2, -((im*sqrt(g)*x)/sqrt(f))))/(2*sqrt(f)*sqrt(g)) - (im*p*PolyLog(2, (im*sqrt(g)*x)/sqrt(f)))/(2*sqrt(f)*sqrt(g)) - (im*p*PolyLog(2, 1 - (2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(2*sqrt(f)*sqrt(g)) + (im*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*(e + d*x))/((im*d*sqrt(f) + e*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*sqrt(f)*sqrt(g))]
    @test_int [log(c*(d + e/x^2)^p)/(f + g*x^2), x, 18, (atan((sqrt(g)*x)/sqrt(f))*log(c*(d + e/x^2)^p))/(sqrt(f)*sqrt(g)) + (2*p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(sqrt(f)*sqrt(g)) - (p*atan((sqrt(g)*x)/sqrt(f))*log(-((2*sqrt(f)*sqrt(g)*(sqrt(e) - sqrt(-d)*x))/((im*sqrt(-d)*sqrt(f) - sqrt(e)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x)))))/(sqrt(f)*sqrt(g)) - (p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f)*sqrt(g)*(sqrt(e) + sqrt(-d)*x))/((im*sqrt(-d)*sqrt(f) + sqrt(e)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(sqrt(f)*sqrt(g)) + (im*p*PolyLog(2, -((im*sqrt(g)*x)/sqrt(f))))/(sqrt(f)*sqrt(g)) - (im*p*PolyLog(2, (im*sqrt(g)*x)/sqrt(f)))/(sqrt(f)*sqrt(g)) - (im*p*PolyLog(2, 1 - (2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(sqrt(f)*sqrt(g)) + (im*p*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*(sqrt(e) - sqrt(-d)*x))/((im*sqrt(-d)*sqrt(f) - sqrt(e)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*sqrt(f)*sqrt(g)) + (im*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*(sqrt(e) + sqrt(-d)*x))/((im*sqrt(-d)*sqrt(f) + sqrt(e)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*sqrt(f)*sqrt(g))]

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

    #= [log(c*(d + e*x^(3/2))^p)/(f + g*x^2), x, 43, (p*log(-((g^(1/4)*((-1)^(1/3)*d^(1/3) - e^(1/3)*sqrt(x)))/(e^(1/3)*sqrt(-sqrt(-f)) - (-1)^(1/3)*d^(1/3)*g^(1/4))))*log(sqrt(-sqrt(-f)) - g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) + (p*log((g^(1/4)*(d^(1/3) + e^(1/3)*sqrt(x)))/(e^(1/3)*sqrt(-sqrt(-f)) + d^(1/3)*g^(1/4)))*log(sqrt(-sqrt(-f)) - g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) + (p*log((g^(1/4)*((-1)^(2/3)*d^(1/3) + e^(1/3)*sqrt(x)))/(e^(1/3)*sqrt(-sqrt(-f)) + (-1)^(2/3)*d^(1/3)*g^(1/4)))*log(sqrt(-sqrt(-f)) - g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) - (p*log(-((g^(1/4)*((-1)^(1/3)*d^(1/3) - e^(1/3)*sqrt(x)))/(e^(1/3)*(-f)^(1/4) - (-1)^(1/3)*d^(1/3)*g^(1/4))))*log((-f)^(1/4) - g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) - (p*log((g^(1/4)*(d^(1/3) + e^(1/3)*sqrt(x)))/(e^(1/3)*(-f)^(1/4) + d^(1/3)*g^(1/4)))*log((-f)^(1/4) - g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) - (p*log((g^(1/4)*((-1)^(2/3)*d^(1/3) + e^(1/3)*sqrt(x)))/(e^(1/3)*(-f)^(1/4) + (-1)^(2/3)*d^(1/3)*g^(1/4)))*log((-f)^(1/4) - g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) + (p*log(-((g^(1/4)*(d^(1/3) + e^(1/3)*sqrt(x)))/(e^(1/3)*sqrt(-sqrt(-f)) - d^(1/3)*g^(1/4))))*log(sqrt(-sqrt(-f)) + g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) + (p*log(-((g^(1/4)*((-1)^(2/3)*d^(1/3) + e^(1/3)*sqrt(x)))/(e^(1/3)*sqrt(-sqrt(-f)) - (-1)^(2/3)*d^(1/3)*g^(1/4))))*log(sqrt(-sqrt(-f)) + g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) + (p*log(((-1)^(1/3)*g^(1/4)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*sqrt(x)))/(e^(1/3)*sqrt(-sqrt(-f)) + (-1)^(1/3)*d^(1/3)*g^(1/4)))*log(sqrt(-sqrt(-f)) + g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) - (p*log(-((g^(1/4)*(d^(1/3) + e^(1/3)*sqrt(x)))/(e^(1/3)*(-f)^(1/4) - d^(1/3)*g^(1/4))))*log((-f)^(1/4) + g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) - (p*log(-((g^(1/4)*((-1)^(2/3)*d^(1/3) + e^(1/3)*sqrt(x)))/(e^(1/3)*(-f)^(1/4) - (-1)^(2/3)*d^(1/3)*g^(1/4))))*log((-f)^(1/4) + g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) - (p*log(((-1)^(1/3)*g^(1/4)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*sqrt(x)))/(e^(1/3)*(-f)^(1/4) + (-1)^(1/3)*d^(1/3)*g^(1/4)))*log((-f)^(1/4) + g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) - (log(sqrt(-sqrt(-f)) - g^(1/4)*sqrt(x))*log(c*(d + e*x^(3/2))^p))/(2*sqrt(-f)*sqrt(g)) + (log((-f)^(1/4) - g^(1/4)*sqrt(x))*log(c*(d + e*x^(3/2))^p))/(2*sqrt(-f)*sqrt(g)) - (log(sqrt(-sqrt(-f)) + g^(1/4)*sqrt(x))*log(c*(d + e*x^(3/2))^p))/(2*sqrt(-f)*sqrt(g)) + (log((-f)^(1/4) + g^(1/4)*sqrt(x))*log(c*(d + e*x^(3/2))^p))/(2*sqrt(-f)*sqrt(g)) + (p*PolyLog(2, (e^(1/3)*(sqrt(-sqrt(-f)) - g^(1/4)*sqrt(x)))/(e^(1/3)*sqrt(-sqrt(-f)) + d^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) + (p*PolyLog(2, (e^(1/3)*(sqrt(-sqrt(-f)) - g^(1/4)*sqrt(x)))/(e^(1/3)*sqrt(-sqrt(-f)) - (-1)^(1/3)*d^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) + (p*PolyLog(2, (e^(1/3)*(sqrt(-sqrt(-f)) - g^(1/4)*sqrt(x)))/(e^(1/3)*sqrt(-sqrt(-f)) + (-1)^(2/3)*d^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) - (p*PolyLog(2, (e^(1/3)*((-f)^(1/4) - g^(1/4)*sqrt(x)))/(e^(1/3)*(-f)^(1/4) + d^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) - (p*PolyLog(2, (e^(1/3)*((-f)^(1/4) - g^(1/4)*sqrt(x)))/(e^(1/3)*(-f)^(1/4) - (-1)^(1/3)*d^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) - (p*PolyLog(2, (e^(1/3)*((-f)^(1/4) - g^(1/4)*sqrt(x)))/(e^(1/3)*(-f)^(1/4) + (-1)^(2/3)*d^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) + (p*PolyLog(2, (e^(1/3)*(sqrt(-sqrt(-f)) + g^(1/4)*sqrt(x)))/(e^(1/3)*sqrt(-sqrt(-f)) - d^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) + (p*PolyLog(2, (e^(1/3)*(sqrt(-sqrt(-f)) + g^(1/4)*sqrt(x)))/(e^(1/3)*sqrt(-sqrt(-f)) + (-1)^(1/3)*d^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) + (p*PolyLog(2, (e^(1/3)*(sqrt(-sqrt(-f)) + g^(1/4)*sqrt(x)))/(e^(1/3)*sqrt(-sqrt(-f)) - (-1)^(2/3)*d^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) - (p*PolyLog(2, (e^(1/3)*((-f)^(1/4) + g^(1/4)*sqrt(x)))/(e^(1/3)*(-f)^(1/4) - d^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) - (p*PolyLog(2, (e^(1/3)*((-f)^(1/4) + g^(1/4)*sqrt(x)))/(e^(1/3)*(-f)^(1/4) + (-1)^(1/3)*d^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) - (p*PolyLog(2, (e^(1/3)*((-f)^(1/4) + g^(1/4)*sqrt(x)))/(e^(1/3)*(-f)^(1/4) - (-1)^(2/3)*d^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g))] =#
    @test_int [log(c*(d + e*x^(1/2))^p)/(f + g*x^2), x, 19, -((log(c*(d + e*sqrt(x))^p)*log((e*(sqrt(-sqrt(-f)) - g^(1/4)*sqrt(x)))/(e*sqrt(-sqrt(-f)) + d*g^(1/4))))/(2*sqrt(-f)*sqrt(g))) + (log(c*(d + e*sqrt(x))^p)*log((e*((-f)^(1/4) - g^(1/4)*sqrt(x)))/(e*(-f)^(1/4) + d*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) - (log(c*(d + e*sqrt(x))^p)*log((e*(sqrt(-sqrt(-f)) + g^(1/4)*sqrt(x)))/(e*sqrt(-sqrt(-f)) - d*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) + (log(c*(d + e*sqrt(x))^p)*log((e*((-f)^(1/4) + g^(1/4)*sqrt(x)))/(e*(-f)^(1/4) - d*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) - (p*PolyLog(2, -((g^(1/4)*(d + e*sqrt(x)))/(e*sqrt(-sqrt(-f)) - d*g^(1/4)))))/(2*sqrt(-f)*sqrt(g)) + (p*PolyLog(2, -((g^(1/4)*(d + e*sqrt(x)))/(e*(-f)^(1/4) - d*g^(1/4)))))/(2*sqrt(-f)*sqrt(g)) - (p*PolyLog(2, (g^(1/4)*(d + e*sqrt(x)))/(e*sqrt(-sqrt(-f)) + d*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) + (p*PolyLog(2, (g^(1/4)*(d + e*sqrt(x)))/(e*(-f)^(1/4) + d*g^(1/4))))/(2*sqrt(-f)*sqrt(g))]
    @test_int [log(c*(d + e/x^(1/2))^p)/(f + g*x^2), x, 20, -((log(c*(d + e/sqrt(x))^p)*log((e*(g^(1/4) - sqrt(-sqrt(-f))/sqrt(x)))/(d*sqrt(-sqrt(-f)) + e*g^(1/4))))/(2*sqrt(-f)*sqrt(g))) - (log(c*(d + e/sqrt(x))^p)*log(-((e*(g^(1/4) + sqrt(-sqrt(-f))/sqrt(x)))/(d*sqrt(-sqrt(-f)) - e*g^(1/4)))))/(2*sqrt(-f)*sqrt(g)) + (log(c*(d + e/sqrt(x))^p)*log((e*(g^(1/4) - (-f)^(1/4)/sqrt(x)))/(d*(-f)^(1/4) + e*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) + (log(c*(d + e/sqrt(x))^p)*log(-((e*(g^(1/4) + (-f)^(1/4)/sqrt(x)))/(d*(-f)^(1/4) - e*g^(1/4)))))/(2*sqrt(-f)*sqrt(g)) - (p*PolyLog(2, (sqrt(-sqrt(-f))*(d + e/sqrt(x)))/(d*sqrt(-sqrt(-f)) - e*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) + (p*PolyLog(2, ((-f)^(1/4)*(d + e/sqrt(x)))/(d*(-f)^(1/4) - e*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) - (p*PolyLog(2, (sqrt(-sqrt(-f))*(d + e/sqrt(x)))/(d*sqrt(-sqrt(-f)) + e*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) + (p*PolyLog(2, ((-f)^(1/4)*(d + e/sqrt(x)))/(d*(-f)^(1/4) + e*g^(1/4))))/(2*sqrt(-f)*sqrt(g))]
    #= [log(c*(d + e/x^(3/2))^p)/(f + g*x^2), x, 0, -((log(c*(d + e/x^(3/2))^p)*log(sqrt(-sqrt(-f)) - g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g))) + (p*log(-((g^(1/4)*((-1)^(1/3)*e^(1/3) - d^(1/3)*sqrt(x)))/(d^(1/3)*sqrt(-sqrt(-f)) - (-1)^(1/3)*e^(1/3)*g^(1/4))))*log(sqrt(-sqrt(-f)) - g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) + (p*log((g^(1/4)*(e^(1/3) + d^(1/3)*sqrt(x)))/(d^(1/3)*sqrt(-sqrt(-f)) + e^(1/3)*g^(1/4)))*log(sqrt(-sqrt(-f)) - g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) + (p*log((g^(1/4)*((-1)^(2/3)*e^(1/3) + d^(1/3)*sqrt(x)))/(d^(1/3)*sqrt(-sqrt(-f)) + (-1)^(2/3)*e^(1/3)*g^(1/4)))*log(sqrt(-sqrt(-f)) - g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) + (log(c*(d + e/x^(3/2))^p)*log((-f)^(1/4) - g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) - (p*log(-((g^(1/4)*((-1)^(1/3)*e^(1/3) - d^(1/3)*sqrt(x)))/(d^(1/3)*(-f)^(1/4) - (-1)^(1/3)*e^(1/3)*g^(1/4))))*log((-f)^(1/4) - g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) - (p*log((g^(1/4)*(e^(1/3) + d^(1/3)*sqrt(x)))/(d^(1/3)*(-f)^(1/4) + e^(1/3)*g^(1/4)))*log((-f)^(1/4) - g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) - (p*log((g^(1/4)*((-1)^(2/3)*e^(1/3) + d^(1/3)*sqrt(x)))/(d^(1/3)*(-f)^(1/4) + (-1)^(2/3)*e^(1/3)*g^(1/4)))*log((-f)^(1/4) - g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) - (log(c*(d + e/x^(3/2))^p)*log(sqrt(-sqrt(-f)) + g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) + (p*log(-((g^(1/4)*(e^(1/3) + d^(1/3)*sqrt(x)))/(d^(1/3)*sqrt(-sqrt(-f)) - e^(1/3)*g^(1/4))))*log(sqrt(-sqrt(-f)) + g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) + (p*log(-((g^(1/4)*((-1)^(2/3)*e^(1/3) + d^(1/3)*sqrt(x)))/(d^(1/3)*sqrt(-sqrt(-f)) - (-1)^(2/3)*e^(1/3)*g^(1/4))))*log(sqrt(-sqrt(-f)) + g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) + (p*log(((-1)^(1/3)*g^(1/4)*(e^(1/3) + (-1)^(2/3)*d^(1/3)*sqrt(x)))/(d^(1/3)*sqrt(-sqrt(-f)) + (-1)^(1/3)*e^(1/3)*g^(1/4)))*log(sqrt(-sqrt(-f)) + g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) + (log(c*(d + e/x^(3/2))^p)*log((-f)^(1/4) + g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) - (p*log(-((g^(1/4)*(e^(1/3) + d^(1/3)*sqrt(x)))/(d^(1/3)*(-f)^(1/4) - e^(1/3)*g^(1/4))))*log((-f)^(1/4) + g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) - (p*log(-((g^(1/4)*((-1)^(2/3)*e^(1/3) + d^(1/3)*sqrt(x)))/(d^(1/3)*(-f)^(1/4) - (-1)^(2/3)*e^(1/3)*g^(1/4))))*log((-f)^(1/4) + g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) - (p*log(((-1)^(1/3)*g^(1/4)*(e^(1/3) + (-1)^(2/3)*d^(1/3)*sqrt(x)))/(d^(1/3)*(-f)^(1/4) + (-1)^(1/3)*e^(1/3)*g^(1/4)))*log((-f)^(1/4) + g^(1/4)*sqrt(x)))/(2*sqrt(-f)*sqrt(g)) - (3*p*log(sqrt(-sqrt(-f)) + g^(1/4)*sqrt(x))*log(-((g^(1/4)*sqrt(x))/sqrt(-sqrt(-f)))))/(2*sqrt(-f)*sqrt(g)) - (3*p*log(sqrt(-sqrt(-f)) - g^(1/4)*sqrt(x))*log((g^(1/4)*sqrt(x))/sqrt(-sqrt(-f))))/(2*sqrt(-f)*sqrt(g)) + (3*p*log((-f)^(1/4) + g^(1/4)*sqrt(x))*log(-((g^(1/4)*sqrt(x))/(-f)^(1/4))))/(2*sqrt(-f)*sqrt(g)) + (3*p*log((-f)^(1/4) - g^(1/4)*sqrt(x))*log((g^(1/4)*sqrt(x))/(-f)^(1/4)))/(2*sqrt(-f)*sqrt(g)) - (3*p*PolyLog(2, (sqrt(-sqrt(-f)) - g^(1/4)*sqrt(x))/sqrt(-sqrt(-f))))/(2*sqrt(-f)*sqrt(g)) + (p*PolyLog(2, (d^(1/3)*(sqrt(-sqrt(-f)) - g^(1/4)*sqrt(x)))/(d^(1/3)*sqrt(-sqrt(-f)) + e^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) + (p*PolyLog(2, (d^(1/3)*(sqrt(-sqrt(-f)) - g^(1/4)*sqrt(x)))/(d^(1/3)*sqrt(-sqrt(-f)) - (-1)^(1/3)*e^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) + (p*PolyLog(2, (d^(1/3)*(sqrt(-sqrt(-f)) - g^(1/4)*sqrt(x)))/(d^(1/3)*sqrt(-sqrt(-f)) + (-1)^(2/3)*e^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) + (3*p*PolyLog(2, ((-f)^(1/4) - g^(1/4)*sqrt(x))/(-f)^(1/4)))/(2*sqrt(-f)*sqrt(g)) - (p*PolyLog(2, (d^(1/3)*((-f)^(1/4) - g^(1/4)*sqrt(x)))/(d^(1/3)*(-f)^(1/4) + e^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) - (p*PolyLog(2, (d^(1/3)*((-f)^(1/4) - g^(1/4)*sqrt(x)))/(d^(1/3)*(-f)^(1/4) - (-1)^(1/3)*e^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) - (p*PolyLog(2, (d^(1/3)*((-f)^(1/4) - g^(1/4)*sqrt(x)))/(d^(1/3)*(-f)^(1/4) + (-1)^(2/3)*e^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) - (3*p*PolyLog(2, (sqrt(-sqrt(-f)) + g^(1/4)*sqrt(x))/sqrt(-sqrt(-f))))/(2*sqrt(-f)*sqrt(g)) + (p*PolyLog(2, (d^(1/3)*(sqrt(-sqrt(-f)) + g^(1/4)*sqrt(x)))/(d^(1/3)*sqrt(-sqrt(-f)) - e^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) + (p*PolyLog(2, (d^(1/3)*(sqrt(-sqrt(-f)) + g^(1/4)*sqrt(x)))/(d^(1/3)*sqrt(-sqrt(-f)) + (-1)^(1/3)*e^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) + (p*PolyLog(2, (d^(1/3)*(sqrt(-sqrt(-f)) + g^(1/4)*sqrt(x)))/(d^(1/3)*sqrt(-sqrt(-f)) - (-1)^(2/3)*e^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) + (3*p*PolyLog(2, ((-f)^(1/4) + g^(1/4)*sqrt(x))/(-f)^(1/4)))/(2*sqrt(-f)*sqrt(g)) - (p*PolyLog(2, (d^(1/3)*((-f)^(1/4) + g^(1/4)*sqrt(x)))/(d^(1/3)*(-f)^(1/4) - e^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) - (p*PolyLog(2, (d^(1/3)*((-f)^(1/4) + g^(1/4)*sqrt(x)))/(d^(1/3)*(-f)^(1/4) + (-1)^(1/3)*e^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g)) - (p*PolyLog(2, (d^(1/3)*((-f)^(1/4) + g^(1/4)*sqrt(x)))/(d^(1/3)*(-f)^(1/4) - (-1)^(2/3)*e^(1/3)*g^(1/4))))/(2*sqrt(-f)*sqrt(g))] =#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f+g*x^2)^q*log(c*(d+e*x^2)^n)^p=#

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

    @test_int [(f + g*x^2)^3*log(c*(d + e*x^2)^p), x, 17, -2*f^3*p*x + (2*d*f^2*g*p*x)/e - (6*d^2*f*g^2*p*x)/(5*e^2) + (2*d^3*g^3*p*x)/(7*e^3) - (2/3)*f^2*g*p*x^3 + (2*d*f*g^2*p*x^3)/(5*e) - (2*d^2*g^3*p*x^3)/(21*e^2) - (6/25)*f*g^2*p*x^5 + (2*d*g^3*p*x^5)/(35*e) - (2/49)*g^3*p*x^7 + (2*sqrt(d)*f^3*p*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) - (2*d^(3/2)*f^2*g*p*atan((sqrt(e)*x)/sqrt(d)))/e^(3/2) + (6*d^(5/2)*f*g^2*p*atan((sqrt(e)*x)/sqrt(d)))/(5*e^(5/2)) - (2*d^(7/2)*g^3*p*atan((sqrt(e)*x)/sqrt(d)))/(7*e^(7/2)) + f^3*x*log(c*(d + e*x^2)^p) + f^2*g*x^3*log(c*(d + e*x^2)^p) + (3/5)*f*g^2*x^5*log(c*(d + e*x^2)^p) + (1/7)*g^3*x^7*log(c*(d + e*x^2)^p)]
    @test_int [(f + g*x^2)^2*log(c*(d + e*x^2)^p), x, 13, -2*f^2*p*x + (4*d*f*g*p*x)/(3*e) - (2*d^2*g^2*p*x)/(5*e^2) - (4/9)*f*g*p*x^3 + (2*d*g^2*p*x^3)/(15*e) - (2/25)*g^2*p*x^5 + (2*sqrt(d)*f^2*p*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) - (4*d^(3/2)*f*g*p*atan((sqrt(e)*x)/sqrt(d)))/(3*e^(3/2)) + (2*d^(5/2)*g^2*p*atan((sqrt(e)*x)/sqrt(d)))/(5*e^(5/2)) + f^2*x*log(c*(d + e*x^2)^p) + (2/3)*f*g*x^3*log(c*(d + e*x^2)^p) + (1/5)*g^2*x^5*log(c*(d + e*x^2)^p)]
    @test_int [(f + g*x^2)^1*log(c*(d + e*x^2)^p), x, 9, -2*f*p*x + (2*d*g*p*x)/(3*e) - (2/9)*g*p*x^3 + (2*sqrt(d)*f*p*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) - (2*d^(3/2)*g*p*atan((sqrt(e)*x)/sqrt(d)))/(3*e^(3/2)) + f*x*log(c*(d + e*x^2)^p) + (1/3)*g*x^3*log(c*(d + e*x^2)^p)]
    @test_int [log(c*(d + e*x^2)^p)/(f + g*x^2)^1, x, 12, (2*p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(sqrt(f)*sqrt(g)) - (p*atan((sqrt(g)*x)/sqrt(f))*log(-((2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x)))))/(sqrt(f)*sqrt(g)) - (p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(sqrt(f)*sqrt(g)) + (atan((sqrt(g)*x)/sqrt(f))*log(c*(d + e*x^2)^p))/(sqrt(f)*sqrt(g)) - (im*p*PolyLog(2, 1 - (2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(sqrt(f)*sqrt(g)) + (im*p*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*sqrt(f)*sqrt(g)) + (im*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*sqrt(f)*sqrt(g))]
    @test_int [log(c*(d + e*x^2)^p)/(f + g*x^2)^2, x, 26, (sqrt(d)*sqrt(e)*p*atan((sqrt(e)*x)/sqrt(d)))/(f*(e*f - d*g)) - (e*p*log(sqrt(-f) - sqrt(g)*x))/(2*sqrt(-f)*sqrt(g)*(e*f - d*g)) + (p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(f^(3/2)*sqrt(g)) - (p*atan((sqrt(g)*x)/sqrt(f))*log(-((2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x)))))/(2*f^(3/2)*sqrt(g)) - (p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*f^(3/2)*sqrt(g)) + (e*p*log(sqrt(-f) + sqrt(g)*x))/(2*sqrt(-f)*sqrt(g)*(e*f - d*g)) - log(c*(d + e*x^2)^p)/(4*f*sqrt(g)*(sqrt(-f) - sqrt(g)*x)) + log(c*(d + e*x^2)^p)/(4*f*sqrt(g)*(sqrt(-f) + sqrt(g)*x)) + (atan((sqrt(g)*x)/sqrt(f))*log(c*(d + e*x^2)^p))/(2*f^(3/2)*sqrt(g)) - (im*p*PolyLog(2, 1 - (2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(2*f^(3/2)*sqrt(g)) + (im*p*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(4*f^(3/2)*sqrt(g)) + (im*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(4*f^(3/2)*sqrt(g))]

    @test_int [(f + g*x^2)^2*log(c*(d + e*x^2)^p)^2, x, 50, 8*f^2*p^2*x - (64*d*f*g*p^2*x)/(9*e) + (184*d^2*g^2*p^2*x)/(75*e^2) + (16/27)*f*g*p^2*x^3 - (64*d*g^2*p^2*x^3)/(225*e) + (8/125)*g^2*p^2*x^5 - (8*sqrt(d)*f^2*p^2*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) + (64*d^(3/2)*f*g*p^2*atan((sqrt(e)*x)/sqrt(d)))/(9*e^(3/2)) - (184*d^(5/2)*g^2*p^2*atan((sqrt(e)*x)/sqrt(d)))/(75*e^(5/2)) + (4*im*sqrt(d)*f^2*p^2*atan((sqrt(e)*x)/sqrt(d))^2)/sqrt(e) - (8*im*d^(3/2)*f*g*p^2*atan((sqrt(e)*x)/sqrt(d))^2)/(3*e^(3/2)) + (4*im*d^(5/2)*g^2*p^2*atan((sqrt(e)*x)/sqrt(d))^2)/(5*e^(5/2)) + (8*sqrt(d)*f^2*p^2*atan((sqrt(e)*x)/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/sqrt(e) - (16*d^(3/2)*f*g*p^2*atan((sqrt(e)*x)/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/(3*e^(3/2)) + (8*d^(5/2)*g^2*p^2*atan((sqrt(e)*x)/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/(5*e^(5/2)) - 4*f^2*p*x*log(c*(d + e*x^2)^p) + (8*d*f*g*p*x*log(c*(d + e*x^2)^p))/(3*e) - (4*d^2*g^2*p*x*log(c*(d + e*x^2)^p))/(5*e^2) - (8/9)*f*g*p*x^3*log(c*(d + e*x^2)^p) + (4*d*g^2*p*x^3*log(c*(d + e*x^2)^p))/(15*e) - (4/25)*g^2*p*x^5*log(c*(d + e*x^2)^p) + (4*sqrt(d)*f^2*p*atan((sqrt(e)*x)/sqrt(d))*log(c*(d + e*x^2)^p))/sqrt(e) - (8*d^(3/2)*f*g*p*atan((sqrt(e)*x)/sqrt(d))*log(c*(d + e*x^2)^p))/(3*e^(3/2)) + (4*d^(5/2)*g^2*p*atan((sqrt(e)*x)/sqrt(d))*log(c*(d + e*x^2)^p))/(5*e^(5/2)) + f^2*x*log(c*(d + e*x^2)^p)^2 + (2/3)*f*g*x^3*log(c*(d + e*x^2)^p)^2 + (1/5)*g^2*x^5*log(c*(d + e*x^2)^p)^2 + (4*im*sqrt(d)*f^2*p^2*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/sqrt(e) - (8*im*d^(3/2)*f*g*p^2*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/(3*e^(3/2)) + (4*im*d^(5/2)*g^2*p^2*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/(5*e^(5/2))]
    @test_int [(f + g*x^2)^1*log(c*(d + e*x^2)^p)^2, x, 30, 8*f*p^2*x - (32*d*g*p^2*x)/(9*e) + (8/27)*g*p^2*x^3 - (8*sqrt(d)*f*p^2*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) + (32*d^(3/2)*g*p^2*atan((sqrt(e)*x)/sqrt(d)))/(9*e^(3/2)) + (4*im*sqrt(d)*f*p^2*atan((sqrt(e)*x)/sqrt(d))^2)/sqrt(e) - (4*im*d^(3/2)*g*p^2*atan((sqrt(e)*x)/sqrt(d))^2)/(3*e^(3/2)) + (8*sqrt(d)*f*p^2*atan((sqrt(e)*x)/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/sqrt(e) - (8*d^(3/2)*g*p^2*atan((sqrt(e)*x)/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/(3*e^(3/2)) - 4*f*p*x*log(c*(d + e*x^2)^p) + (4*d*g*p*x*log(c*(d + e*x^2)^p))/(3*e) - (4/9)*g*p*x^3*log(c*(d + e*x^2)^p) + (4*sqrt(d)*f*p*atan((sqrt(e)*x)/sqrt(d))*log(c*(d + e*x^2)^p))/sqrt(e) - (4*d^(3/2)*g*p*atan((sqrt(e)*x)/sqrt(d))*log(c*(d + e*x^2)^p))/(3*e^(3/2)) + f*x*log(c*(d + e*x^2)^p)^2 + (1/3)*g*x^3*log(c*(d + e*x^2)^p)^2 + (4*im*sqrt(d)*f*p^2*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/sqrt(e) - (4*im*d^(3/2)*g*p^2*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/(3*e^(3/2))]
    @test_int [log(c*(d + e*x^2)^p)^2/(f + g*x^2)^1, x, 0, Unintegrable(log(c*(d + e*x^2)^p)^2/(f + g*x^2), x)]
    @test_int [log(c*(d + e*x^2)^p)^2/(f + g*x^2)^2, x, 0, Unintegrable(log(c*(d + e*x^2)^p)^2/(f + g*x^2)^2, x)]

    @test_int [(f + g*x^2)^1*log(c*(d + e*x^2)^p)^3, x, 48, -48*f*p^3*x + (208*d*g*p^3*x)/(9*e) - (16/27)*g*p^3*x^3 + (48*sqrt(d)*f*p^3*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) - (208*d^(3/2)*g*p^3*atan((sqrt(e)*x)/sqrt(d)))/(9*e^(3/2)) - (24*im*sqrt(d)*f*p^3*atan((sqrt(e)*x)/sqrt(d))^2)/sqrt(e) + (32*im*d^(3/2)*g*p^3*atan((sqrt(e)*x)/sqrt(d))^2)/(3*e^(3/2)) - (48*sqrt(d)*f*p^3*atan((sqrt(e)*x)/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/sqrt(e) + (64*d^(3/2)*g*p^3*atan((sqrt(e)*x)/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/(3*e^(3/2)) + 24*f*p^2*x*log(c*(d + e*x^2)^p) - (32*d*g*p^2*x*log(c*(d + e*x^2)^p))/(3*e) + (8/9)*g*p^2*x^3*log(c*(d + e*x^2)^p) - (24*sqrt(d)*f*p^2*atan((sqrt(e)*x)/sqrt(d))*log(c*(d + e*x^2)^p))/sqrt(e) + (32*d^(3/2)*g*p^2*atan((sqrt(e)*x)/sqrt(d))*log(c*(d + e*x^2)^p))/(3*e^(3/2)) - 6*f*p*x*log(c*(d + e*x^2)^p)^2 + (2*d*g*p*x*log(c*(d + e*x^2)^p)^2)/e - (2/3)*g*p*x^3*log(c*(d + e*x^2)^p)^2 + f*x*log(c*(d + e*x^2)^p)^3 + (1/3)*g*x^3*log(c*(d + e*x^2)^p)^3 - (24*im*sqrt(d)*f*p^3*PolyLog(2, -((sqrt(d) - im*sqrt(e)*x)/(sqrt(d) + im*sqrt(e)*x))))/sqrt(e) + (32*im*d^(3/2)*g*p^3*PolyLog(2, -((sqrt(d) - im*sqrt(e)*x)/(sqrt(d) + im*sqrt(e)*x))))/(3*e^(3/2)) - (2*d*(-3*e*f + d*g)*p*Unintegrable(log(c*(d + e*x^2)^p)^2/(d + e*x^2), x))/e, -48*f*p^3*x + (208*d*g*p^3*x)/(9*e) - (16/27)*g*p^3*x^3 + (48*sqrt(d)*f*p^3*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) - (208*d^(3/2)*g*p^3*atan((sqrt(e)*x)/sqrt(d)))/(9*e^(3/2)) - (24*im*sqrt(d)*f*p^3*atan((sqrt(e)*x)/sqrt(d))^2)/sqrt(e) + (32*im*d^(3/2)*g*p^3*atan((sqrt(e)*x)/sqrt(d))^2)/(3*e^(3/2)) - (48*sqrt(d)*f*p^3*atan((sqrt(e)*x)/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/sqrt(e) + (64*d^(3/2)*g*p^3*atan((sqrt(e)*x)/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/(3*e^(3/2)) + 24*f*p^2*x*log(c*(d + e*x^2)^p) - (32*d*g*p^2*x*log(c*(d + e*x^2)^p))/(3*e) + (8/9)*g*p^2*x^3*log(c*(d + e*x^2)^p) - (24*sqrt(d)*f*p^2*atan((sqrt(e)*x)/sqrt(d))*log(c*(d + e*x^2)^p))/sqrt(e) + (32*d^(3/2)*g*p^2*atan((sqrt(e)*x)/sqrt(d))*log(c*(d + e*x^2)^p))/(3*e^(3/2)) - 6*f*p*x*log(c*(d + e*x^2)^p)^2 + (2*d*g*p*x*log(c*(d + e*x^2)^p)^2)/e - (2/3)*g*p*x^3*log(c*(d + e*x^2)^p)^2 + f*x*log(c*(d + e*x^2)^p)^3 + (1/3)*g*x^3*log(c*(d + e*x^2)^p)^3 - (24*im*sqrt(d)*f*p^3*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/sqrt(e) + (32*im*d^(3/2)*g*p^3*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/(3*e^(3/2)) + 6*d*f*p*Unintegrable(log(c*(d + e*x^2)^p)^2/(d + e*x^2), x) - (2*d^2*g*p*Unintegrable(log(c*(d + e*x^2)^p)^2/(d + e*x^2), x))/e]
    @test_int [log(c*(d + e*x^2)^p)^3/(f + g*x^2)^1, x, 0, Unintegrable(log(c*(d + e*x^2)^p)^3/(f + g*x^2), x)]
    @test_int [log(c*(d + e*x^2)^p)^3/(f + g*x^2)^2, x, 0, Unintegrable(log(c*(d + e*x^2)^p)^3/(f + g*x^2)^2, x)]

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

    @test_int [(f + g*x^2)^2/log(c*(d + e*x^2)^p), x, 0, Unintegrable((f + g*x^2)^2/log(c*(d + e*x^2)^p), x)]
    @test_int [(f + g*x^2)^1/log(c*(d + e*x^2)^p), x, 0, Unintegrable((f + g*x^2)/log(c*(d + e*x^2)^p), x)]
    @test_int [1/((f + g*x^2)^1*log(c*(d + e*x^2)^p)), x, 0, Unintegrable(1/((f + g*x^2)*log(c*(d + e*x^2)^p)), x)]
    @test_int [1/((f + g*x^2)^2*log(c*(d + e*x^2)^p)), x, 0, Unintegrable(1/((f + g*x^2)^2*log(c*(d + e*x^2)^p)), x)]

    @test_int [(f + g*x^2)^2/log(c*(d + e*x^2)^p)^2, x, 0, Unintegrable((f + g*x^2)^2/log(c*(d + e*x^2)^p)^2, x)]
    @test_int [(f + g*x^2)^1/log(c*(d + e*x^2)^p)^2, x, 0, Unintegrable((f + g*x^2)/log(c*(d + e*x^2)^p)^2, x)]
    @test_int [1/((f + g*x^2)^1*log(c*(d + e*x^2)^p)^2), x, 0, Unintegrable(1/((f + g*x^2)*log(c*(d + e*x^2)^p)^2), x)]
    @test_int [1/((f + g*x^2)^2*log(c*(d + e*x^2)^p)^2), x, 0, Unintegrable(1/((f + g*x^2)^2*log(c*(d + e*x^2)^p)^2), x)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f+g*x^3)^q*log(c*(d+e*x^2)^n)^p=#

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

    @test_int [(f + g*x^3)^3*log(c*(d + e*x^2)^p), x, 17, -2*f^3*p*x + (6*d^3*f*g^2*p*x)/(7*e^3) + (3*d*f^2*g*p*x^2)/(4*e) - (d^4*g^3*p*x^2)/(10*e^4) - (2*d^2*f*g^2*p*x^3)/(7*e^2) - (3/8)*f^2*g*p*x^4 + (d^3*g^3*p*x^4)/(20*e^3) + (6*d*f*g^2*p*x^5)/(35*e) - (d^2*g^3*p*x^6)/(30*e^2) - (6/49)*f*g^2*p*x^7 + (d*g^3*p*x^8)/(40*e) - (1/50)*g^3*p*x^10 + (2*sqrt(d)*f^3*p*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) - (6*d^(7/2)*f*g^2*p*atan((sqrt(e)*x)/sqrt(d)))/(7*e^(7/2)) - (3*d^2*f^2*g*p*log(d + e*x^2))/(4*e^2) + (d^5*g^3*p*log(d + e*x^2))/(10*e^5) + f^3*x*log(c*(d + e*x^2)^p) + (3/4)*f^2*g*x^4*log(c*(d + e*x^2)^p) + (3/7)*f*g^2*x^7*log(c*(d + e*x^2)^p) + (1/10)*g^3*x^10*log(c*(d + e*x^2)^p)]
    @test_int [(f + g*x^3)^2*log(c*(d + e*x^2)^p), x, 13, -2*f^2*p*x + (2*d^3*g^2*p*x)/(7*e^3) + (d*f*g*p*x^2)/(2*e) - (2*d^2*g^2*p*x^3)/(21*e^2) - (1/4)*f*g*p*x^4 + (2*d*g^2*p*x^5)/(35*e) - (2/49)*g^2*p*x^7 + (2*sqrt(d)*f^2*p*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) - (2*d^(7/2)*g^2*p*atan((sqrt(e)*x)/sqrt(d)))/(7*e^(7/2)) - (d^2*f*g*p*log(d + e*x^2))/(2*e^2) + f^2*x*log(c*(d + e*x^2)^p) + (1/2)*f*g*x^4*log(c*(d + e*x^2)^p) + (1/7)*g^2*x^7*log(c*(d + e*x^2)^p)]
    @test_int [(f + g*x^3)^1*log(c*(d + e*x^2)^p), x, 9, -2*f*p*x + (d*g*p*x^2)/(4*e) - (1/8)*g*p*x^4 + (2*sqrt(d)*f*p*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) - (d^2*g*p*log(d + e*x^2))/(4*e^2) + f*x*log(c*(d + e*x^2)^p) + (1/4)*g*x^4*log(c*(d + e*x^2)^p)]
    @test_int [log(c*(d + e*x^2)^p)/(f + g*x^3)^1, x, 29, -((p*log((g^(1/3)*(sqrt(-d) - sqrt(e)*x))/(sqrt(e)*f^(1/3) + sqrt(-d)*g^(1/3)))*log(-f^(1/3) - g^(1/3)*x))/(3*f^(2/3)*g^(1/3))) - (p*log(-((g^(1/3)*(sqrt(-d) + sqrt(e)*x))/(sqrt(e)*f^(1/3) - sqrt(-d)*g^(1/3))))*log(-f^(1/3) - g^(1/3)*x))/(3*f^(2/3)*g^(1/3)) - ((-1)^(2/3)*p*log(-(((-1)^(1/3)*g^(1/3)*(sqrt(-d) - sqrt(e)*x))/(sqrt(e)*f^(1/3) - (-1)^(1/3)*sqrt(-d)*g^(1/3))))*log(-f^(1/3) + (-1)^(1/3)*g^(1/3)*x))/(3*f^(2/3)*g^(1/3)) - ((-1)^(2/3)*p*log(((-1)^(1/3)*g^(1/3)*(sqrt(-d) + sqrt(e)*x))/(sqrt(e)*f^(1/3) + (-1)^(1/3)*sqrt(-d)*g^(1/3)))*log(-f^(1/3) + (-1)^(1/3)*g^(1/3)*x))/(3*f^(2/3)*g^(1/3)) + ((-1)^(1/3)*p*log(((-1)^(2/3)*g^(1/3)*(sqrt(-d) - sqrt(e)*x))/(sqrt(e)*f^(1/3) + (-1)^(2/3)*sqrt(-d)*g^(1/3)))*log(-f^(1/3) - (-1)^(2/3)*g^(1/3)*x))/(3*f^(2/3)*g^(1/3)) + ((-1)^(1/3)*p*log(-(((-1)^(2/3)*g^(1/3)*(sqrt(-d) + sqrt(e)*x))/(sqrt(e)*f^(1/3) - (-1)^(2/3)*sqrt(-d)*g^(1/3))))*log(-f^(1/3) - (-1)^(2/3)*g^(1/3)*x))/(3*f^(2/3)*g^(1/3)) + (log(-f^(1/3) - g^(1/3)*x)*log(c*(d + e*x^2)^p))/(3*f^(2/3)*g^(1/3)) + ((-1)^(2/3)*log(-f^(1/3) + (-1)^(1/3)*g^(1/3)*x)*log(c*(d + e*x^2)^p))/(3*f^(2/3)*g^(1/3)) - ((-1)^(1/3)*log(-f^(1/3) - (-1)^(2/3)*g^(1/3)*x)*log(c*(d + e*x^2)^p))/(3*f^(2/3)*g^(1/3)) - (p*PolyLog(2, (sqrt(e)*(f^(1/3) + g^(1/3)*x))/(sqrt(e)*f^(1/3) - sqrt(-d)*g^(1/3))))/(3*f^(2/3)*g^(1/3)) - (p*PolyLog(2, (sqrt(e)*(f^(1/3) + g^(1/3)*x))/(sqrt(e)*f^(1/3) + sqrt(-d)*g^(1/3))))/(3*f^(2/3)*g^(1/3)) - ((-1)^(2/3)*p*PolyLog(2, (sqrt(e)*(f^(1/3) - (-1)^(1/3)*g^(1/3)*x))/(sqrt(e)*f^(1/3) - (-1)^(1/3)*sqrt(-d)*g^(1/3))))/(3*f^(2/3)*g^(1/3)) - ((-1)^(2/3)*p*PolyLog(2, (sqrt(e)*(f^(1/3) - (-1)^(1/3)*g^(1/3)*x))/(sqrt(e)*f^(1/3) + (-1)^(1/3)*sqrt(-d)*g^(1/3))))/(3*f^(2/3)*g^(1/3)) + ((-1)^(1/3)*p*PolyLog(2, (sqrt(e)*(f^(1/3) + (-1)^(2/3)*g^(1/3)*x))/(sqrt(e)*f^(1/3) - (-1)^(2/3)*sqrt(-d)*g^(1/3))))/(3*f^(2/3)*g^(1/3)) + ((-1)^(1/3)*p*PolyLog(2, (sqrt(e)*(f^(1/3) + (-1)^(2/3)*g^(1/3)*x))/(sqrt(e)*f^(1/3) + (-1)^(2/3)*sqrt(-d)*g^(1/3))))/(3*f^(2/3)*g^(1/3))]
    @test_int [log(c*(d + e*x^2)^p)/(f + g*x^3)^2, x, 47, If(13>=8, (2*sqrt(d)*sqrt(e)*p*atan((sqrt(e)*x)/sqrt(d)))/(9*f^(4/3)*(e*f^(2/3) + d*g^(2/3))) + (2*(-1)^(2/3)*sqrt(d)*sqrt(e)*p*atan((sqrt(e)*x)/sqrt(d)))/((1 + (-1)^(1/3))^4*f^(4/3)*(e*f^(2/3) + (-1)^(2/3)*d*g^(2/3))) + (4*sqrt(d)*sqrt(e)*p*atan((sqrt(e)*x)/sqrt(d)))/(9*f^(4/3)*(2*e*f^(2/3) - (1 + im*sqrt(3))*d*g^(2/3))) - (2*e*p*log(f^(1/3) + g^(1/3)*x))/(9*f*(e*f^(2/3) + d*g^(2/3))*g^(1/3)) - (2*p*log((g^(1/3)*(sqrt(-d) - sqrt(e)*x))/(sqrt(e)*f^(1/3) + sqrt(-d)*g^(1/3)))*log(f^(1/3) + g^(1/3)*x))/(9*f^(5/3)*g^(1/3)) - (2*p*log(-((g^(1/3)*(sqrt(-d) + sqrt(e)*x))/(sqrt(e)*f^(1/3) - sqrt(-d)*g^(1/3))))*log(f^(1/3) + g^(1/3)*x))/(9*f^(5/3)*g^(1/3)) + (2*(-1)^(1/3)*e*p*log(f^(1/3) - (-1)^(1/3)*g^(1/3)*x))/((1 + (-1)^(1/3))^4*f*(e*f^(2/3) + (-1)^(2/3)*d*g^(2/3))*g^(1/3)) + (2*im*sqrt(3)*p*log(-(((-1)^(1/3)*g^(1/3)*(sqrt(-d) - sqrt(e)*x))/(sqrt(e)*f^(1/3) - (-1)^(1/3)*sqrt(-d)*g^(1/3))))*log(-f^(1/3) + (-1)^(1/3)*g^(1/3)*x))/((1 + (-1)^(1/3))^5*f^(5/3)*g^(1/3)) + (2*im*sqrt(3)*p*log(((-1)^(1/3)*g^(1/3)*(sqrt(-d) + sqrt(e)*x))/(sqrt(e)*f^(1/3) + (-1)^(1/3)*sqrt(-d)*g^(1/3)))*log(-f^(1/3) + (-1)^(1/3)*g^(1/3)*x))/((1 + (-1)^(1/3))^5*f^(5/3)*g^(1/3)) + (4*(-1)^(1/3)*e*p*log(f^(1/3) + (-1)^(2/3)*g^(1/3)*x))/(9*f*(2*e*f^(2/3) - (1 + im*sqrt(3))*d*g^(2/3))*g^(1/3)) - (2*p*log(((-1)^(2/3)*g^(1/3)*(sqrt(-d) - sqrt(e)*x))/(sqrt(e)*f^(1/3) + (-1)^(2/3)*sqrt(-d)*g^(1/3)))*log(f^(1/3) + (-1)^(2/3)*g^(1/3)*x))/((1 + (-1)^(1/3))^4*f^(5/3)*g^(1/3)) - (2*p*log(-(((-1)^(2/3)*g^(1/3)*(sqrt(-d) + sqrt(e)*x))/(sqrt(e)*f^(1/3) - (-1)^(2/3)*sqrt(-d)*g^(1/3))))*log(f^(1/3) + (-1)^(2/3)*g^(1/3)*x))/((1 + (-1)^(1/3))^4*f^(5/3)*g^(1/3)) + (e*p*log(d + e*x^2))/(9*f*(e*f^(2/3) + d*g^(2/3))*g^(1/3)) - ((-1)^(1/3)*e*p*log(d + e*x^2))/((1 + (-1)^(1/3))^4*f*(e*f^(2/3) + (-1)^(2/3)*d*g^(2/3))*g^(1/3)) - (2*(-1)^(1/3)*e*p*log(d + e*x^2))/(9*f*(2*e*f^(2/3) - (1 + im*sqrt(3))*d*g^(2/3))*g^(1/3)) - log(c*(d + e*x^2)^p)/(9*f^(4/3)*g^(1/3)*(f^(1/3) + g^(1/3)*x)) - log(c*(d + e*x^2)^p)/((1 + (-1)^(1/3))^4*f^(4/3)*g^(1/3)*((-1)^(2/3)*f^(1/3) + g^(1/3)*x)) + ((-1)^(1/3)*log(c*(d + e*x^2)^p))/(9*f^(4/3)*g^(1/3)*(f^(1/3) + (-1)^(2/3)*g^(1/3)*x)) + (2*log(f^(1/3) + g^(1/3)*x)*log(c*(d + e*x^2)^p))/(9*f^(5/3)*g^(1/3)) - (2*im*sqrt(3)*log(-f^(1/3) + (-1)^(1/3)*g^(1/3)*x)*log(c*(d + e*x^2)^p))/((1 + (-1)^(1/3))^5*f^(5/3)*g^(1/3)) + (2*log(f^(1/3) + (-1)^(2/3)*g^(1/3)*x)*log(c*(d + e*x^2)^p))/((1 + (-1)^(1/3))^4*f^(5/3)*g^(1/3)) - (2*p*PolyLog(2, (sqrt(e)*(f^(1/3) + g^(1/3)*x))/(sqrt(e)*f^(1/3) - sqrt(-d)*g^(1/3))))/(9*f^(5/3)*g^(1/3)) - (2*p*PolyLog(2, (sqrt(e)*(f^(1/3) + g^(1/3)*x))/(sqrt(e)*f^(1/3) + sqrt(-d)*g^(1/3))))/(9*f^(5/3)*g^(1/3)) + (2*im*sqrt(3)*p*PolyLog(2, (sqrt(e)*(f^(1/3) - (-1)^(1/3)*g^(1/3)*x))/(sqrt(e)*f^(1/3) - (-1)^(1/3)*sqrt(-d)*g^(1/3))))/((1 + (-1)^(1/3))^5*f^(5/3)*g^(1/3)) + (2*im*sqrt(3)*p*PolyLog(2, (sqrt(e)*(f^(1/3) - (-1)^(1/3)*g^(1/3)*x))/(sqrt(e)*f^(1/3) + (-1)^(1/3)*sqrt(-d)*g^(1/3))))/((1 + (-1)^(1/3))^5*f^(5/3)*g^(1/3)) - (2*p*PolyLog(2, (sqrt(e)*(f^(1/3) + (-1)^(2/3)*g^(1/3)*x))/(sqrt(e)*f^(1/3) - (-1)^(2/3)*sqrt(-d)*g^(1/3))))/((1 + (-1)^(1/3))^4*f^(5/3)*g^(1/3)) - (2*p*PolyLog(2, (sqrt(e)*(f^(1/3) + (-1)^(2/3)*g^(1/3)*x))/(sqrt(e)*f^(1/3) + (-1)^(2/3)*sqrt(-d)*g^(1/3))))/((1 + (-1)^(1/3))^4*f^(5/3)*g^(1/3)), (2*sqrt(d)*sqrt(e)*p*atan((sqrt(e)*x)/sqrt(d)))/(9*f^(4/3)*(e*f^(2/3) + d*g^(2/3))) + (2*(-1)^(2/3)*sqrt(d)*sqrt(e)*p*atan((sqrt(e)*x)/sqrt(d)))/((1 + (-1)^(1/3))^4*f^(4/3)*(e*f^(2/3) + (-1)^(2/3)*d*g^(2/3))) + (4*sqrt(d)*sqrt(e)*p*atan((sqrt(e)*x)/sqrt(d)))/(9*f^(4/3)*(2*e*f^(2/3) - (1 + im*sqrt(3))*d*g^(2/3))) - (2*e*p*log(f^(1/3) + g^(1/3)*x))/(9*f*(e*f^(2/3) + d*g^(2/3))*g^(1/3)) - (2*p*log((g^(1/3)*(sqrt(-d) - sqrt(e)*x))/(sqrt(e)*f^(1/3) + sqrt(-d)*g^(1/3)))*log(f^(1/3) + g^(1/3)*x))/(9*f^(5/3)*g^(1/3)) - (2*p*log(-((g^(1/3)*(sqrt(-d) + sqrt(e)*x))/(sqrt(e)*f^(1/3) - sqrt(-d)*g^(1/3))))*log(f^(1/3) + g^(1/3)*x))/(9*f^(5/3)*g^(1/3)) + (2*(-1)^(1/3)*e*p*log(f^(1/3) - (-1)^(1/3)*g^(1/3)*x))/((1 + (-1)^(1/3))^4*f*(e*f^(2/3) + (-1)^(2/3)*d*g^(2/3))*g^(1/3)) + (4*(-1)^(1/3)*e*p*log(f^(1/3) + (-1)^(2/3)*g^(1/3)*x))/(9*f*(2*e*f^(2/3) - (1 + im*sqrt(3))*d*g^(2/3))*g^(1/3)) + (4*p*log(-(((im + sqrt(3))*g^(1/3)*(sqrt(-d) - sqrt(e)*x))/(2*im*sqrt(e)*f^(1/3) - (im + sqrt(3))*sqrt(-d)*g^(1/3))))*log(2*f^(1/3) - (1 - im*sqrt(3))*g^(1/3)*x))/(9*(1 - im*sqrt(3))*f^(5/3)*g^(1/3)) + (4*p*log(((im + sqrt(3))*g^(1/3)*(sqrt(-d) + sqrt(e)*x))/(2*im*sqrt(e)*f^(1/3) + (im + sqrt(3))*sqrt(-d)*g^(1/3)))*log(2*f^(1/3) - (1 - im*sqrt(3))*g^(1/3)*x))/(9*(1 - im*sqrt(3))*f^(5/3)*g^(1/3)) + (4*p*log(-(((1 + im*sqrt(3))*g^(1/3)*(sqrt(-d) - sqrt(e)*x))/(2*sqrt(e)*f^(1/3) - (1 + im*sqrt(3))*sqrt(-d)*g^(1/3))))*log(2*f^(1/3) - (1 + im*sqrt(3))*g^(1/3)*x))/(9*(1 + im*sqrt(3))*f^(5/3)*g^(1/3)) + (4*p*log(((1 + im*sqrt(3))*g^(1/3)*(sqrt(-d) + sqrt(e)*x))/(2*sqrt(e)*f^(1/3) + (1 + im*sqrt(3))*sqrt(-d)*g^(1/3)))*log(2*f^(1/3) - (1 + im*sqrt(3))*g^(1/3)*x))/(9*(1 + im*sqrt(3))*f^(5/3)*g^(1/3)) + (e*p*log(d + e*x^2))/(9*f*(e*f^(2/3) + d*g^(2/3))*g^(1/3)) - ((-1)^(1/3)*e*p*log(d + e*x^2))/((1 + (-1)^(1/3))^4*f*(e*f^(2/3) + (-1)^(2/3)*d*g^(2/3))*g^(1/3)) - (2*(-1)^(1/3)*e*p*log(d + e*x^2))/(9*f*(2*e*f^(2/3) - (1 + im*sqrt(3))*d*g^(2/3))*g^(1/3)) - log(c*(d + e*x^2)^p)/(9*f^(4/3)*g^(1/3)*(f^(1/3) + g^(1/3)*x)) - log(c*(d + e*x^2)^p)/((1 + (-1)^(1/3))^4*f^(4/3)*g^(1/3)*((-1)^(2/3)*f^(1/3) + g^(1/3)*x)) + ((-1)^(1/3)*log(c*(d + e*x^2)^p))/(9*f^(4/3)*g^(1/3)*(f^(1/3) + (-1)^(2/3)*g^(1/3)*x)) + (2*log(f^(1/3) + g^(1/3)*x)*log(c*(d + e*x^2)^p))/(9*f^(5/3)*g^(1/3)) - (4*log(2*f^(1/3) - (1 - im*sqrt(3))*g^(1/3)*x)*log(c*(d + e*x^2)^p))/(9*(1 - im*sqrt(3))*f^(5/3)*g^(1/3)) - (4*log(2*f^(1/3) - (1 + im*sqrt(3))*g^(1/3)*x)*log(c*(d + e*x^2)^p))/(9*(1 + im*sqrt(3))*f^(5/3)*g^(1/3)) - (2*p*PolyLog(2, (sqrt(e)*(f^(1/3) + g^(1/3)*x))/(sqrt(e)*f^(1/3) - sqrt(-d)*g^(1/3))))/(9*f^(5/3)*g^(1/3)) - (2*p*PolyLog(2, (sqrt(e)*(f^(1/3) + g^(1/3)*x))/(sqrt(e)*f^(1/3) + sqrt(-d)*g^(1/3))))/(9*f^(5/3)*g^(1/3)) + (4*p*PolyLog(2, (sqrt(e)*(2*f^(1/3) - (1 - im*sqrt(3))*g^(1/3)*x))/(2*sqrt(e)*f^(1/3) + (1 - im*sqrt(3))*sqrt(-d)*g^(1/3))))/(9*(1 - im*sqrt(3))*f^(5/3)*g^(1/3)) + (4*p*PolyLog(2, (sqrt(e)*(2*f^(1/3) - (1 - im*sqrt(3))*g^(1/3)*x))/(2*sqrt(e)*f^(1/3) + im*(im + sqrt(3))*sqrt(-d)*g^(1/3))))/(9*(1 - im*sqrt(3))*f^(5/3)*g^(1/3)) + (4*p*PolyLog(2, (sqrt(e)*(2*f^(1/3) - (1 + im*sqrt(3))*g^(1/3)*x))/(2*sqrt(e)*f^(1/3) - (1 + im*sqrt(3))*sqrt(-d)*g^(1/3))))/(9*(1 + im*sqrt(3))*f^(5/3)*g^(1/3)) + (4*p*PolyLog(2, (sqrt(e)*(2*f^(1/3) - (1 + im*sqrt(3))*g^(1/3)*x))/(2*sqrt(e)*f^(1/3) + (1 + im*sqrt(3))*sqrt(-d)*g^(1/3))))/(9*(1 + im*sqrt(3))*f^(5/3)*g^(1/3)))]

    @test_int [(f + g*x^3)^3*log(c*(d + e*x^2)^p)^2, x, 55, 8*f^3*p^2*x - (1408*d^3*f*g^2*p^2*x)/(245*e^3) - (3*d*f^2*g*p^2*x^2)/e + (d^4*g^3*p^2*x^2)/e^4 + (568*d^2*f*g^2*p^2*x^3)/(735*e^2) - (288*d*f*g^2*p^2*x^5)/(1225*e) + (24/343)*f*g^2*p^2*x^7 + (3*f^2*g*p^2*(d + e*x^2)^2)/(8*e^2) - (d^3*g^3*p^2*(d + e*x^2)^2)/(2*e^5) + (2*d^2*g^3*p^2*(d + e*x^2)^3)/(9*e^5) - (d*g^3*p^2*(d + e*x^2)^4)/(16*e^5) + (g^3*p^2*(d + e*x^2)^5)/(125*e^5) - (8*sqrt(d)*f^3*p^2*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) + (1408*d^(7/2)*f*g^2*p^2*atan((sqrt(e)*x)/sqrt(d)))/(245*e^(7/2)) + (4*im*sqrt(d)*f^3*p^2*atan((sqrt(e)*x)/sqrt(d))^2)/sqrt(e) - (12*im*d^(7/2)*f*g^2*p^2*atan((sqrt(e)*x)/sqrt(d))^2)/(7*e^(7/2)) + (8*sqrt(d)*f^3*p^2*atan((sqrt(e)*x)/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/sqrt(e) - (24*d^(7/2)*f*g^2*p^2*atan((sqrt(e)*x)/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/(7*e^(7/2)) - (d^5*g^3*p^2*log(d + e*x^2)^2)/(10*e^5) - 4*f^3*p*x*log(c*(d + e*x^2)^p) + (12*d^3*f*g^2*p*x*log(c*(d + e*x^2)^p))/(7*e^3) - (4*d^2*f*g^2*p*x^3*log(c*(d + e*x^2)^p))/(7*e^2) + (12*d*f*g^2*p*x^5*log(c*(d + e*x^2)^p))/(35*e) - (12/49)*f*g^2*p*x^7*log(c*(d + e*x^2)^p) + (3*d*f^2*g*p*(d + e*x^2)*log(c*(d + e*x^2)^p))/e^2 - (d^4*g^3*p*(d + e*x^2)*log(c*(d + e*x^2)^p))/e^5 - (3*f^2*g*p*(d + e*x^2)^2*log(c*(d + e*x^2)^p))/(4*e^2) + (d^3*g^3*p*(d + e*x^2)^2*log(c*(d + e*x^2)^p))/e^5 - (2*d^2*g^3*p*(d + e*x^2)^3*log(c*(d + e*x^2)^p))/(3*e^5) + (d*g^3*p*(d + e*x^2)^4*log(c*(d + e*x^2)^p))/(4*e^5) - (g^3*p*(d + e*x^2)^5*log(c*(d + e*x^2)^p))/(25*e^5) + (4*sqrt(d)*f^3*p*atan((sqrt(e)*x)/sqrt(d))*log(c*(d + e*x^2)^p))/sqrt(e) - (12*d^(7/2)*f*g^2*p*atan((sqrt(e)*x)/sqrt(d))*log(c*(d + e*x^2)^p))/(7*e^(7/2)) + (d^5*g^3*p*log(d + e*x^2)*log(c*(d + e*x^2)^p))/(5*e^5) + f^3*x*log(c*(d + e*x^2)^p)^2 + (3/7)*f*g^2*x^7*log(c*(d + e*x^2)^p)^2 + (1/10)*g^3*x^10*log(c*(d + e*x^2)^p)^2 - (3*d*f^2*g*(d + e*x^2)*log(c*(d + e*x^2)^p)^2)/(2*e^2) + (3*f^2*g*(d + e*x^2)^2*log(c*(d + e*x^2)^p)^2)/(4*e^2) + (4*im*sqrt(d)*f^3*p^2*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/sqrt(e) - (12*im*d^(7/2)*f*g^2*p^2*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/(7*e^(7/2))]
    @test_int [(f + g*x^3)^2*log(c*(d + e*x^2)^p)^2, x, 47, 8*f^2*p^2*x - (1408*d^3*g^2*p^2*x)/(735*e^3) - (2*d*f*g*p^2*x^2)/e + (568*d^2*g^2*p^2*x^3)/(2205*e^2) - (96*d*g^2*p^2*x^5)/(1225*e) + (8/343)*g^2*p^2*x^7 + (f*g*p^2*(d + e*x^2)^2)/(4*e^2) - (8*sqrt(d)*f^2*p^2*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) + (1408*d^(7/2)*g^2*p^2*atan((sqrt(e)*x)/sqrt(d)))/(735*e^(7/2)) + (4*im*sqrt(d)*f^2*p^2*atan((sqrt(e)*x)/sqrt(d))^2)/sqrt(e) - (4*im*d^(7/2)*g^2*p^2*atan((sqrt(e)*x)/sqrt(d))^2)/(7*e^(7/2)) + (8*sqrt(d)*f^2*p^2*atan((sqrt(e)*x)/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/sqrt(e) - (8*d^(7/2)*g^2*p^2*atan((sqrt(e)*x)/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/(7*e^(7/2)) - 4*f^2*p*x*log(c*(d + e*x^2)^p) + (4*d^3*g^2*p*x*log(c*(d + e*x^2)^p))/(7*e^3) - (4*d^2*g^2*p*x^3*log(c*(d + e*x^2)^p))/(21*e^2) + (4*d*g^2*p*x^5*log(c*(d + e*x^2)^p))/(35*e) - (4/49)*g^2*p*x^7*log(c*(d + e*x^2)^p) + (2*d*f*g*p*(d + e*x^2)*log(c*(d + e*x^2)^p))/e^2 - (f*g*p*(d + e*x^2)^2*log(c*(d + e*x^2)^p))/(2*e^2) + (4*sqrt(d)*f^2*p*atan((sqrt(e)*x)/sqrt(d))*log(c*(d + e*x^2)^p))/sqrt(e) - (4*d^(7/2)*g^2*p*atan((sqrt(e)*x)/sqrt(d))*log(c*(d + e*x^2)^p))/(7*e^(7/2)) + f^2*x*log(c*(d + e*x^2)^p)^2 + (1/7)*g^2*x^7*log(c*(d + e*x^2)^p)^2 - (d*f*g*(d + e*x^2)*log(c*(d + e*x^2)^p)^2)/e^2 + (f*g*(d + e*x^2)^2*log(c*(d + e*x^2)^p)^2)/(2*e^2) + (4*im*sqrt(d)*f^2*p^2*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/sqrt(e) - (4*im*d^(7/2)*g^2*p^2*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/(7*e^(7/2))]
    @test_int [(f + g*x^3)^1*log(c*(d + e*x^2)^p)^2, x, 23, 8*f*p^2*x - (d*g*p^2*x^2)/e + (g*p^2*(d + e*x^2)^2)/(8*e^2) - (8*sqrt(d)*f*p^2*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) + (4*im*sqrt(d)*f*p^2*atan((sqrt(e)*x)/sqrt(d))^2)/sqrt(e) + (8*sqrt(d)*f*p^2*atan((sqrt(e)*x)/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/sqrt(e) - 4*f*p*x*log(c*(d + e*x^2)^p) + (d*g*p*(d + e*x^2)*log(c*(d + e*x^2)^p))/e^2 - (g*p*(d + e*x^2)^2*log(c*(d + e*x^2)^p))/(4*e^2) + (4*sqrt(d)*f*p*atan((sqrt(e)*x)/sqrt(d))*log(c*(d + e*x^2)^p))/sqrt(e) + f*x*log(c*(d + e*x^2)^p)^2 - (d*g*(d + e*x^2)*log(c*(d + e*x^2)^p)^2)/(2*e^2) + (g*(d + e*x^2)^2*log(c*(d + e*x^2)^p)^2)/(4*e^2) + (4*im*sqrt(d)*f*p^2*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/sqrt(e)]
    @test_int [log(c*(d + e*x^2)^p)^2/(f + g*x^3)^1, x, 0, Unintegrable(log(c*(d + e*x^2)^p)^2/(f + g*x^3), x)]
    @test_int [log(c*(d + e*x^2)^p)^2/(f + g*x^3)^2, x, 0, Unintegrable(log(c*(d + e*x^2)^p)^2/(f + g*x^3)^2, x)]

    @test_int [(f + g*x^3)^2*log(c*(d + e*x^2)^p)^3, x, 103, -48*f^2*p^3*x + (351136*d^3*g^2*p^3*x)/(25725*e^3) + (6*d*f*g*p^3*x^2)/e - (55456*d^2*g^2*p^3*x^3)/(77175*e^2) + (5232*d*g^2*p^3*x^5)/(42875*e) - (48*g^2*p^3*x^7)/2401 - (3*f*g*p^3*(d + e*x^2)^2)/(8*e^2) + (48*sqrt(d)*f^2*p^3*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) - (351136*d^(7/2)*g^2*p^3*atan((sqrt(e)*x)/sqrt(d)))/(25725*e^(7/2)) - (24*im*sqrt(d)*f^2*p^3*atan((sqrt(e)*x)/sqrt(d))^2)/sqrt(e) + (1408*im*d^(7/2)*g^2*p^3*atan((sqrt(e)*x)/sqrt(d))^2)/(245*e^(7/2)) - (48*sqrt(d)*f^2*p^3*atan((sqrt(e)*x)/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/sqrt(e) + (2816*d^(7/2)*g^2*p^3*atan((sqrt(e)*x)/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/(245*e^(7/2)) + 24*f^2*p^2*x*log(c*(d + e*x^2)^p) - (1408*d^3*g^2*p^2*x*log(c*(d + e*x^2)^p))/(245*e^3) + (568*d^2*g^2*p^2*x^3*log(c*(d + e*x^2)^p))/(735*e^2) - (288*d*g^2*p^2*x^5*log(c*(d + e*x^2)^p))/(1225*e) + (24/343)*g^2*p^2*x^7*log(c*(d + e*x^2)^p) - (6*d*f*g*p^2*(d + e*x^2)*log(c*(d + e*x^2)^p))/e^2 + (3*f*g*p^2*(d + e*x^2)^2*log(c*(d + e*x^2)^p))/(4*e^2) - (24*sqrt(d)*f^2*p^2*atan((sqrt(e)*x)/sqrt(d))*log(c*(d + e*x^2)^p))/sqrt(e) + (1408*d^(7/2)*g^2*p^2*atan((sqrt(e)*x)/sqrt(d))*log(c*(d + e*x^2)^p))/(245*e^(7/2)) - 6*f^2*p*x*log(c*(d + e*x^2)^p)^2 + (6*d^3*g^2*p*x*log(c*(d + e*x^2)^p)^2)/(7*e^3) - (2*d^2*g^2*p*x^3*log(c*(d + e*x^2)^p)^2)/(7*e^2) + (6*d*g^2*p*x^5*log(c*(d + e*x^2)^p)^2)/(35*e) - (6/49)*g^2*p*x^7*log(c*(d + e*x^2)^p)^2 + (3*d*f*g*p*(d + e*x^2)*log(c*(d + e*x^2)^p)^2)/e^2 - (3*f*g*p*(d + e*x^2)^2*log(c*(d + e*x^2)^p)^2)/(4*e^2) + f^2*x*log(c*(d + e*x^2)^p)^3 + (1/7)*g^2*x^7*log(c*(d + e*x^2)^p)^3 - (d*f*g*(d + e*x^2)*log(c*(d + e*x^2)^p)^3)/e^2 + (f*g*(d + e*x^2)^2*log(c*(d + e*x^2)^p)^3)/(2*e^2) - (24*im*sqrt(d)*f^2*p^3*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/sqrt(e) + (1408*im*d^(7/2)*g^2*p^3*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/(245*e^(7/2)) + 6*d*f^2*p*Unintegrable(log(c*(d + e*x^2)^p)^2/(d + e*x^2), x) - (6*d^4*g^2*p*Unintegrable(log(c*(d + e*x^2)^p)^2/(d + e*x^2), x))/(7*e^3)]
    @test_int [(f + g*x^3)^1*log(c*(d + e*x^2)^p)^3, x, 28, -48*f*p^3*x + (3*d*g*p^3*x^2)/e - (3*g*p^3*(d + e*x^2)^2)/(16*e^2) + (48*sqrt(d)*f*p^3*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) - (24*im*sqrt(d)*f*p^3*atan((sqrt(e)*x)/sqrt(d))^2)/sqrt(e) - (48*sqrt(d)*f*p^3*atan((sqrt(e)*x)/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/sqrt(e) + 24*f*p^2*x*log(c*(d + e*x^2)^p) - (3*d*g*p^2*(d + e*x^2)*log(c*(d + e*x^2)^p))/e^2 + (3*g*p^2*(d + e*x^2)^2*log(c*(d + e*x^2)^p))/(8*e^2) - (24*sqrt(d)*f*p^2*atan((sqrt(e)*x)/sqrt(d))*log(c*(d + e*x^2)^p))/sqrt(e) - 6*f*p*x*log(c*(d + e*x^2)^p)^2 + (3*d*g*p*(d + e*x^2)*log(c*(d + e*x^2)^p)^2)/(2*e^2) - (3*g*p*(d + e*x^2)^2*log(c*(d + e*x^2)^p)^2)/(8*e^2) + f*x*log(c*(d + e*x^2)^p)^3 - (d*g*(d + e*x^2)*log(c*(d + e*x^2)^p)^3)/(2*e^2) + (g*(d + e*x^2)^2*log(c*(d + e*x^2)^p)^3)/(4*e^2) - (24*im*sqrt(d)*f*p^3*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x)))/sqrt(e) + 6*d*f*p*Unintegrable(log(c*(d + e*x^2)^p)^2/(d + e*x^2), x)]
    @test_int [log(c*(d + e*x^2)^p)^3/(f + g*x^3)^1, x, 0, Unintegrable(log(c*(d + e*x^2)^p)^3/(f + g*x^3), x)]
    @test_int [log(c*(d + e*x^2)^p)^3/(f + g*x^3)^2, x, 0, Unintegrable(log(c*(d + e*x^2)^p)^3/(f + g*x^3)^2, x)]

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

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

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

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(h*x)^r*(f+g*x^s)^q*log(c*(d+e*x^m)^n)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^r*(f+g*x^2)^q*log(c*(d+e*x^2)^n)=#

    #= ::Subsubsection::Closed:: =#
    #=q>0=#

    @test_int [x^5*(f + g*x^2)*log(c*(d + e*x^2)^p), x, 5, -((d^2*(4*e*f - 3*d*g)*p*x^2)/(24*e^3)) + (d*(4*e*f - 3*d*g)*p*x^4)/(48*e^2) - ((4*e*f - 3*d*g)*p*x^6)/(72*e) - (1/32)*g*p*x^8 + (d^3*(4*e*f - 3*d*g)*p*log(d + e*x^2))/(24*e^4) + (1/6)*f*x^6*log(c*(d + e*x^2)^p) + (1/8)*g*x^8*log(c*(d + e*x^2)^p)]
    @test_int [x^3*(f + g*x^2)*log(c*(d + e*x^2)^p), x, 5, (d*(3*e*f - 2*d*g)*p*x^2)/(12*e^2) - ((3*e*f - 2*d*g)*p*x^4)/(24*e) - (1/18)*g*p*x^6 - (d^2*(3*e*f - 2*d*g)*p*log(d + e*x^2))/(12*e^3) + (1/4)*f*x^4*log(c*(d + e*x^2)^p) + (1/6)*g*x^6*log(c*(d + e*x^2)^p)]
    @test_int [x^1*(f + g*x^2)*log(c*(d + e*x^2)^p), x, 4, -((e*f - d*g)*p*x^2)/(4*e) - (p*(f + g*x^2)^2)/(8*g) - ((e*f - d*g)^2*p*log(d + e*x^2))/(4*e^2*g) + ((f + g*x^2)^2*log(c*(d + e*x^2)^p))/(4*g)]
    @test_int [((f + g*x^2)*log(c*(d + e*x^2)^p))/x^1, x, 7, (-(1/2))*g*p*x^2 + (g*(d + e*x^2)*log(c*(d + e*x^2)^p))/(2*e) + (1/2)*f*log(-((e*x^2)/d))*log(c*(d + e*x^2)^p) + (1/2)*f*p*PolyLog(2, 1 + (e*x^2)/d)]
    @test_int [((f + g*x^2)*log(c*(d + e*x^2)^p))/x^3, x, 9, (e*f*p*log(x))/d - (e*f*p*log(d + e*x^2))/(2*d) - (f*log(c*(d + e*x^2)^p))/(2*x^2) + (1/2)*g*log(-((e*x^2)/d))*log(c*(d + e*x^2)^p) + (1/2)*g*p*PolyLog(2, 1 + (e*x^2)/d)]
    @test_int [((f + g*x^2)*log(c*(d + e*x^2)^p))/x^5, x, 5, -((e*f*p)/(4*d*x^2)) - (e*(e*f - 2*d*g)*p*log(x))/(2*d^2) + ((e*f - d*g)^2*p*log(d + e*x^2))/(4*d^2*f) - ((f + g*x^2)^2*log(c*(d + e*x^2)^p))/(4*f*x^4)]
    @test_int [((f + g*x^2)*log(c*(d + e*x^2)^p))/x^7, x, 5, -((e*f*p)/(12*d*x^4)) + (e*(2*e*f - 3*d*g)*p)/(12*d^2*x^2) + (e^2*(2*e*f - 3*d*g)*p*log(x))/(6*d^3) - (e^2*(2*e*f - 3*d*g)*p*log(d + e*x^2))/(12*d^3) - (f*log(c*(d + e*x^2)^p))/(6*x^6) - (g*log(c*(d + e*x^2)^p))/(4*x^4)]
    @test_int [((f + g*x^2)*log(c*(d + e*x^2)^p))/x^9, x, 5, -((e*f*p)/(24*d*x^6)) + (e*(3*e*f - 4*d*g)*p)/(48*d^2*x^4) - (e^2*(3*e*f - 4*d*g)*p)/(24*d^3*x^2) - (e^3*(3*e*f - 4*d*g)*p*log(x))/(12*d^4) + (e^3*(3*e*f - 4*d*g)*p*log(d + e*x^2))/(24*d^4) - (f*log(c*(d + e*x^2)^p))/(8*x^8) - (g*log(c*(d + e*x^2)^p))/(6*x^6)]

    @test_int [x^2*(f + g*x^2)*log(c*(d + e*x^2)^p), x, 10, (2*d*f*p*x)/(3*e) - (2*d^2*g*p*x)/(5*e^2) - (2*f*p*x^3)/9 + (2*d*g*p*x^3)/(15*e) - (2*g*p*x^5)/25 - (2*d^(3/2)*f*p*atan((sqrt(e)*x)/sqrt(d)))/(3*e^(3/2)) + (2*d^(5/2)*g*p*atan((sqrt(e)*x)/sqrt(d)))/(5*e^(5/2)) + (f*x^3*log(c*(d + e*x^2)^p))/3 + (g*x^5*log(c*(d + e*x^2)^p))/5]
    @test_int [x^0*(f + g*x^2)*log(c*(d + e*x^2)^p), x, 9, -2*f*p*x + (2*d*g*p*x)/(3*e) - (2*g*p*x^3)/9 + (2*sqrt(d)*f*p*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) - (2*d^(3/2)*g*p*atan((sqrt(e)*x)/sqrt(d)))/(3*e^(3/2)) + f*x*log(c*(d + e*x^2)^p) + (g*x^3*log(c*(d + e*x^2)^p))/3]
    @test_int [(f + g*x^2)*log(c*(d + e*x^2)^p)/x^2, x, 7, -2*g*p*x + (2*(e*f + d*g)*p*atan((sqrt(e)*x)/sqrt(d)))/(sqrt(d)*sqrt(e)) - (f*log(c*(d + e*x^2)^p))/x + g*x*log(c*(d + e*x^2)^p), -2*g*p*x + (2*sqrt(e)*f*p*atan((sqrt(e)*x)/sqrt(d)))/sqrt(d) + (2*sqrt(d)*g*p*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) - (f*log(c*(d + e*x^2)^p))/x + g*x*log(c*(d + e*x^2)^p)]
    @test_int [(f + g*x^2)*log(c*(d + e*x^2)^p)/x^4, x, 7, (-2*e*f*p)/(3*d*x) - (2*e^(3/2)*f*p*atan((sqrt(e)*x)/sqrt(d)))/(3*d^(3/2)) + (2*sqrt(e)*g*p*atan((sqrt(e)*x)/sqrt(d)))/sqrt(d) - (f*log(c*(d + e*x^2)^p))/(3*x^3) - (g*log(c*(d + e*x^2)^p))/x]
    @test_int [(f + g*x^2)*log(c*(d + e*x^2)^p)/x^6, x, 9, -((2*e*f*p)/(15*d*x^3)) + (2*e^2*f*p)/(5*d^2*x) - (2*e*g*p)/(3*d*x) + (2*e^(5/2)*f*p*atan((sqrt(e)*x)/sqrt(d)))/(5*d^(5/2)) - (2*e^(3/2)*g*p*atan((sqrt(e)*x)/sqrt(d)))/(3*d^(3/2)) - (f*log(c*(d + e*x^2)^p))/(5*x^5) - (g*log(c*(d + e*x^2)^p))/(3*x^3)]

    @test_int [x^5*(f + g*x^2)^2*log(c*(d + e*x^2)^p), x, 5, -((d^2*(e*f - d*g)^2*p*x^2)/(2*e^4)) + (d*(e*f - 2*d*g)*(e*f - d*g)*p*(d + e*x^2)^2)/(4*e^5) - ((e^2*f^2 - 6*d*e*f*g + 6*d^2*g^2)*p*(d + e*x^2)^3)/(18*e^5) - (g*(e*f - 2*d*g)*p*(d + e*x^2)^4)/(16*e^5) - (g^2*p*(d + e*x^2)^5)/(50*e^5) + (d^3*(10*e^2*f^2 - 15*d*e*f*g + 6*d^2*g^2)*p*log(d + e*x^2))/(60*e^5) + (1/6)*f^2*x^6*log(c*(d + e*x^2)^p) + (1/4)*f*g*x^8*log(c*(d + e*x^2)^p) + (1/10)*g^2*x^10*log(c*(d + e*x^2)^p)]
    @test_int [x^3*(f + g*x^2)^2*log(c*(d + e*x^2)^p), x, 5, (d*(e*f - d*g)^2*p*x^2)/(2*e^3) - ((e*f - 3*d*g)*(e*f - d*g)*p*(d + e*x^2)^2)/(8*e^4) - (g*(2*e*f - 3*d*g)*p*(d + e*x^2)^3)/(18*e^4) - (g^2*p*(d + e*x^2)^4)/(32*e^4) - (d^2*(6*e^2*f^2 - 8*d*e*f*g + 3*d^2*g^2)*p*log(d + e*x^2))/(24*e^4) + (1/4)*f^2*x^4*log(c*(d + e*x^2)^p) + (1/3)*f*g*x^6*log(c*(d + e*x^2)^p) + (1/8)*g^2*x^8*log(c*(d + e*x^2)^p)]
    @test_int [x^1*(f + g*x^2)^2*log(c*(d + e*x^2)^p), x, 4, -((e*f - d*g)^2*p*x^2)/(6*e^2) - ((e*f - d*g)*p*(f + g*x^2)^2)/(12*e*g) - (p*(f + g*x^2)^3)/(18*g) - ((e*f - d*g)^3*p*log(d + e*x^2))/(6*e^3*g) + ((f + g*x^2)^3*log(c*(d + e*x^2)^p))/(6*g)]
    @test_int [((f + g*x^2)^2*log(c*(d + e*x^2)^p))/x^1, x, 10, (-f)*g*p*x^2 + (d*g^2*p*x^2)/(4*e) - (1/8)*g^2*p*x^4 - (d^2*g^2*p*log(d + e*x^2))/(4*e^2) + (1/4)*g^2*x^4*log(c*(d + e*x^2)^p) + (f*g*(d + e*x^2)*log(c*(d + e*x^2)^p))/e + (1/2)*f^2*log(-((e*x^2)/d))*log(c*(d + e*x^2)^p) + (1/2)*f^2*p*PolyLog(2, 1 + (e*x^2)/d)]
    @test_int [((f + g*x^2)^2*log(c*(d + e*x^2)^p))/x^3, x, 11, (-(1/2))*g^2*p*x^2 + (e*f^2*p*log(x))/d - (e*f^2*p*log(d + e*x^2))/(2*d) - (f^2*log(c*(d + e*x^2)^p))/(2*x^2) + (g^2*(d + e*x^2)*log(c*(d + e*x^2)^p))/(2*e) + f*g*log(-((e*x^2)/d))*log(c*(d + e*x^2)^p) + f*g*p*PolyLog(2, 1 + (e*x^2)/d)]
    @test_int [((f + g*x^2)^2*log(c*(d + e*x^2)^p))/x^5, x, 12, -((e*f^2*p)/(4*d*x^2)) - (e^2*f^2*p*log(x))/(2*d^2) + (2*e*f*g*p*log(x))/d + (e^2*f^2*p*log(d + e*x^2))/(4*d^2) - (e*f*g*p*log(d + e*x^2))/d - (f^2*log(c*(d + e*x^2)^p))/(4*x^4) - (f*g*log(c*(d + e*x^2)^p))/x^2 + (1/2)*g^2*log(-((e*x^2)/d))*log(c*(d + e*x^2)^p) + (1/2)*g^2*p*PolyLog(2, 1 + (e*x^2)/d)]
    @test_int [((f + g*x^2)^2*log(c*(d + e*x^2)^p))/x^7, x, 5, -((e*f^2*p)/(12*d*x^4)) + (e*f*(e*f - 3*d*g)*p)/(6*d^2*x^2) + (e*(e^2*f^2 - 3*d*e*f*g + 3*d^2*g^2)*p*log(x))/(3*d^3) - ((e*f - d*g)^3*p*log(d + e*x^2))/(6*d^3*f) - ((f + g*x^2)^3*log(c*(d + e*x^2)^p))/(6*f*x^6)]
    @test_int [((f + g*x^2)^2*log(c*(d + e*x^2)^p))/x^9, x, 5, -((e*f^2*p)/(24*d*x^6)) + (e*f*(3*e*f - 8*d*g)*p)/(48*d^2*x^4) - (e*(3*e^2*f^2 - 8*d*e*f*g + 6*d^2*g^2)*p)/(24*d^3*x^2) - (e^2*(3*e^2*f^2 - 8*d*e*f*g + 6*d^2*g^2)*p*log(x))/(12*d^4) + (e^2*(3*e^2*f^2 - 8*d*e*f*g + 6*d^2*g^2)*p*log(d + e*x^2))/(24*d^4) - (f^2*log(c*(d + e*x^2)^p))/(8*x^8) - (f*g*log(c*(d + e*x^2)^p))/(3*x^6) - (g^2*log(c*(d + e*x^2)^p))/(4*x^4)]
    @test_int [((f + g*x^2)^2*log(c*(d + e*x^2)^p))/x^11, x, 5, -((e*f^2*p)/(40*d*x^8)) + (e*f*(2*e*f - 5*d*g)*p)/(60*d^2*x^6) - (e*(6*e^2*f^2 - 15*d*e*f*g + 10*d^2*g^2)*p)/(120*d^3*x^4) + (e^2*(6*e^2*f^2 - 15*d*e*f*g + 10*d^2*g^2)*p)/(60*d^4*x^2) + (e^3*(6*e^2*f^2 - 15*d*e*f*g + 10*d^2*g^2)*p*log(x))/(30*d^5) - (e^3*(6*e^2*f^2 - 15*d*e*f*g + 10*d^2*g^2)*p*log(d + e*x^2))/(60*d^5) - (f^2*log(c*(d + e*x^2)^p))/(10*x^10) - (f*g*log(c*(d + e*x^2)^p))/(4*x^8) - (g^2*log(c*(d + e*x^2)^p))/(6*x^6)]

    @test_int [x^2*(f + g*x^2)^2*log(c*(d + e*x^2)^p), x, 14, (2*d*f^2*p*x)/(3*e) - (4*d^2*f*g*p*x)/(5*e^2) + (2*d^3*g^2*p*x)/(7*e^3) - (2*f^2*p*x^3)/9 + (4*d*f*g*p*x^3)/(15*e) - (2*d^2*g^2*p*x^3)/(21*e^2) - (4*f*g*p*x^5)/25 + (2*d*g^2*p*x^5)/(35*e) - (2*g^2*p*x^7)/49 - (2*d^(3/2)*f^2*p*atan((sqrt(e)*x)/sqrt(d)))/(3*e^(3/2)) + (4*d^(5/2)*f*g*p*atan((sqrt(e)*x)/sqrt(d)))/(5*e^(5/2)) - (2*d^(7/2)*g^2*p*atan((sqrt(e)*x)/sqrt(d)))/(7*e^(7/2)) + (f^2*x^3*log(c*(d + e*x^2)^p))/3 + (2*f*g*x^5*log(c*(d + e*x^2)^p))/5 + (g^2*x^7*log(c*(d + e*x^2)^p))/7]
    @test_int [x^0*(f + g*x^2)^2*log(c*(d + e*x^2)^p), x, 13, -2*f^2*p*x + (4*d*f*g*p*x)/(3*e) - (2*d^2*g^2*p*x)/(5*e^2) - (4*f*g*p*x^3)/9 + (2*d*g^2*p*x^3)/(15*e) - (2*g^2*p*x^5)/25 + (2*sqrt(d)*f^2*p*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) - (4*d^(3/2)*f*g*p*atan((sqrt(e)*x)/sqrt(d)))/(3*e^(3/2)) + (2*d^(5/2)*g^2*p*atan((sqrt(e)*x)/sqrt(d)))/(5*e^(5/2)) + f^2*x*log(c*(d + e*x^2)^p) + (2*f*g*x^3*log(c*(d + e*x^2)^p))/3 + (g^2*x^5*log(c*(d + e*x^2)^p))/5]
    @test_int [(f + g*x^2)^2*log(c*(d + e*x^2)^p)/x^2, x, 11, -4*f*g*p*x + (2*d*g^2*p*x)/(3*e) - (2*g^2*p*x^3)/9 + (2*sqrt(e)*f^2*p*atan((sqrt(e)*x)/sqrt(d)))/sqrt(d) + (4*sqrt(d)*f*g*p*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) - (2*d^(3/2)*g^2*p*atan((sqrt(e)*x)/sqrt(d)))/(3*e^(3/2)) - (f^2*log(c*(d + e*x^2)^p))/x + 2*f*g*x*log(c*(d + e*x^2)^p) + (g^2*x^3*log(c*(d + e*x^2)^p))/3]
    @test_int [(f + g*x^2)^2*log(c*(d + e*x^2)^p)/x^4, x, 10, (-2*e*f^2*p)/(3*d*x) - 2*g^2*p*x - (2*e^(3/2)*f^2*p*atan((sqrt(e)*x)/sqrt(d)))/(3*d^(3/2)) + (4*sqrt(e)*f*g*p*atan((sqrt(e)*x)/sqrt(d)))/sqrt(d) + (2*sqrt(d)*g^2*p*atan((sqrt(e)*x)/sqrt(d)))/sqrt(e) - (f^2*log(c*(d + e*x^2)^p))/(3*x^3) - (2*f*g*log(c*(d + e*x^2)^p))/x + g^2*x*log(c*(d + e*x^2)^p)]
    @test_int [(f + g*x^2)^2*log(c*(d + e*x^2)^p)/x^6, x, 11, -((2*e*f^2*p)/(15*d*x^3)) + (2*e^2*f^2*p)/(5*d^2*x) - (4*e*f*g*p)/(3*d*x) + (2*e^(5/2)*f^2*p*atan((sqrt(e)*x)/sqrt(d)))/(5*d^(5/2)) - (4*e^(3/2)*f*g*p*atan((sqrt(e)*x)/sqrt(d)))/(3*d^(3/2)) + (2*sqrt(e)*g^2*p*atan((sqrt(e)*x)/sqrt(d)))/sqrt(d) - (f^2*log(c*(d + e*x^2)^p))/(5*x^5) - (2*f*g*log(c*(d + e*x^2)^p))/(3*x^3) - (g^2*log(c*(d + e*x^2)^p))/x]
    @test_int [(f + g*x^2)^2*log(c*(d + e*x^2)^p)/x^8, x, 14, -((2*e*f^2*p)/(35*d*x^5)) + (2*e^2*f^2*p)/(21*d^2*x^3) - (4*e*f*g*p)/(15*d*x^3) - (2*e^3*f^2*p)/(7*d^3*x) + (4*e^2*f*g*p)/(5*d^2*x) - (2*e*g^2*p)/(3*d*x) - (2*e^(7/2)*f^2*p*atan((sqrt(e)*x)/sqrt(d)))/(7*d^(7/2)) + (4*e^(5/2)*f*g*p*atan((sqrt(e)*x)/sqrt(d)))/(5*d^(5/2)) - (2*e^(3/2)*g^2*p*atan((sqrt(e)*x)/sqrt(d)))/(3*d^(3/2)) - (f^2*log(c*(d + e*x^2)^p))/(7*x^7) - (2*f*g*log(c*(d + e*x^2)^p))/(5*x^5) - (g^2*log(c*(d + e*x^2)^p))/(3*x^3)]

    #= ::Subsubsection::Closed:: =#
    #=q<0=#

    @test_int [(x^5*log(c*(d + e*x^2)^p))/(f + g*x^2), x, 11, (f*p*x^2)/(2*g^2) + (d*p*x^2)/(4*e*g) - (p*x^4)/(8*g) - (d^2*p*log(d + e*x^2))/(4*e^2*g) + (x^4*log(c*(d + e*x^2)^p))/(4*g) - (f*(d + e*x^2)*log(c*(d + e*x^2)^p))/(2*e*g^2) + (f^2*log(c*(d + e*x^2)^p)*log((e*(f + g*x^2))/(e*f - d*g)))/(2*g^3) + (f^2*p*PolyLog(2, -((g*(d + e*x^2))/(e*f - d*g))))/(2*g^3)]
    @test_int [(x^3*log(c*(d + e*x^2)^p))/(f + g*x^2), x, 8, -(p*x^2)/(2*g) + ((d + e*x^2)*log(c*(d + e*x^2)^p))/(2*e*g) - (f*log(c*(d + e*x^2)^p)*log((e*(f + g*x^2))/(e*f - d*g)))/(2*g^2) - (f*p*PolyLog(2, -((g*(d + e*x^2))/(e*f - d*g))))/(2*g^2)]
    @test_int [(x^1*log(c*(d + e*x^2)^p))/(f + g*x^2), x, 4, (log(c*(d + e*x^2)^p)*log((e*(f + g*x^2))/(e*f - d*g)))/(2*g) + (p*PolyLog(2, -((g*(d + e*x^2))/(e*f - d*g))))/(2*g)]
    @test_int [log(c*(d + e*x^2)^p)/(x^1*(f + g*x^2)), x, 8, (log(-((e*x^2)/d))*log(c*(d + e*x^2)^p))/(2*f) - (log(c*(d + e*x^2)^p)*log((e*(f + g*x^2))/(e*f - d*g)))/(2*f) - (p*PolyLog(2, -((g*(d + e*x^2))/(e*f - d*g))))/(2*f) + (p*PolyLog(2, 1 + (e*x^2)/d))/(2*f)]
    @test_int [log(c*(d + e*x^2)^p)/(x^3*(f + g*x^2)), x, 12, (e*p*log(x))/(d*f) - (e*p*log(d + e*x^2))/(2*d*f) - log(c*(d + e*x^2)^p)/(2*f*x^2) - (g*log(-((e*x^2)/d))*log(c*(d + e*x^2)^p))/(2*f^2) + (g*log(c*(d + e*x^2)^p)*log((e*(f + g*x^2))/(e*f - d*g)))/(2*f^2) + (g*p*PolyLog(2, -((g*(d + e*x^2))/(e*f - d*g))))/(2*f^2) - (g*p*PolyLog(2, 1 + (e*x^2)/d))/(2*f^2)]

    @test_int [x^4*log(c*(d + e*x^2)^p)/(f + g*x^2), x, 21, (2*f*p*x)/g^2 + (2*d*p*x)/(3*e*g) - (2*p*x^3)/(9*g) - (2*sqrt(d)*f*p*atan((sqrt(e)*x)/sqrt(d)))/(sqrt(e)*g^2) - (2*d^(3/2)*p*atan((sqrt(e)*x)/sqrt(d)))/(3*e^(3/2)*g) + (2*f^(3/2)*p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/g^(5/2) - (f^(3/2)*p*atan((sqrt(g)*x)/sqrt(f))*log(-((2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x)))))/g^(5/2) - (f^(3/2)*p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/g^(5/2) - (f*x*log(c*(d + e*x^2)^p))/g^2 + (x^3*log(c*(d + e*x^2)^p))/(3*g) + (f^(3/2)*atan((sqrt(g)*x)/sqrt(f))*log(c*(d + e*x^2)^p))/g^(5/2) - (im*f^(3/2)*p*PolyLog(2, 1 - (2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/g^(5/2) + (im*f^(3/2)*p*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*g^(5/2)) + (im*f^(3/2)*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*g^(5/2))]
    @test_int [x^2*log(c*(d + e*x^2)^p)/(f + g*x^2), x, 17, -((2*p*x)/g) + (2*sqrt(d)*p*atan((sqrt(e)*x)/sqrt(d)))/(sqrt(e)*g) - (2*sqrt(f)*p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/g^(3/2) + (sqrt(f)*p*atan((sqrt(g)*x)/sqrt(f))*log(-((2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x)))))/g^(3/2) + (sqrt(f)*p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/g^(3/2) + (x*log(c*(d + e*x^2)^p))/g - (sqrt(f)*atan((sqrt(g)*x)/sqrt(f))*log(c*(d + e*x^2)^p))/g^(3/2) + (im*sqrt(f)*p*PolyLog(2, 1 - (2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/g^(3/2) - (im*sqrt(f)*p*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*g^(3/2)) - (im*sqrt(f)*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*g^(3/2))]
    @test_int [x^0*log(c*(d + e*x^2)^p)/(f + g*x^2), x, 12, (2*p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(sqrt(f)*sqrt(g)) - (p*atan((sqrt(g)*x)/sqrt(f))*log(-((2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x)))))/(sqrt(f)*sqrt(g)) - (p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(sqrt(f)*sqrt(g)) + (atan((sqrt(g)*x)/sqrt(f))*log(c*(d + e*x^2)^p))/(sqrt(f)*sqrt(g)) - (im*p*PolyLog(2, 1 - (2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(sqrt(f)*sqrt(g)) + (im*p*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*sqrt(f)*sqrt(g)) + (im*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*sqrt(f)*sqrt(g))]
    @test_int [log(c*(d + e*x^2)^p)/(x^2*(f + g*x^2)), x, 16, (2*sqrt(e)*p*atan((sqrt(e)*x)/sqrt(d)))/(sqrt(d)*f) - (2*sqrt(g)*p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/f^(3/2) + (sqrt(g)*p*atan((sqrt(g)*x)/sqrt(f))*log(-((2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x)))))/f^(3/2) + (sqrt(g)*p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/f^(3/2) - log(c*(d + e*x^2)^p)/(f*x) - (sqrt(g)*atan((sqrt(g)*x)/sqrt(f))*log(c*(d + e*x^2)^p))/f^(3/2) + (im*sqrt(g)*p*PolyLog(2, 1 - (2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/f^(3/2) - (im*sqrt(g)*p*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*f^(3/2)) - (im*sqrt(g)*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*f^(3/2))]
    @test_int [log(c*(d + e*x^2)^p)/(x^4*(f + g*x^2)), x, 19, -((2*e*p)/(3*d*f*x)) - (2*e^(3/2)*p*atan((sqrt(e)*x)/sqrt(d)))/(3*d^(3/2)*f) - (2*sqrt(e)*g*p*atan((sqrt(e)*x)/sqrt(d)))/(sqrt(d)*f^2) + (2*g^(3/2)*p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/f^(5/2) - (g^(3/2)*p*atan((sqrt(g)*x)/sqrt(f))*log(-((2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x)))))/f^(5/2) - (g^(3/2)*p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/f^(5/2) - log(c*(d + e*x^2)^p)/(3*f*x^3) + (g*log(c*(d + e*x^2)^p))/(f^2*x) + (g^(3/2)*atan((sqrt(g)*x)/sqrt(f))*log(c*(d + e*x^2)^p))/f^(5/2) - (im*g^(3/2)*p*PolyLog(2, 1 - (2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/f^(5/2) + (im*g^(3/2)*p*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*f^(5/2)) + (im*g^(3/2)*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*f^(5/2))]

    @test_int [(x^5*log(c*(d + e*x^2)^p))/(f + g*x^2)^2, x, 12, -(p*x^2)/(2*g^2) + (e*f^2*p*log(d + e*x^2))/(2*g^3*(e*f - d*g)) + ((d + e*x^2)*log(c*(d + e*x^2)^p))/(2*e*g^2) - (f^2*log(c*(d + e*x^2)^p))/(2*g^3*(f + g*x^2)) - (e*f^2*p*log(f + g*x^2))/(2*g^3*(e*f - d*g)) - (f*log(c*(d + e*x^2)^p)*log((e*(f + g*x^2))/(e*f - d*g)))/g^3 - (f*p*PolyLog(2, -((g*(d + e*x^2))/(e*f - d*g))))/g^3]
    @test_int [(x^3*log(c*(d + e*x^2)^p))/(f + g*x^2)^2, x, 10, -(e*f*p*log(d + e*x^2))/(2*g^2*(e*f - d*g)) + (f*log(c*(d + e*x^2)^p))/(2*g^2*(f + g*x^2)) + (e*f*p*log(f + g*x^2))/(2*g^2*(e*f - d*g)) + (log(c*(d + e*x^2)^p)*log((e*(f + g*x^2))/(e*f - d*g)))/(2*g^2) + (p*PolyLog(2, -((g*(d + e*x^2))/(e*f - d*g))))/(2*g^2)]
    @test_int [(x^1*log(c*(d + e*x^2)^p))/(f + g*x^2)^2, x, 5, (e*p*log(d + e*x^2))/(2*g*(e*f - d*g)) - log(c*(d + e*x^2)^p)/(2*g*(f + g*x^2)) - (e*p*log(f + g*x^2))/(2*g*(e*f - d*g))]
    @test_int [log(c*(d + e*x^2)^p)/(x^1*(f + g*x^2)^2), x, 12, -((e*p*log(d + e*x^2))/(2*f*(e*f - d*g))) + log(c*(d + e*x^2)^p)/(2*f*(f + g*x^2)) + (log(-((e*x^2)/d))*log(c*(d + e*x^2)^p))/(2*f^2) + (e*p*log(f + g*x^2))/(2*f*(e*f - d*g)) - (log(c*(d + e*x^2)^p)*log((e*(f + g*x^2))/(e*f - d*g)))/(2*f^2) - (p*PolyLog(2, -((g*(d + e*x^2))/(e*f - d*g))))/(2*f^2) + (p*PolyLog(2, 1 + (e*x^2)/d))/(2*f^2)]
    @test_int [log(c*(d + e*x^2)^p)/(x^3*(f + g*x^2)^2), x, 16, (e*p*log(x))/(d*f^2) - (e*p*log(d + e*x^2))/(2*d*f^2) + (e*g*p*log(d + e*x^2))/(2*f^2*(e*f - d*g)) - log(c*(d + e*x^2)^p)/(2*f^2*x^2) - (g*log(c*(d + e*x^2)^p))/(2*f^2*(f + g*x^2)) - (g*log(-((e*x^2)/d))*log(c*(d + e*x^2)^p))/f^3 - (e*g*p*log(f + g*x^2))/(2*f^2*(e*f - d*g)) + (g*log(c*(d + e*x^2)^p)*log((e*(f + g*x^2))/(e*f - d*g)))/f^3 + (g*p*PolyLog(2, -((g*(d + e*x^2))/(e*f - d*g))))/f^3 - (g*p*PolyLog(2, 1 + (e*x^2)/d))/f^3]

    @test_int [x^4*log(c*(d + e*x^2)^p)/(f + g*x^2)^2, x, 43, -((2*p*x)/g^2) + (2*sqrt(d)*p*atan((sqrt(e)*x)/sqrt(d)))/(sqrt(e)*g^2) + (sqrt(d)*sqrt(e)*f*p*atan((sqrt(e)*x)/sqrt(d)))/(g^2*(e*f - d*g)) - (e*(-f)^(3/2)*p*log(sqrt(-f) - sqrt(g)*x))/(2*g^(5/2)*(e*f - d*g)) - (3*sqrt(f)*p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/g^(5/2) + (3*sqrt(f)*p*atan((sqrt(g)*x)/sqrt(f))*log(-((2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x)))))/(2*g^(5/2)) + (3*sqrt(f)*p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*g^(5/2)) + (e*(-f)^(3/2)*p*log(sqrt(-f) + sqrt(g)*x))/(2*g^(5/2)*(e*f - d*g)) + (x*log(c*(d + e*x^2)^p))/g^2 - (f*log(c*(d + e*x^2)^p))/(4*g^(5/2)*(sqrt(-f) - sqrt(g)*x)) + (f*log(c*(d + e*x^2)^p))/(4*g^(5/2)*(sqrt(-f) + sqrt(g)*x)) - (3*sqrt(f)*atan((sqrt(g)*x)/sqrt(f))*log(c*(d + e*x^2)^p))/(2*g^(5/2)) + (3*im*sqrt(f)*p*PolyLog(2, 1 - (2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(2*g^(5/2)) - (3*im*sqrt(f)*p*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(4*g^(5/2)) - (3*im*sqrt(f)*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(4*g^(5/2))]
    @test_int [x^2*log(c*(d + e*x^2)^p)/(f + g*x^2)^2, x, 40, -((sqrt(d)*sqrt(e)*p*atan((sqrt(e)*x)/sqrt(d)))/(g*(e*f - d*g))) - (e*sqrt(-f)*p*log(sqrt(-f) - sqrt(g)*x))/(2*g^(3/2)*(e*f - d*g)) + (p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(sqrt(f)*g^(3/2)) - (p*atan((sqrt(g)*x)/sqrt(f))*log(-((2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x)))))/(2*sqrt(f)*g^(3/2)) - (p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*sqrt(f)*g^(3/2)) + (e*sqrt(-f)*p*log(sqrt(-f) + sqrt(g)*x))/(2*g^(3/2)*(e*f - d*g)) + log(c*(d + e*x^2)^p)/(4*g^(3/2)*(sqrt(-f) - sqrt(g)*x)) - log(c*(d + e*x^2)^p)/(4*g^(3/2)*(sqrt(-f) + sqrt(g)*x)) + (atan((sqrt(g)*x)/sqrt(f))*log(c*(d + e*x^2)^p))/(2*sqrt(f)*g^(3/2)) - (im*p*PolyLog(2, 1 - (2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(2*sqrt(f)*g^(3/2)) + (im*p*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(4*sqrt(f)*g^(3/2)) + (im*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(4*sqrt(f)*g^(3/2))]
    @test_int [x^0*log(c*(d + e*x^2)^p)/(f + g*x^2)^2, x, 26, (sqrt(d)*sqrt(e)*p*atan((sqrt(e)*x)/sqrt(d)))/(f*(e*f - d*g)) - (e*p*log(sqrt(-f) - sqrt(g)*x))/(2*sqrt(-f)*sqrt(g)*(e*f - d*g)) + (p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(f^(3/2)*sqrt(g)) - (p*atan((sqrt(g)*x)/sqrt(f))*log(-((2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x)))))/(2*f^(3/2)*sqrt(g)) - (p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*f^(3/2)*sqrt(g)) + (e*p*log(sqrt(-f) + sqrt(g)*x))/(2*sqrt(-f)*sqrt(g)*(e*f - d*g)) - log(c*(d + e*x^2)^p)/(4*f*sqrt(g)*(sqrt(-f) - sqrt(g)*x)) + log(c*(d + e*x^2)^p)/(4*f*sqrt(g)*(sqrt(-f) + sqrt(g)*x)) + (atan((sqrt(g)*x)/sqrt(f))*log(c*(d + e*x^2)^p))/(2*f^(3/2)*sqrt(g)) - (im*p*PolyLog(2, 1 - (2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(2*f^(3/2)*sqrt(g)) + (im*p*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(4*f^(3/2)*sqrt(g)) + (im*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(4*f^(3/2)*sqrt(g))]
    @test_int [log(c*(d + e*x^2)^p)/(x^2*(f + g*x^2)^2), x, 42, (2*sqrt(e)*p*atan((sqrt(e)*x)/sqrt(d)))/(sqrt(d)*f^2) - (sqrt(d)*sqrt(e)*g*p*atan((sqrt(e)*x)/sqrt(d)))/(f^2*(e*f - d*g)) - (e*sqrt(g)*p*log(sqrt(-f) - sqrt(g)*x))/(2*(-f)^(3/2)*(e*f - d*g)) - (3*sqrt(g)*p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/f^(5/2) + (3*sqrt(g)*p*atan((sqrt(g)*x)/sqrt(f))*log(-((2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x)))))/(2*f^(5/2)) + (3*sqrt(g)*p*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*f^(5/2)) + (e*sqrt(g)*p*log(sqrt(-f) + sqrt(g)*x))/(2*(-f)^(3/2)*(e*f - d*g)) - log(c*(d + e*x^2)^p)/(f^2*x) + (sqrt(g)*log(c*(d + e*x^2)^p))/(4*f^2*(sqrt(-f) - sqrt(g)*x)) - (sqrt(g)*log(c*(d + e*x^2)^p))/(4*f^2*(sqrt(-f) + sqrt(g)*x)) - (3*sqrt(g)*atan((sqrt(g)*x)/sqrt(f))*log(c*(d + e*x^2)^p))/(2*f^(5/2)) + (3*im*sqrt(g)*p*PolyLog(2, 1 - (2*sqrt(f))/(sqrt(f) - im*sqrt(g)*x)))/(2*f^(5/2)) - (3*im*sqrt(g)*p*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*(sqrt(-d) - sqrt(e)*x))/((im*sqrt(e)*sqrt(f) - sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(4*f^(5/2)) - (3*im*sqrt(g)*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*(sqrt(-d) + sqrt(e)*x))/((im*sqrt(e)*sqrt(f) + sqrt(-d)*sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(4*f^(5/2))]

    @test_int [log(c*(a + b*x^2)^n)/(a + b*x^2), x, 6, (im*n*atan((sqrt(b)*x)/sqrt(a))^2)/(sqrt(a)*sqrt(b)) + (2*n*atan((sqrt(b)*x)/sqrt(a))*log((2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/(sqrt(a)*sqrt(b)) + (atan((sqrt(b)*x)/sqrt(a))*log(c*(a + b*x^2)^n))/(sqrt(a)*sqrt(b)) + (im*n*PolyLog(2, 1 - (2*sqrt(a))/(sqrt(a) + im*sqrt(b)*x)))/(sqrt(a)*sqrt(b))]

    @test_int [log(1 - x^2)/(2 - x^2), x, 12, sqrt(2)*atanh(x/sqrt(2))*log((2*sqrt(2))/(sqrt(2) + x)) - (atanh(x/sqrt(2))*log(-((4*(1 - x))/((2 - sqrt(2))*(sqrt(2) + x)))))/sqrt(2) - (atanh(x/sqrt(2))*log((4*(1 + x))/((2 + sqrt(2))*(sqrt(2) + x))))/sqrt(2) + (atanh(x/sqrt(2))*log(1 - x^2))/sqrt(2) - PolyLog(2, 1 - (2*sqrt(2))/(sqrt(2) + x))/sqrt(2) + PolyLog(2, 1 + (4*(1 - x))/((2 - sqrt(2))*(sqrt(2) + x)))/(2*sqrt(2)) + PolyLog(2, 1 - (4*(1 + x))/((2 + sqrt(2))*(sqrt(2) + x)))/(2*sqrt(2))]
    @test_int [log(d + e*x^2)/(1 - x^2), x, 11, 2*atanh(x)*log(2/(1 + x)) - atanh(x)*log((2*(sqrt(-d) - sqrt(e)*x))/((sqrt(-d) - sqrt(e))*(1 + x))) - atanh(x)*log((2*(sqrt(-d) + sqrt(e)*x))/((sqrt(-d) + sqrt(e))*(1 + x))) + atanh(x)*log(d + e*x^2) - PolyLog(2, 1 - 2/(1 + x)) + (1/2)*PolyLog(2, 1 - (2*(sqrt(-d) - sqrt(e)*x))/((sqrt(-d) - sqrt(e))*(1 + x))) + (1/2)*PolyLog(2, 1 - (2*(sqrt(-d) + sqrt(e)*x))/((sqrt(-d) + sqrt(e))*(1 + x)))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^r*(f+g*x^s)^q*log(c*(d+e*x^m)^n)*when*s=k*n*and*s*symbolic=#

    #= ::Subsubsection::Closed:: =#
    #=r>0=#

    @test_int [(f + g*x^(3*n))*log(c*(d + e*x^n)^p)/x, x, 8, -((d^2*g*p*x^n)/(3*e^2*n)) + (d*g*p*x^(2*n))/(6*e*n) - (g*p*x^(3*n))/(9*n) + (d^3*g*p*log(d + e*x^n))/(3*e^3*n) + (g*x^(3*n)*log(c*(d + e*x^n)^p))/(3*n) + (f*log(-((e*x^n)/d))*log(c*(d + e*x^n)^p))/n + (f*p*PolyLog(2, 1 + (e*x^n)/d))/n]
    @test_int [(f + g*x^(2*n))*log(c*(d + e*x^n)^p)/x, x, 8, (d*g*p*x^n)/(2*e*n) - (g*p*x^(2*n))/(4*n) - (d^2*g*p*log(d + e*x^n))/(2*e^2*n) + (g*x^(2*n)*log(c*(d + e*x^n)^p))/(2*n) + (f*log(-((e*x^n)/d))*log(c*(d + e*x^n)^p))/n + (f*p*PolyLog(2, 1 + (e*x^n)/d))/n]
    @test_int [(f + g*x^(1*n))*log(c*(d + e*x^n)^p)/x, x, 7, -((g*p*x^n)/n) + (g*(d + e*x^n)*log(c*(d + e*x^n)^p))/(e*n) + (f*log(-((e*x^n)/d))*log(c*(d + e*x^n)^p))/n + (f*p*PolyLog(2, 1 + (e*x^n)/d))/n]
    @test_int [(f + g/x^(1*n))*log(c*(d + e*x^n)^p)/x, x, 9, (e*g*p*log(x))/d - (e*g*p*log(d + e*x^n))/(d*n) - (g*log(c*(d + e*x^n)^p))/(x^n*n) + (f*log(-((e*x^n)/d))*log(c*(d + e*x^n)^p))/n + (f*p*PolyLog(2, 1 + (e*x^n)/d))/n]
    @test_int [(f + g/x^(2*n))*log(c*(d + e*x^n)^p)/x, x, 8, -((e*g*p)/(x^n*(2*d*n))) - (e^2*g*p*log(x))/(2*d^2) + (e^2*g*p*log(d + e*x^n))/(2*d^2*n) - (g*log(c*(d + e*x^n)^p))/(x^(2*n)*(2*n)) + (f*log(-((e*x^n)/d))*log(c*(d + e*x^n)^p))/n + (f*p*PolyLog(2, 1 + (e*x^n)/d))/n]

    @test_int [(f + g*x^(3*n))^2*log(c*(d + e*x^n)^p)/x, x, 11, -((2*d^2*f*g*p*x^n)/(3*e^2*n)) + (d^5*g^2*p*x^n)/(6*e^5*n) + (d*f*g*p*x^(2*n))/(3*e*n) - (d^4*g^2*p*x^(2*n))/(12*e^4*n) - (2*f*g*p*x^(3*n))/(9*n) + (d^3*g^2*p*x^(3*n))/(18*e^3*n) - (d^2*g^2*p*x^(4*n))/(24*e^2*n) + (d*g^2*p*x^(5*n))/(30*e*n) - (g^2*p*x^(6*n))/(36*n) + (2*d^3*f*g*p*log(d + e*x^n))/(3*e^3*n) - (d^6*g^2*p*log(d + e*x^n))/(6*e^6*n) + (2*f*g*x^(3*n)*log(c*(d + e*x^n)^p))/(3*n) + (g^2*x^(6*n)*log(c*(d + e*x^n)^p))/(6*n) + (f^2*log(-((e*x^n)/d))*log(c*(d + e*x^n)^p))/n + (f^2*p*PolyLog(2, 1 + (e*x^n)/d))/n]
    @test_int [(f + g*x^(2*n))^2*log(c*(d + e*x^n)^p)/x, x, 11, (d*f*g*p*x^n)/(e*n) + (d^3*g^2*p*x^n)/(4*e^3*n) - (f*g*p*x^(2*n))/(2*n) - (d^2*g^2*p*x^(2*n))/(8*e^2*n) + (d*g^2*p*x^(3*n))/(12*e*n) - (g^2*p*x^(4*n))/(16*n) - (d^2*f*g*p*log(d + e*x^n))/(e^2*n) - (d^4*g^2*p*log(d + e*x^n))/(4*e^4*n) + (f*g*x^(2*n)*log(c*(d + e*x^n)^p))/n + (g^2*x^(4*n)*log(c*(d + e*x^n)^p))/(4*n) + (f^2*log(-((e*x^n)/d))*log(c*(d + e*x^n)^p))/n + (f^2*p*PolyLog(2, 1 + (e*x^n)/d))/n]
    @test_int [(f + g*x^(1*n))^2*log(c*(d + e*x^n)^p)/x, x, 10, -((2*f*g*p*x^n)/n) + (d*g^2*p*x^n)/(2*e*n) - (g^2*p*x^(2*n))/(4*n) - (d^2*g^2*p*log(d + e*x^n))/(2*e^2*n) + (g^2*x^(2*n)*log(c*(d + e*x^n)^p))/(2*n) + (2*f*g*(d + e*x^n)*log(c*(d + e*x^n)^p))/(e*n) + (f^2*log(-((e*x^n)/d))*log(c*(d + e*x^n)^p))/n + (f^2*p*PolyLog(2, 1 + (e*x^n)/d))/n]
    @test_int [(f + g/x^(1*n))^2*log(c*(d + e*x^n)^p)/x, x, 12, -((e*g^2*p)/(x^n*(2*d*n))) + (2*e*f*g*p*log(x))/d - (e^2*g^2*p*log(x))/(2*d^2) - (2*e*f*g*p*log(d + e*x^n))/(d*n) + (e^2*g^2*p*log(d + e*x^n))/(2*d^2*n) - (g^2*log(c*(d + e*x^n)^p))/(x^(2*n)*(2*n)) - (2*f*g*log(c*(d + e*x^n)^p))/(x^n*n) + (f^2*log(-((e*x^n)/d))*log(c*(d + e*x^n)^p))/n + (f^2*p*PolyLog(2, 1 + (e*x^n)/d))/n]
    @test_int [(f + g/x^(2*n))^2*log(c*(d + e*x^n)^p)/x, x, 11, -((e*g^2*p)/(x^(3*n)*(12*d*n))) + (e^2*g^2*p)/(x^(2*n)*(8*d^2*n)) - (e*f*g*p)/(x^n*(d*n)) - (e^3*g^2*p)/(x^n*(4*d^3*n)) - (e^2*f*g*p*log(x))/d^2 - (e^4*g^2*p*log(x))/(4*d^4) + (e^2*f*g*p*log(d + e*x^n))/(d^2*n) + (e^4*g^2*p*log(d + e*x^n))/(4*d^4*n) - (g^2*log(c*(d + e*x^n)^p))/(x^(4*n)*(4*n)) - (f*g*log(c*(d + e*x^n)^p))/(x^(2*n)*n) + (f^2*log(-((e*x^n)/d))*log(c*(d + e*x^n)^p))/n + (f^2*p*PolyLog(2, 1 + (e*x^n)/d))/n]

    #= ::Subsubsection::Closed:: =#
    #=r<0=#

    @test_int [1/(f + g*x^(2*n))*log(c*(d + e*x^n)^p)/x, x, 13, (log(-((e*x^n)/d))*log(c*(d + e*x^n)^p))/(f*n) - (log(c*(d + e*x^n)^p)*log((e*(sqrt(-f) - sqrt(g)*x^n))/(e*sqrt(-f) + d*sqrt(g))))/(2*f*n) - (log(c*(d + e*x^n)^p)*log((e*(sqrt(-f) + sqrt(g)*x^n))/(e*sqrt(-f) - d*sqrt(g))))/(2*f*n) - (p*PolyLog(2, -((sqrt(g)*(d + e*x^n))/(e*sqrt(-f) - d*sqrt(g)))))/(2*f*n) - (p*PolyLog(2, (sqrt(g)*(d + e*x^n))/(e*sqrt(-f) + d*sqrt(g))))/(2*f*n) + (p*PolyLog(2, 1 + (e*x^n)/d))/(f*n)]
    @test_int [1/(f + g*x^(1*n))*log(c*(d + e*x^n)^p)/x, x, 8, (log(-((e*x^n)/d))*log(c*(d + e*x^n)^p))/(f*n) - (log(c*(d + e*x^n)^p)*log((e*(f + g*x^n))/(e*f - d*g)))/(f*n) - (p*PolyLog(2, -((g*(d + e*x^n))/(e*f - d*g))))/(f*n) + (p*PolyLog(2, 1 + (e*x^n)/d))/(f*n)]
    @test_int [1/(f + g/x^(1*n))*log(c*(d + e*x^n)^p)/x, x, 5, (log(c*(d + e*x^n)^p)*log(-((e*(g + f*x^n))/(d*f - e*g))))/(f*n) + (p*PolyLog(2, (f*(d + e*x^n))/(d*f - e*g)))/(f*n)]
    @test_int [1/(f + g/x^(2*n))*log(c*(d + e*x^n)^p)/x, x, 9, (log(c*(d + e*x^n)^p)*log((e*(sqrt(g) - sqrt(-f)*x^n))/(d*sqrt(-f) + e*sqrt(g))))/(2*f*n) + (log(c*(d + e*x^n)^p)*log(-((e*(sqrt(g) + sqrt(-f)*x^n))/(d*sqrt(-f) - e*sqrt(g)))))/(2*f*n) + (p*PolyLog(2, (sqrt(-f)*(d + e*x^n))/(d*sqrt(-f) - e*sqrt(g))))/(2*f*n) + (p*PolyLog(2, (sqrt(-f)*(d + e*x^n))/(d*sqrt(-f) + e*sqrt(g))))/(2*f*n)]

    @test_int [1/(f + g*x^(2*n))^2*log(c*(d + e*x^n)^p)/x, x, 19, -((d*e*sqrt(g)*p*atan((sqrt(g)*x^n)/sqrt(f)))/(2*f^(3/2)*(e^2*f + d^2*g)*n)) - (e^2*p*log(d + e*x^n))/(2*f*(e^2*f + d^2*g)*n) + log(c*(d + e*x^n)^p)/(2*f*n*(f + g*x^(2*n))) + (log(-((e*x^n)/d))*log(c*(d + e*x^n)^p))/(f^2*n) - (log(c*(d + e*x^n)^p)*log((e*(sqrt(-f) - sqrt(g)*x^n))/(e*sqrt(-f) + d*sqrt(g))))/(2*f^2*n) - (log(c*(d + e*x^n)^p)*log((e*(sqrt(-f) + sqrt(g)*x^n))/(e*sqrt(-f) - d*sqrt(g))))/(2*f^2*n) + (e^2*p*log(f + g*x^(2*n)))/(4*f*(e^2*f + d^2*g)*n) - (p*PolyLog(2, -((sqrt(g)*(d + e*x^n))/(e*sqrt(-f) - d*sqrt(g)))))/(2*f^2*n) - (p*PolyLog(2, (sqrt(g)*(d + e*x^n))/(e*sqrt(-f) + d*sqrt(g))))/(2*f^2*n) + (p*PolyLog(2, 1 + (e*x^n)/d))/(f^2*n)]
    @test_int [1/(f + g*x^(1*n))^2*log(c*(d + e*x^n)^p)/x, x, 12, -((e*p*log(d + e*x^n))/(f*(e*f - d*g)*n)) + log(c*(d + e*x^n)^p)/(f*n*(f + g*x^n)) + (log(-((e*x^n)/d))*log(c*(d + e*x^n)^p))/(f^2*n) + (e*p*log(f + g*x^n))/(f*(e*f - d*g)*n) - (log(c*(d + e*x^n)^p)*log((e*(f + g*x^n))/(e*f - d*g)))/(f^2*n) - (p*PolyLog(2, -((g*(d + e*x^n))/(e*f - d*g))))/(f^2*n) + (p*PolyLog(2, 1 + (e*x^n)/d))/(f^2*n)]
    @test_int [1/(f + g/x^(1*n))^2*log(c*(d + e*x^n)^p)/x, x, 10, (e*g*p*log(d + e*x^n))/(f^2*(d*f - e*g)*n) + (g*log(c*(d + e*x^n)^p))/(f^2*n*(g + f*x^n)) - (e*g*p*log(g + f*x^n))/(f^2*(d*f - e*g)*n) + (log(c*(d + e*x^n)^p)*log(-((e*(g + f*x^n))/(d*f - e*g))))/(f^2*n) + (p*PolyLog(2, (f*(d + e*x^n))/(d*f - e*g)))/(f^2*n)]
    @test_int [1/(f + g/x^(2*n))^2*log(c*(d + e*x^n)^p)/x, x, 17, -((d*e*sqrt(g)*p*atan((sqrt(f)*x^n)/sqrt(g)))/(2*f^(3/2)*(d^2*f + e^2*g)*n)) - (e^2*g*p*log(d + e*x^n))/(2*f^2*(d^2*f + e^2*g)*n) + (g*log(c*(d + e*x^n)^p))/(2*f^2*n*(g + f*x^(2*n))) + (log(c*(d + e*x^n)^p)*log((e*(sqrt(g) - sqrt(-f)*x^n))/(d*sqrt(-f) + e*sqrt(g))))/(2*f^2*n) + (log(c*(d + e*x^n)^p)*log(-((e*(sqrt(g) + sqrt(-f)*x^n))/(d*sqrt(-f) - e*sqrt(g)))))/(2*f^2*n) + (e^2*g*p*log(g + f*x^(2*n)))/(4*f^2*(d^2*f + e^2*g)*n) + (p*PolyLog(2, (sqrt(-f)*(d + e*x^n))/(d*sqrt(-f) - e*sqrt(g))))/(2*f^2*n) + (p*PolyLog(2, (sqrt(-f)*(d + e*x^n))/(d*sqrt(-f) + e*sqrt(g))))/(2*f^2*n)]

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

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^r*(f+g*x^s)^q*log(c*(d+e*x^m)^n)^q*when*q*symbolic=#

    #= ::Subsubsection::Closed:: =#
    #=r>0=#

    @test_int [(f + g*x^(2*n))^2*log(c*(d + e*x^n)^p)^q/x, x, 0, (4^(-1 - q)*g^2*(d + e*x^n)^4*Gamma(1 + q, -((4*log(c*(d + e*x^n)^p))/p))*log(c*(d + e*x^n)^p)^q)/((c*(d + e*x^n)^p)^(4/p)*(-(log(c*(d + e*x^n)^p)/p))^q*(e^4*n)) - (d*g^2*(d + e*x^n)^3*Gamma(1 + q, -((3*log(c*(d + e*x^n)^p))/p))*log(c*(d + e*x^n)^p)^q)/(3^q*(c*(d + e*x^n)^p)^(3/p)*(-(log(c*(d + e*x^n)^p)/p))^q*(e^4*n)) + (f*g*(d + e*x^n)^2*Gamma(1 + q, -((2*log(c*(d + e*x^n)^p))/p))*log(c*(d + e*x^n)^p)^q)/(2^q*(c*(d + e*x^n)^p)^(2/p)*(-(log(c*(d + e*x^n)^p)/p))^q*(e^2*n)) + (3*2^(-1 - q)*d^2*g^2*(d + e*x^n)^2*Gamma(1 + q, -((2*log(c*(d + e*x^n)^p))/p))*log(c*(d + e*x^n)^p)^q)/((c*(d + e*x^n)^p)^(2/p)*(-(log(c*(d + e*x^n)^p)/p))^q*(e^4*n)) - (2*d*f*g*(d + e*x^n)*Gamma(1 + q, -(log(c*(d + e*x^n)^p)/p))*log(c*(d + e*x^n)^p)^q)/((c*(d + e*x^n)^p)^p^(-1)*(-(log(c*(d + e*x^n)^p)/p))^q*(e^2*n)) - (d^3*g^2*(d + e*x^n)*Gamma(1 + q, -(log(c*(d + e*x^n)^p)/p))*log(c*(d + e*x^n)^p)^q)/((c*(d + e*x^n)^p)^p^(-1)*(-(log(c*(d + e*x^n)^p)/p))^q*(e^4*n)) + f^2*Unintegrable(log(c*(d + e*x^n)^p)^q/x, x), Unintegrable(((f + g*x^(2*n))^2*log(c*(d + e*x^n)^p)^q)/x, x)]
    @test_int [(f + g*x^(1*n))^2*log(c*(d + e*x^n)^p)^q/x, x, 0, (2^(-1 - q)*g^2*(d + e*x^n)^2*Gamma(1 + q, -((2*log(c*(d + e*x^n)^p))/p))*log(c*(d + e*x^n)^p)^q)/((c*(d + e*x^n)^p)^(2/p)*(-(log(c*(d + e*x^n)^p)/p))^q*(e^2*n)) + (2*f*g*(d + e*x^n)*Gamma(1 + q, -(log(c*(d + e*x^n)^p)/p))*log(c*(d + e*x^n)^p)^q)/((c*(d + e*x^n)^p)^p^(-1)*(-(log(c*(d + e*x^n)^p)/p))^q*(e*n)) - (d*g^2*(d + e*x^n)*Gamma(1 + q, -(log(c*(d + e*x^n)^p)/p))*log(c*(d + e*x^n)^p)^q)/((c*(d + e*x^n)^p)^p^(-1)*(-(log(c*(d + e*x^n)^p)/p))^q*(e^2*n)) + f^2*Unintegrable(log(c*(d + e*x^n)^p)^q/x, x), Unintegrable(((f + g*x^n)^2*log(c*(d + e*x^n)^p)^q)/x, x)]
    @test_int [(f + g/x^(1*n))^2*log(c*(d + e*x^n)^p)^q/x, x, 0, Unintegrable(((f + g/x^n)^2*log(c*(d + e*x^n)^p)^q)/x, x)]
    @test_int [(f + g/x^(2*n))^2*log(c*(d + e*x^n)^p)^q/x, x, 0, Unintegrable(((f + g/x^(2*n))^2*log(c*(d + e*x^n)^p)^q)/x, x)]

    #= ::Subsubsection::Closed:: =#
    #=r<0=#

    @test_int [log(c*(d + e*x^n)^p)^q/(x*(f + g*x^(2*n))), x, 0, Unintegrable(log(c*(d + e*x^n)^p)^q/(x*(f + g*x^(2*n))), x)]
    @test_int [log(c*(d + e*x^n)^p)^q/(x*(f + g*x^(1*n))), x, 0, Unintegrable(log(c*(d + e*x^n)^p)^q/(x*(f + g*x^n)), x)]
    @test_int [log(c*(d + e*x^n)^p)^q/(x*(f + g/x^(1*n))), x, 0, Unintegrable(log(c*(d + e*x^n)^p)^q/(x*(f + g/x^n)), x)]
    @test_int [log(c*(d + e*x^n)^p)^q/(x*(f + g/x^(2*n))), x, 0, Unintegrable(log(c*(d + e*x^n)^p)^q/(x*(f + g/x^(2*n))), x)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(h*x)^r*log(f*x^s)^q*log(c*(d+e*x^m)^n)^p=#

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

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f+g*x)^q*log(c*(d+e*x^m)/x^n)=#

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

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

    @test_int [log((a + b*x)/x)/(c + d*x), x, 9, (log(b + a/x)*log(c + d*x))/d + (log(-((d*x)/c))*log(c + d*x))/d - (log(-((d*(a + b*x))/(b*c - a*d)))*log(c + d*x))/d + PolyLog(2, 1 + (d*x)/c)/d - PolyLog(2, (b*(c + d*x))/(b*c - a*d))/d]
    @test_int [log((a + b*x^2)/x^2)/(c + d*x), x, 14, (log(b + a/x^2)*log(c + d*x))/d + (2*log(-((d*x)/c))*log(c + d*x))/d - (log((d*(sqrt(-a) - sqrt(b)*x))/(sqrt(b)*c + sqrt(-a)*d))*log(c + d*x))/d - (log(-((d*(sqrt(-a) + sqrt(b)*x))/(sqrt(b)*c - sqrt(-a)*d)))*log(c + d*x))/d + (2*PolyLog(2, 1 + (d*x)/c))/d - PolyLog(2, (sqrt(b)*(c + d*x))/(sqrt(b)*c - sqrt(-a)*d))/d - PolyLog(2, (sqrt(b)*(c + d*x))/(sqrt(b)*c + sqrt(-a)*d))/d]
    @test_int [log((a + b*x^n)/x^n)/(c + d*x), x, 1, Unintegrable(log(b + a/x^n)/(c + d*x), x)]

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

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

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

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

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

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

    #= ::Subsubsection::Closed:: =#
    #=m=1=#

    @test_int [x^3*(a + b*log(c*(d + e*sqrt(x))^n)), x, 4, (b*d^7*n*sqrt(x))/(4*e^7) - (b*d^6*n*x)/(8*e^6) + (b*d^5*n*x^(3/2))/(12*e^5) - (b*d^4*n*x^2)/(16*e^4) + (b*d^3*n*x^(5/2))/(20*e^3) - (b*d^2*n*x^3)/(24*e^2) + (b*d*n*x^(7/2))/(28*e) - (1/32)*b*n*x^4 - (b*d^8*n*log(d + e*sqrt(x)))/(4*e^8) + (1/4)*x^4*(a + b*log(c*(d + e*sqrt(x))^n))]
    @test_int [x^2*(a + b*log(c*(d + e*sqrt(x))^n)), x, 4, (b*d^5*n*sqrt(x))/(3*e^5) - (b*d^4*n*x)/(6*e^4) + (b*d^3*n*x^(3/2))/(9*e^3) - (b*d^2*n*x^2)/(12*e^2) + (b*d*n*x^(5/2))/(15*e) - (1/18)*b*n*x^3 - (b*d^6*n*log(d + e*sqrt(x)))/(3*e^6) + (1/3)*x^3*(a + b*log(c*(d + e*sqrt(x))^n))]
    @test_int [x^1*(a + b*log(c*(d + e*sqrt(x))^n)), x, 4, (b*d^3*n*sqrt(x))/(2*e^3) - (b*d^2*n*x)/(4*e^2) + (b*d*n*x^(3/2))/(6*e) - (1/8)*b*n*x^2 - (b*d^4*n*log(d + e*sqrt(x)))/(2*e^4) + (1/2)*x^2*(a + b*log(c*(d + e*sqrt(x))^n))]
    @test_int [x^0*(a + b*log(c*(d + e*sqrt(x))^n)), x, 5, (b*d*n*sqrt(x))/e + a*x - (b*n*x)/2 - (b*d^2*n*log(d + e*sqrt(x)))/e^2 + b*x*log(c*(d + e*sqrt(x))^n)]
    @test_int [(a + b*log(c*(d + e*sqrt(x))^n))/x^1, x, 3, 2*(a + b*log(c*(d + e*sqrt(x))^n))*log(-((e*sqrt(x))/d)) + 2*b*n*PolyLog(2, 1 + (e*sqrt(x))/d)]
    @test_int [(a + b*log(c*(d + e*sqrt(x))^n))/x^2, x, 4, -((b*e*n)/(d*sqrt(x))) + (b*e^2*n*log(d + e*sqrt(x)))/d^2 - (a + b*log(c*(d + e*sqrt(x))^n))/x - (b*e^2*n*log(x))/(2*d^2)]
    @test_int [(a + b*log(c*(d + e*sqrt(x))^n))/x^3, x, 4, -((b*e*n)/(6*d*x^(3/2))) + (b*e^2*n)/(4*d^2*x) - (b*e^3*n)/(2*d^3*sqrt(x)) + (b*e^4*n*log(d + e*sqrt(x)))/(2*d^4) - (a + b*log(c*(d + e*sqrt(x))^n))/(2*x^2) - (b*e^4*n*log(x))/(4*d^4)]
    @test_int [(a + b*log(c*(d + e*sqrt(x))^n))/x^4, x, 4, -((b*e*n)/(15*d*x^(5/2))) + (b*e^2*n)/(12*d^2*x^2) - (b*e^3*n)/(9*d^3*x^(3/2)) + (b*e^4*n)/(6*d^4*x) - (b*e^5*n)/(3*d^5*sqrt(x)) + (b*e^6*n*log(d + e*sqrt(x)))/(3*d^6) - (a + b*log(c*(d + e*sqrt(x))^n))/(3*x^3) - (b*e^6*n*log(x))/(6*d^6)]

    @test_int [x^2*(a + b*log(c*(d + e*sqrt(x))^n))^2, x, 8, (5*b^2*d^4*n^2*(d + e*sqrt(x))^2)/(2*e^6) - (40*b^2*d^3*n^2*(d + e*sqrt(x))^3)/(27*e^6) + (5*b^2*d^2*n^2*(d + e*sqrt(x))^4)/(8*e^6) - (4*b^2*d*n^2*(d + e*sqrt(x))^5)/(25*e^6) + (b^2*n^2*(d + e*sqrt(x))^6)/(54*e^6) - (4*b^2*d^5*n^2*sqrt(x))/e^5 + (b^2*d^6*n^2*log(d + e*sqrt(x))^2)/(3*e^6) + (4*b*d^5*n*(d + e*sqrt(x))*(a + b*log(c*(d + e*sqrt(x))^n)))/e^6 - (5*b*d^4*n*(d + e*sqrt(x))^2*(a + b*log(c*(d + e*sqrt(x))^n)))/e^6 + (40*b*d^3*n*(d + e*sqrt(x))^3*(a + b*log(c*(d + e*sqrt(x))^n)))/(9*e^6) - (5*b*d^2*n*(d + e*sqrt(x))^4*(a + b*log(c*(d + e*sqrt(x))^n)))/(2*e^6) + (4*b*d*n*(d + e*sqrt(x))^5*(a + b*log(c*(d + e*sqrt(x))^n)))/(5*e^6) - (b*n*(d + e*sqrt(x))^6*(a + b*log(c*(d + e*sqrt(x))^n)))/(9*e^6) - (2*b*d^6*n*log(d + e*sqrt(x))*(a + b*log(c*(d + e*sqrt(x))^n)))/(3*e^6) + (1/3)*x^3*(a + b*log(c*(d + e*sqrt(x))^n))^2]
    @test_int [x^1*(a + b*log(c*(d + e*sqrt(x))^n))^2, x, 8, (3*b^2*d^2*n^2*(d + e*sqrt(x))^2)/(2*e^4) - (4*b^2*d*n^2*(d + e*sqrt(x))^3)/(9*e^4) + (b^2*n^2*(d + e*sqrt(x))^4)/(16*e^4) - (4*b^2*d^3*n^2*sqrt(x))/e^3 + (b^2*d^4*n^2*log(d + e*sqrt(x))^2)/(2*e^4) + (4*b*d^3*n*(d + e*sqrt(x))*(a + b*log(c*(d + e*sqrt(x))^n)))/e^4 - (3*b*d^2*n*(d + e*sqrt(x))^2*(a + b*log(c*(d + e*sqrt(x))^n)))/e^4 + (4*b*d*n*(d + e*sqrt(x))^3*(a + b*log(c*(d + e*sqrt(x))^n)))/(3*e^4) - (b*n*(d + e*sqrt(x))^4*(a + b*log(c*(d + e*sqrt(x))^n)))/(4*e^4) - (b*d^4*n*log(d + e*sqrt(x))*(a + b*log(c*(d + e*sqrt(x))^n)))/e^4 + (1/2)*x^2*(a + b*log(c*(d + e*sqrt(x))^n))^2]
    @test_int [x^0*(a + b*log(c*(d + e*sqrt(x))^n))^2, x, 10, (b^2*n^2*(d + e*sqrt(x))^2)/(2*e^2) + (4*a*b*d*n*sqrt(x))/e - (4*b^2*d*n^2*sqrt(x))/e + (4*b^2*d*n*(d + e*sqrt(x))*log(c*(d + e*sqrt(x))^n))/e^2 - (b*n*(d + e*sqrt(x))^2*(a + b*log(c*(d + e*sqrt(x))^n)))/e^2 - (2*d*(d + e*sqrt(x))*(a + b*log(c*(d + e*sqrt(x))^n))^2)/e^2 + ((d + e*sqrt(x))^2*(a + b*log(c*(d + e*sqrt(x))^n))^2)/e^2]
    @test_int [(a + b*log(c*(d + e*sqrt(x))^n))^2/x^1, x, 5, 2*(a + b*log(c*(d + e*sqrt(x))^n))^2*log(-((e*sqrt(x))/d)) + 4*b*n*(a + b*log(c*(d + e*sqrt(x))^n))*PolyLog(2, 1 + (e*sqrt(x))/d) - 4*b^2*n^2*PolyLog(3, 1 + (e*sqrt(x))/d)]
    @test_int [(a + b*log(c*(d + e*sqrt(x))^n))^2/x^2, x, 8, -((2*b*e*n*(d + e*sqrt(x))*(a + b*log(c*(d + e*sqrt(x))^n)))/(d^2*sqrt(x))) - (2*b*e^2*n*log(1 - d/(d + e*sqrt(x)))*(a + b*log(c*(d + e*sqrt(x))^n)))/d^2 - (a + b*log(c*(d + e*sqrt(x))^n))^2/x + (b^2*e^2*n^2*log(x))/d^2 + (2*b^2*e^2*n^2*PolyLog(2, d/(d + e*sqrt(x))))/d^2]
    @test_int [(a + b*log(c*(d + e*sqrt(x))^n))^2/x^3, x, 16, -((b^2*e^2*n^2)/(6*d^2*x)) + (5*b^2*e^3*n^2)/(6*d^3*sqrt(x)) - (5*b^2*e^4*n^2*log(d + e*sqrt(x)))/(6*d^4) - (b*e*n*(a + b*log(c*(d + e*sqrt(x))^n)))/(3*d*x^(3/2)) + (b*e^2*n*(a + b*log(c*(d + e*sqrt(x))^n)))/(2*d^2*x) - (b*e^3*n*(d + e*sqrt(x))*(a + b*log(c*(d + e*sqrt(x))^n)))/(d^4*sqrt(x)) - (b*e^4*n*log(1 - d/(d + e*sqrt(x)))*(a + b*log(c*(d + e*sqrt(x))^n)))/d^4 - (a + b*log(c*(d + e*sqrt(x))^n))^2/(2*x^2) + (11*b^2*e^4*n^2*log(x))/(12*d^4) + (b^2*e^4*n^2*PolyLog(2, d/(d + e*sqrt(x))))/d^4]
    @test_int [(a + b*log(c*(d + e*sqrt(x))^n))^2/x^4, x, 24, -((b^2*e^2*n^2)/(30*d^2*x^2)) + (b^2*e^3*n^2)/(10*d^3*x^(3/2)) - (47*b^2*e^4*n^2)/(180*d^4*x) + (77*b^2*e^5*n^2)/(90*d^5*sqrt(x)) - (77*b^2*e^6*n^2*log(d + e*sqrt(x)))/(90*d^6) - (2*b*e*n*(a + b*log(c*(d + e*sqrt(x))^n)))/(15*d*x^(5/2)) + (b*e^2*n*(a + b*log(c*(d + e*sqrt(x))^n)))/(6*d^2*x^2) - (2*b*e^3*n*(a + b*log(c*(d + e*sqrt(x))^n)))/(9*d^3*x^(3/2)) + (b*e^4*n*(a + b*log(c*(d + e*sqrt(x))^n)))/(3*d^4*x) - (2*b*e^5*n*(d + e*sqrt(x))*(a + b*log(c*(d + e*sqrt(x))^n)))/(3*d^6*sqrt(x)) - (2*b*e^6*n*log(1 - d/(d + e*sqrt(x)))*(a + b*log(c*(d + e*sqrt(x))^n)))/(3*d^6) - (a + b*log(c*(d + e*sqrt(x))^n))^2/(3*x^3) + (137*b^2*e^6*n^2*log(x))/(180*d^6) + (2*b^2*e^6*n^2*PolyLog(2, d/(d + e*sqrt(x))))/(3*d^6)]

    @test_int [x^2*(a + b*log(c*(d + e*sqrt(x))^n))^3, x, 28, -((15*b^3*d^4*n^3*(d + e*sqrt(x))^2)/(4*e^6)) + (40*b^3*d^3*n^3*(d + e*sqrt(x))^3)/(27*e^6) - (15*b^3*d^2*n^3*(d + e*sqrt(x))^4)/(32*e^6) + (12*b^3*d*n^3*(d + e*sqrt(x))^5)/(125*e^6) - (b^3*n^3*(d + e*sqrt(x))^6)/(108*e^6) - (12*a*b^2*d^5*n^2*sqrt(x))/e^5 + (12*b^3*d^5*n^3*sqrt(x))/e^5 - (12*b^3*d^5*n^2*(d + e*sqrt(x))*log(c*(d + e*sqrt(x))^n))/e^6 + (15*b^2*d^4*n^2*(d + e*sqrt(x))^2*(a + b*log(c*(d + e*sqrt(x))^n)))/(2*e^6) - (40*b^2*d^3*n^2*(d + e*sqrt(x))^3*(a + b*log(c*(d + e*sqrt(x))^n)))/(9*e^6) + (15*b^2*d^2*n^2*(d + e*sqrt(x))^4*(a + b*log(c*(d + e*sqrt(x))^n)))/(8*e^6) - (12*b^2*d*n^2*(d + e*sqrt(x))^5*(a + b*log(c*(d + e*sqrt(x))^n)))/(25*e^6) + (b^2*n^2*(d + e*sqrt(x))^6*(a + b*log(c*(d + e*sqrt(x))^n)))/(18*e^6) + (6*b*d^5*n*(d + e*sqrt(x))*(a + b*log(c*(d + e*sqrt(x))^n))^2)/e^6 - (15*b*d^4*n*(d + e*sqrt(x))^2*(a + b*log(c*(d + e*sqrt(x))^n))^2)/(2*e^6) + (20*b*d^3*n*(d + e*sqrt(x))^3*(a + b*log(c*(d + e*sqrt(x))^n))^2)/(3*e^6) - (15*b*d^2*n*(d + e*sqrt(x))^4*(a + b*log(c*(d + e*sqrt(x))^n))^2)/(4*e^6) + (6*b*d*n*(d + e*sqrt(x))^5*(a + b*log(c*(d + e*sqrt(x))^n))^2)/(5*e^6) - (b*n*(d + e*sqrt(x))^6*(a + b*log(c*(d + e*sqrt(x))^n))^2)/(6*e^6) - (2*d^5*(d + e*sqrt(x))*(a + b*log(c*(d + e*sqrt(x))^n))^3)/e^6 + (5*d^4*(d + e*sqrt(x))^2*(a + b*log(c*(d + e*sqrt(x))^n))^3)/e^6 - (20*d^3*(d + e*sqrt(x))^3*(a + b*log(c*(d + e*sqrt(x))^n))^3)/(3*e^6) + (5*d^2*(d + e*sqrt(x))^4*(a + b*log(c*(d + e*sqrt(x))^n))^3)/e^6 - (2*d*(d + e*sqrt(x))^5*(a + b*log(c*(d + e*sqrt(x))^n))^3)/e^6 + ((d + e*sqrt(x))^6*(a + b*log(c*(d + e*sqrt(x))^n))^3)/(3*e^6)]
    @test_int [x^1*(a + b*log(c*(d + e*sqrt(x))^n))^3, x, 20, -((9*b^3*d^2*n^3*(d + e*sqrt(x))^2)/(4*e^4)) + (4*b^3*d*n^3*(d + e*sqrt(x))^3)/(9*e^4) - (3*b^3*n^3*(d + e*sqrt(x))^4)/(64*e^4) - (12*a*b^2*d^3*n^2*sqrt(x))/e^3 + (12*b^3*d^3*n^3*sqrt(x))/e^3 - (12*b^3*d^3*n^2*(d + e*sqrt(x))*log(c*(d + e*sqrt(x))^n))/e^4 + (9*b^2*d^2*n^2*(d + e*sqrt(x))^2*(a + b*log(c*(d + e*sqrt(x))^n)))/(2*e^4) - (4*b^2*d*n^2*(d + e*sqrt(x))^3*(a + b*log(c*(d + e*sqrt(x))^n)))/(3*e^4) + (3*b^2*n^2*(d + e*sqrt(x))^4*(a + b*log(c*(d + e*sqrt(x))^n)))/(16*e^4) + (6*b*d^3*n*(d + e*sqrt(x))*(a + b*log(c*(d + e*sqrt(x))^n))^2)/e^4 - (9*b*d^2*n*(d + e*sqrt(x))^2*(a + b*log(c*(d + e*sqrt(x))^n))^2)/(2*e^4) + (2*b*d*n*(d + e*sqrt(x))^3*(a + b*log(c*(d + e*sqrt(x))^n))^2)/e^4 - (3*b*n*(d + e*sqrt(x))^4*(a + b*log(c*(d + e*sqrt(x))^n))^2)/(8*e^4) - (2*d^3*(d + e*sqrt(x))*(a + b*log(c*(d + e*sqrt(x))^n))^3)/e^4 + (3*d^2*(d + e*sqrt(x))^2*(a + b*log(c*(d + e*sqrt(x))^n))^3)/e^4 - (2*d*(d + e*sqrt(x))^3*(a + b*log(c*(d + e*sqrt(x))^n))^3)/e^4 + ((d + e*sqrt(x))^4*(a + b*log(c*(d + e*sqrt(x))^n))^3)/(2*e^4)]
    @test_int [x^0*(a + b*log(c*(d + e*sqrt(x))^n))^3, x, 12, -((3*b^3*n^3*(d + e*sqrt(x))^2)/(4*e^2)) - (12*a*b^2*d*n^2*sqrt(x))/e + (12*b^3*d*n^3*sqrt(x))/e - (12*b^3*d*n^2*(d + e*sqrt(x))*log(c*(d + e*sqrt(x))^n))/e^2 + (3*b^2*n^2*(d + e*sqrt(x))^2*(a + b*log(c*(d + e*sqrt(x))^n)))/(2*e^2) + (6*b*d*n*(d + e*sqrt(x))*(a + b*log(c*(d + e*sqrt(x))^n))^2)/e^2 - (3*b*n*(d + e*sqrt(x))^2*(a + b*log(c*(d + e*sqrt(x))^n))^2)/(2*e^2) - (2*d*(d + e*sqrt(x))*(a + b*log(c*(d + e*sqrt(x))^n))^3)/e^2 + ((d + e*sqrt(x))^2*(a + b*log(c*(d + e*sqrt(x))^n))^3)/e^2]
    @test_int [(a + b*log(c*(d + e*sqrt(x))^n))^3/x^1, x, 6, 2*(a + b*log(c*(d + e*sqrt(x))^n))^3*log(-((e*sqrt(x))/d)) + 6*b*n*(a + b*log(c*(d + e*sqrt(x))^n))^2*PolyLog(2, 1 + (e*sqrt(x))/d) - 12*b^2*n^2*(a + b*log(c*(d + e*sqrt(x))^n))*PolyLog(3, 1 + (e*sqrt(x))/d) + 12*b^3*n^3*PolyLog(4, 1 + (e*sqrt(x))/d)]
    @test_int [(a + b*log(c*(d + e*sqrt(x))^n))^3/x^2, x, 10, -((3*b*e*n*(d + e*sqrt(x))*(a + b*log(c*(d + e*sqrt(x))^n))^2)/(d^2*sqrt(x))) - (3*b*e^2*n*log(1 - d/(d + e*sqrt(x)))*(a + b*log(c*(d + e*sqrt(x))^n))^2)/d^2 - (a + b*log(c*(d + e*sqrt(x))^n))^3/x + (6*b^2*e^2*n^2*(a + b*log(c*(d + e*sqrt(x))^n))*log(-((e*sqrt(x))/d)))/d^2 + (6*b^2*e^2*n^2*(a + b*log(c*(d + e*sqrt(x))^n))*PolyLog(2, d/(d + e*sqrt(x))))/d^2 + (6*b^3*e^2*n^3*PolyLog(2, 1 + (e*sqrt(x))/d))/d^2 + (6*b^3*e^2*n^3*PolyLog(3, d/(d + e*sqrt(x))))/d^2]
    @test_int [(a + b*log(c*(d + e*sqrt(x))^n))^3/x^3, x, 28, -((b^3*e^3*n^3)/(2*d^3*sqrt(x))) + (b^3*e^4*n^3*log(d + e*sqrt(x)))/(2*d^4) - (b^2*e^2*n^2*(a + b*log(c*(d + e*sqrt(x))^n)))/(2*d^2*x) + (5*b^2*e^3*n^2*(d + e*sqrt(x))*(a + b*log(c*(d + e*sqrt(x))^n)))/(2*d^4*sqrt(x)) + (5*b^2*e^4*n^2*log(1 - d/(d + e*sqrt(x)))*(a + b*log(c*(d + e*sqrt(x))^n)))/(2*d^4) - (b*e*n*(a + b*log(c*(d + e*sqrt(x))^n))^2)/(2*d*x^(3/2)) + (3*b*e^2*n*(a + b*log(c*(d + e*sqrt(x))^n))^2)/(4*d^2*x) - (3*b*e^3*n*(d + e*sqrt(x))*(a + b*log(c*(d + e*sqrt(x))^n))^2)/(2*d^4*sqrt(x)) - (3*b*e^4*n*log(1 - d/(d + e*sqrt(x)))*(a + b*log(c*(d + e*sqrt(x))^n))^2)/(2*d^4) - (a + b*log(c*(d + e*sqrt(x))^n))^3/(2*x^2) + (3*b^2*e^4*n^2*(a + b*log(c*(d + e*sqrt(x))^n))*log(-((e*sqrt(x))/d)))/d^4 - (3*b^3*e^4*n^3*log(x))/(2*d^4) - (5*b^3*e^4*n^3*PolyLog(2, d/(d + e*sqrt(x))))/(2*d^4) + (3*b^2*e^4*n^2*(a + b*log(c*(d + e*sqrt(x))^n))*PolyLog(2, d/(d + e*sqrt(x))))/d^4 + (3*b^3*e^4*n^3*PolyLog(2, 1 + (e*sqrt(x))/d))/d^4 + (3*b^3*e^4*n^3*PolyLog(3, d/(d + e*sqrt(x))))/d^4]

    #= ::Subsubsection::Closed:: =#
    #=m=-1=#

    @test_int [x^3*(a + b*log(c*(d + e/sqrt(x))^n)), x, 4, (b*e^7*n*sqrt(x))/(4*d^7) - (b*e^6*n*x)/(8*d^6) + (b*e^5*n*x^(3/2))/(12*d^5) - (b*e^4*n*x^2)/(16*d^4) + (b*e^3*n*x^(5/2))/(20*d^3) - (b*e^2*n*x^3)/(24*d^2) + (b*e*n*x^(7/2))/(28*d) - (b*e^8*n*log(d + e/sqrt(x)))/(4*d^8) + (x^4*(a + b*log(c*(d + e/sqrt(x))^n)))/4 - (b*e^8*n*log(x))/(8*d^8)]
    @test_int [x^2*(a + b*log(c*(d + e/sqrt(x))^n)), x, 4, (b*e^5*n*sqrt(x))/(3*d^5) - (b*e^4*n*x)/(6*d^4) + (b*e^3*n*x^(3/2))/(9*d^3) - (b*e^2*n*x^2)/(12*d^2) + (b*e*n*x^(5/2))/(15*d) - (b*e^6*n*log(d + e/sqrt(x)))/(3*d^6) + (x^3*(a + b*log(c*(d + e/sqrt(x))^n)))/3 - (b*e^6*n*log(x))/(6*d^6)]
    @test_int [x^1*(a + b*log(c*(d + e/sqrt(x))^n)), x, 4, (b*e^3*n*sqrt(x))/(2*d^3) - (b*e^2*n*x)/(4*d^2) + (b*e*n*x^(3/2))/(6*d) - (b*e^4*n*log(d + e/sqrt(x)))/(2*d^4) + (x^2*(a + b*log(c*(d + e/sqrt(x))^n)))/2 - (b*e^4*n*log(x))/(4*d^4)]
    @test_int [x^0*(a + b*log(c*(d + e/sqrt(x))^n)), x, 6, (b*e*n*sqrt(x))/d + a*x + b*x*log(c*(d + e/sqrt(x))^n) - (b*e^2*n*log(e + d*sqrt(x)))/d^2]
    @test_int [(a + b*log(c*(d + e/sqrt(x))^n))/x^1, x, 3, -2*(a + b*log(c*(d + e/sqrt(x))^n))*log(-(e/(d*sqrt(x)))) - 2*b*n*PolyLog(2, 1 + e/(d*sqrt(x)))]
    @test_int [(a + b*log(c*(d + e/sqrt(x))^n))/x^2, x, 4, (b*n)/(2*x) - (b*d*n)/(e*sqrt(x)) + (b*d^2*n*log(d + e/sqrt(x)))/e^2 - (a + b*log(c*(d + e/sqrt(x))^n))/x]
    @test_int [(a + b*log(c*(d + e/sqrt(x))^n))/x^3, x, 4, (b*n)/(8*x^2) - (b*d*n)/(6*e*x^(3/2)) + (b*d^2*n)/(4*e^2*x) - (b*d^3*n)/(2*e^3*sqrt(x)) + (b*d^4*n*log(d + e/sqrt(x)))/(2*e^4) - (a + b*log(c*(d + e/sqrt(x))^n))/(2*x^2)]
    @test_int [(a + b*log(c*(d + e/sqrt(x))^n))/x^4, x, 4, (b*n)/(18*x^3) - (b*d*n)/(15*e*x^(5/2)) + (b*d^2*n)/(12*e^2*x^2) - (b*d^3*n)/(9*e^3*x^(3/2)) + (b*d^4*n)/(6*e^4*x) - (b*d^5*n)/(3*e^5*sqrt(x)) + (b*d^6*n*log(d + e/sqrt(x)))/(3*e^6) - (a + b*log(c*(d + e/sqrt(x))^n))/(3*x^3)]

    @test_int [x^2*(a + b*log(c*(d + e/sqrt(x))^n))^2, x, 24, -((77*b^2*e^5*n^2*sqrt(x))/(90*d^5)) + (47*b^2*e^4*n^2*x)/(180*d^4) - (b^2*e^3*n^2*x^(3/2))/(10*d^3) + (b^2*e^2*n^2*x^2)/(30*d^2) + (77*b^2*e^6*n^2*log(d + e/sqrt(x)))/(90*d^6) + (2*b*e^5*n*(d + e/sqrt(x))*sqrt(x)*(a + b*log(c*(d + e/sqrt(x))^n)))/(3*d^6) - (b*e^4*n*x*(a + b*log(c*(d + e/sqrt(x))^n)))/(3*d^4) + (2*b*e^3*n*x^(3/2)*(a + b*log(c*(d + e/sqrt(x))^n)))/(9*d^3) - (b*e^2*n*x^2*(a + b*log(c*(d + e/sqrt(x))^n)))/(6*d^2) + (2*b*e*n*x^(5/2)*(a + b*log(c*(d + e/sqrt(x))^n)))/(15*d) + (2*b*e^6*n*log(1 - d/(d + e/sqrt(x)))*(a + b*log(c*(d + e/sqrt(x))^n)))/(3*d^6) + (1/3)*x^3*(a + b*log(c*(d + e/sqrt(x))^n))^2 + (137*b^2*e^6*n^2*log(x))/(180*d^6) - (2*b^2*e^6*n^2*PolyLog(2, d/(d + e/sqrt(x))))/(3*d^6)]
    @test_int [x^1*(a + b*log(c*(d + e/sqrt(x))^n))^2, x, 16, -((5*b^2*e^3*n^2*sqrt(x))/(6*d^3)) + (b^2*e^2*n^2*x)/(6*d^2) + (5*b^2*e^4*n^2*log(d + e/sqrt(x)))/(6*d^4) + (b*e^3*n*(d + e/sqrt(x))*sqrt(x)*(a + b*log(c*(d + e/sqrt(x))^n)))/d^4 - (b*e^2*n*x*(a + b*log(c*(d + e/sqrt(x))^n)))/(2*d^2) + (b*e*n*x^(3/2)*(a + b*log(c*(d + e/sqrt(x))^n)))/(3*d) + (b*e^4*n*log(1 - d/(d + e/sqrt(x)))*(a + b*log(c*(d + e/sqrt(x))^n)))/d^4 + (1/2)*x^2*(a + b*log(c*(d + e/sqrt(x))^n))^2 + (11*b^2*e^4*n^2*log(x))/(12*d^4) - (b^2*e^4*n^2*PolyLog(2, d/(d + e/sqrt(x))))/d^4]
    @test_int [x^0*(a + b*log(c*(d + e/sqrt(x))^n))^2, x, 9, (2*b*e*n*(d + e/sqrt(x))*sqrt(x)*(a + b*log(c*(d + e/sqrt(x))^n)))/d^2 + (2*b*e^2*n*log(1 - d/(d + e/sqrt(x)))*(a + b*log(c*(d + e/sqrt(x))^n)))/d^2 + x*(a + b*log(c*(d + e/sqrt(x))^n))^2 + (b^2*e^2*n^2*log(x))/d^2 - (2*b^2*e^2*n^2*PolyLog(2, d/(d + e/sqrt(x))))/d^2]
    @test_int [(a + b*log(c*(d + e/sqrt(x))^n))^2/x^1, x, 5, -2*(a + b*log(c*(d + e/sqrt(x))^n))^2*log(-(e/(d*sqrt(x)))) - 4*b*n*(a + b*log(c*(d + e/sqrt(x))^n))*PolyLog(2, 1 + e/(d*sqrt(x))) + 4*b^2*n^2*PolyLog(3, 1 + e/(d*sqrt(x)))]
    @test_int [(a + b*log(c*(d + e/sqrt(x))^n))^2/x^2, x, 10, -(b^2*n^2*(d + e/sqrt(x))^2)/(2*e^2) - (4*a*b*d*n)/(e*sqrt(x)) + (4*b^2*d*n^2)/(e*sqrt(x)) - (4*b^2*d*n*(d + e/sqrt(x))*log(c*(d + e/sqrt(x))^n))/e^2 + (b*n*(d + e/sqrt(x))^2*(a + b*log(c*(d + e/sqrt(x))^n)))/e^2 + (2*d*(d + e/sqrt(x))*(a + b*log(c*(d + e/sqrt(x))^n))^2)/e^2 - ((d + e/sqrt(x))^2*(a + b*log(c*(d + e/sqrt(x))^n))^2)/e^2]
    @test_int [(a + b*log(c*(d + e/sqrt(x))^n))^2/x^3, x, 8, -((3*b^2*d^2*n^2*(d + e/sqrt(x))^2)/(2*e^4)) + (4*b^2*d*n^2*(d + e/sqrt(x))^3)/(9*e^4) - (b^2*n^2*(d + e/sqrt(x))^4)/(16*e^4) + (4*b^2*d^3*n^2)/(e^3*sqrt(x)) - (b^2*d^4*n^2*log(d + e/sqrt(x))^2)/(2*e^4) - (4*b*d^3*n*(d + e/sqrt(x))*(a + b*log(c*(d + e/sqrt(x))^n)))/e^4 + (3*b*d^2*n*(d + e/sqrt(x))^2*(a + b*log(c*(d + e/sqrt(x))^n)))/e^4 - (4*b*d*n*(d + e/sqrt(x))^3*(a + b*log(c*(d + e/sqrt(x))^n)))/(3*e^4) + (b*n*(d + e/sqrt(x))^4*(a + b*log(c*(d + e/sqrt(x))^n)))/(4*e^4) + (b*d^4*n*log(d + e/sqrt(x))*(a + b*log(c*(d + e/sqrt(x))^n)))/e^4 - (a + b*log(c*(d + e/sqrt(x))^n))^2/(2*x^2)]
    @test_int [(a + b*log(c*(d + e/sqrt(x))^n))^2/x^4, x, 8, -((5*b^2*d^4*n^2*(d + e/sqrt(x))^2)/(2*e^6)) + (40*b^2*d^3*n^2*(d + e/sqrt(x))^3)/(27*e^6) - (5*b^2*d^2*n^2*(d + e/sqrt(x))^4)/(8*e^6) + (4*b^2*d*n^2*(d + e/sqrt(x))^5)/(25*e^6) - (b^2*n^2*(d + e/sqrt(x))^6)/(54*e^6) + (4*b^2*d^5*n^2)/(e^5*sqrt(x)) - (b^2*d^6*n^2*log(d + e/sqrt(x))^2)/(3*e^6) - (4*b*d^5*n*(d + e/sqrt(x))*(a + b*log(c*(d + e/sqrt(x))^n)))/e^6 + (5*b*d^4*n*(d + e/sqrt(x))^2*(a + b*log(c*(d + e/sqrt(x))^n)))/e^6 - (40*b*d^3*n*(d + e/sqrt(x))^3*(a + b*log(c*(d + e/sqrt(x))^n)))/(9*e^6) + (5*b*d^2*n*(d + e/sqrt(x))^4*(a + b*log(c*(d + e/sqrt(x))^n)))/(2*e^6) - (4*b*d*n*(d + e/sqrt(x))^5*(a + b*log(c*(d + e/sqrt(x))^n)))/(5*e^6) + (b*n*(d + e/sqrt(x))^6*(a + b*log(c*(d + e/sqrt(x))^n)))/(9*e^6) + (2*b*d^6*n*log(d + e/sqrt(x))*(a + b*log(c*(d + e/sqrt(x))^n)))/(3*e^6) - (a + b*log(c*(d + e/sqrt(x))^n))^2/(3*x^3)]

    @test_int [x^1*(a + b*log(c*(d + e/sqrt(x))^n))^3, x, 28, (b^3*e^3*n^3*sqrt(x))/(2*d^3) - (b^3*e^4*n^3*log(d + e/sqrt(x)))/(2*d^4) - (5*b^2*e^3*n^2*(d + e/sqrt(x))*sqrt(x)*(a + b*log(c*(d + e/sqrt(x))^n)))/(2*d^4) + (b^2*e^2*n^2*x*(a + b*log(c*(d + e/sqrt(x))^n)))/(2*d^2) - (5*b^2*e^4*n^2*log(1 - d/(d + e/sqrt(x)))*(a + b*log(c*(d + e/sqrt(x))^n)))/(2*d^4) + (3*b*e^3*n*(d + e/sqrt(x))*sqrt(x)*(a + b*log(c*(d + e/sqrt(x))^n))^2)/(2*d^4) - (3*b*e^2*n*x*(a + b*log(c*(d + e/sqrt(x))^n))^2)/(4*d^2) + (b*e*n*x^(3/2)*(a + b*log(c*(d + e/sqrt(x))^n))^2)/(2*d) + (3*b*e^4*n*log(1 - d/(d + e/sqrt(x)))*(a + b*log(c*(d + e/sqrt(x))^n))^2)/(2*d^4) + (1/2)*x^2*(a + b*log(c*(d + e/sqrt(x))^n))^3 - (3*b^2*e^4*n^2*(a + b*log(c*(d + e/sqrt(x))^n))*log(-(e/(d*sqrt(x)))))/d^4 - (3*b^3*e^4*n^3*log(x))/(2*d^4) + (5*b^3*e^4*n^3*PolyLog(2, d/(d + e/sqrt(x))))/(2*d^4) - (3*b^2*e^4*n^2*(a + b*log(c*(d + e/sqrt(x))^n))*PolyLog(2, d/(d + e/sqrt(x))))/d^4 - (3*b^3*e^4*n^3*PolyLog(2, 1 + e/(d*sqrt(x))))/d^4 - (3*b^3*e^4*n^3*PolyLog(3, d/(d + e/sqrt(x))))/d^4]
    @test_int [x^0*(a + b*log(c*(d + e/sqrt(x))^n))^3, x, 11, (3*b*e*n*(d + e/sqrt(x))*sqrt(x)*(a + b*log(c*(d + e/sqrt(x))^n))^2)/d^2 + (3*b*e^2*n*log(1 - d/(d + e/sqrt(x)))*(a + b*log(c*(d + e/sqrt(x))^n))^2)/d^2 + x*(a + b*log(c*(d + e/sqrt(x))^n))^3 - (6*b^2*e^2*n^2*(a + b*log(c*(d + e/sqrt(x))^n))*log(-(e/(d*sqrt(x)))))/d^2 - (6*b^2*e^2*n^2*(a + b*log(c*(d + e/sqrt(x))^n))*PolyLog(2, d/(d + e/sqrt(x))))/d^2 - (6*b^3*e^2*n^3*PolyLog(2, 1 + e/(d*sqrt(x))))/d^2 - (6*b^3*e^2*n^3*PolyLog(3, d/(d + e/sqrt(x))))/d^2]
    @test_int [(a + b*log(c*(d + e/sqrt(x))^n))^3/x^1, x, 6, -2*(a + b*log(c*(d + e/sqrt(x))^n))^3*log(-(e/(d*sqrt(x)))) - 6*b*n*(a + b*log(c*(d + e/sqrt(x))^n))^2*PolyLog(2, 1 + e/(d*sqrt(x))) + 12*b^2*n^2*(a + b*log(c*(d + e/sqrt(x))^n))*PolyLog(3, 1 + e/(d*sqrt(x))) - 12*b^3*n^3*PolyLog(4, 1 + e/(d*sqrt(x)))]
    @test_int [(a + b*log(c*(d + e/sqrt(x))^n))^3/x^2, x, 12, (3*b^3*n^3*(d + e/sqrt(x))^2)/(4*e^2) + (12*a*b^2*d*n^2)/(e*sqrt(x)) - (12*b^3*d*n^3)/(e*sqrt(x)) + (12*b^3*d*n^2*(d + e/sqrt(x))*log(c*(d + e/sqrt(x))^n))/e^2 - (3*b^2*n^2*(d + e/sqrt(x))^2*(a + b*log(c*(d + e/sqrt(x))^n)))/(2*e^2) - (6*b*d*n*(d + e/sqrt(x))*(a + b*log(c*(d + e/sqrt(x))^n))^2)/e^2 + (3*b*n*(d + e/sqrt(x))^2*(a + b*log(c*(d + e/sqrt(x))^n))^2)/(2*e^2) + (2*d*(d + e/sqrt(x))*(a + b*log(c*(d + e/sqrt(x))^n))^3)/e^2 - ((d + e/sqrt(x))^2*(a + b*log(c*(d + e/sqrt(x))^n))^3)/e^2]
    @test_int [(a + b*log(c*(d + e/sqrt(x))^n))^3/x^3, x, 20, (9*b^3*d^2*n^3*(d + e/sqrt(x))^2)/(4*e^4) - (4*b^3*d*n^3*(d + e/sqrt(x))^3)/(9*e^4) + (3*b^3*n^3*(d + e/sqrt(x))^4)/(64*e^4) + (12*a*b^2*d^3*n^2)/(e^3*sqrt(x)) - (12*b^3*d^3*n^3)/(e^3*sqrt(x)) + (12*b^3*d^3*n^2*(d + e/sqrt(x))*log(c*(d + e/sqrt(x))^n))/e^4 - (9*b^2*d^2*n^2*(d + e/sqrt(x))^2*(a + b*log(c*(d + e/sqrt(x))^n)))/(2*e^4) + (4*b^2*d*n^2*(d + e/sqrt(x))^3*(a + b*log(c*(d + e/sqrt(x))^n)))/(3*e^4) - (3*b^2*n^2*(d + e/sqrt(x))^4*(a + b*log(c*(d + e/sqrt(x))^n)))/(16*e^4) - (6*b*d^3*n*(d + e/sqrt(x))*(a + b*log(c*(d + e/sqrt(x))^n))^2)/e^4 + (9*b*d^2*n*(d + e/sqrt(x))^2*(a + b*log(c*(d + e/sqrt(x))^n))^2)/(2*e^4) - (2*b*d*n*(d + e/sqrt(x))^3*(a + b*log(c*(d + e/sqrt(x))^n))^2)/e^4 + (3*b*n*(d + e/sqrt(x))^4*(a + b*log(c*(d + e/sqrt(x))^n))^2)/(8*e^4) + (2*d^3*(d + e/sqrt(x))*(a + b*log(c*(d + e/sqrt(x))^n))^3)/e^4 - (3*d^2*(d + e/sqrt(x))^2*(a + b*log(c*(d + e/sqrt(x))^n))^3)/e^4 + (2*d*(d + e/sqrt(x))^3*(a + b*log(c*(d + e/sqrt(x))^n))^3)/e^4 - ((d + e/sqrt(x))^4*(a + b*log(c*(d + e/sqrt(x))^n))^3)/(2*e^4)]
    @test_int [(a + b*log(c*(d + e/sqrt(x))^n))^3/x^4, x, 28, (15*b^3*d^4*n^3*(d + e/sqrt(x))^2)/(4*e^6) - (40*b^3*d^3*n^3*(d + e/sqrt(x))^3)/(27*e^6) + (15*b^3*d^2*n^3*(d + e/sqrt(x))^4)/(32*e^6) - (12*b^3*d*n^3*(d + e/sqrt(x))^5)/(125*e^6) + (b^3*n^3*(d + e/sqrt(x))^6)/(108*e^6) + (12*a*b^2*d^5*n^2)/(e^5*sqrt(x)) - (12*b^3*d^5*n^3)/(e^5*sqrt(x)) + (12*b^3*d^5*n^2*(d + e/sqrt(x))*log(c*(d + e/sqrt(x))^n))/e^6 - (15*b^2*d^4*n^2*(d + e/sqrt(x))^2*(a + b*log(c*(d + e/sqrt(x))^n)))/(2*e^6) + (40*b^2*d^3*n^2*(d + e/sqrt(x))^3*(a + b*log(c*(d + e/sqrt(x))^n)))/(9*e^6) - (15*b^2*d^2*n^2*(d + e/sqrt(x))^4*(a + b*log(c*(d + e/sqrt(x))^n)))/(8*e^6) + (12*b^2*d*n^2*(d + e/sqrt(x))^5*(a + b*log(c*(d + e/sqrt(x))^n)))/(25*e^6) - (b^2*n^2*(d + e/sqrt(x))^6*(a + b*log(c*(d + e/sqrt(x))^n)))/(18*e^6) - (6*b*d^5*n*(d + e/sqrt(x))*(a + b*log(c*(d + e/sqrt(x))^n))^2)/e^6 + (15*b*d^4*n*(d + e/sqrt(x))^2*(a + b*log(c*(d + e/sqrt(x))^n))^2)/(2*e^6) - (20*b*d^3*n*(d + e/sqrt(x))^3*(a + b*log(c*(d + e/sqrt(x))^n))^2)/(3*e^6) + (15*b*d^2*n*(d + e/sqrt(x))^4*(a + b*log(c*(d + e/sqrt(x))^n))^2)/(4*e^6) - (6*b*d*n*(d + e/sqrt(x))^5*(a + b*log(c*(d + e/sqrt(x))^n))^2)/(5*e^6) + (b*n*(d + e/sqrt(x))^6*(a + b*log(c*(d + e/sqrt(x))^n))^2)/(6*e^6) + (2*d^5*(d + e/sqrt(x))*(a + b*log(c*(d + e/sqrt(x))^n))^3)/e^6 - (5*d^4*(d + e/sqrt(x))^2*(a + b*log(c*(d + e/sqrt(x))^n))^3)/e^6 + (20*d^3*(d + e/sqrt(x))^3*(a + b*log(c*(d + e/sqrt(x))^n))^3)/(3*e^6) - (5*d^2*(d + e/sqrt(x))^4*(a + b*log(c*(d + e/sqrt(x))^n))^3)/e^6 + (2*d*(d + e/sqrt(x))^5*(a + b*log(c*(d + e/sqrt(x))^n))^3)/e^6 - ((d + e/sqrt(x))^6*(a + b*log(c*(d + e/sqrt(x))^n))^3)/(3*e^6)]

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

    #= ::Subsubsection::Closed:: =#
    #=m=1=#

    @test_int [x^3*(a + b*log(c*(d + e*x^(1/3))^n)), x, 4, (b*d^11*n*x^(1/3))/(4*e^11) - (b*d^10*n*x^(2/3))/(8*e^10) + (b*d^9*n*x)/(12*e^9) - (b*d^8*n*x^(4/3))/(16*e^8) + (b*d^7*n*x^(5/3))/(20*e^7) - (b*d^6*n*x^2)/(24*e^6) + (b*d^5*n*x^(7/3))/(28*e^5) - (b*d^4*n*x^(8/3))/(32*e^4) + (b*d^3*n*x^3)/(36*e^3) - (b*d^2*n*x^(10/3))/(40*e^2) + (b*d*n*x^(11/3))/(44*e) - (1/48)*b*n*x^4 - (b*d^12*n*log(d + e*x^(1/3)))/(4*e^12) + (1/4)*x^4*(a + b*log(c*(d + e*x^(1/3))^n))]
    @test_int [x^2*(a + b*log(c*(d + e*x^(1/3))^n)), x, 4, -((b*d^8*n*x^(1/3))/(3*e^8)) + (b*d^7*n*x^(2/3))/(6*e^7) - (b*d^6*n*x)/(9*e^6) + (b*d^5*n*x^(4/3))/(12*e^5) - (b*d^4*n*x^(5/3))/(15*e^4) + (b*d^3*n*x^2)/(18*e^3) - (b*d^2*n*x^(7/3))/(21*e^2) + (b*d*n*x^(8/3))/(24*e) - (1/27)*b*n*x^3 + (b*d^9*n*log(d + e*x^(1/3)))/(3*e^9) + (1/3)*x^3*(a + b*log(c*(d + e*x^(1/3))^n))]
    @test_int [x^1*(a + b*log(c*(d + e*x^(1/3))^n)), x, 4, (b*d^5*n*x^(1/3))/(2*e^5) - (b*d^4*n*x^(2/3))/(4*e^4) + (b*d^3*n*x)/(6*e^3) - (b*d^2*n*x^(4/3))/(8*e^2) + (b*d*n*x^(5/3))/(10*e) - (1/12)*b*n*x^2 - (b*d^6*n*log(d + e*x^(1/3)))/(2*e^6) + (1/2)*x^2*(a + b*log(c*(d + e*x^(1/3))^n))]
    @test_int [x^0*(a + b*log(c*(d + e*x^(1/3))^n)), x, 5, -((b*d^2*n*x^(1/3))/e^2) + (b*d*n*x^(2/3))/(2*e) + a*x - (b*n*x)/3 + (b*d^3*n*log(d + e*x^(1/3)))/e^3 + b*x*log(c*(d + e*x^(1/3))^n)]
    @test_int [(a + b*log(c*(d + e*x^(1/3))^n))/x^1, x, 3, 3*(a + b*log(c*(d + e*x^(1/3))^n))*log(-((e*x^(1/3))/d)) + 3*b*n*PolyLog(2, 1 + (e*x^(1/3))/d)]
    @test_int [(a + b*log(c*(d + e*x^(1/3))^n))/x^2, x, 4, -((b*e*n)/(2*d*x^(2/3))) + (b*e^2*n)/(d^2*x^(1/3)) - (b*e^3*n*log(d + e*x^(1/3)))/d^3 - (a + b*log(c*(d + e*x^(1/3))^n))/x + (b*e^3*n*log(x))/(3*d^3)]
    @test_int [(a + b*log(c*(d + e*x^(1/3))^n))/x^3, x, 4, -((b*e*n)/(10*d*x^(5/3))) + (b*e^2*n)/(8*d^2*x^(4/3)) - (b*e^3*n)/(6*d^3*x) + (b*e^4*n)/(4*d^4*x^(2/3)) - (b*e^5*n)/(2*d^5*x^(1/3)) + (b*e^6*n*log(d + e*x^(1/3)))/(2*d^6) - (a + b*log(c*(d + e*x^(1/3))^n))/(2*x^2) - (b*e^6*n*log(x))/(6*d^6)]
    @test_int [(a + b*log(c*(d + e*x^(1/3))^n))/x^4, x, 4, -((b*e*n)/(24*d*x^(8/3))) + (b*e^2*n)/(21*d^2*x^(7/3)) - (b*e^3*n)/(18*d^3*x^2) + (b*e^4*n)/(15*d^4*x^(5/3)) - (b*e^5*n)/(12*d^5*x^(4/3)) + (b*e^6*n)/(9*d^6*x) - (b*e^7*n)/(6*d^7*x^(2/3)) + (b*e^8*n)/(3*d^8*x^(1/3)) - (b*e^9*n*log(d + e*x^(1/3)))/(3*d^9) - (a + b*log(c*(d + e*x^(1/3))^n))/(3*x^3) + (b*e^9*n*log(x))/(9*d^9)]

    @test_int [x^2*(a + b*log(c*(d + e*x^(1/3))^n))^2, x, 8, -((6*b^2*d^7*n^2*(d + e*x^(1/3))^2)/e^9) + (56*b^2*d^6*n^2*(d + e*x^(1/3))^3)/(9*e^9) - (21*b^2*d^5*n^2*(d + e*x^(1/3))^4)/(4*e^9) + (84*b^2*d^4*n^2*(d + e*x^(1/3))^5)/(25*e^9) - (14*b^2*d^3*n^2*(d + e*x^(1/3))^6)/(9*e^9) + (24*b^2*d^2*n^2*(d + e*x^(1/3))^7)/(49*e^9) - (3*b^2*d*n^2*(d + e*x^(1/3))^8)/(32*e^9) + (2*b^2*n^2*(d + e*x^(1/3))^9)/(243*e^9) + (6*b^2*d^8*n^2*x^(1/3))/e^8 - (b^2*d^9*n^2*log(d + e*x^(1/3))^2)/(3*e^9) - (6*b*d^8*n*(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n)))/e^9 + (12*b*d^7*n*(d + e*x^(1/3))^2*(a + b*log(c*(d + e*x^(1/3))^n)))/e^9 - (56*b*d^6*n*(d + e*x^(1/3))^3*(a + b*log(c*(d + e*x^(1/3))^n)))/(3*e^9) + (21*b*d^5*n*(d + e*x^(1/3))^4*(a + b*log(c*(d + e*x^(1/3))^n)))/e^9 - (84*b*d^4*n*(d + e*x^(1/3))^5*(a + b*log(c*(d + e*x^(1/3))^n)))/(5*e^9) + (28*b*d^3*n*(d + e*x^(1/3))^6*(a + b*log(c*(d + e*x^(1/3))^n)))/(3*e^9) - (24*b*d^2*n*(d + e*x^(1/3))^7*(a + b*log(c*(d + e*x^(1/3))^n)))/(7*e^9) + (3*b*d*n*(d + e*x^(1/3))^8*(a + b*log(c*(d + e*x^(1/3))^n)))/(4*e^9) - (2*b*n*(d + e*x^(1/3))^9*(a + b*log(c*(d + e*x^(1/3))^n)))/(27*e^9) + (2*b*d^9*n*log(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n)))/(3*e^9) + (1/3)*x^3*(a + b*log(c*(d + e*x^(1/3))^n))^2]
    @test_int [x^1*(a + b*log(c*(d + e*x^(1/3))^n))^2, x, 8, (15*b^2*d^4*n^2*(d + e*x^(1/3))^2)/(4*e^6) - (20*b^2*d^3*n^2*(d + e*x^(1/3))^3)/(9*e^6) + (15*b^2*d^2*n^2*(d + e*x^(1/3))^4)/(16*e^6) - (6*b^2*d*n^2*(d + e*x^(1/3))^5)/(25*e^6) + (b^2*n^2*(d + e*x^(1/3))^6)/(36*e^6) - (6*b^2*d^5*n^2*x^(1/3))/e^5 + (b^2*d^6*n^2*log(d + e*x^(1/3))^2)/(2*e^6) + (6*b*d^5*n*(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n)))/e^6 - (15*b*d^4*n*(d + e*x^(1/3))^2*(a + b*log(c*(d + e*x^(1/3))^n)))/(2*e^6) + (20*b*d^3*n*(d + e*x^(1/3))^3*(a + b*log(c*(d + e*x^(1/3))^n)))/(3*e^6) - (15*b*d^2*n*(d + e*x^(1/3))^4*(a + b*log(c*(d + e*x^(1/3))^n)))/(4*e^6) + (6*b*d*n*(d + e*x^(1/3))^5*(a + b*log(c*(d + e*x^(1/3))^n)))/(5*e^6) - (b*n*(d + e*x^(1/3))^6*(a + b*log(c*(d + e*x^(1/3))^n)))/(6*e^6) - (b*d^6*n*log(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n)))/e^6 + (1/2)*x^2*(a + b*log(c*(d + e*x^(1/3))^n))^2]
    @test_int [x^0*(a + b*log(c*(d + e*x^(1/3))^n))^2, x, 8, -((3*b^2*d*n^2*(d + e*x^(1/3))^2)/(2*e^3)) + (2*b^2*n^2*(d + e*x^(1/3))^3)/(9*e^3) + (6*b^2*d^2*n^2*x^(1/3))/e^2 - (b^2*d^3*n^2*log(d + e*x^(1/3))^2)/e^3 - (6*b*d^2*n*(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n)))/e^3 + (3*b*d*n*(d + e*x^(1/3))^2*(a + b*log(c*(d + e*x^(1/3))^n)))/e^3 - (2*b*n*(d + e*x^(1/3))^3*(a + b*log(c*(d + e*x^(1/3))^n)))/(3*e^3) + (2*b*d^3*n*log(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n)))/e^3 + x*(a + b*log(c*(d + e*x^(1/3))^n))^2]
    @test_int [(a + b*log(c*(d + e*x^(1/3))^n))^2/x^1, x, 5, 3*(a + b*log(c*(d + e*x^(1/3))^n))^2*log(-((e*x^(1/3))/d)) + 6*b*n*(a + b*log(c*(d + e*x^(1/3))^n))*PolyLog(2, 1 + (e*x^(1/3))/d) - 6*b^2*n^2*PolyLog(3, 1 + (e*x^(1/3))/d)]
    @test_int [(a + b*log(c*(d + e*x^(1/3))^n))^2/x^2, x, 12, -((b^2*e^2*n^2)/(d^2*x^(1/3))) + (b^2*e^3*n^2*log(d + e*x^(1/3)))/d^3 - (b*e*n*(a + b*log(c*(d + e*x^(1/3))^n)))/(d*x^(2/3)) + (2*b*e^2*n*(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n)))/(d^3*x^(1/3)) + (2*b*e^3*n*log(1 - d/(d + e*x^(1/3)))*(a + b*log(c*(d + e*x^(1/3))^n)))/d^3 - (a + b*log(c*(d + e*x^(1/3))^n))^2/x - (b^2*e^3*n^2*log(x))/d^3 - (2*b^2*e^3*n^2*PolyLog(2, d/(d + e*x^(1/3))))/d^3]
    @test_int [(a + b*log(c*(d + e*x^(1/3))^n))^2/x^3, x, 24, -((b^2*e^2*n^2)/(20*d^2*x^(4/3))) + (3*b^2*e^3*n^2)/(20*d^3*x) - (47*b^2*e^4*n^2)/(120*d^4*x^(2/3)) + (77*b^2*e^5*n^2)/(60*d^5*x^(1/3)) - (77*b^2*e^6*n^2*log(d + e*x^(1/3)))/(60*d^6) - (b*e*n*(a + b*log(c*(d + e*x^(1/3))^n)))/(5*d*x^(5/3)) + (b*e^2*n*(a + b*log(c*(d + e*x^(1/3))^n)))/(4*d^2*x^(4/3)) - (b*e^3*n*(a + b*log(c*(d + e*x^(1/3))^n)))/(3*d^3*x) + (b*e^4*n*(a + b*log(c*(d + e*x^(1/3))^n)))/(2*d^4*x^(2/3)) - (b*e^5*n*(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n)))/(d^6*x^(1/3)) - (b*e^6*n*log(1 - d/(d + e*x^(1/3)))*(a + b*log(c*(d + e*x^(1/3))^n)))/d^6 - (a + b*log(c*(d + e*x^(1/3))^n))^2/(2*x^2) + (137*b^2*e^6*n^2*log(x))/(180*d^6) + (b^2*e^6*n^2*PolyLog(2, d/(d + e*x^(1/3))))/d^6]

    @test_int [x^3*(a + b*log(c*(d + e*x^(1/3))^n))^3, x, 52, (-99*b^3*d^10*n^3*(d + e*x^(1/3))^2)/(8*e^12) + (110*b^3*d^9*n^3*(d + e*x^(1/3))^3)/(9*e^12) - (1485*b^3*d^8*n^3*(d + e*x^(1/3))^4)/(128*e^12) + (1188*b^3*d^7*n^3*(d + e*x^(1/3))^5)/(125*e^12) - (77*b^3*d^6*n^3*(d + e*x^(1/3))^6)/(12*e^12) + (1188*b^3*d^5*n^3*(d + e*x^(1/3))^7)/(343*e^12) - (1485*b^3*d^4*n^3*(d + e*x^(1/3))^8)/(1024*e^12) + (110*b^3*d^3*n^3*(d + e*x^(1/3))^9)/(243*e^12) - (99*b^3*d^2*n^3*(d + e*x^(1/3))^10)/(1000*e^12) + (18*b^3*d*n^3*(d + e*x^(1/3))^11)/(1331*e^12) - (b^3*n^3*(d + e*x^(1/3))^12)/(1152*e^12) - (18*a*b^2*d^11*n^2*x^(1/3))/e^11 + (18*b^3*d^11*n^3*x^(1/3))/e^11 - (18*b^3*d^11*n^2*(d + e*x^(1/3))*log(c*(d + e*x^(1/3))^n))/e^12 + (99*b^2*d^10*n^2*(d + e*x^(1/3))^2*(a + b*log(c*(d + e*x^(1/3))^n)))/(4*e^12) - (110*b^2*d^9*n^2*(d + e*x^(1/3))^3*(a + b*log(c*(d + e*x^(1/3))^n)))/(3*e^12) + (1485*b^2*d^8*n^2*(d + e*x^(1/3))^4*(a + b*log(c*(d + e*x^(1/3))^n)))/(32*e^12) - (1188*b^2*d^7*n^2*(d + e*x^(1/3))^5*(a + b*log(c*(d + e*x^(1/3))^n)))/(25*e^12) + (77*b^2*d^6*n^2*(d + e*x^(1/3))^6*(a + b*log(c*(d + e*x^(1/3))^n)))/(2*e^12) - (1188*b^2*d^5*n^2*(d + e*x^(1/3))^7*(a + b*log(c*(d + e*x^(1/3))^n)))/(49*e^12) + (1485*b^2*d^4*n^2*(d + e*x^(1/3))^8*(a + b*log(c*(d + e*x^(1/3))^n)))/(128*e^12) - (110*b^2*d^3*n^2*(d + e*x^(1/3))^9*(a + b*log(c*(d + e*x^(1/3))^n)))/(27*e^12) + (99*b^2*d^2*n^2*(d + e*x^(1/3))^10*(a + b*log(c*(d + e*x^(1/3))^n)))/(100*e^12) - (18*b^2*d*n^2*(d + e*x^(1/3))^11*(a + b*log(c*(d + e*x^(1/3))^n)))/(121*e^12) + (b^2*n^2*(d + e*x^(1/3))^12*(a + b*log(c*(d + e*x^(1/3))^n)))/(96*e^12) + (9*b*d^11*n*(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n))^2)/e^12 - (99*b*d^10*n*(d + e*x^(1/3))^2*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(4*e^12) + (55*b*d^9*n*(d + e*x^(1/3))^3*(a + b*log(c*(d + e*x^(1/3))^n))^2)/e^12 - (1485*b*d^8*n*(d + e*x^(1/3))^4*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(16*e^12) + (594*b*d^7*n*(d + e*x^(1/3))^5*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(5*e^12) - (231*b*d^6*n*(d + e*x^(1/3))^6*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(2*e^12) + (594*b*d^5*n*(d + e*x^(1/3))^7*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(7*e^12) - (1485*b*d^4*n*(d + e*x^(1/3))^8*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(32*e^12) + (55*b*d^3*n*(d + e*x^(1/3))^9*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(3*e^12) - (99*b*d^2*n*(d + e*x^(1/3))^10*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(20*e^12) + (9*b*d*n*(d + e*x^(1/3))^11*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(11*e^12) - (b*n*(d + e*x^(1/3))^12*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(16*e^12) - (3*d^11*(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^12 + (33*d^10*(d + e*x^(1/3))^2*(a + b*log(c*(d + e*x^(1/3))^n))^3)/(2*e^12) - (55*d^9*(d + e*x^(1/3))^3*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^12 + (495*d^8*(d + e*x^(1/3))^4*(a + b*log(c*(d + e*x^(1/3))^n))^3)/(4*e^12) - (198*d^7*(d + e*x^(1/3))^5*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^12 + (231*d^6*(d + e*x^(1/3))^6*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^12 - (198*d^5*(d + e*x^(1/3))^7*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^12 + (495*d^4*(d + e*x^(1/3))^8*(a + b*log(c*(d + e*x^(1/3))^n))^3)/(4*e^12) - (55*d^3*(d + e*x^(1/3))^9*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^12 + (33*d^2*(d + e*x^(1/3))^10*(a + b*log(c*(d + e*x^(1/3))^n))^3)/(2*e^12) - (3*d*(d + e*x^(1/3))^11*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^12 + ((d + e*x^(1/3))^12*(a + b*log(c*(d + e*x^(1/3))^n))^3)/(4*e^12)]
    @test_int [x^2*(a + b*log(c*(d + e*x^(1/3))^n))^3, x, 40, (9*b^3*d^7*n^3*(d + e*x^(1/3))^2)/e^9 - (56*b^3*d^6*n^3*(d + e*x^(1/3))^3)/(9*e^9) + (63*b^3*d^5*n^3*(d + e*x^(1/3))^4)/(16*e^9) - (252*b^3*d^4*n^3*(d + e*x^(1/3))^5)/(125*e^9) + (7*b^3*d^3*n^3*(d + e*x^(1/3))^6)/(9*e^9) - (72*b^3*d^2*n^3*(d + e*x^(1/3))^7)/(343*e^9) + (9*b^3*d*n^3*(d + e*x^(1/3))^8)/(256*e^9) - (2*b^3*n^3*(d + e*x^(1/3))^9)/(729*e^9) + (18*a*b^2*d^8*n^2*x^(1/3))/e^8 - (18*b^3*d^8*n^3*x^(1/3))/e^8 + (18*b^3*d^8*n^2*(d + e*x^(1/3))*log(c*(d + e*x^(1/3))^n))/e^9 - (18*b^2*d^7*n^2*(d + e*x^(1/3))^2*(a + b*log(c*(d + e*x^(1/3))^n)))/e^9 + (56*b^2*d^6*n^2*(d + e*x^(1/3))^3*(a + b*log(c*(d + e*x^(1/3))^n)))/(3*e^9) - (63*b^2*d^5*n^2*(d + e*x^(1/3))^4*(a + b*log(c*(d + e*x^(1/3))^n)))/(4*e^9) + (252*b^2*d^4*n^2*(d + e*x^(1/3))^5*(a + b*log(c*(d + e*x^(1/3))^n)))/(25*e^9) - (14*b^2*d^3*n^2*(d + e*x^(1/3))^6*(a + b*log(c*(d + e*x^(1/3))^n)))/(3*e^9) + (72*b^2*d^2*n^2*(d + e*x^(1/3))^7*(a + b*log(c*(d + e*x^(1/3))^n)))/(49*e^9) - (9*b^2*d*n^2*(d + e*x^(1/3))^8*(a + b*log(c*(d + e*x^(1/3))^n)))/(32*e^9) + (2*b^2*n^2*(d + e*x^(1/3))^9*(a + b*log(c*(d + e*x^(1/3))^n)))/(81*e^9) - (9*b*d^8*n*(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n))^2)/e^9 + (18*b*d^7*n*(d + e*x^(1/3))^2*(a + b*log(c*(d + e*x^(1/3))^n))^2)/e^9 - (28*b*d^6*n*(d + e*x^(1/3))^3*(a + b*log(c*(d + e*x^(1/3))^n))^2)/e^9 + (63*b*d^5*n*(d + e*x^(1/3))^4*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(2*e^9) - (126*b*d^4*n*(d + e*x^(1/3))^5*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(5*e^9) + (14*b*d^3*n*(d + e*x^(1/3))^6*(a + b*log(c*(d + e*x^(1/3))^n))^2)/e^9 - (36*b*d^2*n*(d + e*x^(1/3))^7*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(7*e^9) + (9*b*d*n*(d + e*x^(1/3))^8*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(8*e^9) - (b*n*(d + e*x^(1/3))^9*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(9*e^9) + (3*d^8*(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^9 - (12*d^7*(d + e*x^(1/3))^2*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^9 + (28*d^6*(d + e*x^(1/3))^3*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^9 - (42*d^5*(d + e*x^(1/3))^4*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^9 + (42*d^4*(d + e*x^(1/3))^5*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^9 - (28*d^3*(d + e*x^(1/3))^6*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^9 + (12*d^2*(d + e*x^(1/3))^7*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^9 - (3*d*(d + e*x^(1/3))^8*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^9 + ((d + e*x^(1/3))^9*(a + b*log(c*(d + e*x^(1/3))^n))^3)/(3*e^9)]
    @test_int [x^1*(a + b*log(c*(d + e*x^(1/3))^n))^3, x, 28, (-45*b^3*d^4*n^3*(d + e*x^(1/3))^2)/(8*e^6) + (20*b^3*d^3*n^3*(d + e*x^(1/3))^3)/(9*e^6) - (45*b^3*d^2*n^3*(d + e*x^(1/3))^4)/(64*e^6) + (18*b^3*d*n^3*(d + e*x^(1/3))^5)/(125*e^6) - (b^3*n^3*(d + e*x^(1/3))^6)/(72*e^6) - (18*a*b^2*d^5*n^2*x^(1/3))/e^5 + (18*b^3*d^5*n^3*x^(1/3))/e^5 - (18*b^3*d^5*n^2*(d + e*x^(1/3))*log(c*(d + e*x^(1/3))^n))/e^6 + (45*b^2*d^4*n^2*(d + e*x^(1/3))^2*(a + b*log(c*(d + e*x^(1/3))^n)))/(4*e^6) - (20*b^2*d^3*n^2*(d + e*x^(1/3))^3*(a + b*log(c*(d + e*x^(1/3))^n)))/(3*e^6) + (45*b^2*d^2*n^2*(d + e*x^(1/3))^4*(a + b*log(c*(d + e*x^(1/3))^n)))/(16*e^6) - (18*b^2*d*n^2*(d + e*x^(1/3))^5*(a + b*log(c*(d + e*x^(1/3))^n)))/(25*e^6) + (b^2*n^2*(d + e*x^(1/3))^6*(a + b*log(c*(d + e*x^(1/3))^n)))/(12*e^6) + (9*b*d^5*n*(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n))^2)/e^6 - (45*b*d^4*n*(d + e*x^(1/3))^2*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(4*e^6) + (10*b*d^3*n*(d + e*x^(1/3))^3*(a + b*log(c*(d + e*x^(1/3))^n))^2)/e^6 - (45*b*d^2*n*(d + e*x^(1/3))^4*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(8*e^6) + (9*b*d*n*(d + e*x^(1/3))^5*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(5*e^6) - (b*n*(d + e*x^(1/3))^6*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(4*e^6) - (3*d^5*(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^6 + (15*d^4*(d + e*x^(1/3))^2*(a + b*log(c*(d + e*x^(1/3))^n))^3)/(2*e^6) - (10*d^3*(d + e*x^(1/3))^3*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^6 + (15*d^2*(d + e*x^(1/3))^4*(a + b*log(c*(d + e*x^(1/3))^n))^3)/(2*e^6) - (3*d*(d + e*x^(1/3))^5*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^6 + ((d + e*x^(1/3))^6*(a + b*log(c*(d + e*x^(1/3))^n))^3)/(2*e^6)]
    @test_int [x^0*(a + b*log(c*(d + e*x^(1/3))^n))^3, x, 16, (9*b^3*d*n^3*(d + e*x^(1/3))^2)/(4*e^3) - (2*b^3*n^3*(d + e*x^(1/3))^3)/(9*e^3) + (18*a*b^2*d^2*n^2*x^(1/3))/e^2 - (18*b^3*d^2*n^3*x^(1/3))/e^2 + (18*b^3*d^2*n^2*(d + e*x^(1/3))*log(c*(d + e*x^(1/3))^n))/e^3 - (9*b^2*d*n^2*(d + e*x^(1/3))^2*(a + b*log(c*(d + e*x^(1/3))^n)))/(2*e^3) + (2*b^2*n^2*(d + e*x^(1/3))^3*(a + b*log(c*(d + e*x^(1/3))^n)))/(3*e^3) - (9*b*d^2*n*(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n))^2)/e^3 + (9*b*d*n*(d + e*x^(1/3))^2*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(2*e^3) - (b*n*(d + e*x^(1/3))^3*(a + b*log(c*(d + e*x^(1/3))^n))^2)/e^3 + (3*d^2*(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^3 - (3*d*(d + e*x^(1/3))^2*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^3 + ((d + e*x^(1/3))^3*(a + b*log(c*(d + e*x^(1/3))^n))^3)/e^3]
    @test_int [(a + b*log(c*(d + e*x^(1/3))^n))^3/x^1, x, 6, 3*(a + b*log(c*(d + e*x^(1/3))^n))^3*log(-((e*x^(1/3))/d)) + 9*b*n*(a + b*log(c*(d + e*x^(1/3))^n))^2*PolyLog(2, 1 + (e*x^(1/3))/d) - 18*b^2*n^2*(a + b*log(c*(d + e*x^(1/3))^n))*PolyLog(3, 1 + (e*x^(1/3))/d) + 18*b^3*n^3*PolyLog(4, 1 + (e*x^(1/3))/d)]
    @test_int [(a + b*log(c*(d + e*x^(1/3))^n))^3/x^2, x, 17, -((3*b^2*e^2*n^2*(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n)))/(d^3*x^(1/3))) - (3*b^2*e^3*n^2*log(1 - d/(d + e*x^(1/3)))*(a + b*log(c*(d + e*x^(1/3))^n)))/d^3 - (3*b*e*n*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(2*d*x^(2/3)) + (3*b*e^2*n*(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(d^3*x^(1/3)) + (3*b*e^3*n*log(1 - d/(d + e*x^(1/3)))*(a + b*log(c*(d + e*x^(1/3))^n))^2)/d^3 - (a + b*log(c*(d + e*x^(1/3))^n))^3/x - (6*b^2*e^3*n^2*(a + b*log(c*(d + e*x^(1/3))^n))*log(-((e*x^(1/3))/d)))/d^3 + (b^3*e^3*n^3*log(x))/d^3 + (3*b^3*e^3*n^3*PolyLog(2, d/(d + e*x^(1/3))))/d^3 - (6*b^2*e^3*n^2*(a + b*log(c*(d + e*x^(1/3))^n))*PolyLog(2, d/(d + e*x^(1/3))))/d^3 - (6*b^3*e^3*n^3*PolyLog(2, 1 + (e*x^(1/3))/d))/d^3 - (6*b^3*e^3*n^3*PolyLog(3, d/(d + e*x^(1/3))))/d^3]
    @test_int [(a + b*log(c*(d + e*x^(1/3))^n))^3/x^3, x, 62, -((b^3*e^3*n^3)/(20*d^3*x)) + (3*b^3*e^4*n^3)/(10*d^4*x^(2/3)) - (71*b^3*e^5*n^3)/(40*d^5*x^(1/3)) + (71*b^3*e^6*n^3*log(d + e*x^(1/3)))/(40*d^6) - (3*b^2*e^2*n^2*(a + b*log(c*(d + e*x^(1/3))^n)))/(20*d^2*x^(4/3)) + (9*b^2*e^3*n^2*(a + b*log(c*(d + e*x^(1/3))^n)))/(20*d^3*x) - (47*b^2*e^4*n^2*(a + b*log(c*(d + e*x^(1/3))^n)))/(40*d^4*x^(2/3)) + (77*b^2*e^5*n^2*(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n)))/(20*d^6*x^(1/3)) + (77*b^2*e^6*n^2*log(1 - d/(d + e*x^(1/3)))*(a + b*log(c*(d + e*x^(1/3))^n)))/(20*d^6) - (3*b*e*n*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(10*d*x^(5/3)) + (3*b*e^2*n*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(8*d^2*x^(4/3)) - (b*e^3*n*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(2*d^3*x) + (3*b*e^4*n*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(4*d^4*x^(2/3)) - (3*b*e^5*n*(d + e*x^(1/3))*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(2*d^6*x^(1/3)) - (3*b*e^6*n*log(1 - d/(d + e*x^(1/3)))*(a + b*log(c*(d + e*x^(1/3))^n))^2)/(2*d^6) - (a + b*log(c*(d + e*x^(1/3))^n))^3/(2*x^2) + (3*b^2*e^6*n^2*(a + b*log(c*(d + e*x^(1/3))^n))*log(-((e*x^(1/3))/d)))/d^6 - (15*b^3*e^6*n^3*log(x))/(8*d^6) - (77*b^3*e^6*n^3*PolyLog(2, d/(d + e*x^(1/3))))/(20*d^6) + (3*b^2*e^6*n^2*(a + b*log(c*(d + e*x^(1/3))^n))*PolyLog(2, d/(d + e*x^(1/3))))/d^6 + (3*b^3*e^6*n^3*PolyLog(2, 1 + (e*x^(1/3))/d))/d^6 + (3*b^3*e^6*n^3*PolyLog(3, d/(d + e*x^(1/3))))/d^6]

    #= ::Subsubsection::Closed:: =#
    #=m=2=#

    @test_int [x^3*(a + b*log(c*(d + e*x^(2/3))^n)), x, 4, (b*d^5*n*x^(2/3))/(4*e^5) - (b*d^4*n*x^(4/3))/(8*e^4) + (b*d^3*n*x^2)/(12*e^3) - (b*d^2*n*x^(8/3))/(16*e^2) + (b*d*n*x^(10/3))/(20*e) - (1/24)*b*n*x^4 - (b*d^6*n*log(d + e*x^(2/3)))/(4*e^6) + (1/4)*x^4*(a + b*log(c*(d + e*x^(2/3))^n))]
    @test_int [x^2*(a + b*log(c*(d + e*x^(2/3))^n)), x, 5, -((2*b*d^4*n*x^(1/3))/(3*e^4)) + (2*b*d^3*n*x)/(9*e^3) - (2*b*d^2*n*x^(5/3))/(15*e^2) + (2*b*d*n*x^(7/3))/(21*e) - (2/27)*b*n*x^3 + (2*b*d^(9/2)*n*atan((sqrt(e)*x^(1/3))/sqrt(d)))/(3*e^(9/2)) + (1/3)*x^3*(a + b*log(c*(d + e*x^(2/3))^n))]
    @test_int [x^1*(a + b*log(c*(d + e*x^(2/3))^n)), x, 4, -((b*d^2*n*x^(2/3))/(2*e^2)) + (b*d*n*x^(4/3))/(4*e) - (1/6)*b*n*x^2 + (b*d^3*n*log(d + e*x^(2/3)))/(2*e^3) + (1/2)*x^2*(a + b*log(c*(d + e*x^(2/3))^n))]
    @test_int [x^0*(a + b*log(c*(d + e*x^(2/3))^n)), x, 6, (2*b*d*n*x^(1/3))/e + a*x - (2*b*n*x)/3 - (2*b*d^(3/2)*n*atan((sqrt(e)*x^(1/3))/sqrt(d)))/e^(3/2) + b*x*log(c*(d + e*x^(2/3))^n)]
    @test_int [(a + b*log(c*(d + e*x^(2/3))^n))/x^1, x, 3, (3/2)*(a + b*log(c*(d + e*x^(2/3))^n))*log(-((e*x^(2/3))/d)) + (3/2)*b*n*PolyLog(2, 1 + (e*x^(2/3))/d)]
    @test_int [(a + b*log(c*(d + e*x^(2/3))^n))/x^2, x, 4, -((2*b*e*n)/(d*x^(1/3))) - (2*b*e^(3/2)*n*atan((sqrt(e)*x^(1/3))/sqrt(d)))/d^(3/2) - (a + b*log(c*(d + e*x^(2/3))^n))/x]
    @test_int [(a + b*log(c*(d + e*x^(2/3))^n))/x^3, x, 4, -((b*e*n)/(4*d*x^(4/3))) + (b*e^2*n)/(2*d^2*x^(2/3)) - (b*e^3*n*log(d + e*x^(2/3)))/(2*d^3) - (a + b*log(c*(d + e*x^(2/3))^n))/(2*x^2) + (b*e^3*n*log(x))/(3*d^3)]
    @test_int [(a + b*log(c*(d + e*x^(2/3))^n))/x^4, x, 7, -((2*b*e*n)/(21*d*x^(7/3))) + (2*b*e^2*n)/(15*d^2*x^(5/3)) - (2*b*e^3*n)/(9*d^3*x) + (2*b*e^4*n)/(3*d^4*x^(1/3)) + (2*b*e^(9/2)*n*atan((sqrt(e)*x^(1/3))/sqrt(d)))/(3*d^(9/2)) - (a + b*log(c*(d + e*x^(2/3))^n))/(3*x^3)]

    @test_int [x^3*(a + b*log(c*(d + e*x^(2/3))^n))^2, x, 8, (15*b^2*d^4*n^2*(d + e*x^(2/3))^2)/(8*e^6) - (10*b^2*d^3*n^2*(d + e*x^(2/3))^3)/(9*e^6) + (15*b^2*d^2*n^2*(d + e*x^(2/3))^4)/(32*e^6) - (3*b^2*d*n^2*(d + e*x^(2/3))^5)/(25*e^6) + (b^2*n^2*(d + e*x^(2/3))^6)/(72*e^6) - (3*b^2*d^5*n^2*x^(2/3))/e^5 + (b^2*d^6*n^2*log(d + e*x^(2/3))^2)/(4*e^6) + (3*b*d^5*n*(d + e*x^(2/3))*(a + b*log(c*(d + e*x^(2/3))^n)))/e^6 - (15*b*d^4*n*(d + e*x^(2/3))^2*(a + b*log(c*(d + e*x^(2/3))^n)))/(4*e^6) + (10*b*d^3*n*(d + e*x^(2/3))^3*(a + b*log(c*(d + e*x^(2/3))^n)))/(3*e^6) - (15*b*d^2*n*(d + e*x^(2/3))^4*(a + b*log(c*(d + e*x^(2/3))^n)))/(8*e^6) + (3*b*d*n*(d + e*x^(2/3))^5*(a + b*log(c*(d + e*x^(2/3))^n)))/(5*e^6) - (b*n*(d + e*x^(2/3))^6*(a + b*log(c*(d + e*x^(2/3))^n)))/(12*e^6) - (b*d^6*n*log(d + e*x^(2/3))*(a + b*log(c*(d + e*x^(2/3))^n)))/(2*e^6) + (1/4)*x^4*(a + b*log(c*(d + e*x^(2/3))^n))^2]
    @test_int [x^1*(a + b*log(c*(d + e*x^(2/3))^n))^2, x, 8, -((3*b^2*d*n^2*(d + e*x^(2/3))^2)/(4*e^3)) + (b^2*n^2*(d + e*x^(2/3))^3)/(9*e^3) + (3*b^2*d^2*n^2*x^(2/3))/e^2 - (b^2*d^3*n^2*log(d + e*x^(2/3))^2)/(2*e^3) - (3*b*d^2*n*(d + e*x^(2/3))*(a + b*log(c*(d + e*x^(2/3))^n)))/e^3 + (3*b*d*n*(d + e*x^(2/3))^2*(a + b*log(c*(d + e*x^(2/3))^n)))/(2*e^3) - (b*n*(d + e*x^(2/3))^3*(a + b*log(c*(d + e*x^(2/3))^n)))/(3*e^3) + (b*d^3*n*log(d + e*x^(2/3))*(a + b*log(c*(d + e*x^(2/3))^n)))/e^3 + (1/2)*x^2*(a + b*log(c*(d + e*x^(2/3))^n))^2]
    @test_int [(a + b*log(c*(d + e*x^(2/3))^n))^2/x^1, x, 5, (3/2)*(a + b*log(c*(d + e*x^(2/3))^n))^2*log(-((e*x^(2/3))/d)) + 3*b*n*(a + b*log(c*(d + e*x^(2/3))^n))*PolyLog(2, 1 + (e*x^(2/3))/d) - 3*b^2*n^2*PolyLog(3, 1 + (e*x^(2/3))/d)]
    @test_int [(a + b*log(c*(d + e*x^(2/3))^n))^2/x^3, x, 12, -((b^2*e^2*n^2)/(2*d^2*x^(2/3))) + (b^2*e^3*n^2*log(d + e*x^(2/3)))/(2*d^3) - (b*e*n*(a + b*log(c*(d + e*x^(2/3))^n)))/(2*d*x^(4/3)) + (b*e^2*n*(d + e*x^(2/3))*(a + b*log(c*(d + e*x^(2/3))^n)))/(d^3*x^(2/3)) + (b*e^3*n*log(1 - d/(d + e*x^(2/3)))*(a + b*log(c*(d + e*x^(2/3))^n)))/d^3 - (a + b*log(c*(d + e*x^(2/3))^n))^2/(2*x^2) - (b^2*e^3*n^2*log(x))/d^3 - (b^2*e^3*n^2*PolyLog(2, d/(d + e*x^(2/3))))/d^3]
    @test_int [(a + b*log(c*(d + e*x^(2/3))^n))^2/x^5, x, 24, -((b^2*e^2*n^2)/(40*d^2*x^(8/3))) + (3*b^2*e^3*n^2)/(40*d^3*x^2) - (47*b^2*e^4*n^2)/(240*d^4*x^(4/3)) + (77*b^2*e^5*n^2)/(120*d^5*x^(2/3)) - (77*b^2*e^6*n^2*log(d + e*x^(2/3)))/(120*d^6) - (b*e*n*(a + b*log(c*(d + e*x^(2/3))^n)))/(10*d*x^(10/3)) + (b*e^2*n*(a + b*log(c*(d + e*x^(2/3))^n)))/(8*d^2*x^(8/3)) - (b*e^3*n*(a + b*log(c*(d + e*x^(2/3))^n)))/(6*d^3*x^2) + (b*e^4*n*(a + b*log(c*(d + e*x^(2/3))^n)))/(4*d^4*x^(4/3)) - (b*e^5*n*(d + e*x^(2/3))*(a + b*log(c*(d + e*x^(2/3))^n)))/(2*d^6*x^(2/3)) - (b*e^6*n*log(1 - d/(d + e*x^(2/3)))*(a + b*log(c*(d + e*x^(2/3))^n)))/(2*d^6) - (a + b*log(c*(d + e*x^(2/3))^n))^2/(4*x^4) + (137*b^2*e^6*n^2*log(x))/(180*d^6) + (b^2*e^6*n^2*PolyLog(2, d/(d + e*x^(2/3))))/(2*d^6)]

    @test_int [x^2*(a + b*log(c*(d + e*x^(2/3))^n))^2, x, 30, -((4*a*b*d^4*n*x^(1/3))/(3*e^4)) + (4504*b^2*d^4*n^2*x^(1/3))/(945*e^4) - (1984*b^2*d^3*n^2*x)/(2835*e^3) + (1144*b^2*d^2*n^2*x^(5/3))/(4725*e^2) - (128*b^2*d*n^2*x^(7/3))/(1323*e) + (8/243)*b^2*n^2*x^3 - (4504*b^2*d^(9/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d)))/(945*e^(9/2)) + (4*im*b^2*d^(9/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d))^2)/(3*e^(9/2)) + (8*b^2*d^(9/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/(3*e^(9/2)) - (4*b^2*d^4*n*x^(1/3)*log(c*(d + e*x^(2/3))^n))/(3*e^4) + (4*b*d^3*n*x*(a + b*log(c*(d + e*x^(2/3))^n)))/(9*e^3) - (4*b*d^2*n*x^(5/3)*(a + b*log(c*(d + e*x^(2/3))^n)))/(15*e^2) + (4*b*d*n*x^(7/3)*(a + b*log(c*(d + e*x^(2/3))^n)))/(21*e) - (4/27)*b*n*x^3*(a + b*log(c*(d + e*x^(2/3))^n)) + (4*b*d^(9/2)*n*atan((sqrt(e)*x^(1/3))/sqrt(d))*(a + b*log(c*(d + e*x^(2/3))^n)))/(3*e^(9/2)) + (1/3)*x^3*(a + b*log(c*(d + e*x^(2/3))^n))^2 + (4*im*b^2*d^(9/2)*n^2*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/(3*e^(9/2))]
    @test_int [x^0*(a + b*log(c*(d + e*x^(2/3))^n))^2, x, 18, (4*a*b*d*n*x^(1/3))/e - (32*b^2*d*n^2*x^(1/3))/(3*e) + (8/9)*b^2*n^2*x + (32*b^2*d^(3/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d)))/(3*e^(3/2)) - (4*im*b^2*d^(3/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d))^2)/e^(3/2) - (8*b^2*d^(3/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/e^(3/2) + (4*b^2*d*n*x^(1/3)*log(c*(d + e*x^(2/3))^n))/e - (4/3)*b*n*x*(a + b*log(c*(d + e*x^(2/3))^n)) - (4*b*d^(3/2)*n*atan((sqrt(e)*x^(1/3))/sqrt(d))*(a + b*log(c*(d + e*x^(2/3))^n)))/e^(3/2) + x*(a + b*log(c*(d + e*x^(2/3))^n))^2 - (4*im*b^2*d^(3/2)*n^2*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/e^(3/2)]
    @test_int [(a + b*log(c*(d + e*x^(2/3))^n))^2/x^2, x, 12, (8*b^2*e^(3/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d)))/d^(3/2) - (4*im*b^2*e^(3/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d))^2)/d^(3/2) - (8*b^2*e^(3/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/d^(3/2) - (4*b*e*n*(a + b*log(c*(d + e*x^(2/3))^n)))/(d*x^(1/3)) - (4*b*e^(3/2)*n*atan((sqrt(e)*x^(1/3))/sqrt(d))*(a + b*log(c*(d + e*x^(2/3))^n)))/d^(3/2) - (a + b*log(c*(d + e*x^(2/3))^n))^2/x - (4*im*b^2*e^(3/2)*n^2*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/d^(3/2)]
    @test_int [(a + b*log(c*(d + e*x^(2/3))^n))^2/x^4, x, 24, -((8*b^2*e^2*n^2)/(105*d^2*x^(5/3))) + (32*b^2*e^3*n^2)/(105*d^3*x) - (568*b^2*e^4*n^2)/(315*d^4*x^(1/3)) - (1408*b^2*e^(9/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d)))/(315*d^(9/2)) + (4*im*b^2*e^(9/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d))^2)/(3*d^(9/2)) + (8*b^2*e^(9/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/(3*d^(9/2)) - (4*b*e*n*(a + b*log(c*(d + e*x^(2/3))^n)))/(21*d*x^(7/3)) + (4*b*e^2*n*(a + b*log(c*(d + e*x^(2/3))^n)))/(15*d^2*x^(5/3)) - (4*b*e^3*n*(a + b*log(c*(d + e*x^(2/3))^n)))/(9*d^3*x) + (4*b*e^4*n*(a + b*log(c*(d + e*x^(2/3))^n)))/(3*d^4*x^(1/3)) + (4*b*e^(9/2)*n*atan((sqrt(e)*x^(1/3))/sqrt(d))*(a + b*log(c*(d + e*x^(2/3))^n)))/(3*d^(9/2)) - (a + b*log(c*(d + e*x^(2/3))^n))^2/(3*x^3) + (4*im*b^2*e^(9/2)*n^2*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/(3*d^(9/2))]
    @test_int [(a + b*log(c*(d + e*x^(2/3))^n))^2/x^6, x, 45, -((8*b^2*e^2*n^2)/(715*d^2*x^(11/3))) + (64*b^2*e^3*n^2)/(2145*d^3*x^3) - (2872*b^2*e^4*n^2)/(45045*d^4*x^(7/3)) + (1216*b^2*e^5*n^2)/(9009*d^5*x^(5/3)) - (224072*b^2*e^6*n^2)/(675675*d^6*x) + (344192*b^2*e^7*n^2)/(225225*d^7*x^(1/3)) + (704552*b^2*e^(15/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d)))/(225225*d^(15/2)) - (4*im*b^2*e^(15/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d))^2)/(5*d^(15/2)) - (8*b^2*e^(15/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/(5*d^(15/2)) - (4*b*e*n*(a + b*log(c*(d + e*x^(2/3))^n)))/(65*d*x^(13/3)) + (4*b*e^2*n*(a + b*log(c*(d + e*x^(2/3))^n)))/(55*d^2*x^(11/3)) - (4*b*e^3*n*(a + b*log(c*(d + e*x^(2/3))^n)))/(45*d^3*x^3) + (4*b*e^4*n*(a + b*log(c*(d + e*x^(2/3))^n)))/(35*d^4*x^(7/3)) - (4*b*e^5*n*(a + b*log(c*(d + e*x^(2/3))^n)))/(25*d^5*x^(5/3)) + (4*b*e^6*n*(a + b*log(c*(d + e*x^(2/3))^n)))/(15*d^6*x) - (4*b*e^7*n*(a + b*log(c*(d + e*x^(2/3))^n)))/(5*d^7*x^(1/3)) - (4*b*e^(15/2)*n*atan((sqrt(e)*x^(1/3))/sqrt(d))*(a + b*log(c*(d + e*x^(2/3))^n)))/(5*d^(15/2)) - (a + b*log(c*(d + e*x^(2/3))^n))^2/(5*x^5) - (4*im*b^2*e^(15/2)*n^2*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/(5*d^(15/2))]

    @test_int [x^3*(a + b*log(c*(d + e*x^(2/3))^n))^3, x, 28, (-45*b^3*d^4*n^3*(d + e*x^(2/3))^2)/(16*e^6) + (10*b^3*d^3*n^3*(d + e*x^(2/3))^3)/(9*e^6) - (45*b^3*d^2*n^3*(d + e*x^(2/3))^4)/(128*e^6) + (9*b^3*d*n^3*(d + e*x^(2/3))^5)/(125*e^6) - (b^3*n^3*(d + e*x^(2/3))^6)/(144*e^6) - (9*a*b^2*d^5*n^2*x^(2/3))/e^5 + (9*b^3*d^5*n^3*x^(2/3))/e^5 - (9*b^3*d^5*n^2*(d + e*x^(2/3))*log(c*(d + e*x^(2/3))^n))/e^6 + (45*b^2*d^4*n^2*(d + e*x^(2/3))^2*(a + b*log(c*(d + e*x^(2/3))^n)))/(8*e^6) - (10*b^2*d^3*n^2*(d + e*x^(2/3))^3*(a + b*log(c*(d + e*x^(2/3))^n)))/(3*e^6) + (45*b^2*d^2*n^2*(d + e*x^(2/3))^4*(a + b*log(c*(d + e*x^(2/3))^n)))/(32*e^6) - (9*b^2*d*n^2*(d + e*x^(2/3))^5*(a + b*log(c*(d + e*x^(2/3))^n)))/(25*e^6) + (b^2*n^2*(d + e*x^(2/3))^6*(a + b*log(c*(d + e*x^(2/3))^n)))/(24*e^6) + (9*b*d^5*n*(d + e*x^(2/3))*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(2*e^6) - (45*b*d^4*n*(d + e*x^(2/3))^2*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(8*e^6) + (5*b*d^3*n*(d + e*x^(2/3))^3*(a + b*log(c*(d + e*x^(2/3))^n))^2)/e^6 - (45*b*d^2*n*(d + e*x^(2/3))^4*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(16*e^6) + (9*b*d*n*(d + e*x^(2/3))^5*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(10*e^6) - (b*n*(d + e*x^(2/3))^6*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(8*e^6) - (3*d^5*(d + e*x^(2/3))*(a + b*log(c*(d + e*x^(2/3))^n))^3)/(2*e^6) + (15*d^4*(d + e*x^(2/3))^2*(a + b*log(c*(d + e*x^(2/3))^n))^3)/(4*e^6) - (5*d^3*(d + e*x^(2/3))^3*(a + b*log(c*(d + e*x^(2/3))^n))^3)/e^6 + (15*d^2*(d + e*x^(2/3))^4*(a + b*log(c*(d + e*x^(2/3))^n))^3)/(4*e^6) - (3*d*(d + e*x^(2/3))^5*(a + b*log(c*(d + e*x^(2/3))^n))^3)/(2*e^6) + ((d + e*x^(2/3))^6*(a + b*log(c*(d + e*x^(2/3))^n))^3)/(4*e^6)]
    @test_int [x^1*(a + b*log(c*(d + e*x^(2/3))^n))^3, x, 16, (9*b^3*d*n^3*(d + e*x^(2/3))^2)/(8*e^3) - (b^3*n^3*(d + e*x^(2/3))^3)/(9*e^3) + (9*a*b^2*d^2*n^2*x^(2/3))/e^2 - (9*b^3*d^2*n^3*x^(2/3))/e^2 + (9*b^3*d^2*n^2*(d + e*x^(2/3))*log(c*(d + e*x^(2/3))^n))/e^3 - (9*b^2*d*n^2*(d + e*x^(2/3))^2*(a + b*log(c*(d + e*x^(2/3))^n)))/(4*e^3) + (b^2*n^2*(d + e*x^(2/3))^3*(a + b*log(c*(d + e*x^(2/3))^n)))/(3*e^3) - (9*b*d^2*n*(d + e*x^(2/3))*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(2*e^3) + (9*b*d*n*(d + e*x^(2/3))^2*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(4*e^3) - (b*n*(d + e*x^(2/3))^3*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(2*e^3) + (3*d^2*(d + e*x^(2/3))*(a + b*log(c*(d + e*x^(2/3))^n))^3)/(2*e^3) - (3*d*(d + e*x^(2/3))^2*(a + b*log(c*(d + e*x^(2/3))^n))^3)/(2*e^3) + ((d + e*x^(2/3))^3*(a + b*log(c*(d + e*x^(2/3))^n))^3)/(2*e^3)]
    @test_int [(a + b*log(c*(d + e*x^(2/3))^n))^3/x^1, x, 6, (3*(a + b*log(c*(d + e*x^(2/3))^n))^3*log(-((e*x^(2/3))/d)))/2 + (9*b*n*(a + b*log(c*(d + e*x^(2/3))^n))^2*PolyLog(2, 1 + (e*x^(2/3))/d))/2 - 9*b^2*n^2*(a + b*log(c*(d + e*x^(2/3))^n))*PolyLog(3, 1 + (e*x^(2/3))/d) + 9*b^3*n^3*PolyLog(4, 1 + (e*x^(2/3))/d)]
    @test_int [(a + b*log(c*(d + e*x^(2/3))^n))^3/x^3, x, 17, -((3*b^2*e^2*n^2*(d + e*x^(2/3))*(a + b*log(c*(d + e*x^(2/3))^n)))/(2*d^3*x^(2/3))) - (3*b^2*e^3*n^2*log(1 - d/(d + e*x^(2/3)))*(a + b*log(c*(d + e*x^(2/3))^n)))/(2*d^3) - (3*b*e*n*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(4*d*x^(4/3)) + (3*b*e^2*n*(d + e*x^(2/3))*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(2*d^3*x^(2/3)) + (3*b*e^3*n*log(1 - d/(d + e*x^(2/3)))*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(2*d^3) - (a + b*log(c*(d + e*x^(2/3))^n))^3/(2*x^2) - (3*b^2*e^3*n^2*(a + b*log(c*(d + e*x^(2/3))^n))*log(-((e*x^(2/3))/d)))/d^3 + (b^3*e^3*n^3*log(x))/d^3 + (3*b^3*e^3*n^3*PolyLog(2, d/(d + e*x^(2/3))))/(2*d^3) - (3*b^2*e^3*n^2*(a + b*log(c*(d + e*x^(2/3))^n))*PolyLog(2, d/(d + e*x^(2/3))))/d^3 - (3*b^3*e^3*n^3*PolyLog(2, 1 + (e*x^(2/3))/d))/d^3 - (3*b^3*e^3*n^3*PolyLog(3, d/(d + e*x^(2/3))))/d^3]

    @test_int [x^2*(a + b*log(c*(d + e*x^(2/3))^n))^3, x, 109, (4504*a*b^2*d^4*n^2*x^(1/3))/(315*e^4) - (3475504*b^3*d^4*n^3*x^(1/3))/(99225*e^4) + (637984*b^3*d^3*n^3*x)/(297675*e^3) - (221344*b^3*d^2*n^3*x^(5/3))/(496125*e^2) + (3088*b^3*d*n^3*x^(7/3))/(27783*e) - (16*b^3*n^3*x^3)/729 + (3475504*b^3*d^(9/2)*n^3*atan((sqrt(e)*x^(1/3))/sqrt(d)))/(99225*e^(9/2)) - (((4504*im)/315)*b^3*d^(9/2)*n^3*atan((sqrt(e)*x^(1/3))/sqrt(d))^2)/e^(9/2) - (9008*b^3*d^(9/2)*n^3*atan((sqrt(e)*x^(1/3))/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/(315*e^(9/2)) + (4504*b^3*d^4*n^2*x^(1/3)*log(c*(d + e*x^(2/3))^n))/(315*e^4) - (1984*b^2*d^3*n^2*x*(a + b*log(c*(d + e*x^(2/3))^n)))/(945*e^3) + (1144*b^2*d^2*n^2*x^(5/3)*(a + b*log(c*(d + e*x^(2/3))^n)))/(1575*e^2) - (128*b^2*d*n^2*x^(7/3)*(a + b*log(c*(d + e*x^(2/3))^n)))/(441*e) + (8*b^2*n^2*x^3*(a + b*log(c*(d + e*x^(2/3))^n)))/81 - (4504*b^2*d^(9/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d))*(a + b*log(c*(d + e*x^(2/3))^n)))/(315*e^(9/2)) - (2*b*d^4*n*x^(1/3)*(a + b*log(c*(d + e*x^(2/3))^n))^2)/e^4 + (2*b*d^3*n*x*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(3*e^3) - (2*b*d^2*n*x^(5/3)*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(5*e^2) + (2*b*d*n*x^(7/3)*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(7*e) - (2*b*n*x^3*(a + b*log(c*(d + e*x^(2/3))^n))^2)/9 + (x^3*(a + b*log(c*(d + e*x^(2/3))^n))^3)/3 - (((4504*im)/315)*b^3*d^(9/2)*n^3*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/e^(9/2) + (2*b*d^5*n*Unintegrable((a + b*log(c*(d + e*x^(2/3))^n))^2/((d + e*x^(2/3))*x^(2/3)), x))/(3*e^4)]
    @test_int [x^0*(a + b*log(c*(d + e*x^(2/3))^n))^3, x, 34, (-32*a*b^2*d*n^2*x^(1/3))/e + (208*b^3*d*n^3*x^(1/3))/(3*e) - (16*b^3*n^3*x)/9 - (208*b^3*d^(3/2)*n^3*atan((sqrt(e)*x^(1/3))/sqrt(d)))/(3*e^(3/2)) + ((32*im)*b^3*d^(3/2)*n^3*atan((sqrt(e)*x^(1/3))/sqrt(d))^2)/e^(3/2) + (64*b^3*d^(3/2)*n^3*atan((sqrt(e)*x^(1/3))/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/e^(3/2) - (32*b^3*d*n^2*x^(1/3)*log(c*(d + e*x^(2/3))^n))/e + (8*b^2*n^2*x*(a + b*log(c*(d + e*x^(2/3))^n)))/3 + (32*b^2*d^(3/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d))*(a + b*log(c*(d + e*x^(2/3))^n)))/e^(3/2) + (6*b*d*n*x^(1/3)*(a + b*log(c*(d + e*x^(2/3))^n))^2)/e - 2*b*n*x*(a + b*log(c*(d + e*x^(2/3))^n))^2 + x*(a + b*log(c*(d + e*x^(2/3))^n))^3 + ((32*im)*b^3*d^(3/2)*n^3*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/e^(3/2) - (2*b*d^2*n*Unintegrable((a + b*log(c*(d + e*x^(2/3))^n))^2/((d + e*x^(2/3))*x^(2/3)), x))/e]
    @test_int [(a + b*log(c*(d + e*x^(2/3))^n))^3/x^2, x, 11, ((24*im)*b^3*e^(3/2)*n^3*atan((sqrt(e)*x^(1/3))/sqrt(d))^2)/d^(3/2) + (48*b^3*e^(3/2)*n^3*atan((sqrt(e)*x^(1/3))/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/d^(3/2) + (24*b^2*e^(3/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d))*(a + b*log(c*(d + e*x^(2/3))^n)))/d^(3/2) - (6*b*e*n*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(d*x^(1/3)) - (a + b*log(c*(d + e*x^(2/3))^n))^3/x + ((24*im)*b^3*e^(3/2)*n^3*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/d^(3/2) - (2*b*e^2*n*Unintegrable((a + b*log(c*(d + e*x^(2/3))^n))^2/((d + e*x^(2/3))*x^(2/3)), x))/d]
    @test_int [(a + b*log(c*(d + e*x^(2/3))^n))^3/x^4, x, 54, -((16*b^3*e^3*n^3)/(105*d^3*x)) + (16*b^3*e^4*n^3)/(7*d^4*x^(1/3)) + (1376*b^3*e^(9/2)*n^3*atan((sqrt(e)*x^(1/3))/sqrt(d)))/(105*d^(9/2)) - (1408*im*b^3*e^(9/2)*n^3*atan((sqrt(e)*x^(1/3))/sqrt(d))^2)/(105*d^(9/2)) - (2816*b^3*e^(9/2)*n^3*atan((sqrt(e)*x^(1/3))/sqrt(d))*log((2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/(105*d^(9/2)) - (8*b^2*e^2*n^2*(a + b*log(c*(d + e*x^(2/3))^n)))/(35*d^2*x^(5/3)) + (32*b^2*e^3*n^2*(a + b*log(c*(d + e*x^(2/3))^n)))/(35*d^3*x) - (568*b^2*e^4*n^2*(a + b*log(c*(d + e*x^(2/3))^n)))/(105*d^4*x^(1/3)) - (1408*b^2*e^(9/2)*n^2*atan((sqrt(e)*x^(1/3))/sqrt(d))*(a + b*log(c*(d + e*x^(2/3))^n)))/(105*d^(9/2)) - (2*b*e*n*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(7*d*x^(7/3)) + (2*b*e^2*n*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(5*d^2*x^(5/3)) - (2*b*e^3*n*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(3*d^3*x) + (2*b*e^4*n*(a + b*log(c*(d + e*x^(2/3))^n))^2)/(d^4*x^(1/3)) - (a + b*log(c*(d + e*x^(2/3))^n))^3/(3*x^3) - (1408*im*b^3*e^(9/2)*n^3*PolyLog(2, 1 - (2*sqrt(d))/(sqrt(d) + im*sqrt(e)*x^(1/3))))/(105*d^(9/2)) + (2*b*e^5*n*Unintegrable((a + b*log(c*(d + e*x^(2/3))^n))^2/((d + e*x^(2/3))*x^(2/3)), x))/(3*d^4)]

    #= ::Subsubsection::Closed:: =#
    #=m=-1=#

    @test_int [x^3*(a + b*log(c*(d + e/x^(1/3))^n)), x, 4, (b*e^11*n*x^(1/3))/(4*d^11) - (b*e^10*n*x^(2/3))/(8*d^10) + (b*e^9*n*x)/(12*d^9) - (b*e^8*n*x^(4/3))/(16*d^8) + (b*e^7*n*x^(5/3))/(20*d^7) - (b*e^6*n*x^2)/(24*d^6) + (b*e^5*n*x^(7/3))/(28*d^5) - (b*e^4*n*x^(8/3))/(32*d^4) + (b*e^3*n*x^3)/(36*d^3) - (b*e^2*n*x^(10/3))/(40*d^2) + (b*e*n*x^(11/3))/(44*d) - (b*e^12*n*log(d + e/x^(1/3)))/(4*d^12) + (x^4*(a + b*log(c*(d + e/x^(1/3))^n)))/4 - (b*e^12*n*log(x))/(12*d^12)]
    @test_int [x^2*(a + b*log(c*(d + e/x^(1/3))^n)), x, 4, -(b*e^8*n*x^(1/3))/(3*d^8) + (b*e^7*n*x^(2/3))/(6*d^7) - (b*e^6*n*x)/(9*d^6) + (b*e^5*n*x^(4/3))/(12*d^5) - (b*e^4*n*x^(5/3))/(15*d^4) + (b*e^3*n*x^2)/(18*d^3) - (b*e^2*n*x^(7/3))/(21*d^2) + (b*e*n*x^(8/3))/(24*d) + (b*e^9*n*log(d + e/x^(1/3)))/(3*d^9) + (x^3*(a + b*log(c*(d + e/x^(1/3))^n)))/3 + (b*e^9*n*log(x))/(9*d^9)]
    @test_int [x^1*(a + b*log(c*(d + e/x^(1/3))^n)), x, 4, (b*e^5*n*x^(1/3))/(2*d^5) - (b*e^4*n*x^(2/3))/(4*d^4) + (b*e^3*n*x)/(6*d^3) - (b*e^2*n*x^(4/3))/(8*d^2) + (b*e*n*x^(5/3))/(10*d) - (b*e^6*n*log(d + e/x^(1/3)))/(2*d^6) + (x^2*(a + b*log(c*(d + e/x^(1/3))^n)))/2 - (b*e^6*n*log(x))/(6*d^6)]
    @test_int [x^0*(a + b*log(c*(d + e/x^(1/3))^n)), x, 6, -((b*e^2*n*x^(1/3))/d^2) + (b*e*n*x^(2/3))/(2*d) + a*x + b*x*log(c*(d + e/x^(1/3))^n) + (b*e^3*n*log(e + d*x^(1/3)))/d^3]
    @test_int [(a + b*log(c*(d + e/x^(1/3))^n))/x^1, x, 3, -3*(a + b*log(c*(d + e/x^(1/3))^n))*log(-(e/(d*x^(1/3)))) - 3*b*n*PolyLog(2, 1 + e/(d*x^(1/3)))]
    @test_int [(a + b*log(c*(d + e/x^(1/3))^n))/x^2, x, 4, (b*n)/(3*x) - (b*d*n)/(2*e*x^(2/3)) + (b*d^2*n)/(e^2*x^(1/3)) - (b*d^3*n*log(d + e/x^(1/3)))/e^3 - (a + b*log(c*(d + e/x^(1/3))^n))/x]
    @test_int [(a + b*log(c*(d + e/x^(1/3))^n))/x^3, x, 4, (b*n)/(12*x^2) - (b*d*n)/(10*e*x^(5/3)) + (b*d^2*n)/(8*e^2*x^(4/3)) - (b*d^3*n)/(6*e^3*x) + (b*d^4*n)/(4*e^4*x^(2/3)) - (b*d^5*n)/(2*e^5*x^(1/3)) + (b*d^6*n*log(d + e/x^(1/3)))/(2*e^6) - (a + b*log(c*(d + e/x^(1/3))^n))/(2*x^2)]
    @test_int [(a + b*log(c*(d + e/x^(1/3))^n))/x^4, x, 4, (b*n)/(27*x^3) - (b*d*n)/(24*e*x^(8/3)) + (b*d^2*n)/(21*e^2*x^(7/3)) - (b*d^3*n)/(18*e^3*x^2) + (b*d^4*n)/(15*e^4*x^(5/3)) - (b*d^5*n)/(12*e^5*x^(4/3)) + (b*d^6*n)/(9*e^6*x) - (b*d^7*n)/(6*e^7*x^(2/3)) + (b*d^8*n)/(3*e^8*x^(1/3)) - (b*d^9*n*log(d + e/x^(1/3)))/(3*e^9) - (a + b*log(c*(d + e/x^(1/3))^n))/(3*x^3)]

    @test_int [x^2*(a + b*log(c*(d + e/x^(1/3))^n))^2, x, 36, (481*b^2*e^8*n^2*x^(1/3))/(420*d^8) - (341*b^2*e^7*n^2*x^(2/3))/(840*d^7) + (743*b^2*e^6*n^2*x)/(3780*d^6) - (533*b^2*e^5*n^2*x^(4/3))/(5040*d^5) + (73*b^2*e^4*n^2*x^(5/3))/(1260*d^4) - (5*b^2*e^3*n^2*x^2)/(168*d^3) + (b^2*e^2*n^2*x^(7/3))/(84*d^2) - (481*b^2*e^9*n^2*log(d + e/x^(1/3)))/(420*d^9) - (2*b*e^8*n*(d + e/x^(1/3))*x^(1/3)*(a + b*log(c*(d + e/x^(1/3))^n)))/(3*d^9) + (b*e^7*n*x^(2/3)*(a + b*log(c*(d + e/x^(1/3))^n)))/(3*d^7) - (2*b*e^6*n*x*(a + b*log(c*(d + e/x^(1/3))^n)))/(9*d^6) + (b*e^5*n*x^(4/3)*(a + b*log(c*(d + e/x^(1/3))^n)))/(6*d^5) - (2*b*e^4*n*x^(5/3)*(a + b*log(c*(d + e/x^(1/3))^n)))/(15*d^4) + (b*e^3*n*x^2*(a + b*log(c*(d + e/x^(1/3))^n)))/(9*d^3) - (2*b*e^2*n*x^(7/3)*(a + b*log(c*(d + e/x^(1/3))^n)))/(21*d^2) + (b*e*n*x^(8/3)*(a + b*log(c*(d + e/x^(1/3))^n)))/(12*d) - (2*b*e^9*n*log(1 - d/(d + e/x^(1/3)))*(a + b*log(c*(d + e/x^(1/3))^n)))/(3*d^9) + (1/3)*x^3*(a + b*log(c*(d + e/x^(1/3))^n))^2 - (761*b^2*e^9*n^2*log(x))/(1260*d^9) + (2*b^2*e^9*n^2*PolyLog(2, d/(d + e/x^(1/3))))/(3*d^9)]
    @test_int [x^1*(a + b*log(c*(d + e/x^(1/3))^n))^2, x, 24, -((77*b^2*e^5*n^2*x^(1/3))/(60*d^5)) + (47*b^2*e^4*n^2*x^(2/3))/(120*d^4) - (3*b^2*e^3*n^2*x)/(20*d^3) + (b^2*e^2*n^2*x^(4/3))/(20*d^2) + (77*b^2*e^6*n^2*log(d + e/x^(1/3)))/(60*d^6) + (b*e^5*n*(d + e/x^(1/3))*x^(1/3)*(a + b*log(c*(d + e/x^(1/3))^n)))/d^6 - (b*e^4*n*x^(2/3)*(a + b*log(c*(d + e/x^(1/3))^n)))/(2*d^4) + (b*e^3*n*x*(a + b*log(c*(d + e/x^(1/3))^n)))/(3*d^3) - (b*e^2*n*x^(4/3)*(a + b*log(c*(d + e/x^(1/3))^n)))/(4*d^2) + (b*e*n*x^(5/3)*(a + b*log(c*(d + e/x^(1/3))^n)))/(5*d) + (b*e^6*n*log(1 - d/(d + e/x^(1/3)))*(a + b*log(c*(d + e/x^(1/3))^n)))/d^6 + (1/2)*x^2*(a + b*log(c*(d + e/x^(1/3))^n))^2 + (137*b^2*e^6*n^2*log(x))/(180*d^6) - (b^2*e^6*n^2*PolyLog(2, d/(d + e/x^(1/3))))/d^6]
    @test_int [x^0*(a + b*log(c*(d + e/x^(1/3))^n))^2, x, 13, (b^2*e^2*n^2*x^(1/3))/d^2 - (b^2*e^3*n^2*log(d + e/x^(1/3)))/d^3 - (2*b*e^2*n*(d + e/x^(1/3))*x^(1/3)*(a + b*log(c*(d + e/x^(1/3))^n)))/d^3 + (b*e*n*x^(2/3)*(a + b*log(c*(d + e/x^(1/3))^n)))/d - (2*b*e^3*n*log(1 - d/(d + e/x^(1/3)))*(a + b*log(c*(d + e/x^(1/3))^n)))/d^3 + x*(a + b*log(c*(d + e/x^(1/3))^n))^2 - (b^2*e^3*n^2*log(x))/d^3 + (2*b^2*e^3*n^2*PolyLog(2, d/(d + e/x^(1/3))))/d^3]
    @test_int [(a + b*log(c*(d + e/x^(1/3))^n))^2/x^1, x, 5, -3*(a + b*log(c*(d + e/x^(1/3))^n))^2*log(-(e/(d*x^(1/3)))) - 6*b*n*(a + b*log(c*(d + e/x^(1/3))^n))*PolyLog(2, 1 + e/(d*x^(1/3))) + 6*b^2*n^2*PolyLog(3, 1 + e/(d*x^(1/3)))]
    @test_int [(a + b*log(c*(d + e/x^(1/3))^n))^2/x^2, x, 8, (3*b^2*d*n^2*(d + e/x^(1/3))^2)/(2*e^3) - (2*b^2*n^2*(d + e/x^(1/3))^3)/(9*e^3) - (6*b^2*d^2*n^2)/(e^2*x^(1/3)) + (b^2*d^3*n^2*log(d + e/x^(1/3))^2)/e^3 + (6*b*d^2*n*(d + e/x^(1/3))*(a + b*log(c*(d + e/x^(1/3))^n)))/e^3 - (3*b*d*n*(d + e/x^(1/3))^2*(a + b*log(c*(d + e/x^(1/3))^n)))/e^3 + (2*b*n*(d + e/x^(1/3))^3*(a + b*log(c*(d + e/x^(1/3))^n)))/(3*e^3) - (2*b*d^3*n*log(d + e/x^(1/3))*(a + b*log(c*(d + e/x^(1/3))^n)))/e^3 - (a + b*log(c*(d + e/x^(1/3))^n))^2/x]
    @test_int [(a + b*log(c*(d + e/x^(1/3))^n))^2/x^3, x, 8, -((15*b^2*d^4*n^2*(d + e/x^(1/3))^2)/(4*e^6)) + (20*b^2*d^3*n^2*(d + e/x^(1/3))^3)/(9*e^6) - (15*b^2*d^2*n^2*(d + e/x^(1/3))^4)/(16*e^6) + (6*b^2*d*n^2*(d + e/x^(1/3))^5)/(25*e^6) - (b^2*n^2*(d + e/x^(1/3))^6)/(36*e^6) + (6*b^2*d^5*n^2)/(e^5*x^(1/3)) - (b^2*d^6*n^2*log(d + e/x^(1/3))^2)/(2*e^6) - (6*b*d^5*n*(d + e/x^(1/3))*(a + b*log(c*(d + e/x^(1/3))^n)))/e^6 + (15*b*d^4*n*(d + e/x^(1/3))^2*(a + b*log(c*(d + e/x^(1/3))^n)))/(2*e^6) - (20*b*d^3*n*(d + e/x^(1/3))^3*(a + b*log(c*(d + e/x^(1/3))^n)))/(3*e^6) + (15*b*d^2*n*(d + e/x^(1/3))^4*(a + b*log(c*(d + e/x^(1/3))^n)))/(4*e^6) - (6*b*d*n*(d + e/x^(1/3))^5*(a + b*log(c*(d + e/x^(1/3))^n)))/(5*e^6) + (b*n*(d + e/x^(1/3))^6*(a + b*log(c*(d + e/x^(1/3))^n)))/(6*e^6) + (b*d^6*n*log(d + e/x^(1/3))*(a + b*log(c*(d + e/x^(1/3))^n)))/e^6 - (a + b*log(c*(d + e/x^(1/3))^n))^2/(2*x^2)]

    @test_int [x^1*(a + b*log(c*(d + e/x^(1/3))^n))^3, x, 62, (71*b^3*e^5*n^3*x^(1/3))/(40*d^5) - (3*b^3*e^4*n^3*x^(2/3))/(10*d^4) + (b^3*e^3*n^3*x)/(20*d^3) - (71*b^3*e^6*n^3*log(d + e/x^(1/3)))/(40*d^6) - (77*b^2*e^5*n^2*(d + e/x^(1/3))*x^(1/3)*(a + b*log(c*(d + e/x^(1/3))^n)))/(20*d^6) + (47*b^2*e^4*n^2*x^(2/3)*(a + b*log(c*(d + e/x^(1/3))^n)))/(40*d^4) - (9*b^2*e^3*n^2*x*(a + b*log(c*(d + e/x^(1/3))^n)))/(20*d^3) + (3*b^2*e^2*n^2*x^(4/3)*(a + b*log(c*(d + e/x^(1/3))^n)))/(20*d^2) - (77*b^2*e^6*n^2*log(1 - d/(d + e/x^(1/3)))*(a + b*log(c*(d + e/x^(1/3))^n)))/(20*d^6) + (3*b*e^5*n*(d + e/x^(1/3))*x^(1/3)*(a + b*log(c*(d + e/x^(1/3))^n))^2)/(2*d^6) - (3*b*e^4*n*x^(2/3)*(a + b*log(c*(d + e/x^(1/3))^n))^2)/(4*d^4) + (b*e^3*n*x*(a + b*log(c*(d + e/x^(1/3))^n))^2)/(2*d^3) - (3*b*e^2*n*x^(4/3)*(a + b*log(c*(d + e/x^(1/3))^n))^2)/(8*d^2) + (3*b*e*n*x^(5/3)*(a + b*log(c*(d + e/x^(1/3))^n))^2)/(10*d) + (3*b*e^6*n*log(1 - d/(d + e/x^(1/3)))*(a + b*log(c*(d + e/x^(1/3))^n))^2)/(2*d^6) + (1/2)*x^2*(a + b*log(c*(d + e/x^(1/3))^n))^3 - (3*b^2*e^6*n^2*(a + b*log(c*(d + e/x^(1/3))^n))*log(-(e/(d*x^(1/3)))))/d^6 - (15*b^3*e^6*n^3*log(x))/(8*d^6) + (77*b^3*e^6*n^3*PolyLog(2, d/(d + e/x^(1/3))))/(20*d^6) - (3*b^2*e^6*n^2*(a + b*log(c*(d + e/x^(1/3))^n))*PolyLog(2, d/(d + e/x^(1/3))))/d^6 - (3*b^3*e^6*n^3*PolyLog(2, 1 + e/(d*x^(1/3))))/d^6 - (3*b^3*e^6*n^3*PolyLog(3, d/(d + e/x^(1/3))))/d^6]
    @test_int [x^0*(a + b*log(c*(d + e/x^(1/3))^n))^3, x, 18, (3*b^2*e^2*n^2*(d + e/x^(1/3))*x^(1/3)*(a + b*log(c*(d + e/x^(1/3))^n)))/d^3 + (3*b^2*e^3*n^2*log(1 - d/(d + e/x^(1/3)))*(a + b*log(c*(d + e/x^(1/3))^n)))/d^3 - (3*b*e^2*n*(d + e/x^(1/3))*x^(1/3)*(a + b*log(c*(d + e/x^(1/3))^n))^2)/d^3 + (3*b*e*n*x^(2/3)*(a + b*log(c*(d + e/x^(1/3))^n))^2)/(2*d) - (3*b*e^3*n*log(1 - d/(d + e/x^(1/3)))*(a + b*log(c*(d + e/x^(1/3))^n))^2)/d^3 + x*(a + b*log(c*(d + e/x^(1/3))^n))^3 + (6*b^2*e^3*n^2*(a + b*log(c*(d + e/x^(1/3))^n))*log(-(e/(d*x^(1/3)))))/d^3 + (b^3*e^3*n^3*log(x))/d^3 - (3*b^3*e^3*n^3*PolyLog(2, d/(d + e/x^(1/3))))/d^3 + (6*b^2*e^3*n^2*(a + b*log(c*(d + e/x^(1/3))^n))*PolyLog(2, d/(d + e/x^(1/3))))/d^3 + (6*b^3*e^3*n^3*PolyLog(2, 1 + e/(d*x^(1/3))))/d^3 + (6*b^3*e^3*n^3*PolyLog(3, d/(d + e/x^(1/3))))/d^3]
    @test_int [(a + b*log(c*(d + e/x^(1/3))^n))^3/x^1, x, 6, -3*(a + b*log(c*(d + e/x^(1/3))^n))^3*log(-(e/(d*x^(1/3)))) - 9*b*n*(a + b*log(c*(d + e/x^(1/3))^n))^2*PolyLog(2, 1 + e/(d*x^(1/3))) + 18*b^2*n^2*(a + b*log(c*(d + e/x^(1/3))^n))*PolyLog(3, 1 + e/(d*x^(1/3))) - 18*b^3*n^3*PolyLog(4, 1 + e/(d*x^(1/3)))]
    @test_int [(a + b*log(c*(d + e/x^(1/3))^n))^3/x^2, x, 16, (-9*b^3*d*n^3*(d + e/x^(1/3))^2)/(4*e^3) + (2*b^3*n^3*(d + e/x^(1/3))^3)/(9*e^3) - (18*a*b^2*d^2*n^2)/(e^2*x^(1/3)) + (18*b^3*d^2*n^3)/(e^2*x^(1/3)) - (18*b^3*d^2*n^2*(d + e/x^(1/3))*log(c*(d + e/x^(1/3))^n))/e^3 + (9*b^2*d*n^2*(d + e/x^(1/3))^2*(a + b*log(c*(d + e/x^(1/3))^n)))/(2*e^3) - (2*b^2*n^2*(d + e/x^(1/3))^3*(a + b*log(c*(d + e/x^(1/3))^n)))/(3*e^3) + (9*b*d^2*n*(d + e/x^(1/3))*(a + b*log(c*(d + e/x^(1/3))^n))^2)/e^3 - (9*b*d*n*(d + e/x^(1/3))^2*(a + b*log(c*(d + e/x^(1/3))^n))^2)/(2*e^3) + (b*n*(d + e/x^(1/3))^3*(a + b*log(c*(d + e/x^(1/3))^n))^2)/e^3 - (3*d^2*(d + e/x^(1/3))*(a + b*log(c*(d + e/x^(1/3))^n))^3)/e^3 + (3*d*(d + e/x^(1/3))^2*(a + b*log(c*(d + e/x^(1/3))^n))^3)/e^3 - ((d + e/x^(1/3))^3*(a + b*log(c*(d + e/x^(1/3))^n))^3)/e^3]
    @test_int [(a + b*log(c*(d + e/x^(1/3))^n))^3/x^3, x, 28, (45*b^3*d^4*n^3*(d + e/x^(1/3))^2)/(8*e^6) - (20*b^3*d^3*n^3*(d + e/x^(1/3))^3)/(9*e^6) + (45*b^3*d^2*n^3*(d + e/x^(1/3))^4)/(64*e^6) - (18*b^3*d*n^3*(d + e/x^(1/3))^5)/(125*e^6) + (b^3*n^3*(d + e/x^(1/3))^6)/(72*e^6) + (18*a*b^2*d^5*n^2)/(e^5*x^(1/3)) - (18*b^3*d^5*n^3)/(e^5*x^(1/3)) + (18*b^3*d^5*n^2*(d + e/x^(1/3))*log(c*(d + e/x^(1/3))^n))/e^6 - (45*b^2*d^4*n^2*(d + e/x^(1/3))^2*(a + b*log(c*(d + e/x^(1/3))^n)))/(4*e^6) + (20*b^2*d^3*n^2*(d + e/x^(1/3))^3*(a + b*log(c*(d + e/x^(1/3))^n)))/(3*e^6) - (45*b^2*d^2*n^2*(d + e/x^(1/3))^4*(a + b*log(c*(d + e/x^(1/3))^n)))/(16*e^6) + (18*b^2*d*n^2*(d + e/x^(1/3))^5*(a + b*log(c*(d + e/x^(1/3))^n)))/(25*e^6) - (b^2*n^2*(d + e/x^(1/3))^6*(a + b*log(c*(d + e/x^(1/3))^n)))/(12*e^6) - (9*b*d^5*n*(d + e/x^(1/3))*(a + b*log(c*(d + e/x^(1/3))^n))^2)/e^6 + (45*b*d^4*n*(d + e/x^(1/3))^2*(a + b*log(c*(d + e/x^(1/3))^n))^2)/(4*e^6) - (10*b*d^3*n*(d + e/x^(1/3))^3*(a + b*log(c*(d + e/x^(1/3))^n))^2)/e^6 + (45*b*d^2*n*(d + e/x^(1/3))^4*(a + b*log(c*(d + e/x^(1/3))^n))^2)/(8*e^6) - (9*b*d*n*(d + e/x^(1/3))^5*(a + b*log(c*(d + e/x^(1/3))^n))^2)/(5*e^6) + (b*n*(d + e/x^(1/3))^6*(a + b*log(c*(d + e/x^(1/3))^n))^2)/(4*e^6) + (3*d^5*(d + e/x^(1/3))*(a + b*log(c*(d + e/x^(1/3))^n))^3)/e^6 - (15*d^4*(d + e/x^(1/3))^2*(a + b*log(c*(d + e/x^(1/3))^n))^3)/(2*e^6) + (10*d^3*(d + e/x^(1/3))^3*(a + b*log(c*(d + e/x^(1/3))^n))^3)/e^6 - (15*d^2*(d + e/x^(1/3))^4*(a + b*log(c*(d + e/x^(1/3))^n))^3)/(2*e^6) + (3*d*(d + e/x^(1/3))^5*(a + b*log(c*(d + e/x^(1/3))^n))^3)/e^6 - ((d + e/x^(1/3))^6*(a + b*log(c*(d + e/x^(1/3))^n))^3)/(2*e^6)]

    #= ::Subsubsection::Closed:: =#
    #=m=-2=#

    @test_int [x^3*(a + b*log(c*(d + e/x^(2/3))^n)), x, 4, (b*e^5*n*x^(2/3))/(4*d^5) - (b*e^4*n*x^(4/3))/(8*d^4) + (b*e^3*n*x^2)/(12*d^3) - (b*e^2*n*x^(8/3))/(16*d^2) + (b*e*n*x^(10/3))/(20*d) - (b*e^6*n*log(d + e/x^(2/3)))/(4*d^6) + (x^4*(a + b*log(c*(d + e/x^(2/3))^n)))/4 - (b*e^6*n*log(x))/(6*d^6)]
    @test_int [x^2*(a + b*log(c*(d + e/x^(2/3))^n)), x, 6, (-2*b*e^4*n*x^(1/3))/(3*d^4) + (2*b*e^3*n*x)/(9*d^3) - (2*b*e^2*n*x^(5/3))/(15*d^2) + (2*b*e*n*x^(7/3))/(21*d) + (2*b*e^(9/2)*n*atan((sqrt(d)*x^(1/3))/sqrt(e)))/(3*d^(9/2)) + (x^3*(a + b*log(c*(d + e/x^(2/3))^n)))/3]
    @test_int [x^1*(a + b*log(c*(d + e/x^(2/3))^n)), x, 4, -(b*e^2*n*x^(2/3))/(2*d^2) + (b*e*n*x^(4/3))/(4*d) + (b*e^3*n*log(d + e/x^(2/3)))/(2*d^3) + (x^2*(a + b*log(c*(d + e/x^(2/3))^n)))/2 + (b*e^3*n*log(x))/(3*d^3)]
    @test_int [x^0*(a + b*log(c*(d + e/x^(2/3))^n)), x, 6, (2*b*e*n*x^(1/3))/d + a*x - (2*b*e^(3/2)*n*atan((sqrt(d)*x^(1/3))/sqrt(e)))/d^(3/2) + b*x*log(c*(d + e/x^(2/3))^n)]
    @test_int [(a + b*log(c*(d + e/x^(2/3))^n))/x^1, x, 3, (-3*(a + b*log(c*(d + e/x^(2/3))^n))*log(-(e/(d*x^(2/3)))))/2 - (3*b*n*PolyLog(2, 1 + e/(d*x^(2/3))))/2]
    @test_int [(a + b*log(c*(d + e/x^(2/3))^n))/x^2, x, 6, (2*b*n)/(3*x) - (2*b*d*n)/(e*x^(1/3)) - (2*b*d^(3/2)*n*atan((sqrt(d)*x^(1/3))/sqrt(e)))/e^(3/2) - (a + b*log(c*(d + e/x^(2/3))^n))/x]
    @test_int [(a + b*log(c*(d + e/x^(2/3))^n))/x^3, x, 4, (b*n)/(6*x^2) - (b*d*n)/(4*e*x^(4/3)) + (b*d^2*n)/(2*e^2*x^(2/3)) - (b*d^3*n*log(d + e/x^(2/3)))/(2*e^3) - (a + b*log(c*(d + e/x^(2/3))^n))/(2*x^2)]
    @test_int [(a + b*log(c*(d + e/x^(2/3))^n))/x^4, x, 9, (2*b*n)/(27*x^3) - (2*b*d*n)/(21*e*x^(7/3)) + (2*b*d^2*n)/(15*e^2*x^(5/3)) - (2*b*d^3*n)/(9*e^3*x) + (2*b*d^4*n)/(3*e^4*x^(1/3)) + (2*b*d^(9/2)*n*atan((sqrt(d)*x^(1/3))/sqrt(e)))/(3*e^(9/2)) - (a + b*log(c*(d + e/x^(2/3))^n))/(3*x^3)]

    @test_int [x^3*(a + b*log(c*(d + e/x^(2/3))^n))^2, x, 24, -((77*b^2*e^5*n^2*x^(2/3))/(120*d^5)) + (47*b^2*e^4*n^2*x^(4/3))/(240*d^4) - (3*b^2*e^3*n^2*x^2)/(40*d^3) + (b^2*e^2*n^2*x^(8/3))/(40*d^2) + (77*b^2*e^6*n^2*log(d + e/x^(2/3)))/(120*d^6) + (b*e^5*n*(d + e/x^(2/3))*x^(2/3)*(a + b*log(c*(d + e/x^(2/3))^n)))/(2*d^6) - (b*e^4*n*x^(4/3)*(a + b*log(c*(d + e/x^(2/3))^n)))/(4*d^4) + (b*e^3*n*x^2*(a + b*log(c*(d + e/x^(2/3))^n)))/(6*d^3) - (b*e^2*n*x^(8/3)*(a + b*log(c*(d + e/x^(2/3))^n)))/(8*d^2) + (b*e*n*x^(10/3)*(a + b*log(c*(d + e/x^(2/3))^n)))/(10*d) + (b*e^6*n*log(1 - d/(d + e/x^(2/3)))*(a + b*log(c*(d + e/x^(2/3))^n)))/(2*d^6) + (1/4)*x^4*(a + b*log(c*(d + e/x^(2/3))^n))^2 + (137*b^2*e^6*n^2*log(x))/(180*d^6) - (b^2*e^6*n^2*PolyLog(2, d/(d + e/x^(2/3))))/(2*d^6)]
    @test_int [x^1*(a + b*log(c*(d + e/x^(2/3))^n))^2, x, 12, (b^2*e^2*n^2*x^(2/3))/(2*d^2) - (b^2*e^3*n^2*log(d + e/x^(2/3)))/(2*d^3) - (b*e^2*n*(d + e/x^(2/3))*x^(2/3)*(a + b*log(c*(d + e/x^(2/3))^n)))/d^3 + (b*e*n*x^(4/3)*(a + b*log(c*(d + e/x^(2/3))^n)))/(2*d) - (b*e^3*n*log(1 - d/(d + e/x^(2/3)))*(a + b*log(c*(d + e/x^(2/3))^n)))/d^3 + (1/2)*x^2*(a + b*log(c*(d + e/x^(2/3))^n))^2 - (b^2*e^3*n^2*log(x))/d^3 + (b^2*e^3*n^2*PolyLog(2, d/(d + e/x^(2/3))))/d^3]
    @test_int [(a + b*log(c*(d + e/x^(2/3))^n))^2/x^1, x, 5, (-3*(a + b*log(c*(d + e/x^(2/3))^n))^2*log(-(e/(d*x^(2/3)))))/2 - 3*b*n*(a + b*log(c*(d + e/x^(2/3))^n))*PolyLog(2, 1 + e/(d*x^(2/3))) + 3*b^2*n^2*PolyLog(3, 1 + e/(d*x^(2/3)))]
    @test_int [(a + b*log(c*(d + e/x^(2/3))^n))^2/x^3, x, 8, (3*b^2*d*n^2*(d + e/x^(2/3))^2)/(4*e^3) - (b^2*n^2*(d + e/x^(2/3))^3)/(9*e^3) - (3*b^2*d^2*n^2)/(e^2*x^(2/3)) + (b^2*d^3*n^2*log(d + e/x^(2/3))^2)/(2*e^3) + (3*b*d^2*n*(d + e/x^(2/3))*(a + b*log(c*(d + e/x^(2/3))^n)))/e^3 - (3*b*d*n*(d + e/x^(2/3))^2*(a + b*log(c*(d + e/x^(2/3))^n)))/(2*e^3) + (b*n*(d + e/x^(2/3))^3*(a + b*log(c*(d + e/x^(2/3))^n)))/(3*e^3) - (b*d^3*n*log(d + e/x^(2/3))*(a + b*log(c*(d + e/x^(2/3))^n)))/e^3 - (a + b*log(c*(d + e/x^(2/3))^n))^2/(2*x^2)]
    @test_int [(a + b*log(c*(d + e/x^(2/3))^n))^2/x^5, x, 8, -((15*b^2*d^4*n^2*(d + e/x^(2/3))^2)/(8*e^6)) + (10*b^2*d^3*n^2*(d + e/x^(2/3))^3)/(9*e^6) - (15*b^2*d^2*n^2*(d + e/x^(2/3))^4)/(32*e^6) + (3*b^2*d*n^2*(d + e/x^(2/3))^5)/(25*e^6) - (b^2*n^2*(d + e/x^(2/3))^6)/(72*e^6) + (3*b^2*d^5*n^2)/(e^5*x^(2/3)) - (b^2*d^6*n^2*log(d + e/x^(2/3))^2)/(4*e^6) - (3*b*d^5*n*(d + e/x^(2/3))*(a + b*log(c*(d + e/x^(2/3))^n)))/e^6 + (15*b*d^4*n*(d + e/x^(2/3))^2*(a + b*log(c*(d + e/x^(2/3))^n)))/(4*e^6) - (10*b*d^3*n*(d + e/x^(2/3))^3*(a + b*log(c*(d + e/x^(2/3))^n)))/(3*e^6) + (15*b*d^2*n*(d + e/x^(2/3))^4*(a + b*log(c*(d + e/x^(2/3))^n)))/(8*e^6) - (3*b*d*n*(d + e/x^(2/3))^5*(a + b*log(c*(d + e/x^(2/3))^n)))/(5*e^6) + (b*n*(d + e/x^(2/3))^6*(a + b*log(c*(d + e/x^(2/3))^n)))/(12*e^6) + (b*d^6*n*log(d + e/x^(2/3))*(a + b*log(c*(d + e/x^(2/3))^n)))/(2*e^6) - (a + b*log(c*(d + e/x^(2/3))^n))^2/(4*x^4)]

    @test_int [x^2*(a + b*log(c*(d + e/x^(2/3))^n))^2, x, 28, (-4*a*b*e^4*n*x^(1/3))/(3*d^4) + (568*b^2*e^4*n^2*x^(1/3))/(315*d^4) - (32*b^2*e^3*n^2*x)/(105*d^3) + (8*b^2*e^2*n^2*x^(5/3))/(105*d^2) - (1408*b^2*e^(9/2)*n^2*atan((sqrt(d)*x^(1/3))/sqrt(e)))/(315*d^(9/2)) - (((4*im)/3)*b^2*e^(9/2)*n^2*atan((sqrt(d)*x^(1/3))/sqrt(e))^2)/d^(9/2) + (8*b^2*e^(9/2)*n^2*atan((sqrt(d)*x^(1/3))/sqrt(e))*log(2 - (2*sqrt(e))/(sqrt(e) - im*sqrt(d)*x^(1/3))))/(3*d^(9/2)) - (4*b^2*e^4*n*x^(1/3)*log(c*(d + e/x^(2/3))^n))/(3*d^4) + (4*b*e^3*n*x*(a + b*log(c*(d + e/x^(2/3))^n)))/(9*d^3) - (4*b*e^2*n*x^(5/3)*(a + b*log(c*(d + e/x^(2/3))^n)))/(15*d^2) + (4*b*e*n*x^(7/3)*(a + b*log(c*(d + e/x^(2/3))^n)))/(21*d) + (4*b*e^(9/2)*n*atan((sqrt(d)*x^(1/3))/sqrt(e))*(a + b*log(c*(d + e/x^(2/3))^n)))/(3*d^(9/2)) + (x^3*(a + b*log(c*(d + e/x^(2/3))^n))^2)/3 - (((4*im)/3)*b^2*e^(9/2)*n^2*PolyLog(2, -1 + (2*sqrt(e))/(sqrt(e) - im*sqrt(d)*x^(1/3))))/d^(9/2)]
    @test_int [x^0*(a + b*log(c*(d + e/x^(2/3))^n))^2, x, 14, (4*a*b*e*n*x^(1/3))/d + (8*b^2*e^(3/2)*n^2*atan((sqrt(d)*x^(1/3))/sqrt(e)))/d^(3/2) + ((4*im)*b^2*e^(3/2)*n^2*atan((sqrt(d)*x^(1/3))/sqrt(e))^2)/d^(3/2) - (8*b^2*e^(3/2)*n^2*atan((sqrt(d)*x^(1/3))/sqrt(e))*log(2 - (2*sqrt(e))/(sqrt(e) - im*sqrt(d)*x^(1/3))))/d^(3/2) + (4*b^2*e*n*x^(1/3)*log(c*(d + e/x^(2/3))^n))/d - (4*b*e^(3/2)*n*atan((sqrt(d)*x^(1/3))/sqrt(e))*(a + b*log(c*(d + e/x^(2/3))^n)))/d^(3/2) + x*(a + b*log(c*(d + e/x^(2/3))^n))^2 + ((4*im)*b^2*e^(3/2)*n^2*PolyLog(2, -1 + (2*sqrt(e))/(sqrt(e) - im*sqrt(d)*x^(1/3))))/d^(3/2)]
    @test_int [(a + b*log(c*(d + e/x^(2/3))^n))^2/x^2, x, 19, (-8*b^2*n^2)/(9*x) + (32*b^2*d*n^2)/(3*e*x^(1/3)) + (32*b^2*d^(3/2)*n^2*atan((sqrt(d)*x^(1/3))/sqrt(e)))/(3*e^(3/2)) + ((4*im)*b^2*d^(3/2)*n^2*atan((sqrt(d)*x^(1/3))/sqrt(e))^2)/e^(3/2) - (8*b^2*d^(3/2)*n^2*atan((sqrt(d)*x^(1/3))/sqrt(e))*log(2 - (2*sqrt(e))/(sqrt(e) - im*sqrt(d)*x^(1/3))))/e^(3/2) + (4*b*n*(a + b*log(c*(d + e/x^(2/3))^n)))/(3*x) - (4*b*d*n*(a + b*log(c*(d + e/x^(2/3))^n)))/(e*x^(1/3)) - (4*b*d^(3/2)*n*atan((sqrt(d)*x^(1/3))/sqrt(e))*(a + b*log(c*(d + e/x^(2/3))^n)))/e^(3/2) - (a + b*log(c*(d + e/x^(2/3))^n))^2/x + ((4*im)*b^2*d^(3/2)*n^2*PolyLog(2, -1 + (2*sqrt(e))/(sqrt(e) - im*sqrt(d)*x^(1/3))))/e^(3/2)]
    #= [(a + b*log(c*(d + e/x^(2/3))^n))^2/x^4, x, 40, -((8*b^2*n^2)/(243*x^3)) + (128*b^2*d*n^2)/(1323*e*x^(7/3)) - (1144*b^2*d^2*n^2)/(4725*e^2*x^(5/3)) + (1984*b^2*d^3*n^2)/(2835*e^3*x) - (4504*b^2*d^4*n^2)/(945*e^4*x^(1/3)) - (4504*b^2*d^(9/2)*n^2*atan((sqrt(d)*x^(1/3))/sqrt(e)))/(945*e^(9/2)) - (4*im*b^2*d^(9/2)*n^2*atan((sqrt(d)*x^(1/3))/sqrt(e))^2)/(3*e^(9/2)) + (8*b^2*d^(9/2)*n^2*atan((sqrt(d)*x^(1/3))/sqrt(e))*log(2 - (2*sqrt(e))/(sqrt(e) - im*sqrt(d)*x^(1/3))))/(3*e^(9/2)) + (4*b*n*(a + b*log(c*(d + e/x^(2/3))^n)))/(27*x^3) - (4*b*d*n*(a + b*log(c*(d + e/x^(2/3))^n)))/(21*e*x^(7/3)) + (4*b*d^2*n*(a + b*log(c*(d + e/x^(2/3))^n)))/(15*e^2*x^(5/3)) - (4*b*d^3*n*(a + b*log(c*(d + e/x^(2/3))^n)))/(9*e^3*x) + (4*b*d^4*n*(a + b*log(c*(d + e/x^(2/3))^n)))/(3*e^4*x^(1/3)) + (4*b*d^(9/2)*n*atan((sqrt(d)*x^(1/3))/sqrt(e))*(a + b*log(c*(d + e/x^(2/3))^n)))/(3*e^(9/2)) - (a + b*log(c*(d + e/x^(2/3))^n))^2/(3*x^3) - (4*im*b^2*d^(9/2)*n^2*PolyLog(2, -1 + (2*sqrt(e))/(sqrt(e) - im*sqrt(d)*x^(1/3))))/(3*e^(9/2))] =#

    @test_int [x^3*(a + b*log(c*(d + e/x^(2/3))^n))^3, x, 62, (71*b^3*e^5*n^3*x^(2/3))/(80*d^5) - (3*b^3*e^4*n^3*x^(4/3))/(20*d^4) + (b^3*e^3*n^3*x^2)/(40*d^3) - (71*b^3*e^6*n^3*log(d + e/x^(2/3)))/(80*d^6) - (77*b^2*e^5*n^2*(d + e/x^(2/3))*x^(2/3)*(a + b*log(c*(d + e/x^(2/3))^n)))/(40*d^6) + (47*b^2*e^4*n^2*x^(4/3)*(a + b*log(c*(d + e/x^(2/3))^n)))/(80*d^4) - (9*b^2*e^3*n^2*x^2*(a + b*log(c*(d + e/x^(2/3))^n)))/(40*d^3) + (3*b^2*e^2*n^2*x^(8/3)*(a + b*log(c*(d + e/x^(2/3))^n)))/(40*d^2) - (77*b^2*e^6*n^2*log(1 - d/(d + e/x^(2/3)))*(a + b*log(c*(d + e/x^(2/3))^n)))/(40*d^6) + (3*b*e^5*n*(d + e/x^(2/3))*x^(2/3)*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(4*d^6) - (3*b*e^4*n*x^(4/3)*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(8*d^4) + (b*e^3*n*x^2*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(4*d^3) - (3*b*e^2*n*x^(8/3)*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(16*d^2) + (3*b*e*n*x^(10/3)*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(20*d) + (3*b*e^6*n*log(1 - d/(d + e/x^(2/3)))*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(4*d^6) + (1/4)*x^4*(a + b*log(c*(d + e/x^(2/3))^n))^3 - (3*b^2*e^6*n^2*(a + b*log(c*(d + e/x^(2/3))^n))*log(-(e/(d*x^(2/3)))))/(2*d^6) - (15*b^3*e^6*n^3*log(x))/(8*d^6) + (77*b^3*e^6*n^3*PolyLog(2, d/(d + e/x^(2/3))))/(40*d^6) - (3*b^2*e^6*n^2*(a + b*log(c*(d + e/x^(2/3))^n))*PolyLog(2, d/(d + e/x^(2/3))))/(2*d^6) - (3*b^3*e^6*n^3*PolyLog(2, 1 + e/(d*x^(2/3))))/(2*d^6) - (3*b^3*e^6*n^3*PolyLog(3, d/(d + e/x^(2/3))))/(2*d^6)]
    @test_int [x^1*(a + b*log(c*(d + e/x^(2/3))^n))^3, x, 17, (3*b^2*e^2*n^2*(d + e/x^(2/3))*x^(2/3)*(a + b*log(c*(d + e/x^(2/3))^n)))/(2*d^3) + (3*b^2*e^3*n^2*log(1 - d/(d + e/x^(2/3)))*(a + b*log(c*(d + e/x^(2/3))^n)))/(2*d^3) - (3*b*e^2*n*(d + e/x^(2/3))*x^(2/3)*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(2*d^3) + (3*b*e*n*x^(4/3)*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(4*d) - (3*b*e^3*n*log(1 - d/(d + e/x^(2/3)))*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(2*d^3) + (1/2)*x^2*(a + b*log(c*(d + e/x^(2/3))^n))^3 + (3*b^2*e^3*n^2*(a + b*log(c*(d + e/x^(2/3))^n))*log(-(e/(d*x^(2/3)))))/d^3 + (b^3*e^3*n^3*log(x))/d^3 - (3*b^3*e^3*n^3*PolyLog(2, d/(d + e/x^(2/3))))/(2*d^3) + (3*b^2*e^3*n^2*(a + b*log(c*(d + e/x^(2/3))^n))*PolyLog(2, d/(d + e/x^(2/3))))/d^3 + (3*b^3*e^3*n^3*PolyLog(2, 1 + e/(d*x^(2/3))))/d^3 + (3*b^3*e^3*n^3*PolyLog(3, d/(d + e/x^(2/3))))/d^3]
    @test_int [(a + b*log(c*(d + e/x^(2/3))^n))^3/x^1, x, 6, (-3*(a + b*log(c*(d + e/x^(2/3))^n))^3*log(-(e/(d*x^(2/3)))))/2 - (9*b*n*(a + b*log(c*(d + e/x^(2/3))^n))^2*PolyLog(2, 1 + e/(d*x^(2/3))))/2 + 9*b^2*n^2*(a + b*log(c*(d + e/x^(2/3))^n))*PolyLog(3, 1 + e/(d*x^(2/3))) - 9*b^3*n^3*PolyLog(4, 1 + e/(d*x^(2/3)))]
    @test_int [(a + b*log(c*(d + e/x^(2/3))^n))^3/x^3, x, 16, (-9*b^3*d*n^3*(d + e/x^(2/3))^2)/(8*e^3) + (b^3*n^3*(d + e/x^(2/3))^3)/(9*e^3) - (9*a*b^2*d^2*n^2)/(e^2*x^(2/3)) + (9*b^3*d^2*n^3)/(e^2*x^(2/3)) - (9*b^3*d^2*n^2*(d + e/x^(2/3))*log(c*(d + e/x^(2/3))^n))/e^3 + (9*b^2*d*n^2*(d + e/x^(2/3))^2*(a + b*log(c*(d + e/x^(2/3))^n)))/(4*e^3) - (b^2*n^2*(d + e/x^(2/3))^3*(a + b*log(c*(d + e/x^(2/3))^n)))/(3*e^3) + (9*b*d^2*n*(d + e/x^(2/3))*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(2*e^3) - (9*b*d*n*(d + e/x^(2/3))^2*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(4*e^3) + (b*n*(d + e/x^(2/3))^3*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(2*e^3) - (3*d^2*(d + e/x^(2/3))*(a + b*log(c*(d + e/x^(2/3))^n))^3)/(2*e^3) + (3*d*(d + e/x^(2/3))^2*(a + b*log(c*(d + e/x^(2/3))^n))^3)/(2*e^3) - ((d + e/x^(2/3))^3*(a + b*log(c*(d + e/x^(2/3))^n))^3)/(2*e^3)]

    @test_int [x^2*(a + b*log(c*(d + e/x^(2/3))^n))^3, x, 83, (568*a*b^2*e^4*n^2*x^(1/3))/(105*d^4) - (16*b^3*e^4*n^3*x^(1/3))/(7*d^4) + (16*b^3*e^3*n^3*x)/(105*d^3) + (1376*b^3*e^(9/2)*n^3*atan((sqrt(d)*x^(1/3))/sqrt(e)))/(105*d^(9/2)) + (((568*im)/105)*b^3*e^(9/2)*n^3*atan((sqrt(d)*x^(1/3))/sqrt(e))^2)/d^(9/2) - (1136*b^3*e^(9/2)*n^3*atan((sqrt(d)*x^(1/3))/sqrt(e))*log(2 - (2*sqrt(e))/(sqrt(e) - im*sqrt(d)*x^(1/3))))/(105*d^(9/2)) + (568*b^3*e^4*n^2*x^(1/3)*log(c*(d + e/x^(2/3))^n))/(105*d^4) - (32*b^2*e^3*n^2*x*(a + b*log(c*(d + e/x^(2/3))^n)))/(35*d^3) + (8*b^2*e^2*n^2*x^(5/3)*(a + b*log(c*(d + e/x^(2/3))^n)))/(35*d^2) - (568*b^2*e^(9/2)*n^2*atan((sqrt(d)*x^(1/3))/sqrt(e))*(a + b*log(c*(d + e/x^(2/3))^n)))/(105*d^(9/2)) - (2*b*e^4*n*x^(1/3)*(a + b*log(c*(d + e/x^(2/3))^n))^2)/d^4 + (2*b*e^3*n*x*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(3*d^3) - (2*b*e^2*n*x^(5/3)*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(5*d^2) + (2*b*e*n*x^(7/3)*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(7*d) + (x^3*(a + b*log(c*(d + e/x^(2/3))^n))^3)/3 + (4*b^2*e^(9/2)*n^2*(a + b*log(c*(d + e/x^(2/3))^n))*log(sqrt(e) - sqrt(-d)*x^(1/3)))/(-d)^(9/2) - (2*b^3*e^(9/2)*n^3*log(sqrt(e) - sqrt(-d)*x^(1/3))^2)/(-d)^(9/2) - (4*b^2*e^(9/2)*n^2*(a + b*log(c*(d + e/x^(2/3))^n))*log(sqrt(e) + sqrt(-d)*x^(1/3)))/(-d)^(9/2) + (2*b^3*e^(9/2)*n^3*log(sqrt(e) + sqrt(-d)*x^(1/3))^2)/(-d)^(9/2) + (4*b^3*e^(9/2)*n^3*log(sqrt(e) + sqrt(-d)*x^(1/3))*log(1/2 - (sqrt(-d)*x^(1/3))/(2*sqrt(e))))/(-d)^(9/2) - (4*b^3*e^(9/2)*n^3*log(sqrt(e) - sqrt(-d)*x^(1/3))*log((1 + (sqrt(-d)*x^(1/3))/sqrt(e))/2))/(-d)^(9/2) - (8*b^3*e^(9/2)*n^3*log(sqrt(e) + sqrt(-d)*x^(1/3))*log(-((sqrt(-d)*x^(1/3))/sqrt(e))))/(-d)^(9/2) + (8*b^3*e^(9/2)*n^3*log(sqrt(e) - sqrt(-d)*x^(1/3))*log((sqrt(-d)*x^(1/3))/sqrt(e)))/(-d)^(9/2) + (((568*im)/105)*b^3*e^(9/2)*n^3*PolyLog(2, -1 + (2*sqrt(e))/(sqrt(e) - im*sqrt(d)*x^(1/3))))/d^(9/2) + (8*b^3*e^(9/2)*n^3*PolyLog(2, 1 - (sqrt(-d)*x^(1/3))/sqrt(e)))/(-d)^(9/2) - (4*b^3*e^(9/2)*n^3*PolyLog(2, 1/2 - (sqrt(-d)*x^(1/3))/(2*sqrt(e))))/(-d)^(9/2) + (4*b^3*e^(9/2)*n^3*PolyLog(2, (1 + (sqrt(-d)*x^(1/3))/sqrt(e))/2))/(-d)^(9/2) - (8*b^3*e^(9/2)*n^3*PolyLog(2, 1 + (sqrt(-d)*x^(1/3))/sqrt(e)))/(-d)^(9/2) + (2*b*e^5*n*Unintegrable((a + b*log(c*(d + e/x^(2/3))^n))^2/((e + d*x^(2/3))*x^(2/3)), x))/(3*d^4)]
    @test_int [x^0*(a + b*log(c*(d + e/x^(2/3))^n))^3, x, 31, (6*b*e*n*x^(1/3)*(a + b*log(c*(d + e/x^(2/3))^n))^2)/d + x*(a + b*log(c*(d + e/x^(2/3))^n))^3 + (12*b^2*e^(3/2)*n^2*(a + b*log(c*(d + e/x^(2/3))^n))*log(sqrt(e) - sqrt(-d)*x^(1/3)))/(-d)^(3/2) - (6*b^3*e^(3/2)*n^3*log(sqrt(e) - sqrt(-d)*x^(1/3))^2)/(-d)^(3/2) - (12*b^2*e^(3/2)*n^2*(a + b*log(c*(d + e/x^(2/3))^n))*log(sqrt(e) + sqrt(-d)*x^(1/3)))/(-d)^(3/2) + (6*b^3*e^(3/2)*n^3*log(sqrt(e) + sqrt(-d)*x^(1/3))^2)/(-d)^(3/2) + (12*b^3*e^(3/2)*n^3*log(sqrt(e) + sqrt(-d)*x^(1/3))*log(1/2 - (sqrt(-d)*x^(1/3))/(2*sqrt(e))))/(-d)^(3/2) - (12*b^3*e^(3/2)*n^3*log(sqrt(e) - sqrt(-d)*x^(1/3))*log((1 + (sqrt(-d)*x^(1/3))/sqrt(e))/2))/(-d)^(3/2) - (24*b^3*e^(3/2)*n^3*log(sqrt(e) + sqrt(-d)*x^(1/3))*log(-((sqrt(-d)*x^(1/3))/sqrt(e))))/(-d)^(3/2) + (24*b^3*e^(3/2)*n^3*log(sqrt(e) - sqrt(-d)*x^(1/3))*log((sqrt(-d)*x^(1/3))/sqrt(e)))/(-d)^(3/2) + (24*b^3*e^(3/2)*n^3*PolyLog(2, 1 - (sqrt(-d)*x^(1/3))/sqrt(e)))/(-d)^(3/2) - (12*b^3*e^(3/2)*n^3*PolyLog(2, 1/2 - (sqrt(-d)*x^(1/3))/(2*sqrt(e))))/(-d)^(3/2) + (12*b^3*e^(3/2)*n^3*PolyLog(2, (1 + (sqrt(-d)*x^(1/3))/sqrt(e))/2))/(-d)^(3/2) - (24*b^3*e^(3/2)*n^3*PolyLog(2, 1 + (sqrt(-d)*x^(1/3))/sqrt(e)))/(-d)^(3/2) - (2*b*e^2*n*Unintegrable((a + b*log(c*(d + e/x^(2/3))^n))^2/((e + d*x^(2/3))*x^(2/3)), x))/d]
    @test_int [(a + b*log(c*(d + e/x^(2/3))^n))^3/x^2, x, 35, (16*b^3*n^3)/(9*x) - (208*b^3*d*n^3)/(3*e*x^(1/3)) - (208*b^3*d^(3/2)*n^3*atan((sqrt(d)*x^(1/3))/sqrt(e)))/(3*e^(3/2)) - ((32*im)*b^3*d^(3/2)*n^3*atan((sqrt(d)*x^(1/3))/sqrt(e))^2)/e^(3/2) + (64*b^3*d^(3/2)*n^3*atan((sqrt(d)*x^(1/3))/sqrt(e))*log(2 - (2*sqrt(e))/(sqrt(e) - im*sqrt(d)*x^(1/3))))/e^(3/2) - (8*b^2*n^2*(a + b*log(c*(d + e/x^(2/3))^n)))/(3*x) + (32*b^2*d*n^2*(a + b*log(c*(d + e/x^(2/3))^n)))/(e*x^(1/3)) + (32*b^2*d^(3/2)*n^2*atan((sqrt(d)*x^(1/3))/sqrt(e))*(a + b*log(c*(d + e/x^(2/3))^n)))/e^(3/2) + (2*b*n*(a + b*log(c*(d + e/x^(2/3))^n))^2)/x - (6*b*d*n*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(e*x^(1/3)) - (a + b*log(c*(d + e/x^(2/3))^n))^3/x - ((32*im)*b^3*d^(3/2)*n^3*PolyLog(2, -1 + (2*sqrt(e))/(sqrt(e) - im*sqrt(d)*x^(1/3))))/e^(3/2) - (2*b*d^2*n*Unintegrable((a + b*log(c*(d + e/x^(2/3))^n))^2/((e + d*x^(2/3))*x^(2/3)), x))/e]
    @test_int [(a + b*log(c*(d + e/x^(2/3))^n))^3/x^4, x, 129, (16*b^3*n^3)/(729*x^3) - (3088*b^3*d*n^3)/(27783*e*x^(7/3)) + (221344*b^3*d^2*n^3)/(496125*e^2*x^(5/3)) - (637984*b^3*d^3*n^3)/(297675*e^3*x) + (3475504*b^3*d^4*n^3)/(99225*e^4*x^(1/3)) + (3475504*b^3*d^(9/2)*n^3*atan((sqrt(d)*x^(1/3))/sqrt(e)))/(99225*e^(9/2)) + (4504*im*b^3*d^(9/2)*n^3*atan((sqrt(d)*x^(1/3))/sqrt(e))^2)/(315*e^(9/2)) - (9008*b^3*d^(9/2)*n^3*atan((sqrt(d)*x^(1/3))/sqrt(e))*log(2 - (2*sqrt(e))/(sqrt(e) - im*sqrt(d)*x^(1/3))))/(315*e^(9/2)) - (8*b^2*n^2*(a + b*log(c*(d + e/x^(2/3))^n)))/(81*x^3) + (128*b^2*d*n^2*(a + b*log(c*(d + e/x^(2/3))^n)))/(441*e*x^(7/3)) - (1144*b^2*d^2*n^2*(a + b*log(c*(d + e/x^(2/3))^n)))/(1575*e^2*x^(5/3)) + (1984*b^2*d^3*n^2*(a + b*log(c*(d + e/x^(2/3))^n)))/(945*e^3*x) - (4504*b^2*d^4*n^2*(a + b*log(c*(d + e/x^(2/3))^n)))/(315*e^4*x^(1/3)) - (4504*b^2*d^(9/2)*n^2*atan((sqrt(d)*x^(1/3))/sqrt(e))*(a + b*log(c*(d + e/x^(2/3))^n)))/(315*e^(9/2)) + (2*b*n*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(9*x^3) - (2*b*d*n*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(7*e*x^(7/3)) + (2*b*d^2*n*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(5*e^2*x^(5/3)) - (2*b*d^3*n*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(3*e^3*x) + (2*b*d^4*n*(a + b*log(c*(d + e/x^(2/3))^n))^2)/(e^4*x^(1/3)) - (a + b*log(c*(d + e/x^(2/3))^n))^3/(3*x^3) + (4504*im*b^3*d^(9/2)*n^3*PolyLog(2, -1 + (2*sqrt(e))/(sqrt(e) - im*sqrt(d)*x^(1/3))))/(315*e^(9/2)) + (2*b*d^5*n*Unintegrable((a + b*log(c*(d + e/x^(2/3))^n))^2/((e + d*x^(2/3))*x^(2/3)), x))/(3*e^4)]

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

    #= ::Subsubsection::Closed:: =#
    #=m=1=#

    @test_int [x^3*(a + b*log(c*(d + e*sqrt(x))))^p, x, 27, (2^(-2 - 3*p)*Gamma(1 + p, -((8*(a + b*log(c*(d + e*sqrt(x)))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(ℯ^((8*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c^8*e^8)) - (2*d*Gamma(1 + p, -((7*(a + b*log(c*(d + e*sqrt(x)))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(7^p*ℯ^((7*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c^7*e^8)) + (7*d^2*Gamma(1 + p, -((6*(a + b*log(c*(d + e*sqrt(x)))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(6^p*ℯ^((6*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c^6*e^8)) - (14*d^3*Gamma(1 + p, -((5*(a + b*log(c*(d + e*sqrt(x)))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(5^p*ℯ^((5*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c^5*e^8)) + (35*2^(-1 - 2*p)*d^4*Gamma(1 + p, -((4*(a + b*log(c*(d + e*sqrt(x)))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(ℯ^((4*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c^4*e^8)) - (14*d^5*Gamma(1 + p, -((3*(a + b*log(c*(d + e*sqrt(x)))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(3^p*ℯ^((3*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c^3*e^8)) + (7*d^6*Gamma(1 + p, -((2*(a + b*log(c*(d + e*sqrt(x)))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(2^p*ℯ^((2*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c^2*e^8)) - (2*d^7*Gamma(1 + p, -((a + b*log(c*(d + e*sqrt(x))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c*e^8))]
    @test_int [x^2*(a + b*log(c*(d + e*sqrt(x))))^p, x, 21, (3^(-1 - p)*Gamma(1 + p, -((6*(a + b*log(c*(d + e*sqrt(x)))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(2^p*ℯ^((6*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c^6*e^6)) - (2*d*Gamma(1 + p, -((5*(a + b*log(c*(d + e*sqrt(x)))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(5^p*ℯ^((5*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c^5*e^6)) + (5*d^2*Gamma(1 + p, -((4*(a + b*log(c*(d + e*sqrt(x)))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(4^p*ℯ^((4*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c^4*e^6)) - (20*3^(-1 - p)*d^3*Gamma(1 + p, -((3*(a + b*log(c*(d + e*sqrt(x)))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(ℯ^((3*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c^3*e^6)) + (5*d^4*Gamma(1 + p, -((2*(a + b*log(c*(d + e*sqrt(x)))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(2^p*ℯ^((2*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c^2*e^6)) - (2*d^5*Gamma(1 + p, -((a + b*log(c*(d + e*sqrt(x))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c*e^6))]
    @test_int [x^1*(a + b*log(c*(d + e*sqrt(x))))^p, x, 15, (2^(-1 - 2*p)*Gamma(1 + p, -((4*(a + b*log(c*(d + e*sqrt(x)))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(ℯ^((4*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c^4*e^4)) - (2*d*Gamma(1 + p, -((3*(a + b*log(c*(d + e*sqrt(x)))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(3^p*ℯ^((3*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c^3*e^4)) + (3*d^2*Gamma(1 + p, -((2*(a + b*log(c*(d + e*sqrt(x)))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(2^p*ℯ^((2*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c^2*e^4)) - (2*d^3*Gamma(1 + p, -((a + b*log(c*(d + e*sqrt(x))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c*e^4))]
    @test_int [x^0*(a + b*log(c*(d + e*sqrt(x))))^p, x, 9, (Gamma(1 + p, -((2*(a + b*log(c*(d + e*sqrt(x)))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(2^p*ℯ^((2*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c^2*e^2)) - (2*d*Gamma(1 + p, -((a + b*log(c*(d + e*sqrt(x))))/b))*(a + b*log(c*(d + e*sqrt(x))))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e*sqrt(x))))/b))^p*(c*e^2))]
    @test_int [(a + b*log(c*(d + e*sqrt(x))))^p/x^1, x, 1, Unintegrable((a + b*log(c*(d + e*sqrt(x))))^p/x, x)]
    @test_int [(a + b*log(c*(d + e*sqrt(x))))^p/x^2, x, 1, Unintegrable((a + b*log(c*(d + e*sqrt(x))))^p/x^2, x)]

    @test_int [x^3*(a + b*log(c*(d + e*sqrt(x))^2))^p, x, 27, (Gamma(1 + p, -((4*(a + b*log(c*(d + e*sqrt(x))^2)))/b))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(2^(2*(1 + p))*ℯ^((4*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(c^4*e^8)) - (2^(1 + p)*d*(d + e*sqrt(x))^7*Gamma(1 + p, -((7*(a + b*log(c*(d + e*sqrt(x))^2)))/(2*b)))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(7^p*ℯ^((7*a)/(2*b))*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(e^8*(c*(d + e*sqrt(x))^2)^(7/2))) + (7*d^2*Gamma(1 + p, -((3*(a + b*log(c*(d + e*sqrt(x))^2)))/b))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(3^p*ℯ^((3*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(c^3*e^8)) - (7*2^(1 + p)*d^3*(d + e*sqrt(x))^5*Gamma(1 + p, -((5*(a + b*log(c*(d + e*sqrt(x))^2)))/(2*b)))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(5^p*ℯ^((5*a)/(2*b))*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(e^8*(c*(d + e*sqrt(x))^2)^(5/2))) + (35*2^(-1 - p)*d^4*Gamma(1 + p, -((2*(a + b*log(c*(d + e*sqrt(x))^2)))/b))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(ℯ^((2*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(c^2*e^8)) - (7*2^(1 + p)*d^5*(d + e*sqrt(x))^3*Gamma(1 + p, -((3*(a + b*log(c*(d + e*sqrt(x))^2)))/(2*b)))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(3^p*ℯ^((3*a)/(2*b))*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(e^8*(c*(d + e*sqrt(x))^2)^(3/2))) + (7*d^6*Gamma(1 + p, -((a + b*log(c*(d + e*sqrt(x))^2))/b))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(c*e^8)) - (2^(1 + p)*d^7*(d + e*sqrt(x))*Gamma(1 + p, -((a + b*log(c*(d + e*sqrt(x))^2))/(2*b)))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(ℯ^(a/(2*b))*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(e^8*sqrt(c*(d + e*sqrt(x))^2)))]
    @test_int [x^2*(a + b*log(c*(d + e*sqrt(x))^2))^p, x, 21, (3^(-1 - p)*Gamma(1 + p, -((3*(a + b*log(c*(d + e*sqrt(x))^2)))/b))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(ℯ^((3*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(c^3*e^6)) - (2^(1 + p)*d*(d + e*sqrt(x))^5*Gamma(1 + p, -((5*(a + b*log(c*(d + e*sqrt(x))^2)))/(2*b)))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(5^p*ℯ^((5*a)/(2*b))*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(e^6*(c*(d + e*sqrt(x))^2)^(5/2))) + (5*d^2*Gamma(1 + p, -((2*(a + b*log(c*(d + e*sqrt(x))^2)))/b))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(2^p*ℯ^((2*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(c^2*e^6)) - (5*2^(2 + p)*3^(-1 - p)*d^3*(d + e*sqrt(x))^3*Gamma(1 + p, -((3*(a + b*log(c*(d + e*sqrt(x))^2)))/(2*b)))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(ℯ^((3*a)/(2*b))*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(e^6*(c*(d + e*sqrt(x))^2)^(3/2))) + (5*d^4*Gamma(1 + p, -((a + b*log(c*(d + e*sqrt(x))^2))/b))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(c*e^6)) - (2^(1 + p)*d^5*(d + e*sqrt(x))*Gamma(1 + p, -((a + b*log(c*(d + e*sqrt(x))^2))/(2*b)))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(ℯ^(a/(2*b))*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(e^6*sqrt(c*(d + e*sqrt(x))^2)))]
    @test_int [x^1*(a + b*log(c*(d + e*sqrt(x))^2))^p, x, 15, (2^(-1 - p)*Gamma(1 + p, -((2*(a + b*log(c*(d + e*sqrt(x))^2)))/b))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(ℯ^((2*a)/b)*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(c^2*e^4)) - (2^(1 + p)*d*(d + e*sqrt(x))^3*Gamma(1 + p, -((3*(a + b*log(c*(d + e*sqrt(x))^2)))/(2*b)))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(3^p*ℯ^((3*a)/(2*b))*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(e^4*(c*(d + e*sqrt(x))^2)^(3/2))) + (3*d^2*Gamma(1 + p, -((a + b*log(c*(d + e*sqrt(x))^2))/b))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(c*e^4)) - (2^(1 + p)*d^3*(d + e*sqrt(x))*Gamma(1 + p, -((a + b*log(c*(d + e*sqrt(x))^2))/(2*b)))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(ℯ^(a/(2*b))*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(e^4*sqrt(c*(d + e*sqrt(x))^2)))]
    @test_int [x^0*(a + b*log(c*(d + e*sqrt(x))^2))^p, x, 9, (Gamma(1 + p, -((a + b*log(c*(d + e*sqrt(x))^2))/b))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(c*e^2)) - (2^(1 + p)*d*(d + e*sqrt(x))*Gamma(1 + p, -((a + b*log(c*(d + e*sqrt(x))^2))/(2*b)))*(a + b*log(c*(d + e*sqrt(x))^2))^p)/(ℯ^(a/(2*b))*(-((a + b*log(c*(d + e*sqrt(x))^2))/b))^p*(e^2*sqrt(c*(d + e*sqrt(x))^2)))]
    @test_int [(a + b*log(c*(d + e*sqrt(x))^2))^p/x^1, x, 1, Unintegrable((a + b*log(c*(d + e*sqrt(x))^2))^p/x, x)]
    @test_int [(a + b*log(c*(d + e*sqrt(x))^2))^p/x^2, x, 1, Unintegrable((a + b*log(c*(d + e*sqrt(x))^2))^p/x^2, x)]

    #= ::Subsubsection::Closed:: =#
    #=m=-1=#

    @test_int [x^1*(a + b*log(c*(d + e/sqrt(x))))^p, x, 1, Unintegrable(x*(a + b*log(c*(d + e/sqrt(x))))^p, x)]
    @test_int [x^0*(a + b*log(c*(d + e/sqrt(x))))^p, x, 1, Unintegrable((a + b*log(c*(d + e/sqrt(x))))^p, x)]
    @test_int [(a + b*log(c*(d + e/sqrt(x))))^p/x^1, x, 1, Unintegrable((a + b*log(c*(d + e/sqrt(x))))^p/x, x)]
    @test_int [(a + b*log(c*(d + e/sqrt(x))))^p/x^2, x, 9, -((Gamma(1 + p, (-2*(a + b*log(c*(d + e/sqrt(x)))))/b)*(a + b*log(c*(d + e/sqrt(x))))^p)/(2^p*c^2*e^2*ℯ^((2*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p)) + (2*d*Gamma(1 + p, -((a + b*log(c*(d + e/sqrt(x))))/b))*(a + b*log(c*(d + e/sqrt(x))))^p)/(c*e^2*ℯ^(a/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p)]
    @test_int [(a + b*log(c*(d + e/sqrt(x))))^p/x^4, x, 21, -((3^(-1 - p)*Gamma(1 + p, -((6*(a + b*log(c*(d + e/sqrt(x)))))/b))*(a + b*log(c*(d + e/sqrt(x))))^p)/(2^p*ℯ^((6*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p*(c^6*e^6))) + (2*d*Gamma(1 + p, -((5*(a + b*log(c*(d + e/sqrt(x)))))/b))*(a + b*log(c*(d + e/sqrt(x))))^p)/(5^p*ℯ^((5*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p*(c^5*e^6)) - (5*d^2*Gamma(1 + p, -((4*(a + b*log(c*(d + e/sqrt(x)))))/b))*(a + b*log(c*(d + e/sqrt(x))))^p)/(4^p*ℯ^((4*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p*(c^4*e^6)) + (20*3^(-1 - p)*d^3*Gamma(1 + p, -((3*(a + b*log(c*(d + e/sqrt(x)))))/b))*(a + b*log(c*(d + e/sqrt(x))))^p)/(ℯ^((3*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p*(c^3*e^6)) - (5*d^4*Gamma(1 + p, -((2*(a + b*log(c*(d + e/sqrt(x)))))/b))*(a + b*log(c*(d + e/sqrt(x))))^p)/(2^p*ℯ^((2*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p*(c^2*e^6)) + (2*d^5*Gamma(1 + p, -((a + b*log(c*(d + e/sqrt(x))))/b))*(a + b*log(c*(d + e/sqrt(x))))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p*(c*e^6))]
    @test_int [(a + b*log(c*(d + e/sqrt(x))))^p/x^6, x, 33, -((5^(-1 - p)*Gamma(1 + p, -((10*(a + b*log(c*(d + e/sqrt(x)))))/b))*(a + b*log(c*(d + e/sqrt(x))))^p)/(2^p*ℯ^((10*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p*(c^10*e^10))) + (2*d*Gamma(1 + p, -((9*(a + b*log(c*(d + e/sqrt(x)))))/b))*(a + b*log(c*(d + e/sqrt(x))))^p)/(9^p*ℯ^((9*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p*(c^9*e^10)) - (9*d^2*Gamma(1 + p, -((8*(a + b*log(c*(d + e/sqrt(x)))))/b))*(a + b*log(c*(d + e/sqrt(x))))^p)/(8^p*ℯ^((8*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p*(c^8*e^10)) + (24*d^3*Gamma(1 + p, -((7*(a + b*log(c*(d + e/sqrt(x)))))/b))*(a + b*log(c*(d + e/sqrt(x))))^p)/(7^p*ℯ^((7*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p*(c^7*e^10)) - (7*6^(1 - p)*d^4*Gamma(1 + p, -((6*(a + b*log(c*(d + e/sqrt(x)))))/b))*(a + b*log(c*(d + e/sqrt(x))))^p)/(ℯ^((6*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p*(c^6*e^10)) + (252*5^(-1 - p)*d^5*Gamma(1 + p, -((5*(a + b*log(c*(d + e/sqrt(x)))))/b))*(a + b*log(c*(d + e/sqrt(x))))^p)/(ℯ^((5*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p*(c^5*e^10)) - (21*2^(1 - 2*p)*d^6*Gamma(1 + p, -((4*(a + b*log(c*(d + e/sqrt(x)))))/b))*(a + b*log(c*(d + e/sqrt(x))))^p)/(ℯ^((4*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p*(c^4*e^10)) + (8*3^(1 - p)*d^7*Gamma(1 + p, -((3*(a + b*log(c*(d + e/sqrt(x)))))/b))*(a + b*log(c*(d + e/sqrt(x))))^p)/(ℯ^((3*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p*(c^3*e^10)) - (9*d^8*Gamma(1 + p, -((2*(a + b*log(c*(d + e/sqrt(x)))))/b))*(a + b*log(c*(d + e/sqrt(x))))^p)/(2^p*ℯ^((2*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p*(c^2*e^10)) + (2*d^9*Gamma(1 + p, -((a + b*log(c*(d + e/sqrt(x))))/b))*(a + b*log(c*(d + e/sqrt(x))))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e/sqrt(x))))/b))^p*(c*e^10))]

    @test_int [x^1*(a + b*log(c*(d + e/sqrt(x))^2))^p, x, 1, Unintegrable(x*(a + b*log(c*(d + e/sqrt(x))^2))^p, x)]
    @test_int [x^0*(a + b*log(c*(d + e/sqrt(x))^2))^p, x, 1, Unintegrable((a + b*log(c*(d + e/sqrt(x))^2))^p, x)]
    @test_int [(a + b*log(c*(d + e/sqrt(x))^2))^p/x^1, x, 1, Unintegrable((a + b*log(c*(d + e/sqrt(x))^2))^p/x, x)]
    @test_int [(a + b*log(c*(d + e/sqrt(x))^2))^p/x^2, x, 9, -((Gamma(1 + p, -((a + b*log(c*(d + e/sqrt(x))^2))/b))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(c*e^2*ℯ^(a/b)*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p)) + (2^(1 + p)*d*(d + e/sqrt(x))*Gamma(1 + p, -(a + b*log(c*(d + e/sqrt(x))^2))/(2*b))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(e^2*ℯ^(a/(2*b))*sqrt(c*(d + e/sqrt(x))^2)*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p)]
    @test_int [(a + b*log(c*(d + e/sqrt(x))^2))^p/x^4, x, 21, -((3^(-1 - p)*Gamma(1 + p, -((3*(a + b*log(c*(d + e/sqrt(x))^2)))/b))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(ℯ^((3*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p*(c^3*e^6))) + (2^(1 + p)*d*(d + e/sqrt(x))^5*Gamma(1 + p, -((5*(a + b*log(c*(d + e/sqrt(x))^2)))/(2*b)))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(5^p*ℯ^((5*a)/(2*b))*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p*(e^6*(c*(d + e/sqrt(x))^2)^(5/2))) - (5*d^2*Gamma(1 + p, -((2*(a + b*log(c*(d + e/sqrt(x))^2)))/b))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(2^p*ℯ^((2*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p*(c^2*e^6)) + (5*2^(2 + p)*3^(-1 - p)*d^3*(d + e/sqrt(x))^3*Gamma(1 + p, -((3*(a + b*log(c*(d + e/sqrt(x))^2)))/(2*b)))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(ℯ^((3*a)/(2*b))*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p*(e^6*(c*(d + e/sqrt(x))^2)^(3/2))) - (5*d^4*Gamma(1 + p, -((a + b*log(c*(d + e/sqrt(x))^2))/b))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p*(c*e^6)) + (2^(1 + p)*d^5*(d + e/sqrt(x))*Gamma(1 + p, -((a + b*log(c*(d + e/sqrt(x))^2))/(2*b)))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(ℯ^(a/(2*b))*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p*(e^6*sqrt(c*(d + e/sqrt(x))^2)))]
    @test_int [(a + b*log(c*(d + e/sqrt(x))^2))^p/x^6, x, 33, -((5^(-1 - p)*Gamma(1 + p, -((5*(a + b*log(c*(d + e/sqrt(x))^2)))/b))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(ℯ^((5*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p*(c^5*e^10))) + (2^(1 + p)*d*(d + e/sqrt(x))^9*Gamma(1 + p, -((9*(a + b*log(c*(d + e/sqrt(x))^2)))/(2*b)))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(9^p*ℯ^((9*a)/(2*b))*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p*(e^10*(c*(d + e/sqrt(x))^2)^(9/2))) - (9*d^2*Gamma(1 + p, -((4*(a + b*log(c*(d + e/sqrt(x))^2)))/b))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(4^p*ℯ^((4*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p*(c^4*e^10)) + (3*2^(3 + p)*d^3*(d + e/sqrt(x))^7*Gamma(1 + p, -((7*(a + b*log(c*(d + e/sqrt(x))^2)))/(2*b)))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(7^p*ℯ^((7*a)/(2*b))*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p*(e^10*(c*(d + e/sqrt(x))^2)^(7/2))) - (14*3^(1 - p)*d^4*Gamma(1 + p, -((3*(a + b*log(c*(d + e/sqrt(x))^2)))/b))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(ℯ^((3*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p*(c^3*e^10)) + (63*2^(2 + p)*5^(-1 - p)*d^5*(d + e/sqrt(x))^5*Gamma(1 + p, -((5*(a + b*log(c*(d + e/sqrt(x))^2)))/(2*b)))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(ℯ^((5*a)/(2*b))*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p*(e^10*(c*(d + e/sqrt(x))^2)^(5/2))) - (21*2^(1 - p)*d^6*Gamma(1 + p, -((2*(a + b*log(c*(d + e/sqrt(x))^2)))/b))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(ℯ^((2*a)/b)*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p*(c^2*e^10)) + (2^(3 + p)*3^(1 - p)*d^7*(d + e/sqrt(x))^3*Gamma(1 + p, -((3*(a + b*log(c*(d + e/sqrt(x))^2)))/(2*b)))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(ℯ^((3*a)/(2*b))*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p*(e^10*(c*(d + e/sqrt(x))^2)^(3/2))) - (9*d^8*Gamma(1 + p, -((a + b*log(c*(d + e/sqrt(x))^2))/b))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p*(c*e^10)) + (2^(1 + p)*d^9*(d + e/sqrt(x))*Gamma(1 + p, -((a + b*log(c*(d + e/sqrt(x))^2))/(2*b)))*(a + b*log(c*(d + e/sqrt(x))^2))^p)/(ℯ^(a/(2*b))*(-((a + b*log(c*(d + e/sqrt(x))^2))/b))^p*(e^10*sqrt(c*(d + e/sqrt(x))^2)))]

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

    #= ::Subsubsection::Closed:: =#
    #=m=1=#

    @test_int [x^3*(a + b*log(c*(d + e*x^(1/3))))^p, x, 39, (4^(-1 - p)*Gamma(1 + p, -((12*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(3^p*ℯ^((12*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^12*e^12)) - (3*d*Gamma(1 + p, -((11*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(11^p*ℯ^((11*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^11*e^12)) + (33*2^(-1 - p)*d^2*Gamma(1 + p, -((10*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(5^p*ℯ^((10*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^10*e^12)) - (55*d^3*Gamma(1 + p, -((9*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(9^p*ℯ^((9*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^9*e^12)) + (495*2^(-2 - 3*p)*d^4*Gamma(1 + p, -((8*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(ℯ^((8*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^8*e^12)) - (198*d^5*Gamma(1 + p, -((7*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(7^p*ℯ^((7*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^7*e^12)) + (77*3^(1 - p)*d^6*Gamma(1 + p, -((6*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(2^p*ℯ^((6*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^6*e^12)) - (198*d^7*Gamma(1 + p, -((5*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(5^p*ℯ^((5*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^5*e^12)) + (495*4^(-1 - p)*d^8*Gamma(1 + p, -((4*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(ℯ^((4*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^4*e^12)) - (55*d^9*Gamma(1 + p, -((3*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(3^p*ℯ^((3*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^3*e^12)) + (33*2^(-1 - p)*d^10*Gamma(1 + p, -((2*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(ℯ^((2*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^2*e^12)) - (3*d^11*Gamma(1 + p, -((a + b*log(c*(d + e*x^(1/3))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c*e^12))]
    @test_int [x^2*(a + b*log(c*(d + e*x^(1/3))))^p, x, 30, (3^(-1 - 2*p)*Gamma(1 + p, -((9*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(ℯ^((9*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^9*e^9)) - (3*d*Gamma(1 + p, -((8*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(8^p*ℯ^((8*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^8*e^9)) + (12*d^2*Gamma(1 + p, -((7*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(7^p*ℯ^((7*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^7*e^9)) - (7*2^(2 - p)*d^3*Gamma(1 + p, -((6*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(3^p*ℯ^((6*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^6*e^9)) + (42*d^4*Gamma(1 + p, -((5*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(5^p*ℯ^((5*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^5*e^9)) - (21*2^(1 - 2*p)*d^5*Gamma(1 + p, -((4*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(ℯ^((4*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^4*e^9)) + (28*d^6*Gamma(1 + p, -((3*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(3^p*ℯ^((3*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^3*e^9)) - (3*2^(2 - p)*d^7*Gamma(1 + p, -((2*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(ℯ^((2*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^2*e^9)) + (3*d^8*Gamma(1 + p, -((a + b*log(c*(d + e*x^(1/3))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c*e^9))]
    @test_int [x^1*(a + b*log(c*(d + e*x^(1/3))))^p, x, 21, (2^(-1 - p)*Gamma(1 + p, -((6*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(3^p*ℯ^((6*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^6*e^6)) - (3*d*Gamma(1 + p, -((5*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(5^p*ℯ^((5*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^5*e^6)) + (15*2^(-1 - 2*p)*d^2*Gamma(1 + p, -((4*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(ℯ^((4*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^4*e^6)) - (10*d^3*Gamma(1 + p, -((3*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(3^p*ℯ^((3*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^3*e^6)) + (15*2^(-1 - p)*d^4*Gamma(1 + p, -((2*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(ℯ^((2*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^2*e^6)) - (3*d^5*Gamma(1 + p, -((a + b*log(c*(d + e*x^(1/3))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c*e^6))]
    @test_int [x^0*(a + b*log(c*(d + e*x^(1/3))))^p, x, 12, (Gamma(1 + p, -((3*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(3^p*ℯ^((3*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^3*e^3)) - (3*d*Gamma(1 + p, -((2*(a + b*log(c*(d + e*x^(1/3)))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(2^p*ℯ^((2*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c^2*e^3)) + (3*d^2*Gamma(1 + p, -((a + b*log(c*(d + e*x^(1/3))))/b))*(a + b*log(c*(d + e*x^(1/3))))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e*x^(1/3))))/b))^p*(c*e^3))]
    @test_int [(a + b*log(c*(d + e*x^(1/3))))^p/x^1, x, 1, Unintegrable((a + b*log(c*(d + e*x^(1/3))))^p/x, x)]
    @test_int [(a + b*log(c*(d + e*x^(1/3))))^p/x^2, x, 1, Unintegrable((a + b*log(c*(d + e*x^(1/3))))^p/x^2, x)]

    @test_int [x^3*(a + b*log(c*(d + e*x^(1/3))^2))^p, x, 39, (2^(-2 - p)*Gamma(1 + p, -((6*(a + b*log(c*(d + e*x^(1/3))^2)))/b))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(3^p*ℯ^((6*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(c^6*e^12)) - (3*(2/11)^p*d*(d + e*x^(1/3))^11*Gamma(1 + p, -((11*(a + b*log(c*(d + e*x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^((11*a)/(2*b))*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(e^12*(c*(d + e*x^(1/3))^2)^(11/2))) + (33*d^2*Gamma(1 + p, -((5*(a + b*log(c*(d + e*x^(1/3))^2)))/b))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(5^p*ℯ^((5*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(2*c^5*e^12)) - (55*(2/9)^p*d^3*(d + e*x^(1/3))^9*Gamma(1 + p, -((9*(a + b*log(c*(d + e*x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^((9*a)/(2*b))*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(e^12*(c*(d + e*x^(1/3))^2)^(9/2))) + (495*d^4*Gamma(1 + p, -((4*(a + b*log(c*(d + e*x^(1/3))^2)))/b))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(2^(2*(1 + p))*ℯ^((4*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(c^4*e^12)) - (99*2^(1 + p)*d^5*(d + e*x^(1/3))^7*Gamma(1 + p, -((7*(a + b*log(c*(d + e*x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(7^p*ℯ^((7*a)/(2*b))*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(e^12*(c*(d + e*x^(1/3))^2)^(7/2))) + (77*3^(1 - p)*d^6*Gamma(1 + p, -((3*(a + b*log(c*(d + e*x^(1/3))^2)))/b))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^((3*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(c^3*e^12)) - (99*2^(1 + p)*d^7*(d + e*x^(1/3))^5*Gamma(1 + p, -((5*(a + b*log(c*(d + e*x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(5^p*ℯ^((5*a)/(2*b))*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(e^12*(c*(d + e*x^(1/3))^2)^(5/2))) + (495*2^(-2 - p)*d^8*Gamma(1 + p, -((2*(a + b*log(c*(d + e*x^(1/3))^2)))/b))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^((2*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(c^2*e^12)) - (55*(2/3)^p*d^9*(d + e*x^(1/3))^3*Gamma(1 + p, -((3*(a + b*log(c*(d + e*x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^((3*a)/(2*b))*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(e^12*(c*(d + e*x^(1/3))^2)^(3/2))) + (33*d^10*Gamma(1 + p, -((a + b*log(c*(d + e*x^(1/3))^2))/b))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(2*c*e^12)) - (3*2^p*d^11*(d + e*x^(1/3))*Gamma(1 + p, -((a + b*log(c*(d + e*x^(1/3))^2))/(2*b)))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^(a/(2*b))*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(e^12*sqrt(c*(d + e*x^(1/3))^2)))]
    @test_int [x^2*(a + b*log(c*(d + e*x^(1/3))^2))^p, x, 30, (2^p*3^(-1 - 2*p)*(d + e*x^(1/3))^9*Gamma(1 + p, -((9*(a + b*log(c*(d + e*x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^((9*a)/(2*b))*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(e^9*(c*(d + e*x^(1/3))^2)^(9/2))) - (3*d*Gamma(1 + p, -((4*(a + b*log(c*(d + e*x^(1/3))^2)))/b))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(4^p*ℯ^((4*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(c^4*e^9)) + (3*2^(2 + p)*d^2*(d + e*x^(1/3))^7*Gamma(1 + p, -((7*(a + b*log(c*(d + e*x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(7^p*ℯ^((7*a)/(2*b))*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(e^9*(c*(d + e*x^(1/3))^2)^(7/2))) - (28*d^3*Gamma(1 + p, -((3*(a + b*log(c*(d + e*x^(1/3))^2)))/b))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(3^p*ℯ^((3*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(c^3*e^9)) + (21*2^(1 + p)*d^4*(d + e*x^(1/3))^5*Gamma(1 + p, -((5*(a + b*log(c*(d + e*x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(5^p*ℯ^((5*a)/(2*b))*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(e^9*(c*(d + e*x^(1/3))^2)^(5/2))) - (21*2^(1 - p)*d^5*Gamma(1 + p, -((2*(a + b*log(c*(d + e*x^(1/3))^2)))/b))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^((2*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(c^2*e^9)) + (7*2^(2 + p)*d^6*(d + e*x^(1/3))^3*Gamma(1 + p, -((3*(a + b*log(c*(d + e*x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(3^p*ℯ^((3*a)/(2*b))*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(e^9*(c*(d + e*x^(1/3))^2)^(3/2))) - (12*d^7*Gamma(1 + p, -((a + b*log(c*(d + e*x^(1/3))^2))/b))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(c*e^9)) + (3*2^p*d^8*(d + e*x^(1/3))*Gamma(1 + p, -((a + b*log(c*(d + e*x^(1/3))^2))/(2*b)))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^(a/(2*b))*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(e^9*sqrt(c*(d + e*x^(1/3))^2)))]
    @test_int [x^1*(a + b*log(c*(d + e*x^(1/3))^2))^p, x, 21, (Gamma(1 + p, -((3*(a + b*log(c*(d + e*x^(1/3))^2)))/b))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(3^p*ℯ^((3*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(2*c^3*e^6)) - (3*(2/5)^p*d*(d + e*x^(1/3))^5*Gamma(1 + p, -((5*(a + b*log(c*(d + e*x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^((5*a)/(2*b))*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(e^6*(c*(d + e*x^(1/3))^2)^(5/2))) + (15*2^(-1 - p)*d^2*Gamma(1 + p, -((2*(a + b*log(c*(d + e*x^(1/3))^2)))/b))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^((2*a)/b)*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(c^2*e^6)) - (5*2^(1 + p)*d^3*(d + e*x^(1/3))^3*Gamma(1 + p, -((3*(a + b*log(c*(d + e*x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(3^p*ℯ^((3*a)/(2*b))*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(e^6*(c*(d + e*x^(1/3))^2)^(3/2))) + (15*d^4*Gamma(1 + p, -((a + b*log(c*(d + e*x^(1/3))^2))/b))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(2*c*e^6)) - (3*2^p*d^5*(d + e*x^(1/3))*Gamma(1 + p, -((a + b*log(c*(d + e*x^(1/3))^2))/(2*b)))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^(a/(2*b))*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(e^6*sqrt(c*(d + e*x^(1/3))^2)))]
    @test_int [x^0*(a + b*log(c*(d + e*x^(1/3))^2))^p, x, 12, ((2/3)^p*(d + e*x^(1/3))^3*Gamma(1 + p, -((3*(a + b*log(c*(d + e*x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^((3*a)/(2*b))*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(e^3*(c*(d + e*x^(1/3))^2)^(3/2))) - (3*d*Gamma(1 + p, -((a + b*log(c*(d + e*x^(1/3))^2))/b))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(c*e^3)) + (3*2^p*d^2*(d + e*x^(1/3))*Gamma(1 + p, -((a + b*log(c*(d + e*x^(1/3))^2))/(2*b)))*(a + b*log(c*(d + e*x^(1/3))^2))^p)/(ℯ^(a/(2*b))*(-((a + b*log(c*(d + e*x^(1/3))^2))/b))^p*(e^3*sqrt(c*(d + e*x^(1/3))^2)))]
    @test_int [(a + b*log(c*(d + e*x^(1/3))^2))^p/x^1, x, 1, Unintegrable((a + b*log(c*(d + e*x^(1/3))^2))^p/x, x)]
    @test_int [(a + b*log(c*(d + e*x^(1/3))^2))^p/x^2, x, 1, Unintegrable((a + b*log(c*(d + e*x^(1/3))^2))^p/x^2, x)]

    #= ::Subsubsection::Closed:: =#
    #=m=2=#

    @test_int [x^3*(a + b*log(c*(d + e*x^(2/3))))^p, x, 21, (2^(-2 - p)*Gamma(1 + p, (-6*(a + b*log(c*(d + e*x^(2/3)))))/b)*(a + b*log(c*(d + e*x^(2/3))))^p)/(3^p*c^6*e^6*ℯ^((6*a)/b)*(-((a + b*log(c*(d + e*x^(2/3))))/b))^p) - (3*d*Gamma(1 + p, (-5*(a + b*log(c*(d + e*x^(2/3)))))/b)*(a + b*log(c*(d + e*x^(2/3))))^p)/(2*5^p*c^5*e^6*ℯ^((5*a)/b)*(-((a + b*log(c*(d + e*x^(2/3))))/b))^p) + (15*d^2*Gamma(1 + p, (-4*(a + b*log(c*(d + e*x^(2/3)))))/b)*(a + b*log(c*(d + e*x^(2/3))))^p)/(2^(2*(1 + p))*c^4*e^6*ℯ^((4*a)/b)*(-((a + b*log(c*(d + e*x^(2/3))))/b))^p) - (5*d^3*Gamma(1 + p, (-3*(a + b*log(c*(d + e*x^(2/3)))))/b)*(a + b*log(c*(d + e*x^(2/3))))^p)/(3^p*c^3*e^6*ℯ^((3*a)/b)*(-((a + b*log(c*(d + e*x^(2/3))))/b))^p) + (15*2^(-2 - p)*d^4*Gamma(1 + p, (-2*(a + b*log(c*(d + e*x^(2/3)))))/b)*(a + b*log(c*(d + e*x^(2/3))))^p)/(c^2*e^6*ℯ^((2*a)/b)*(-((a + b*log(c*(d + e*x^(2/3))))/b))^p) - (3*d^5*Gamma(1 + p, -((a + b*log(c*(d + e*x^(2/3))))/b))*(a + b*log(c*(d + e*x^(2/3))))^p)/(2*c*e^6*ℯ^(a/b)*(-((a + b*log(c*(d + e*x^(2/3))))/b))^p)]
    @test_int [x^1*(a + b*log(c*(d + e*x^(2/3))))^p, x, 12, (Gamma(1 + p, (-3*(a + b*log(c*(d + e*x^(2/3)))))/b)*(a + b*log(c*(d + e*x^(2/3))))^p)/(2*3^p*c^3*e^3*ℯ^((3*a)/b)*(-((a + b*log(c*(d + e*x^(2/3))))/b))^p) - (3*2^(-1 - p)*d*Gamma(1 + p, (-2*(a + b*log(c*(d + e*x^(2/3)))))/b)*(a + b*log(c*(d + e*x^(2/3))))^p)/(c^2*e^3*ℯ^((2*a)/b)*(-((a + b*log(c*(d + e*x^(2/3))))/b))^p) + (3*d^2*Gamma(1 + p, -((a + b*log(c*(d + e*x^(2/3))))/b))*(a + b*log(c*(d + e*x^(2/3))))^p)/(2*c*e^3*ℯ^(a/b)*(-((a + b*log(c*(d + e*x^(2/3))))/b))^p)]
    @test_int [(a + b*log(c*(d + e*x^(2/3))))^p/x^1, x, 1, Unintegrable((a + b*log(c*(d + e*x^(2/3))))^p/x, x)]
    @test_int [(a + b*log(c*(d + e*x^(2/3))))^p/x^3, x, 1, Unintegrable((a + b*log(c*(d + e*x^(2/3))))^p/x^3, x)]

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

    @test_int [x^3*(a + b*log(c*(d + e*x^(2/3))^2))^p, x, 21, (Gamma(1 + p, (-3*(a + b*log(c*(d + e*x^(2/3))^2)))/b)*(a + b*log(c*(d + e*x^(2/3))^2))^p)/(4*3^p*c^3*e^6*ℯ^((3*a)/b)*(-((a + b*log(c*(d + e*x^(2/3))^2))/b))^p) - (3*2^(-1 + p)*d*(d + e*x^(2/3))^5*Gamma(1 + p, (-5*(a + b*log(c*(d + e*x^(2/3))^2)))/(2*b))*(a + b*log(c*(d + e*x^(2/3))^2))^p)/(5^p*e^6*ℯ^((5*a)/(2*b))*(c*(d + e*x^(2/3))^2)^(5/2)*(-((a + b*log(c*(d + e*x^(2/3))^2))/b))^p) + (15*2^(-2 - p)*d^2*Gamma(1 + p, (-2*(a + b*log(c*(d + e*x^(2/3))^2)))/b)*(a + b*log(c*(d + e*x^(2/3))^2))^p)/(c^2*e^6*ℯ^((2*a)/b)*(-((a + b*log(c*(d + e*x^(2/3))^2))/b))^p) - (5*(2/3)^p*d^3*(d + e*x^(2/3))^3*Gamma(1 + p, (-3*(a + b*log(c*(d + e*x^(2/3))^2)))/(2*b))*(a + b*log(c*(d + e*x^(2/3))^2))^p)/(e^6*ℯ^((3*a)/(2*b))*(c*(d + e*x^(2/3))^2)^(3/2)*(-((a + b*log(c*(d + e*x^(2/3))^2))/b))^p) + (15*d^4*Gamma(1 + p, -((a + b*log(c*(d + e*x^(2/3))^2))/b))*(a + b*log(c*(d + e*x^(2/3))^2))^p)/(4*c*e^6*ℯ^(a/b)*(-((a + b*log(c*(d + e*x^(2/3))^2))/b))^p) - (3*2^(-1 + p)*d^5*(d + e*x^(2/3))*Gamma(1 + p, -(a + b*log(c*(d + e*x^(2/3))^2))/(2*b))*(a + b*log(c*(d + e*x^(2/3))^2))^p)/(e^6*ℯ^(a/(2*b))*sqrt(c*(d + e*x^(2/3))^2)*(-((a + b*log(c*(d + e*x^(2/3))^2))/b))^p)]
    @test_int [x^1*(a + b*log(c*(d + e*x^(2/3))^2))^p, x, 12, (2^(-1 + p)*(d + e*x^(2/3))^3*Gamma(1 + p, (-3*(a + b*log(c*(d + e*x^(2/3))^2)))/(2*b))*(a + b*log(c*(d + e*x^(2/3))^2))^p)/(3^p*e^3*ℯ^((3*a)/(2*b))*(c*(d + e*x^(2/3))^2)^(3/2)*(-((a + b*log(c*(d + e*x^(2/3))^2))/b))^p) - (3*d*Gamma(1 + p, -((a + b*log(c*(d + e*x^(2/3))^2))/b))*(a + b*log(c*(d + e*x^(2/3))^2))^p)/(2*c*e^3*ℯ^(a/b)*(-((a + b*log(c*(d + e*x^(2/3))^2))/b))^p) + (3*2^(-1 + p)*d^2*(d + e*x^(2/3))*Gamma(1 + p, -(a + b*log(c*(d + e*x^(2/3))^2))/(2*b))*(a + b*log(c*(d + e*x^(2/3))^2))^p)/(e^3*ℯ^(a/(2*b))*sqrt(c*(d + e*x^(2/3))^2)*(-((a + b*log(c*(d + e*x^(2/3))^2))/b))^p)]
    @test_int [(a + b*log(c*(d + e*x^(2/3))^2))^p/x^1, x, 1, Unintegrable((a + b*log(c*(d + e*x^(2/3))^2))^p/x, x)]
    @test_int [(a + b*log(c*(d + e*x^(2/3))^2))^p/x^3, x, 1, Unintegrable((a + b*log(c*(d + e*x^(2/3))^2))^p/x^3, x)]

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

    #= ::Subsubsection::Closed:: =#
    #=m=-1=#

    @test_int [x^1*(a + b*log(c*(d + e/x^(1/3))))^p, x, 1, Unintegrable(x*(a + b*log(c*(d + e/x^(1/3))))^p, x)]
    @test_int [x^0*(a + b*log(c*(d + e/x^(1/3))))^p, x, 1, Unintegrable((a + b*log(c*(d + e/x^(1/3))))^p, x)]
    @test_int [(a + b*log(c*(d + e/x^(1/3))))^p/x^1, x, 1, Unintegrable((a + b*log(c*(d + e/x^(1/3))))^p/x, x)]
    @test_int [(a + b*log(c*(d + e/x^(1/3))))^p/x^2, x, 12, -((Gamma(1 + p, (-3*(a + b*log(c*(d + e/x^(1/3)))))/b)*(a + b*log(c*(d + e/x^(1/3))))^p)/(3^p*c^3*e^3*ℯ^((3*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p)) + (3*d*Gamma(1 + p, (-2*(a + b*log(c*(d + e/x^(1/3)))))/b)*(a + b*log(c*(d + e/x^(1/3))))^p)/(2^p*c^2*e^3*ℯ^((2*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p) - (3*d^2*Gamma(1 + p, -((a + b*log(c*(d + e/x^(1/3))))/b))*(a + b*log(c*(d + e/x^(1/3))))^p)/(c*e^3*ℯ^(a/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p)]
    @test_int [(a + b*log(c*(d + e/x^(1/3))))^p/x^3, x, 21, -((2^(-1 - p)*Gamma(1 + p, -((6*(a + b*log(c*(d + e/x^(1/3)))))/b))*(a + b*log(c*(d + e/x^(1/3))))^p)/(3^p*ℯ^((6*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p*(c^6*e^6))) + (3*d*Gamma(1 + p, -((5*(a + b*log(c*(d + e/x^(1/3)))))/b))*(a + b*log(c*(d + e/x^(1/3))))^p)/(5^p*ℯ^((5*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p*(c^5*e^6)) - (15*2^(-1 - 2*p)*d^2*Gamma(1 + p, -((4*(a + b*log(c*(d + e/x^(1/3)))))/b))*(a + b*log(c*(d + e/x^(1/3))))^p)/(ℯ^((4*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p*(c^4*e^6)) + (10*d^3*Gamma(1 + p, -((3*(a + b*log(c*(d + e/x^(1/3)))))/b))*(a + b*log(c*(d + e/x^(1/3))))^p)/(3^p*ℯ^((3*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p*(c^3*e^6)) - (15*2^(-1 - p)*d^4*Gamma(1 + p, -((2*(a + b*log(c*(d + e/x^(1/3)))))/b))*(a + b*log(c*(d + e/x^(1/3))))^p)/(ℯ^((2*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p*(c^2*e^6)) + (3*d^5*Gamma(1 + p, -((a + b*log(c*(d + e/x^(1/3))))/b))*(a + b*log(c*(d + e/x^(1/3))))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p*(c*e^6))]
    @test_int [(a + b*log(c*(d + e/x^(1/3))))^p/x^4, x, 30, -((3^(-1 - 2*p)*Gamma(1 + p, -((9*(a + b*log(c*(d + e/x^(1/3)))))/b))*(a + b*log(c*(d + e/x^(1/3))))^p)/(ℯ^((9*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p*(c^9*e^9))) + (3*d*Gamma(1 + p, -((8*(a + b*log(c*(d + e/x^(1/3)))))/b))*(a + b*log(c*(d + e/x^(1/3))))^p)/(8^p*ℯ^((8*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p*(c^8*e^9)) - (12*d^2*Gamma(1 + p, -((7*(a + b*log(c*(d + e/x^(1/3)))))/b))*(a + b*log(c*(d + e/x^(1/3))))^p)/(7^p*ℯ^((7*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p*(c^7*e^9)) + (7*2^(2 - p)*d^3*Gamma(1 + p, -((6*(a + b*log(c*(d + e/x^(1/3)))))/b))*(a + b*log(c*(d + e/x^(1/3))))^p)/(3^p*ℯ^((6*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p*(c^6*e^9)) - (42*d^4*Gamma(1 + p, -((5*(a + b*log(c*(d + e/x^(1/3)))))/b))*(a + b*log(c*(d + e/x^(1/3))))^p)/(5^p*ℯ^((5*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p*(c^5*e^9)) + (21*2^(1 - 2*p)*d^5*Gamma(1 + p, -((4*(a + b*log(c*(d + e/x^(1/3)))))/b))*(a + b*log(c*(d + e/x^(1/3))))^p)/(ℯ^((4*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p*(c^4*e^9)) - (28*d^6*Gamma(1 + p, -((3*(a + b*log(c*(d + e/x^(1/3)))))/b))*(a + b*log(c*(d + e/x^(1/3))))^p)/(3^p*ℯ^((3*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p*(c^3*e^9)) + (3*2^(2 - p)*d^7*Gamma(1 + p, -((2*(a + b*log(c*(d + e/x^(1/3)))))/b))*(a + b*log(c*(d + e/x^(1/3))))^p)/(ℯ^((2*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p*(c^2*e^9)) - (3*d^8*Gamma(1 + p, -((a + b*log(c*(d + e/x^(1/3))))/b))*(a + b*log(c*(d + e/x^(1/3))))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e/x^(1/3))))/b))^p*(c*e^9))]

    @test_int [x^1*(a + b*log(c*(d + e/x^(1/3))^2))^p, x, 1, Unintegrable(x*(a + b*log(c*(d + e/x^(1/3))^2))^p, x)]
    @test_int [x^0*(a + b*log(c*(d + e/x^(1/3))^2))^p, x, 1, Unintegrable((a + b*log(c*(d + e/x^(1/3))^2))^p, x)]
    @test_int [(a + b*log(c*(d + e/x^(1/3))^2))^p/x^1, x, 1, Unintegrable((a + b*log(c*(d + e/x^(1/3))^2))^p/x, x)]
    @test_int [(a + b*log(c*(d + e/x^(1/3))^2))^p/x^2, x, 12, -(((2/3)^p*(d + e/x^(1/3))^3*Gamma(1 + p, (-3*(a + b*log(c*(d + e/x^(1/3))^2)))/(2*b))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(e^3*ℯ^((3*a)/(2*b))*(c*(d + e/x^(1/3))^2)^(3/2)*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p)) + (3*d*Gamma(1 + p, -((a + b*log(c*(d + e/x^(1/3))^2))/b))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(c*e^3*ℯ^(a/b)*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p) - (3*2^p*d^2*(d + e/x^(1/3))*Gamma(1 + p, -(a + b*log(c*(d + e/x^(1/3))^2))/(2*b))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(e^3*ℯ^(a/(2*b))*sqrt(c*(d + e/x^(1/3))^2)*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p)]
    @test_int [(a + b*log(c*(d + e/x^(1/3))^2))^p/x^3, x, 21, -((Gamma(1 + p, -((3*(a + b*log(c*(d + e/x^(1/3))^2)))/b))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(3^p*ℯ^((3*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p*(2*c^3*e^6))) + (3*(2/5)^p*d*(d + e/x^(1/3))^5*Gamma(1 + p, -((5*(a + b*log(c*(d + e/x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(ℯ^((5*a)/(2*b))*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p*(e^6*(c*(d + e/x^(1/3))^2)^(5/2))) - (15*2^(-1 - p)*d^2*Gamma(1 + p, -((2*(a + b*log(c*(d + e/x^(1/3))^2)))/b))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(ℯ^((2*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p*(c^2*e^6)) + (5*2^(1 + p)*d^3*(d + e/x^(1/3))^3*Gamma(1 + p, -((3*(a + b*log(c*(d + e/x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(3^p*ℯ^((3*a)/(2*b))*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p*(e^6*(c*(d + e/x^(1/3))^2)^(3/2))) - (15*d^4*Gamma(1 + p, -((a + b*log(c*(d + e/x^(1/3))^2))/b))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p*(2*c*e^6)) + (3*2^p*d^5*(d + e/x^(1/3))*Gamma(1 + p, -((a + b*log(c*(d + e/x^(1/3))^2))/(2*b)))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(ℯ^(a/(2*b))*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p*(e^6*sqrt(c*(d + e/x^(1/3))^2)))]
    @test_int [(a + b*log(c*(d + e/x^(1/3))^2))^p/x^4, x, 30, -((2^p*3^(-1 - 2*p)*(d + e/x^(1/3))^9*Gamma(1 + p, -((9*(a + b*log(c*(d + e/x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(ℯ^((9*a)/(2*b))*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p*(e^9*(c*(d + e/x^(1/3))^2)^(9/2)))) + (3*d*Gamma(1 + p, -((4*(a + b*log(c*(d + e/x^(1/3))^2)))/b))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(4^p*ℯ^((4*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p*(c^4*e^9)) - (3*2^(2 + p)*d^2*(d + e/x^(1/3))^7*Gamma(1 + p, -((7*(a + b*log(c*(d + e/x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(7^p*ℯ^((7*a)/(2*b))*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p*(e^9*(c*(d + e/x^(1/3))^2)^(7/2))) + (28*d^3*Gamma(1 + p, -((3*(a + b*log(c*(d + e/x^(1/3))^2)))/b))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(3^p*ℯ^((3*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p*(c^3*e^9)) - (21*2^(1 + p)*d^4*(d + e/x^(1/3))^5*Gamma(1 + p, -((5*(a + b*log(c*(d + e/x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(5^p*ℯ^((5*a)/(2*b))*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p*(e^9*(c*(d + e/x^(1/3))^2)^(5/2))) + (21*2^(1 - p)*d^5*Gamma(1 + p, -((2*(a + b*log(c*(d + e/x^(1/3))^2)))/b))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(ℯ^((2*a)/b)*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p*(c^2*e^9)) - (7*2^(2 + p)*d^6*(d + e/x^(1/3))^3*Gamma(1 + p, -((3*(a + b*log(c*(d + e/x^(1/3))^2)))/(2*b)))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(3^p*ℯ^((3*a)/(2*b))*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p*(e^9*(c*(d + e/x^(1/3))^2)^(3/2))) + (12*d^7*Gamma(1 + p, -((a + b*log(c*(d + e/x^(1/3))^2))/b))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(ℯ^(a/b)*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p*(c*e^9)) - (3*2^p*d^8*(d + e/x^(1/3))*Gamma(1 + p, -((a + b*log(c*(d + e/x^(1/3))^2))/(2*b)))*(a + b*log(c*(d + e/x^(1/3))^2))^p)/(ℯ^(a/(2*b))*(-((a + b*log(c*(d + e/x^(1/3))^2))/b))^p*(e^9*sqrt(c*(d + e/x^(1/3))^2)))]

    #= ::Subsubsection::Closed:: =#
    #=m=-2=#

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

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

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

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

    #= ::Subsubsection::Closed:: =#
    #=r>0=#

    @test_int [(f + g*x)*(a + b*log(c*(d + e*x^2)^p))/(h*x)^(1/2), x, 26, (2*a*f*sqrt(h*x))/h - (8*b*f*p*sqrt(h*x))/h - (8*b*g*p*(h*x)^(3/2))/(9*h^2) - (2*sqrt(2)*b*d^(1/4)*f*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(e^(1/4)*sqrt(h)) - (2*sqrt(2)*b*d^(3/4)*g*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(3*e^(3/4)*sqrt(h)) + (2*sqrt(2)*b*d^(1/4)*f*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(e^(1/4)*sqrt(h)) + (2*sqrt(2)*b*d^(3/4)*g*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(3*e^(3/4)*sqrt(h)) + (2*b*f*sqrt(h*x)*log(c*(d + e*x^2)^p))/h + (2*g*(h*x)^(3/2)*(a + b*log(c*(d + e*x^2)^p)))/(3*h^2) - (sqrt(2)*b*d^(1/4)*f*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(e^(1/4)*sqrt(h)) + (sqrt(2)*b*d^(3/4)*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(3*e^(3/4)*sqrt(h)) + (sqrt(2)*b*d^(1/4)*f*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(e^(1/4)*sqrt(h)) - (sqrt(2)*b*d^(3/4)*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(3*e^(3/4)*sqrt(h))]
    @test_int [(f + g*x)*(a + b*log(c*(d + e*x^2)^p))/(h*x)^(3/2), x, 25, (2*a*g*sqrt(h*x))/h^2 - (8*b*g*p*sqrt(h*x))/h^2 - (2*sqrt(2)*b*e^(1/4)*f*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(d^(1/4)*h^(3/2)) - (2*sqrt(2)*b*d^(1/4)*g*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(e^(1/4)*h^(3/2)) + (2*sqrt(2)*b*e^(1/4)*f*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(d^(1/4)*h^(3/2)) + (2*sqrt(2)*b*d^(1/4)*g*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(e^(1/4)*h^(3/2)) + (2*b*g*sqrt(h*x)*log(c*(d + e*x^2)^p))/h^2 - (2*f*(a + b*log(c*(d + e*x^2)^p)))/(h*sqrt(h*x)) + (sqrt(2)*b*e^(1/4)*f*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(d^(1/4)*h^(3/2)) - (sqrt(2)*b*d^(1/4)*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(e^(1/4)*h^(3/2)) - (sqrt(2)*b*e^(1/4)*f*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(d^(1/4)*h^(3/2)) + (sqrt(2)*b*d^(1/4)*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(e^(1/4)*h^(3/2))]
    @test_int [(f + g*x)*(a + b*log(c*(d + e*x^2)^p))/(h*x)^(5/2), x, 23, -((2*sqrt(2)*b*e^(3/4)*f*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(3*d^(3/4)*h^(5/2))) - (2*sqrt(2)*b*e^(1/4)*g*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(d^(1/4)*h^(5/2)) + (2*sqrt(2)*b*e^(3/4)*f*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(3*d^(3/4)*h^(5/2)) + (2*sqrt(2)*b*e^(1/4)*g*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(d^(1/4)*h^(5/2)) - (2*f*(a + b*log(c*(d + e*x^2)^p)))/(3*h*(h*x)^(3/2)) - (2*g*(a + b*log(c*(d + e*x^2)^p)))/(h^2*sqrt(h*x)) - (sqrt(2)*b*e^(3/4)*f*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(3*d^(3/4)*h^(5/2)) + (sqrt(2)*b*e^(1/4)*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(d^(1/4)*h^(5/2)) + (sqrt(2)*b*e^(3/4)*f*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(3*d^(3/4)*h^(5/2)) - (sqrt(2)*b*e^(1/4)*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(d^(1/4)*h^(5/2))]
    @test_int [(f + g*x)*(a + b*log(c*(d + e*x^2)^p))/(h*x)^(7/2), x, 24, -((8*b*e*f*p)/(5*d*h^3*sqrt(h*x))) + (2*sqrt(2)*b*e^(5/4)*f*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(5*d^(5/4)*h^(7/2)) - (2*sqrt(2)*b*e^(3/4)*g*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(3*d^(3/4)*h^(7/2)) - (2*sqrt(2)*b*e^(5/4)*f*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(5*d^(5/4)*h^(7/2)) + (2*sqrt(2)*b*e^(3/4)*g*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(3*d^(3/4)*h^(7/2)) - (2*f*(a + b*log(c*(d + e*x^2)^p)))/(5*h*(h*x)^(5/2)) - (2*g*(a + b*log(c*(d + e*x^2)^p)))/(3*h^2*(h*x)^(3/2)) - (sqrt(2)*b*e^(5/4)*f*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(5*d^(5/4)*h^(7/2)) - (sqrt(2)*b*e^(3/4)*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(3*d^(3/4)*h^(7/2)) + (sqrt(2)*b*e^(5/4)*f*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(5*d^(5/4)*h^(7/2)) + (sqrt(2)*b*e^(3/4)*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(3*d^(3/4)*h^(7/2))]
    @test_int [(f + g*x)*(a + b*log(c*(d + e*x^2)^p))/(h*x)^(9/2), x, 25, -((8*b*e*f*p)/(21*d*h^3*(h*x)^(3/2))) - (8*b*e*g*p)/(5*d*h^4*sqrt(h*x)) + (2*sqrt(2)*b*e^(7/4)*f*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(7*d^(7/4)*h^(9/2)) + (2*sqrt(2)*b*e^(5/4)*g*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(5*d^(5/4)*h^(9/2)) - (2*sqrt(2)*b*e^(7/4)*f*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(7*d^(7/4)*h^(9/2)) - (2*sqrt(2)*b*e^(5/4)*g*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(5*d^(5/4)*h^(9/2)) - (2*f*(a + b*log(c*(d + e*x^2)^p)))/(7*h*(h*x)^(7/2)) - (2*g*(a + b*log(c*(d + e*x^2)^p)))/(5*h^2*(h*x)^(5/2)) + (sqrt(2)*b*e^(7/4)*f*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(7*d^(7/4)*h^(9/2)) - (sqrt(2)*b*e^(5/4)*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(5*d^(5/4)*h^(9/2)) - (sqrt(2)*b*e^(7/4)*f*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(7*d^(7/4)*h^(9/2)) + (sqrt(2)*b*e^(5/4)*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(5*d^(5/4)*h^(9/2))]

    @test_int [(f + g*x)^2*(a + b*log(c*(d + e*x^2)^p))/(h*x)^(1/2), x, 38, (2*a*f^2*sqrt(h*x))/h - (8*b*f^2*p*sqrt(h*x))/h + (8*b*d*g^2*p*sqrt(h*x))/(5*e*h) - (16*b*f*g*p*(h*x)^(3/2))/(9*h^2) - (8*b*g^2*p*(h*x)^(5/2))/(25*h^3) - (2*sqrt(2)*b*d^(1/4)*f^2*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(e^(1/4)*sqrt(h)) - (4*sqrt(2)*b*d^(3/4)*f*g*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(3*e^(3/4)*sqrt(h)) + (2*sqrt(2)*b*d^(5/4)*g^2*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(5*e^(5/4)*sqrt(h)) + (2*sqrt(2)*b*d^(1/4)*f^2*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(e^(1/4)*sqrt(h)) + (4*sqrt(2)*b*d^(3/4)*f*g*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(3*e^(3/4)*sqrt(h)) - (2*sqrt(2)*b*d^(5/4)*g^2*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(5*e^(5/4)*sqrt(h)) + (2*b*f^2*sqrt(h*x)*log(c*(d + e*x^2)^p))/h + (4*f*g*(h*x)^(3/2)*(a + b*log(c*(d + e*x^2)^p)))/(3*h^2) + (2*g^2*(h*x)^(5/2)*(a + b*log(c*(d + e*x^2)^p)))/(5*h^3) - (sqrt(2)*b*d^(1/4)*f^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(e^(1/4)*sqrt(h)) + (2*sqrt(2)*b*d^(3/4)*f*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(3*e^(3/4)*sqrt(h)) + (sqrt(2)*b*d^(5/4)*g^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(5*e^(5/4)*sqrt(h)) + (sqrt(2)*b*d^(1/4)*f^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(e^(1/4)*sqrt(h)) - (2*sqrt(2)*b*d^(3/4)*f*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(3*e^(3/4)*sqrt(h)) - (sqrt(2)*b*d^(5/4)*g^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(5*e^(5/4)*sqrt(h))]
    @test_int [(f + g*x)^2*(a + b*log(c*(d + e*x^2)^p))/(h*x)^(3/2), x, 36, (4*a*f*g*sqrt(h*x))/h^2 - (16*b*f*g*p*sqrt(h*x))/h^2 - (8*b*g^2*p*(h*x)^(3/2))/(9*h^3) - (2*sqrt(2)*b*e^(1/4)*f^2*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(d^(1/4)*h^(3/2)) - (4*sqrt(2)*b*d^(1/4)*f*g*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(e^(1/4)*h^(3/2)) - (2*sqrt(2)*b*d^(3/4)*g^2*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(3*e^(3/4)*h^(3/2)) + (2*sqrt(2)*b*e^(1/4)*f^2*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(d^(1/4)*h^(3/2)) + (4*sqrt(2)*b*d^(1/4)*f*g*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(e^(1/4)*h^(3/2)) + (2*sqrt(2)*b*d^(3/4)*g^2*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(3*e^(3/4)*h^(3/2)) + (4*b*f*g*sqrt(h*x)*log(c*(d + e*x^2)^p))/h^2 - (2*f^2*(a + b*log(c*(d + e*x^2)^p)))/(h*sqrt(h*x)) + (2*g^2*(h*x)^(3/2)*(a + b*log(c*(d + e*x^2)^p)))/(3*h^3) + (sqrt(2)*b*e^(1/4)*f^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(d^(1/4)*h^(3/2)) - (2*sqrt(2)*b*d^(1/4)*f*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(e^(1/4)*h^(3/2)) + (sqrt(2)*b*d^(3/4)*g^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(3*e^(3/4)*h^(3/2)) - (sqrt(2)*b*e^(1/4)*f^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(d^(1/4)*h^(3/2)) + (2*sqrt(2)*b*d^(1/4)*f*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(e^(1/4)*h^(3/2)) - (sqrt(2)*b*d^(3/4)*g^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(3*e^(3/4)*h^(3/2))]
    @test_int [(f + g*x)^2*(a + b*log(c*(d + e*x^2)^p))/(h*x)^(5/2), x, 35, (2*a*g^2*sqrt(h*x))/h^3 - (8*b*g^2*p*sqrt(h*x))/h^3 - (2*sqrt(2)*b*e^(3/4)*f^2*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(3*d^(3/4)*h^(5/2)) - (4*sqrt(2)*b*e^(1/4)*f*g*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(d^(1/4)*h^(5/2)) - (2*sqrt(2)*b*d^(1/4)*g^2*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(e^(1/4)*h^(5/2)) + (2*sqrt(2)*b*e^(3/4)*f^2*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(3*d^(3/4)*h^(5/2)) + (4*sqrt(2)*b*e^(1/4)*f*g*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(d^(1/4)*h^(5/2)) + (2*sqrt(2)*b*d^(1/4)*g^2*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(e^(1/4)*h^(5/2)) + (2*b*g^2*sqrt(h*x)*log(c*(d + e*x^2)^p))/h^3 - (2*f^2*(a + b*log(c*(d + e*x^2)^p)))/(3*h*(h*x)^(3/2)) - (4*f*g*(a + b*log(c*(d + e*x^2)^p)))/(h^2*sqrt(h*x)) - (sqrt(2)*b*e^(3/4)*f^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(3*d^(3/4)*h^(5/2)) + (2*sqrt(2)*b*e^(1/4)*f*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(d^(1/4)*h^(5/2)) - (sqrt(2)*b*d^(1/4)*g^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(e^(1/4)*h^(5/2)) + (sqrt(2)*b*e^(3/4)*f^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(3*d^(3/4)*h^(5/2)) - (2*sqrt(2)*b*e^(1/4)*f*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(d^(1/4)*h^(5/2)) + (sqrt(2)*b*d^(1/4)*g^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(e^(1/4)*h^(5/2))]
    @test_int [(f + g*x)^2*(a + b*log(c*(d + e*x^2)^p))/(h*x)^(7/2), x, 34, -((8*b*e*f^2*p)/(5*d*h^3*sqrt(h*x))) + (2*sqrt(2)*b*e^(5/4)*f^2*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(5*d^(5/4)*h^(7/2)) - (4*sqrt(2)*b*e^(3/4)*f*g*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(3*d^(3/4)*h^(7/2)) - (2*sqrt(2)*b*e^(1/4)*g^2*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(d^(1/4)*h^(7/2)) - (2*sqrt(2)*b*e^(5/4)*f^2*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(5*d^(5/4)*h^(7/2)) + (4*sqrt(2)*b*e^(3/4)*f*g*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(3*d^(3/4)*h^(7/2)) + (2*sqrt(2)*b*e^(1/4)*g^2*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(d^(1/4)*h^(7/2)) - (2*f^2*(a + b*log(c*(d + e*x^2)^p)))/(5*h*(h*x)^(5/2)) - (4*f*g*(a + b*log(c*(d + e*x^2)^p)))/(3*h^2*(h*x)^(3/2)) - (2*g^2*(a + b*log(c*(d + e*x^2)^p)))/(h^3*sqrt(h*x)) - (sqrt(2)*b*e^(5/4)*f^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(5*d^(5/4)*h^(7/2)) - (2*sqrt(2)*b*e^(3/4)*f*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(3*d^(3/4)*h^(7/2)) + (sqrt(2)*b*e^(1/4)*g^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(d^(1/4)*h^(7/2)) + (sqrt(2)*b*e^(5/4)*f^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(5*d^(5/4)*h^(7/2)) + (2*sqrt(2)*b*e^(3/4)*f*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(3*d^(3/4)*h^(7/2)) - (sqrt(2)*b*e^(1/4)*g^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(d^(1/4)*h^(7/2))]
    @test_int [(f + g*x)^2*(a + b*log(c*(d + e*x^2)^p))/(h*x)^(9/2), x, 35, -((8*b*e*f^2*p)/(21*d*h^3*(h*x)^(3/2))) - (16*b*e*f*g*p)/(5*d*h^4*sqrt(h*x)) + (2*sqrt(2)*b*e^(7/4)*f^2*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(7*d^(7/4)*h^(9/2)) + (4*sqrt(2)*b*e^(5/4)*f*g*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(5*d^(5/4)*h^(9/2)) - (2*sqrt(2)*b*e^(3/4)*g^2*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(3*d^(3/4)*h^(9/2)) - (2*sqrt(2)*b*e^(7/4)*f^2*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(7*d^(7/4)*h^(9/2)) - (4*sqrt(2)*b*e^(5/4)*f*g*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(5*d^(5/4)*h^(9/2)) + (2*sqrt(2)*b*e^(3/4)*g^2*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(3*d^(3/4)*h^(9/2)) - (2*f^2*(a + b*log(c*(d + e*x^2)^p)))/(7*h*(h*x)^(7/2)) - (4*f*g*(a + b*log(c*(d + e*x^2)^p)))/(5*h^2*(h*x)^(5/2)) - (2*g^2*(a + b*log(c*(d + e*x^2)^p)))/(3*h^3*(h*x)^(3/2)) + (sqrt(2)*b*e^(7/4)*f^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(7*d^(7/4)*h^(9/2)) - (2*sqrt(2)*b*e^(5/4)*f*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(5*d^(5/4)*h^(9/2)) - (sqrt(2)*b*e^(3/4)*g^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(3*d^(3/4)*h^(9/2)) - (sqrt(2)*b*e^(7/4)*f^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(7*d^(7/4)*h^(9/2)) + (2*sqrt(2)*b*e^(5/4)*f*g*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(5*d^(5/4)*h^(9/2)) + (sqrt(2)*b*e^(3/4)*g^2*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(3*d^(3/4)*h^(9/2))]

    #= ::Subsubsection::Closed:: =#
    #=r<0=#

    @test_int [(h*x)^(1/2)*(a + b*log(c*(d + e*x^2)^p))/(f + g*x), x, 39, (2*a*sqrt(h*x))/g - (8*b*p*sqrt(h*x))/g - (2*sqrt(2)*b*d^(1/4)*sqrt(h)*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(e^(1/4)*g) + (2*sqrt(2)*b*d^(1/4)*sqrt(h)*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(e^(1/4)*g) + (2*b*sqrt(h*x)*log(c*(d + e*x^2)^p))/g - (2*sqrt(f)*sqrt(h)*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*(a + b*log(c*(d + e*x^2)^p)))/g^(3/2) - (sqrt(2)*b*d^(1/4)*sqrt(h)*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(e^(1/4)*g) + (sqrt(2)*b*d^(1/4)*sqrt(h)*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(e^(1/4)*g) - (8*b*sqrt(f)*sqrt(h)*p*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*log((2*sqrt(f)*sqrt(h))/(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x))))/g^(3/2) + (2*b*sqrt(f)*sqrt(h)*p*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*log((2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h) - e^(1/4)*sqrt(h*x)))/(((-d)^(1/4)*sqrt(g)*sqrt(-h) - im*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/g^(3/2) + (2*b*sqrt(f)*sqrt(h)*p*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*log(-((2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h) - e^(1/4)*sqrt(h*x)))/((im*e^(1/4)*sqrt(f) - (-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x))))))/g^(3/2) + (2*b*sqrt(f)*sqrt(h)*p*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*log((2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h) + e^(1/4)*sqrt(h*x)))/(((-d)^(1/4)*sqrt(g)*sqrt(-h) + im*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/g^(3/2) + (2*b*sqrt(f)*sqrt(h)*p*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*log((2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h) + e^(1/4)*sqrt(h*x)))/((im*e^(1/4)*sqrt(f) + (-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/g^(3/2) + (4*im*b*sqrt(f)*sqrt(h)*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(h))/(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x))))/g^(3/2) - (im*b*sqrt(f)*sqrt(h)*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h) - e^(1/4)*sqrt(h*x)))/(((-d)^(1/4)*sqrt(g)*sqrt(-h) - im*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/g^(3/2) - (im*b*sqrt(f)*sqrt(h)*p*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h) - e^(1/4)*sqrt(h*x)))/((im*e^(1/4)*sqrt(f) - (-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/g^(3/2) - (im*b*sqrt(f)*sqrt(h)*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h) + e^(1/4)*sqrt(h*x)))/(((-d)^(1/4)*sqrt(g)*sqrt(-h) + im*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/g^(3/2) - (im*b*sqrt(f)*sqrt(h)*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h) + e^(1/4)*sqrt(h*x)))/((im*e^(1/4)*sqrt(f) + (-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/g^(3/2)]
    @test_int [(a + b*log(c*(d + e*x^2)^p))/((f + g*x)*(h*x)^(1/2)), x, 25, (2*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*(a + b*log(c*(d + e*x^2)^p)))/(sqrt(f)*sqrt(g)*sqrt(h)) + (8*b*p*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*log((2*sqrt(f)*sqrt(h))/(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x))))/(sqrt(f)*sqrt(g)*sqrt(h)) - (2*b*p*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*log((2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h) - e^(1/4)*sqrt(h*x)))/(((-d)^(1/4)*sqrt(g)*sqrt(-h) - im*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/(sqrt(f)*sqrt(g)*sqrt(h)) - (2*b*p*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*log(-((2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h) - e^(1/4)*sqrt(h*x)))/((im*e^(1/4)*sqrt(f) - (-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x))))))/(sqrt(f)*sqrt(g)*sqrt(h)) - (2*b*p*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*log((2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h) + e^(1/4)*sqrt(h*x)))/(((-d)^(1/4)*sqrt(g)*sqrt(-h) + im*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/(sqrt(f)*sqrt(g)*sqrt(h)) - (2*b*p*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*log((2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h) + e^(1/4)*sqrt(h*x)))/((im*e^(1/4)*sqrt(f) + (-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/(sqrt(f)*sqrt(g)*sqrt(h)) - (4*im*b*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(h))/(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x))))/(sqrt(f)*sqrt(g)*sqrt(h)) + (im*b*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h) - e^(1/4)*sqrt(h*x)))/(((-d)^(1/4)*sqrt(g)*sqrt(-h) - im*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/(sqrt(f)*sqrt(g)*sqrt(h)) + (im*b*p*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h) - e^(1/4)*sqrt(h*x)))/((im*e^(1/4)*sqrt(f) - (-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/(sqrt(f)*sqrt(g)*sqrt(h)) + (im*b*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h) + e^(1/4)*sqrt(h*x)))/(((-d)^(1/4)*sqrt(g)*sqrt(-h) + im*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/(sqrt(f)*sqrt(g)*sqrt(h)) + (im*b*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h) + e^(1/4)*sqrt(h*x)))/((im*e^(1/4)*sqrt(f) + (-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/(sqrt(f)*sqrt(g)*sqrt(h))]
    @test_int [(a + b*log(c*(d + e*x^2)^p))/((f + g*x)*(h*x)^(3/2)), x, 37, -((2*sqrt(2)*b*e^(1/4)*p*atan(1 - (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(d^(1/4)*f*h^(3/2))) + (2*sqrt(2)*b*e^(1/4)*p*atan(1 + (sqrt(2)*e^(1/4)*sqrt(h*x))/(d^(1/4)*sqrt(h))))/(d^(1/4)*f*h^(3/2)) - (2*(a + b*log(c*(d + e*x^2)^p)))/(f*h*sqrt(h*x)) - (2*sqrt(g)*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*(a + b*log(c*(d + e*x^2)^p)))/(f^(3/2)*h^(3/2)) + (sqrt(2)*b*e^(1/4)*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x - sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(d^(1/4)*f*h^(3/2)) - (sqrt(2)*b*e^(1/4)*p*log(sqrt(d)*sqrt(h) + sqrt(e)*sqrt(h)*x + sqrt(2)*d^(1/4)*e^(1/4)*sqrt(h*x)))/(d^(1/4)*f*h^(3/2)) - (8*b*sqrt(g)*p*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*log((2*sqrt(f)*sqrt(h))/(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x))))/(f^(3/2)*h^(3/2)) + (2*b*sqrt(g)*p*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*log((2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h) - e^(1/4)*sqrt(h*x)))/(((-d)^(1/4)*sqrt(g)*sqrt(-h) - im*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/(f^(3/2)*h^(3/2)) + (2*b*sqrt(g)*p*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*log(-((2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h) - e^(1/4)*sqrt(h*x)))/((im*e^(1/4)*sqrt(f) - (-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x))))))/(f^(3/2)*h^(3/2)) + (2*b*sqrt(g)*p*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*log((2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h) + e^(1/4)*sqrt(h*x)))/(((-d)^(1/4)*sqrt(g)*sqrt(-h) + im*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/(f^(3/2)*h^(3/2)) + (2*b*sqrt(g)*p*atan((sqrt(g)*sqrt(h*x))/(sqrt(f)*sqrt(h)))*log((2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h) + e^(1/4)*sqrt(h*x)))/((im*e^(1/4)*sqrt(f) + (-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/(f^(3/2)*h^(3/2)) + (4*im*b*sqrt(g)*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(h))/(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x))))/(f^(3/2)*h^(3/2)) - (im*b*sqrt(g)*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h) - e^(1/4)*sqrt(h*x)))/(((-d)^(1/4)*sqrt(g)*sqrt(-h) - im*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/(f^(3/2)*h^(3/2)) - (im*b*sqrt(g)*p*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h) - e^(1/4)*sqrt(h*x)))/((im*e^(1/4)*sqrt(f) - (-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/(f^(3/2)*h^(3/2)) - (im*b*sqrt(g)*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h) + e^(1/4)*sqrt(h*x)))/(((-d)^(1/4)*sqrt(g)*sqrt(-h) + im*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/(f^(3/2)*h^(3/2)) - (im*b*sqrt(g)*p*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h) + e^(1/4)*sqrt(h*x)))/((im*e^(1/4)*sqrt(f) + (-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h) - im*sqrt(g)*sqrt(h*x)))))/(f^(3/2)*h^(3/2))]

    #= ::Subsection:: =#
    #=Integrands*of*the*form*(h*x)^(r/2)*(f+g*x)^q*(a+b*log(c*(d+e*x^2)^n))^2=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(h*x)^s*log(f*x^r)^q*(a+b*log(c*(d+e*x^m)^n))=#

    @test_int [log(f*x^p)*log(1 + e*x^m)/x, x, 2, -((log(f*x^p)*PolyLog(2, (-e)*x^m))/m) + (p*PolyLog(3, (-e)*x^m))/m^2]

    @test_int [x^(-1 + m)*log(f*x^p)^2/(d + e*x^m), x, 3, (log(f*x^p)^2*log(1 + (e*x^m)/d))/(e*m) + (2*p*log(f*x^p)*PolyLog(2, -((e*x^m)/d)))/(e*m^2) - (2*p^2*PolyLog(3, -((e*x^m)/d)))/(e*m^3)]

    @test_int [log(f*x^p)^3*(a + b*log(c*(d + e*x^m)^n))/x, x, 6, (log(f*x^p)^4*(a + b*log(c*(d + e*x^m)^n)))/(4*p) - (b*n*log(f*x^p)^4*log(1 + (e*x^m)/d))/(4*p) - (b*n*log(f*x^p)^3*PolyLog(2, -((e*x^m)/d)))/m + (3*b*n*p*log(f*x^p)^2*PolyLog(3, -((e*x^m)/d)))/m^2 - (6*b*n*p^2*log(f*x^p)*PolyLog(4, -((e*x^m)/d)))/m^3 + (6*b*n*p^3*PolyLog(5, -((e*x^m)/d)))/m^4]
    @test_int [log(f*x^p)^2*(a + b*log(c*(d + e*x^m)^n))/x, x, 5, (log(f*x^p)^3*(a + b*log(c*(d + e*x^m)^n)))/(3*p) - (b*n*log(f*x^p)^3*log(1 + (e*x^m)/d))/(3*p) - (b*n*log(f*x^p)^2*PolyLog(2, -((e*x^m)/d)))/m + (2*b*n*p*log(f*x^p)*PolyLog(3, -((e*x^m)/d)))/m^2 - (2*b*n*p^2*PolyLog(4, -((e*x^m)/d)))/m^3]
    @test_int [log(f*x^p)^1*(a + b*log(c*(d + e*x^m)^n))/x, x, 4, (log(f*x^p)^2*(a + b*log(c*(d + e*x^m)^n)))/(2*p) - (b*n*log(f*x^p)^2*log(1 + (e*x^m)/d))/(2*p) - (b*n*log(f*x^p)*PolyLog(2, -((e*x^m)/d)))/m + (b*n*p*PolyLog(3, -((e*x^m)/d)))/m^2]
    @test_int [log(f*x^p)^0*(a + b*log(c*(d + e*x^m)^n))/x, x, 3, (log(-((e*x^m)/d))*(a + b*log(c*(d + e*x^m)^n)))/m + (b*n*PolyLog(2, 1 + (e*x^m)/d))/m]
    @test_int [(a + b*log(c*(d + e*x^m)^n))/(x*log(f*x^p)^1), x, 4, (a*log(log(f*x^p)))/p + b*Unintegrable(log(c*(d + e*x^m)^n)/(x*log(f*x^p)), x)]
    @test_int [(a + b*log(c*(d + e*x^m)^n))/(x*log(f*x^p)^2), x, 1, -((a + b*log(c*(d + e*x^m)^n))/(p*log(f*x^p))) + (b*e*m*n*Unintegrable(x^(-1 + m)/((d + e*x^m)*log(f*x^p)), x))/p]
    @test_int [(a + b*log(c*(d + e*x^m)^n))/(x*log(f*x^p)^3), x, 1, -((a + b*log(c*(d + e*x^m)^n))/(2*p*log(f*x^p)^2)) + (b*e*m*n*Unintegrable(x^(-1 + m)/((d + e*x^m)*log(f*x^p)^2), x))/(2*p)]

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

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

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

    @test_int [log(c*(d + e*(f + g*x)^p)^q), x, 3, -((e*p*q*(f + g*x)^(1 + p)*HypergeometricFunctions._₂F₁(1, 1 + 1/p, 2 + 1/p, -((e*(f + g*x)^p)/d)))/(d*g*(1 + p))) + ((f + g*x)*log(c*(d + e*(f + g*x)^p)^q))/g]

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

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

    @test_int [(a + b*log(c*(d + e/(f + g*x))^p))^n, x, 0, Unintegrable((a + b*log(c*(d + e/(f + g*x))^p))^n, x)]

    @test_int [(a + b*log(c*(d + e/(f + g*x))^p))^4, x, 8, -((4*b*e*p*log(-(e/(d*(f + g*x))))*(a + b*log(c*(d + e/(f + g*x))^p))^3)/(d*g)) + ((e + d*(f + g*x))*(a + b*log(c*(d + e/(f + g*x))^p))^4)/(d*g) - (12*b^2*e*p^2*(a + b*log(c*(d + e/(f + g*x))^p))^2*PolyLog(2, 1 + e/(d*(f + g*x))))/(d*g) + (24*b^3*e*p^3*(a + b*log(c*(d + e/(f + g*x))^p))*PolyLog(3, 1 + e/(d*(f + g*x))))/(d*g) - (24*b^4*e*p^4*PolyLog(4, 1 + e/(d*(f + g*x))))/(d*g)]
    @test_int [(a + b*log(c*(d + e/(f + g*x))^p))^3, x, 7, -((3*b*e*p*log(-(e/(d*(f + g*x))))*(a + b*log(c*(d + e/(f + g*x))^p))^2)/(d*g)) + ((e + d*(f + g*x))*(a + b*log(c*(d + e/(f + g*x))^p))^3)/(d*g) - (6*b^2*e*p^2*(a + b*log(c*(d + e/(f + g*x))^p))*PolyLog(2, 1 + e/(d*(f + g*x))))/(d*g) + (6*b^3*e*p^3*PolyLog(3, 1 + e/(d*(f + g*x))))/(d*g)]
    @test_int [(a + b*log(c*(d + e/(f + g*x))^p))^2, x, 5, -((2*b*e*p*log(-(e/(d*(f + g*x))))*(a + b*log(c*(d + e/(f + g*x))^p)))/(d*g)) + ((e + d*(f + g*x))*(a + b*log(c*(d + e/(f + g*x))^p))^2)/(d*g) - (2*b^2*e*p^2*PolyLog(2, 1 + e/(d*(f + g*x))))/(d*g)]
    @test_int [(a + b*log(c*(d + e/(f + g*x))^p))^1, x, 5, a*x + (b*(f + g*x)*log(c*(d + e/(f + g*x))^p))/g + (b*e*p*log(e + d*(f + g*x)))/(d*g)]
    @test_int [1/(a + b*log(c*(d + e/(f + g*x))^p))^1, x, 0, Unintegrable(1/(a + b*log(c*(d + e/(f + g*x))^p)), x)]
    @test_int [1/(a + b*log(c*(d + e/(f + g*x))^p))^2, x, 0, Unintegrable(1/(a + b*log(c*(d + e/(f + g*x))^p))^2, x)]
    end

max_stars_repo_path: test/3 Logarithms/3.4 u (a+b log(c (d+e x^m)^n))^p.jl