text:
@testset "3.1.5 u (a+b log(c x^n))^p" begin
    (a, b, c, d, e, f, g, k, m, n, p, q, r, x, ) = @variables a b c d e f g k m n p q r x

    #= ::Package:: =#

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

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

    @test_int [(a + b*log(c*x^n))/(d + e*x + f*x^2), x, 6, ((a + b*log(c*x^n))*log(1 + (2*f*x)/(e - sqrt(e^2 - 4*d*f))))/sqrt(e^2 - 4*d*f) - ((a + b*log(c*x^n))*log(1 + (2*f*x)/(e + sqrt(e^2 - 4*d*f))))/sqrt(e^2 - 4*d*f) + (b*n*PolyLog(2, -((2*f*x)/(e - sqrt(e^2 - 4*d*f)))))/sqrt(e^2 - 4*d*f) - (b*n*PolyLog(2, -((2*f*x)/(e + sqrt(e^2 - 4*d*f)))))/sqrt(e^2 - 4*d*f)]

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

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

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

    @test_int [x^3*(a + b*log(c*x^n))*log(1 + e*x), x, 6, -((5*b*n*x)/(16*e^3)) + (3*b*n*x^2)/(32*e^2) - (7*b*n*x^3)/(144*e) + (1/32)*b*n*x^4 + (x*(a + b*log(c*x^n)))/(4*e^3) - (x^2*(a + b*log(c*x^n)))/(8*e^2) + (x^3*(a + b*log(c*x^n)))/(12*e) - (1/16)*x^4*(a + b*log(c*x^n)) + (b*n*log(1 + e*x))/(16*e^4) - (1/16)*b*n*x^4*log(1 + e*x) - ((a + b*log(c*x^n))*log(1 + e*x))/(4*e^4) + (1/4)*x^4*(a + b*log(c*x^n))*log(1 + e*x) - (b*n*PolyLog(2, (-e)*x))/(4*e^4)]
    @test_int [x^2*(a + b*log(c*x^n))*log(1 + e*x), x, 6, (4*b*n*x)/(9*e^2) - (5*b*n*x^2)/(36*e) + (2/27)*b*n*x^3 - (x*(a + b*log(c*x^n)))/(3*e^2) + (x^2*(a + b*log(c*x^n)))/(6*e) - (1/9)*x^3*(a + b*log(c*x^n)) - (b*n*log(1 + e*x))/(9*e^3) - (1/9)*b*n*x^3*log(1 + e*x) + ((a + b*log(c*x^n))*log(1 + e*x))/(3*e^3) + (1/3)*x^3*(a + b*log(c*x^n))*log(1 + e*x) + (b*n*PolyLog(2, (-e)*x))/(3*e^3)]
    @test_int [x^1*(a + b*log(c*x^n))*log(1 + e*x), x, 6, -((3*b*n*x)/(4*e)) + (1/4)*b*n*x^2 + (x*(a + b*log(c*x^n)))/(2*e) - (1/4)*x^2*(a + b*log(c*x^n)) + (b*n*log(1 + e*x))/(4*e^2) - (1/4)*b*n*x^2*log(1 + e*x) - ((a + b*log(c*x^n))*log(1 + e*x))/(2*e^2) + (1/2)*x^2*(a + b*log(c*x^n))*log(1 + e*x) - (b*n*PolyLog(2, (-e)*x))/(2*e^2)]
    @test_int [x^0*(a + b*log(c*x^n))*log(1 + e*x), x, 7, 2*b*n*x - x*(a + b*log(c*x^n)) - (b*n*(1 + e*x)*log(1 + e*x))/e + ((1 + e*x)*(a + b*log(c*x^n))*log(1 + e*x))/e + (b*n*PolyLog(2, (-e)*x))/e]
    @test_int [(a + b*log(c*x^n))*log(1 + e*x)/x^1, x, 2, -((a + b*log(c*x^n))*PolyLog(2, (-e)*x)) + b*n*PolyLog(3, (-e)*x)]
    @test_int [(a + b*log(c*x^n))*log(1 + e*x)/x^2, x, 8, b*e*n*log(x) - (1/2)*b*e*n*log(x)^2 + e*log(x)*(a + b*log(c*x^n)) - b*e*n*log(1 + e*x) - (b*n*log(1 + e*x))/x - e*(a + b*log(c*x^n))*log(1 + e*x) - ((a + b*log(c*x^n))*log(1 + e*x))/x - b*e*n*PolyLog(2, (-e)*x)]
    @test_int [(a + b*log(c*x^n))*log(1 + e*x)/x^3, x, 7, -((3*b*e*n)/(4*x)) - (1/4)*b*e^2*n*log(x) + (1/4)*b*e^2*n*log(x)^2 - (e*(a + b*log(c*x^n)))/(2*x) - (1/2)*e^2*log(x)*(a + b*log(c*x^n)) + (1/4)*b*e^2*n*log(1 + e*x) - (b*n*log(1 + e*x))/(4*x^2) + (1/2)*e^2*(a + b*log(c*x^n))*log(1 + e*x) - ((a + b*log(c*x^n))*log(1 + e*x))/(2*x^2) + (1/2)*b*e^2*n*PolyLog(2, (-e)*x)]
    @test_int [(a + b*log(c*x^n))*log(1 + e*x)/x^4, x, 7, -((5*b*e*n)/(36*x^2)) + (4*b*e^2*n)/(9*x) + (1/9)*b*e^3*n*log(x) - (1/6)*b*e^3*n*log(x)^2 - (e*(a + b*log(c*x^n)))/(6*x^2) + (e^2*(a + b*log(c*x^n)))/(3*x) + (1/3)*e^3*log(x)*(a + b*log(c*x^n)) - (1/9)*b*e^3*n*log(1 + e*x) - (b*n*log(1 + e*x))/(9*x^3) - (1/3)*e^3*(a + b*log(c*x^n))*log(1 + e*x) - ((a + b*log(c*x^n))*log(1 + e*x))/(3*x^3) - (1/3)*b*e^3*n*PolyLog(2, (-e)*x)]

    @test_int [x^3*(a + b*log(c*x^n))^2*log(1 + e*x), x, 15, -((a*b*n*x)/(2*e^3)) + (21*b^2*n^2*x)/(32*e^3) - (7*b^2*n^2*x^2)/(64*e^2) + (37*b^2*n^2*x^3)/(864*e) - (3/128)*b^2*n^2*x^4 - (b^2*n*x*log(c*x^n))/(2*e^3) - (b*n*x*(a + b*log(c*x^n)))/(8*e^3) + (3*b*n*x^2*(a + b*log(c*x^n)))/(16*e^2) - (7*b*n*x^3*(a + b*log(c*x^n)))/(72*e) + (1/16)*b*n*x^4*(a + b*log(c*x^n)) + (x*(a + b*log(c*x^n))^2)/(4*e^3) - (x^2*(a + b*log(c*x^n))^2)/(8*e^2) + (x^3*(a + b*log(c*x^n))^2)/(12*e) - (1/16)*x^4*(a + b*log(c*x^n))^2 - (b^2*n^2*log(1 + e*x))/(32*e^4) + (1/32)*b^2*n^2*x^4*log(1 + e*x) + (b*n*(a + b*log(c*x^n))*log(1 + e*x))/(8*e^4) - (1/8)*b*n*x^4*(a + b*log(c*x^n))*log(1 + e*x) - ((a + b*log(c*x^n))^2*log(1 + e*x))/(4*e^4) + (1/4)*x^4*(a + b*log(c*x^n))^2*log(1 + e*x) + (b^2*n^2*PolyLog(2, (-e)*x))/(8*e^4) - (b*n*(a + b*log(c*x^n))*PolyLog(2, (-e)*x))/(2*e^4) + (b^2*n^2*PolyLog(3, (-e)*x))/(2*e^4)]
    @test_int [x^2*(a + b*log(c*x^n))^2*log(1 + e*x), x, 14, (2*a*b*n*x)/(3*e^2) - (26*b^2*n^2*x)/(27*e^2) + (19*b^2*n^2*x^2)/(108*e) - (2/27)*b^2*n^2*x^3 + (2*b^2*n*x*log(c*x^n))/(3*e^2) + (2*b*n*x*(a + b*log(c*x^n)))/(9*e^2) - (5*b*n*x^2*(a + b*log(c*x^n)))/(18*e) + (4/27)*b*n*x^3*(a + b*log(c*x^n)) - (x*(a + b*log(c*x^n))^2)/(3*e^2) + (x^2*(a + b*log(c*x^n))^2)/(6*e) - (1/9)*x^3*(a + b*log(c*x^n))^2 + (2*b^2*n^2*log(1 + e*x))/(27*e^3) + (2/27)*b^2*n^2*x^3*log(1 + e*x) - (2*b*n*(a + b*log(c*x^n))*log(1 + e*x))/(9*e^3) - (2/9)*b*n*x^3*(a + b*log(c*x^n))*log(1 + e*x) + ((a + b*log(c*x^n))^2*log(1 + e*x))/(3*e^3) + (1/3)*x^3*(a + b*log(c*x^n))^2*log(1 + e*x) - (2*b^2*n^2*PolyLog(2, (-e)*x))/(9*e^3) + (2*b*n*(a + b*log(c*x^n))*PolyLog(2, (-e)*x))/(3*e^3) - (2*b^2*n^2*PolyLog(3, (-e)*x))/(3*e^3)]
    @test_int [x^1*(a + b*log(c*x^n))^2*log(1 + e*x), x, 13, -((a*b*n*x)/e) + (7*b^2*n^2*x)/(4*e) - (3/8)*b^2*n^2*x^2 - (b^2*n*x*log(c*x^n))/e - (b*n*x*(a + b*log(c*x^n)))/(2*e) + (1/2)*b*n*x^2*(a + b*log(c*x^n)) + (x*(a + b*log(c*x^n))^2)/(2*e) - (1/4)*x^2*(a + b*log(c*x^n))^2 - (b^2*n^2*log(1 + e*x))/(4*e^2) + (1/4)*b^2*n^2*x^2*log(1 + e*x) + (b*n*(a + b*log(c*x^n))*log(1 + e*x))/(2*e^2) - (1/2)*b*n*x^2*(a + b*log(c*x^n))*log(1 + e*x) - ((a + b*log(c*x^n))^2*log(1 + e*x))/(2*e^2) + (1/2)*x^2*(a + b*log(c*x^n))^2*log(1 + e*x) + (b^2*n^2*PolyLog(2, (-e)*x))/(2*e^2) - (b*n*(a + b*log(c*x^n))*PolyLog(2, (-e)*x))/e^2 + (b^2*n^2*PolyLog(3, (-e)*x))/e^2]
    @test_int [x^0*(a + b*log(c*x^n))^2*log(1 + e*x), x, 14, 2*a*b*n*x - 6*b^2*n^2*x + 2*b^2*n*x*log(c*x^n) + 2*b*n*x*(a + b*log(c*x^n)) - x*(a + b*log(c*x^n))^2 + (2*b^2*n^2*(1 + e*x)*log(1 + e*x))/e - (2*b*n*(1 + e*x)*(a + b*log(c*x^n))*log(1 + e*x))/e + ((1 + e*x)*(a + b*log(c*x^n))^2*log(1 + e*x))/e - (2*b^2*n^2*PolyLog(2, (-e)*x))/e + (2*b*n*(a + b*log(c*x^n))*PolyLog(2, (-e)*x))/e - (2*b^2*n^2*PolyLog(3, (-e)*x))/e]
    @test_int [(a + b*log(c*x^n))^2*log(1 + e*x)/x^1, x, 3, (-(a + b*log(c*x^n))^2)*PolyLog(2, (-e)*x) + 2*b*n*(a + b*log(c*x^n))*PolyLog(3, (-e)*x) - 2*b^2*n^2*PolyLog(4, (-e)*x)]
    @test_int [(a + b*log(c*x^n))^2*log(1 + e*x)/x^2, x, 10, 2*b^2*e*n^2*log(x) - 2*b*e*n*log(1 + 1/(e*x))*(a + b*log(c*x^n)) - e*log(1 + 1/(e*x))*(a + b*log(c*x^n))^2 - 2*b^2*e*n^2*log(1 + e*x) - (2*b^2*n^2*log(1 + e*x))/x - (2*b*n*(a + b*log(c*x^n))*log(1 + e*x))/x - ((a + b*log(c*x^n))^2*log(1 + e*x))/x + 2*b^2*e*n^2*PolyLog(2, -(1/(e*x))) + 2*b*e*n*(a + b*log(c*x^n))*PolyLog(2, -(1/(e*x))) + 2*b^2*e*n^2*PolyLog(3, -(1/(e*x)))]
    @test_int [(a + b*log(c*x^n))^2*log(1 + e*x)/x^3, x, 14, -((7*b^2*e*n^2)/(4*x)) - (1/4)*b^2*e^2*n^2*log(x) - (3*b*e*n*(a + b*log(c*x^n)))/(2*x) + (1/2)*b*e^2*n*log(1 + 1/(e*x))*(a + b*log(c*x^n)) - (e*(a + b*log(c*x^n))^2)/(2*x) + (1/2)*e^2*log(1 + 1/(e*x))*(a + b*log(c*x^n))^2 + (1/4)*b^2*e^2*n^2*log(1 + e*x) - (b^2*n^2*log(1 + e*x))/(4*x^2) - (b*n*(a + b*log(c*x^n))*log(1 + e*x))/(2*x^2) - ((a + b*log(c*x^n))^2*log(1 + e*x))/(2*x^2) - (1/2)*b^2*e^2*n^2*PolyLog(2, -(1/(e*x))) - b*e^2*n*(a + b*log(c*x^n))*PolyLog(2, -(1/(e*x))) - b^2*e^2*n^2*PolyLog(3, -(1/(e*x)))]

    @test_int [x^3*(a + b*log(c*x^n))^3*log(1 + e*x), x, 29, (15*a*b^2*n^2*x)/(8*e^3) - (255*b^3*n^3*x)/(128*e^3) + (45*b^3*n^3*x^2)/(256*e^2) - (175*b^3*n^3*x^3)/(3456*e) + (3/128)*b^3*n^3*x^4 + (15*b^3*n^2*x*log(c*x^n))/(8*e^3) + (3*b^2*n^2*x*(a + b*log(c*x^n)))/(32*e^3) - (21*b^2*n^2*x^2*(a + b*log(c*x^n)))/(64*e^2) + (37*b^2*n^2*x^3*(a + b*log(c*x^n)))/(288*e) - (9/128)*b^2*n^2*x^4*(a + b*log(c*x^n)) - (15*b*n*x*(a + b*log(c*x^n))^2)/(16*e^3) + (9*b*n*x^2*(a + b*log(c*x^n))^2)/(32*e^2) - (7*b*n*x^3*(a + b*log(c*x^n))^2)/(48*e) + (3/32)*b*n*x^4*(a + b*log(c*x^n))^2 + (x*(a + b*log(c*x^n))^3)/(4*e^3) - (x^2*(a + b*log(c*x^n))^3)/(8*e^2) + (x^3*(a + b*log(c*x^n))^3)/(12*e) - (1/16)*x^4*(a + b*log(c*x^n))^3 + (3*b^3*n^3*log(1 + e*x))/(128*e^4) - (3/128)*b^3*n^3*x^4*log(1 + e*x) - (3*b^2*n^2*(a + b*log(c*x^n))*log(1 + e*x))/(32*e^4) + (3/32)*b^2*n^2*x^4*(a + b*log(c*x^n))*log(1 + e*x) + (3*b*n*(a + b*log(c*x^n))^2*log(1 + e*x))/(16*e^4) - (3/16)*b*n*x^4*(a + b*log(c*x^n))^2*log(1 + e*x) - ((a + b*log(c*x^n))^3*log(1 + e*x))/(4*e^4) + (1/4)*x^4*(a + b*log(c*x^n))^3*log(1 + e*x) - (3*b^3*n^3*PolyLog(2, (-e)*x))/(32*e^4) + (3*b^2*n^2*(a + b*log(c*x^n))*PolyLog(2, (-e)*x))/(8*e^4) - (3*b*n*(a + b*log(c*x^n))^2*PolyLog(2, (-e)*x))/(4*e^4) - (3*b^3*n^3*PolyLog(3, (-e)*x))/(8*e^4) + (3*b^2*n^2*(a + b*log(c*x^n))*PolyLog(3, (-e)*x))/(2*e^4) - (3*b^3*n^3*PolyLog(4, (-e)*x))/(2*e^4)]
    @test_int [x^2*(a + b*log(c*x^n))^3*log(1 + e*x), x, 26, -((8*a*b^2*n^2*x)/(3*e^2)) + (80*b^3*n^3*x)/(27*e^2) - (65*b^3*n^3*x^2)/(216*e) + (8/81)*b^3*n^3*x^3 - (8*b^3*n^2*x*log(c*x^n))/(3*e^2) - (2*b^2*n^2*x*(a + b*log(c*x^n)))/(9*e^2) + (19*b^2*n^2*x^2*(a + b*log(c*x^n)))/(36*e) - (2/9)*b^2*n^2*x^3*(a + b*log(c*x^n)) + (4*b*n*x*(a + b*log(c*x^n))^2)/(3*e^2) - (5*b*n*x^2*(a + b*log(c*x^n))^2)/(12*e) + (2/9)*b*n*x^3*(a + b*log(c*x^n))^2 - (x*(a + b*log(c*x^n))^3)/(3*e^2) + (x^2*(a + b*log(c*x^n))^3)/(6*e) - (1/9)*x^3*(a + b*log(c*x^n))^3 - (2*b^3*n^3*log(1 + e*x))/(27*e^3) - (2/27)*b^3*n^3*x^3*log(1 + e*x) + (2*b^2*n^2*(a + b*log(c*x^n))*log(1 + e*x))/(9*e^3) + (2/9)*b^2*n^2*x^3*(a + b*log(c*x^n))*log(1 + e*x) - (b*n*(a + b*log(c*x^n))^2*log(1 + e*x))/(3*e^3) - (1/3)*b*n*x^3*(a + b*log(c*x^n))^2*log(1 + e*x) + ((a + b*log(c*x^n))^3*log(1 + e*x))/(3*e^3) + (1/3)*x^3*(a + b*log(c*x^n))^3*log(1 + e*x) + (2*b^3*n^3*PolyLog(2, (-e)*x))/(9*e^3) - (2*b^2*n^2*(a + b*log(c*x^n))*PolyLog(2, (-e)*x))/(3*e^3) + (b*n*(a + b*log(c*x^n))^2*PolyLog(2, (-e)*x))/e^3 + (2*b^3*n^3*PolyLog(3, (-e)*x))/(3*e^3) - (2*b^2*n^2*(a + b*log(c*x^n))*PolyLog(3, (-e)*x))/e^3 + (2*b^3*n^3*PolyLog(4, (-e)*x))/e^3]
    @test_int [x^1*(a + b*log(c*x^n))^3*log(1 + e*x), x, 23, (9*a*b^2*n^2*x)/(2*e) - (45*b^3*n^3*x)/(8*e) + (3/4)*b^3*n^3*x^2 + (9*b^3*n^2*x*log(c*x^n))/(2*e) + (3*b^2*n^2*x*(a + b*log(c*x^n)))/(4*e) - (9/8)*b^2*n^2*x^2*(a + b*log(c*x^n)) - (9*b*n*x*(a + b*log(c*x^n))^2)/(4*e) + (3/4)*b*n*x^2*(a + b*log(c*x^n))^2 + (x*(a + b*log(c*x^n))^3)/(2*e) - (1/4)*x^2*(a + b*log(c*x^n))^3 + (3*b^3*n^3*log(1 + e*x))/(8*e^2) - (3/8)*b^3*n^3*x^2*log(1 + e*x) - (3*b^2*n^2*(a + b*log(c*x^n))*log(1 + e*x))/(4*e^2) + (3/4)*b^2*n^2*x^2*(a + b*log(c*x^n))*log(1 + e*x) + (3*b*n*(a + b*log(c*x^n))^2*log(1 + e*x))/(4*e^2) - (3/4)*b*n*x^2*(a + b*log(c*x^n))^2*log(1 + e*x) - ((a + b*log(c*x^n))^3*log(1 + e*x))/(2*e^2) + (1/2)*x^2*(a + b*log(c*x^n))^3*log(1 + e*x) - (3*b^3*n^3*PolyLog(2, (-e)*x))/(4*e^2) + (3*b^2*n^2*(a + b*log(c*x^n))*PolyLog(2, (-e)*x))/(2*e^2) - (3*b*n*(a + b*log(c*x^n))^2*PolyLog(2, (-e)*x))/(2*e^2) - (3*b^3*n^3*PolyLog(3, (-e)*x))/(2*e^2) + (3*b^2*n^2*(a + b*log(c*x^n))*PolyLog(3, (-e)*x))/e^2 - (3*b^3*n^3*PolyLog(4, (-e)*x))/e^2]
    @test_int [x^0*(a + b*log(c*x^n))^3*log(1 + e*x), x, 24, -12*a*b^2*n^2*x + 24*b^3*n^3*x - 12*b^3*n^2*x*log(c*x^n) - 6*b^2*n^2*x*(a + b*log(c*x^n)) + 6*b*n*x*(a + b*log(c*x^n))^2 - x*(a + b*log(c*x^n))^3 - (6*b^3*n^3*(1 + e*x)*log(1 + e*x))/e + (6*b^2*n^2*(1 + e*x)*(a + b*log(c*x^n))*log(1 + e*x))/e - (3*b*n*(1 + e*x)*(a + b*log(c*x^n))^2*log(1 + e*x))/e + ((1 + e*x)*(a + b*log(c*x^n))^3*log(1 + e*x))/e + (6*b^3*n^3*PolyLog(2, (-e)*x))/e - (6*b^2*n^2*(a + b*log(c*x^n))*PolyLog(2, (-e)*x))/e + (3*b*n*(a + b*log(c*x^n))^2*PolyLog(2, (-e)*x))/e + (6*b^3*n^3*PolyLog(3, (-e)*x))/e - (6*b^2*n^2*(a + b*log(c*x^n))*PolyLog(3, (-e)*x))/e + (6*b^3*n^3*PolyLog(4, (-e)*x))/e]
    @test_int [(a + b*log(c*x^n))^3*log(1 + e*x)/x^1, x, 4, (-(a + b*log(c*x^n))^3)*PolyLog(2, (-e)*x) + 3*b*n*(a + b*log(c*x^n))^2*PolyLog(3, (-e)*x) - 6*b^2*n^2*(a + b*log(c*x^n))*PolyLog(4, (-e)*x) + 6*b^3*n^3*PolyLog(5, (-e)*x)]
    @test_int [(a + b*log(c*x^n))^3*log(1 + e*x)/x^2, x, 14, 6*b^3*e*n^3*log(x) - 6*b^2*e*n^2*log(1 + 1/(e*x))*(a + b*log(c*x^n)) - 3*b*e*n*log(1 + 1/(e*x))*(a + b*log(c*x^n))^2 - e*log(1 + 1/(e*x))*(a + b*log(c*x^n))^3 - 6*b^3*e*n^3*log(1 + e*x) - (6*b^3*n^3*log(1 + e*x))/x - (6*b^2*n^2*(a + b*log(c*x^n))*log(1 + e*x))/x - (3*b*n*(a + b*log(c*x^n))^2*log(1 + e*x))/x - ((a + b*log(c*x^n))^3*log(1 + e*x))/x + 6*b^3*e*n^3*PolyLog(2, -(1/(e*x))) + 6*b^2*e*n^2*(a + b*log(c*x^n))*PolyLog(2, -(1/(e*x))) + 3*b*e*n*(a + b*log(c*x^n))^2*PolyLog(2, -(1/(e*x))) + 6*b^3*e*n^3*PolyLog(3, -(1/(e*x))) + 6*b^2*e*n^2*(a + b*log(c*x^n))*PolyLog(3, -(1/(e*x))) + 6*b^3*e*n^3*PolyLog(4, -(1/(e*x)))]
    @test_int [(a + b*log(c*x^n))^3*log(1 + e*x)/x^3, x, 22, -((45*b^3*e*n^3)/(8*x)) - (3/8)*b^3*e^2*n^3*log(x) - (21*b^2*e*n^2*(a + b*log(c*x^n)))/(4*x) + (3/4)*b^2*e^2*n^2*log(1 + 1/(e*x))*(a + b*log(c*x^n)) - (9*b*e*n*(a + b*log(c*x^n))^2)/(4*x) + (3/4)*b*e^2*n*log(1 + 1/(e*x))*(a + b*log(c*x^n))^2 - (e*(a + b*log(c*x^n))^3)/(2*x) + (1/2)*e^2*log(1 + 1/(e*x))*(a + b*log(c*x^n))^3 + (3/8)*b^3*e^2*n^3*log(1 + e*x) - (3*b^3*n^3*log(1 + e*x))/(8*x^2) - (3*b^2*n^2*(a + b*log(c*x^n))*log(1 + e*x))/(4*x^2) - (3*b*n*(a + b*log(c*x^n))^2*log(1 + e*x))/(4*x^2) - ((a + b*log(c*x^n))^3*log(1 + e*x))/(2*x^2) - (3/4)*b^3*e^2*n^3*PolyLog(2, -(1/(e*x))) - (3/2)*b^2*e^2*n^2*(a + b*log(c*x^n))*PolyLog(2, -(1/(e*x))) - (3/2)*b*e^2*n*(a + b*log(c*x^n))^2*PolyLog(2, -(1/(e*x))) - (3/2)*b^3*e^2*n^3*PolyLog(3, -(1/(e*x))) - 3*b^2*e^2*n^2*(a + b*log(c*x^n))*PolyLog(3, -(1/(e*x))) - 3*b^3*e^2*n^3*PolyLog(4, -(1/(e*x)))]

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

    @test_int [x^3*(a + b*log(c*x^n))*log(d*(1/d + f*x^2)), x, 7, -((3*b*n*x^2)/(16*d*f)) + (1/16)*b*n*x^4 + (x^2*(a + b*log(c*x^n)))/(4*d*f) - (1/8)*x^4*(a + b*log(c*x^n)) + (b*n*log(1 + d*f*x^2))/(16*d^2*f^2) - (1/16)*b*n*x^4*log(1 + d*f*x^2) - ((a + b*log(c*x^n))*log(1 + d*f*x^2))/(4*d^2*f^2) + (1/4)*x^4*(a + b*log(c*x^n))*log(1 + d*f*x^2) - (b*n*PolyLog(2, (-d)*f*x^2))/(8*d^2*f^2)]
    @test_int [x^1*(a + b*log(c*x^n))*log(d*(1/d + f*x^2)), x, 8, (1/2)*b*n*x^2 - (1/2)*x^2*(a + b*log(c*x^n)) - (b*n*(1 + d*f*x^2)*log(1 + d*f*x^2))/(4*d*f) + ((1 + d*f*x^2)*(a + b*log(c*x^n))*log(1 + d*f*x^2))/(2*d*f) + (b*n*PolyLog(2, (-d)*f*x^2))/(4*d*f)]
    @test_int [(a + b*log(c*x^n))*log(d*(1/d + f*x^2))/x^1, x, 2, (-(1/2))*(a + b*log(c*x^n))*PolyLog(2, (-d)*f*x^2) + (1/4)*b*n*PolyLog(3, (-d)*f*x^2)]
    @test_int [(a + b*log(c*x^n))*log(d*(1/d + f*x^2))/x^3, x, 9, (1/2)*b*d*f*n*log(x) - (1/2)*b*d*f*n*log(x)^2 + d*f*log(x)*(a + b*log(c*x^n)) - (1/4)*b*d*f*n*log(1 + d*f*x^2) - (b*n*log(1 + d*f*x^2))/(4*x^2) - (1/2)*d*f*(a + b*log(c*x^n))*log(1 + d*f*x^2) - ((a + b*log(c*x^n))*log(1 + d*f*x^2))/(2*x^2) - (1/4)*b*d*f*n*PolyLog(2, (-d)*f*x^2)]

    @test_int [x^2*(a + b*log(c*x^n))*log(d*(1/d + f*x^2)), x, 9, -((8*b*n*x)/(9*d*f)) + (4/27)*b*n*x^3 + (2*b*n*atan(sqrt(d)*sqrt(f)*x))/(9*d^(3/2)*f^(3/2)) + (2*x*(a + b*log(c*x^n)))/(3*d*f) - (2/9)*x^3*(a + b*log(c*x^n)) - (2*atan(sqrt(d)*sqrt(f)*x)*(a + b*log(c*x^n)))/(3*d^(3/2)*f^(3/2)) - (1/9)*b*n*x^3*log(1 + d*f*x^2) + (1/3)*x^3*(a + b*log(c*x^n))*log(1 + d*f*x^2) + (im*b*n*PolyLog(2, (-im)*sqrt(d)*sqrt(f)*x))/(3*d^(3/2)*f^(3/2)) - (im*b*n*PolyLog(2, im*sqrt(d)*sqrt(f)*x))/(3*d^(3/2)*f^(3/2))]
    @test_int [x^0*(a + b*log(c*x^n))*log(d*(1/d + f*x^2)), x, 8, 4*b*n*x - (2*b*n*atan(sqrt(d)*sqrt(f)*x))/(sqrt(d)*sqrt(f)) - 2*x*(a + b*log(c*x^n)) + (2*atan(sqrt(d)*sqrt(f)*x)*(a + b*log(c*x^n)))/(sqrt(d)*sqrt(f)) - b*n*x*log(1 + d*f*x^2) + x*(a + b*log(c*x^n))*log(1 + d*f*x^2) - (im*b*n*PolyLog(2, (-im)*sqrt(d)*sqrt(f)*x))/(sqrt(d)*sqrt(f)) + (im*b*n*PolyLog(2, im*sqrt(d)*sqrt(f)*x))/(sqrt(d)*sqrt(f))]
    @test_int [(a + b*log(c*x^n))*log(d*(1/d + f*x^2))/x^2, x, 7, 2*b*sqrt(d)*sqrt(f)*n*atan(sqrt(d)*sqrt(f)*x) + 2*sqrt(d)*sqrt(f)*atan(sqrt(d)*sqrt(f)*x)*(a + b*log(c*x^n)) - (b*n*log(1 + d*f*x^2))/x - ((a + b*log(c*x^n))*log(1 + d*f*x^2))/x - im*b*sqrt(d)*sqrt(f)*n*PolyLog(2, (-im)*sqrt(d)*sqrt(f)*x) + im*b*sqrt(d)*sqrt(f)*n*PolyLog(2, im*sqrt(d)*sqrt(f)*x)]
    @test_int [(a + b*log(c*x^n))*log(d*(1/d + f*x^2))/x^4, x, 8, -((8*b*d*f*n)/(9*x)) - (2/9)*b*d^(3/2)*f^(3/2)*n*atan(sqrt(d)*sqrt(f)*x) - (2*d*f*(a + b*log(c*x^n)))/(3*x) - (2/3)*d^(3/2)*f^(3/2)*atan(sqrt(d)*sqrt(f)*x)*(a + b*log(c*x^n)) - (b*n*log(1 + d*f*x^2))/(9*x^3) - ((a + b*log(c*x^n))*log(1 + d*f*x^2))/(3*x^3) + (1/3)*im*b*d^(3/2)*f^(3/2)*n*PolyLog(2, (-im)*sqrt(d)*sqrt(f)*x) - (1/3)*im*b*d^(3/2)*f^(3/2)*n*PolyLog(2, im*sqrt(d)*sqrt(f)*x)]

    @test_int [x^3*(a + b*log(c*x^n))^2*log(d*(1/d + f*x^2)), x, 13, (7*b^2*n^2*x^2)/(32*d*f) - (3/64)*b^2*n^2*x^4 - (3*b*n*x^2*(a + b*log(c*x^n)))/(8*d*f) + (1/8)*b*n*x^4*(a + b*log(c*x^n)) + (x^2*(a + b*log(c*x^n))^2)/(4*d*f) - (1/8)*x^4*(a + b*log(c*x^n))^2 - (b^2*n^2*log(1 + d*f*x^2))/(32*d^2*f^2) + (1/32)*b^2*n^2*x^4*log(1 + d*f*x^2) + (b*n*(a + b*log(c*x^n))*log(1 + d*f*x^2))/(8*d^2*f^2) - (1/8)*b*n*x^4*(a + b*log(c*x^n))*log(1 + d*f*x^2) - ((a + b*log(c*x^n))^2*log(1 + d*f*x^2))/(4*d^2*f^2) + (1/4)*x^4*(a + b*log(c*x^n))^2*log(1 + d*f*x^2) + (b^2*n^2*PolyLog(2, (-d)*f*x^2))/(16*d^2*f^2) - (b*n*(a + b*log(c*x^n))*PolyLog(2, (-d)*f*x^2))/(4*d^2*f^2) + (b^2*n^2*PolyLog(3, (-d)*f*x^2))/(8*d^2*f^2)]
    @test_int [x^1*(a + b*log(c*x^n))^2*log(d*(1/d + f*x^2)), x, 15, (-(3/4))*b^2*n^2*x^2 + b*n*x^2*(a + b*log(c*x^n)) - (1/2)*x^2*(a + b*log(c*x^n))^2 + (b^2*n^2*(1 + d*f*x^2)*log(1 + d*f*x^2))/(4*d*f) - (b*n*(1 + d*f*x^2)*(a + b*log(c*x^n))*log(1 + d*f*x^2))/(2*d*f) + ((1 + d*f*x^2)*(a + b*log(c*x^n))^2*log(1 + d*f*x^2))/(2*d*f) - (b^2*n^2*PolyLog(2, (-d)*f*x^2))/(4*d*f) + (b*n*(a + b*log(c*x^n))*PolyLog(2, (-d)*f*x^2))/(2*d*f) - (b^2*n^2*PolyLog(3, (-d)*f*x^2))/(4*d*f)]
    @test_int [(a + b*log(c*x^n))^2*log(d*(1/d + f*x^2))/x^1, x, 3, (-(1/2))*(a + b*log(c*x^n))^2*PolyLog(2, (-d)*f*x^2) + (1/2)*b*n*(a + b*log(c*x^n))*PolyLog(3, (-d)*f*x^2) - (1/4)*b^2*n^2*PolyLog(4, (-d)*f*x^2)]
    @test_int [(a + b*log(c*x^n))^2*log(d*(1/d + f*x^2))/x^3, x, 11, (1/2)*b^2*d*f*n^2*log(x) - (1/2)*b*d*f*n*log(1 + 1/(d*f*x^2))*(a + b*log(c*x^n)) - (1/2)*d*f*log(1 + 1/(d*f*x^2))*(a + b*log(c*x^n))^2 - (1/4)*b^2*d*f*n^2*log(1 + d*f*x^2) - (b^2*n^2*log(1 + d*f*x^2))/(4*x^2) - (b*n*(a + b*log(c*x^n))*log(1 + d*f*x^2))/(2*x^2) - ((a + b*log(c*x^n))^2*log(1 + d*f*x^2))/(2*x^2) + (1/4)*b^2*d*f*n^2*PolyLog(2, -(1/(d*f*x^2))) + (1/2)*b*d*f*n*(a + b*log(c*x^n))*PolyLog(2, -(1/(d*f*x^2))) + (1/4)*b^2*d*f*n^2*PolyLog(3, -(1/(d*f*x^2)))]

    @test_int [x^2*(a + b*log(c*x^n))^2*log(d*(1/d + f*x^2)), x, 30, -((16*a*b*n*x)/(9*d*f)) + (52*b^2*n^2*x)/(27*d*f) - (4/27)*b^2*n^2*x^3 - (4*b^2*n^2*atan(sqrt(d)*sqrt(f)*x))/(27*d^(3/2)*f^(3/2)) - (16*b^2*n*x*log(c*x^n))/(9*d*f) + (8/27)*b*n*x^3*(a + b*log(c*x^n)) + (4*b*n*atan(sqrt(d)*sqrt(f)*x)*(a + b*log(c*x^n)))/(9*d^(3/2)*f^(3/2)) + (2*x*(a + b*log(c*x^n))^2)/(3*d*f) - (2/9)*x^3*(a + b*log(c*x^n))^2 - ((a + b*log(c*x^n))^2*log(1 - sqrt(-d)*sqrt(f)*x))/(3*(-d)^(3/2)*f^(3/2)) + ((a + b*log(c*x^n))^2*log(1 + sqrt(-d)*sqrt(f)*x))/(3*(-d)^(3/2)*f^(3/2)) + (2/27)*b^2*n^2*x^3*log(1 + d*f*x^2) - (2/9)*b*n*x^3*(a + b*log(c*x^n))*log(1 + d*f*x^2) + (1/3)*x^3*(a + b*log(c*x^n))^2*log(1 + d*f*x^2) + (2*b*n*(a + b*log(c*x^n))*PolyLog(2, (-sqrt(-d))*sqrt(f)*x))/(3*(-d)^(3/2)*f^(3/2)) - (2*b*n*(a + b*log(c*x^n))*PolyLog(2, sqrt(-d)*sqrt(f)*x))/(3*(-d)^(3/2)*f^(3/2)) - (2*im*b^2*n^2*PolyLog(2, (-im)*sqrt(d)*sqrt(f)*x))/(9*d^(3/2)*f^(3/2)) + (2*im*b^2*n^2*PolyLog(2, im*sqrt(d)*sqrt(f)*x))/(9*d^(3/2)*f^(3/2)) - (2*b^2*n^2*PolyLog(3, (-sqrt(-d))*sqrt(f)*x))/(3*(-d)^(3/2)*f^(3/2)) + (2*b^2*n^2*PolyLog(3, sqrt(-d)*sqrt(f)*x))/(3*(-d)^(3/2)*f^(3/2))]
    @test_int [x^0*(a + b*log(c*x^n))^2*log(d*(1/d + f*x^2)), x, 26, 4*a*b*n*x - 8*b^2*n^2*x + 4*b*n*(a - b*n)*x - (4*b*n*(a - b*n)*atan(sqrt(d)*sqrt(f)*x))/(sqrt(d)*sqrt(f)) + 8*b^2*n*x*log(c*x^n) - (4*b^2*n*atan(sqrt(d)*sqrt(f)*x)*log(c*x^n))/(sqrt(d)*sqrt(f)) - 2*x*(a + b*log(c*x^n))^2 - ((a + b*log(c*x^n))^2*log(1 - sqrt(-d)*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) + ((a + b*log(c*x^n))^2*log(1 + sqrt(-d)*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) - 2*a*b*n*x*log(1 + d*f*x^2) + 2*b^2*n^2*x*log(1 + d*f*x^2) - 2*b^2*n*x*log(c*x^n)*log(1 + d*f*x^2) + x*(a + b*log(c*x^n))^2*log(1 + d*f*x^2) + (2*b*n*(a + b*log(c*x^n))*PolyLog(2, (-sqrt(-d))*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) - (2*b*n*(a + b*log(c*x^n))*PolyLog(2, sqrt(-d)*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) + (2*im*b^2*n^2*PolyLog(2, (-im)*sqrt(d)*sqrt(f)*x))/(sqrt(d)*sqrt(f)) - (2*im*b^2*n^2*PolyLog(2, im*sqrt(d)*sqrt(f)*x))/(sqrt(d)*sqrt(f)) - (2*b^2*n^2*PolyLog(3, (-sqrt(-d))*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) + (2*b^2*n^2*PolyLog(3, sqrt(-d)*sqrt(f)*x))/(sqrt(-d)*sqrt(f))]
    @test_int [(a + b*log(c*x^n))^2*log(d*(1/d + f*x^2))/x^2, x, 16, 4*b^2*sqrt(d)*sqrt(f)*n^2*atan(sqrt(d)*sqrt(f)*x) + 4*b*sqrt(d)*sqrt(f)*n*atan(sqrt(d)*sqrt(f)*x)*(a + b*log(c*x^n)) + sqrt(-d)*sqrt(f)*(a + b*log(c*x^n))^2*log(1 - sqrt(-d)*sqrt(f)*x) - sqrt(-d)*sqrt(f)*(a + b*log(c*x^n))^2*log(1 + sqrt(-d)*sqrt(f)*x) - (2*b^2*n^2*log(1 + d*f*x^2))/x - (2*b*n*(a + b*log(c*x^n))*log(1 + d*f*x^2))/x - ((a + b*log(c*x^n))^2*log(1 + d*f*x^2))/x - 2*b*sqrt(-d)*sqrt(f)*n*(a + b*log(c*x^n))*PolyLog(2, (-sqrt(-d))*sqrt(f)*x) + 2*b*sqrt(-d)*sqrt(f)*n*(a + b*log(c*x^n))*PolyLog(2, sqrt(-d)*sqrt(f)*x) - 2*im*b^2*sqrt(d)*sqrt(f)*n^2*PolyLog(2, (-im)*sqrt(d)*sqrt(f)*x) + 2*im*b^2*sqrt(d)*sqrt(f)*n^2*PolyLog(2, im*sqrt(d)*sqrt(f)*x) + 2*b^2*sqrt(-d)*sqrt(f)*n^2*PolyLog(3, (-sqrt(-d))*sqrt(f)*x) - 2*b^2*sqrt(-d)*sqrt(f)*n^2*PolyLog(3, sqrt(-d)*sqrt(f)*x)]
    @test_int [(a + b*log(c*x^n))^2*log(d*(1/d + f*x^2))/x^4, x, 22, -((52*b^2*d*f*n^2)/(27*x)) - (4/27)*b^2*d^(3/2)*f^(3/2)*n^2*atan(sqrt(d)*sqrt(f)*x) - (16*b*d*f*n*(a + b*log(c*x^n)))/(9*x) - (4/9)*b*d^(3/2)*f^(3/2)*n*atan(sqrt(d)*sqrt(f)*x)*(a + b*log(c*x^n)) - (2*d*f*(a + b*log(c*x^n))^2)/(3*x) + (1/3)*(-d)^(3/2)*f^(3/2)*(a + b*log(c*x^n))^2*log(1 - sqrt(-d)*sqrt(f)*x) - (1/3)*(-d)^(3/2)*f^(3/2)*(a + b*log(c*x^n))^2*log(1 + sqrt(-d)*sqrt(f)*x) - (2*b^2*n^2*log(1 + d*f*x^2))/(27*x^3) - (2*b*n*(a + b*log(c*x^n))*log(1 + d*f*x^2))/(9*x^3) - ((a + b*log(c*x^n))^2*log(1 + d*f*x^2))/(3*x^3) - (2/3)*b*(-d)^(3/2)*f^(3/2)*n*(a + b*log(c*x^n))*PolyLog(2, (-sqrt(-d))*sqrt(f)*x) + (2/3)*b*(-d)^(3/2)*f^(3/2)*n*(a + b*log(c*x^n))*PolyLog(2, sqrt(-d)*sqrt(f)*x) + (2/9)*im*b^2*d^(3/2)*f^(3/2)*n^2*PolyLog(2, (-im)*sqrt(d)*sqrt(f)*x) - (2/9)*im*b^2*d^(3/2)*f^(3/2)*n^2*PolyLog(2, im*sqrt(d)*sqrt(f)*x) + (2/3)*b^2*(-d)^(3/2)*f^(3/2)*n^2*PolyLog(3, (-sqrt(-d))*sqrt(f)*x) - (2/3)*b^2*(-d)^(3/2)*f^(3/2)*n^2*PolyLog(3, sqrt(-d)*sqrt(f)*x)]

    @test_int [x^3*(a + b*log(c*x^n))^3*log(d*(1/d + f*x^2)), x, 22, -((45*b^3*n^3*x^2)/(128*d*f)) + (3/64)*b^3*n^3*x^4 + (21*b^2*n^2*x^2*(a + b*log(c*x^n)))/(32*d*f) - (9/64)*b^2*n^2*x^4*(a + b*log(c*x^n)) - (9*b*n*x^2*(a + b*log(c*x^n))^2)/(16*d*f) + (3/16)*b*n*x^4*(a + b*log(c*x^n))^2 + (x^2*(a + b*log(c*x^n))^3)/(4*d*f) - (1/8)*x^4*(a + b*log(c*x^n))^3 + (3*b^3*n^3*log(1 + d*f*x^2))/(128*d^2*f^2) - (3/128)*b^3*n^3*x^4*log(1 + d*f*x^2) - (3*b^2*n^2*(a + b*log(c*x^n))*log(1 + d*f*x^2))/(32*d^2*f^2) + (3/32)*b^2*n^2*x^4*(a + b*log(c*x^n))*log(1 + d*f*x^2) + (3*b*n*(a + b*log(c*x^n))^2*log(1 + d*f*x^2))/(16*d^2*f^2) - (3/16)*b*n*x^4*(a + b*log(c*x^n))^2*log(1 + d*f*x^2) - ((a + b*log(c*x^n))^3*log(1 + d*f*x^2))/(4*d^2*f^2) + (1/4)*x^4*(a + b*log(c*x^n))^3*log(1 + d*f*x^2) - (3*b^3*n^3*PolyLog(2, (-d)*f*x^2))/(64*d^2*f^2) + (3*b^2*n^2*(a + b*log(c*x^n))*PolyLog(2, (-d)*f*x^2))/(16*d^2*f^2) - (3*b*n*(a + b*log(c*x^n))^2*PolyLog(2, (-d)*f*x^2))/(8*d^2*f^2) - (3*b^3*n^3*PolyLog(3, (-d)*f*x^2))/(32*d^2*f^2) + (3*b^2*n^2*(a + b*log(c*x^n))*PolyLog(3, (-d)*f*x^2))/(8*d^2*f^2) - (3*b^3*n^3*PolyLog(4, (-d)*f*x^2))/(16*d^2*f^2)]
    @test_int [x^1*(a + b*log(c*x^n))^3*log(d*(1/d + f*x^2)), x, 24, (3/2)*b^3*n^3*x^2 - (9/4)*b^2*n^2*x^2*(a + b*log(c*x^n)) + (3/2)*b*n*x^2*(a + b*log(c*x^n))^2 - (1/2)*x^2*(a + b*log(c*x^n))^3 - (3*b^3*n^3*(1 + d*f*x^2)*log(1 + d*f*x^2))/(8*d*f) + (3*b^2*n^2*(1 + d*f*x^2)*(a + b*log(c*x^n))*log(1 + d*f*x^2))/(4*d*f) - (3*b*n*(1 + d*f*x^2)*(a + b*log(c*x^n))^2*log(1 + d*f*x^2))/(4*d*f) + ((1 + d*f*x^2)*(a + b*log(c*x^n))^3*log(1 + d*f*x^2))/(2*d*f) + (3*b^3*n^3*PolyLog(2, (-d)*f*x^2))/(8*d*f) - (3*b^2*n^2*(a + b*log(c*x^n))*PolyLog(2, (-d)*f*x^2))/(4*d*f) + (3*b*n*(a + b*log(c*x^n))^2*PolyLog(2, (-d)*f*x^2))/(4*d*f) + (3*b^3*n^3*PolyLog(3, (-d)*f*x^2))/(8*d*f) - (3*b^2*n^2*(a + b*log(c*x^n))*PolyLog(3, (-d)*f*x^2))/(4*d*f) + (3*b^3*n^3*PolyLog(4, (-d)*f*x^2))/(8*d*f)]
    @test_int [(a + b*log(c*x^n))^3*log(d*(1/d + f*x^2))/x^1, x, 4, (-(1/2))*(a + b*log(c*x^n))^3*PolyLog(2, (-d)*f*x^2) + (3/4)*b*n*(a + b*log(c*x^n))^2*PolyLog(3, (-d)*f*x^2) - (3/4)*b^2*n^2*(a + b*log(c*x^n))*PolyLog(4, (-d)*f*x^2) + (3/8)*b^3*n^3*PolyLog(5, (-d)*f*x^2)]
    @test_int [(a + b*log(c*x^n))^3*log(d*(1/d + f*x^2))/x^3, x, 15, (3/4)*b^3*d*f*n^3*log(x) - (3/4)*b^2*d*f*n^2*log(1 + 1/(d*f*x^2))*(a + b*log(c*x^n)) - (3/4)*b*d*f*n*log(1 + 1/(d*f*x^2))*(a + b*log(c*x^n))^2 - (1/2)*d*f*log(1 + 1/(d*f*x^2))*(a + b*log(c*x^n))^3 - (3/8)*b^3*d*f*n^3*log(1 + d*f*x^2) - (3*b^3*n^3*log(1 + d*f*x^2))/(8*x^2) - (3*b^2*n^2*(a + b*log(c*x^n))*log(1 + d*f*x^2))/(4*x^2) - (3*b*n*(a + b*log(c*x^n))^2*log(1 + d*f*x^2))/(4*x^2) - ((a + b*log(c*x^n))^3*log(1 + d*f*x^2))/(2*x^2) + (3/8)*b^3*d*f*n^3*PolyLog(2, -(1/(d*f*x^2))) + (3/4)*b^2*d*f*n^2*(a + b*log(c*x^n))*PolyLog(2, -(1/(d*f*x^2))) + (3/4)*b*d*f*n*(a + b*log(c*x^n))^2*PolyLog(2, -(1/(d*f*x^2))) + (3/8)*b^3*d*f*n^3*PolyLog(3, -(1/(d*f*x^2))) + (3/4)*b^2*d*f*n^2*(a + b*log(c*x^n))*PolyLog(3, -(1/(d*f*x^2))) + (3/8)*b^3*d*f*n^3*PolyLog(4, -(1/(d*f*x^2)))]

    @test_int [x^0*(a + b*log(c*x^n))^3*log(d*(1/d + f*x^2)), x, 42, -24*a*b^2*n^2*x + 36*b^3*n^3*x - 12*b^2*n^2*(a - b*n)*x + (12*b^2*n^2*(a - b*n)*atan(sqrt(d)*sqrt(f)*x))/(sqrt(d)*sqrt(f)) - 36*b^3*n^2*x*log(c*x^n) + (12*b^3*n^2*atan(sqrt(d)*sqrt(f)*x)*log(c*x^n))/(sqrt(d)*sqrt(f)) + 12*b*n*x*(a + b*log(c*x^n))^2 - 2*x*(a + b*log(c*x^n))^3 + (3*b*n*(a + b*log(c*x^n))^2*log(1 - sqrt(-d)*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) - ((a + b*log(c*x^n))^3*log(1 - sqrt(-d)*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) - (3*b*n*(a + b*log(c*x^n))^2*log(1 + sqrt(-d)*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) + ((a + b*log(c*x^n))^3*log(1 + sqrt(-d)*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) + 6*a*b^2*n^2*x*log(1 + d*f*x^2) - 6*b^3*n^3*x*log(1 + d*f*x^2) + 6*b^3*n^2*x*log(c*x^n)*log(1 + d*f*x^2) - 3*b*n*x*(a + b*log(c*x^n))^2*log(1 + d*f*x^2) + x*(a + b*log(c*x^n))^3*log(1 + d*f*x^2) - (6*b^2*n^2*(a + b*log(c*x^n))*PolyLog(2, (-sqrt(-d))*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) + (3*b*n*(a + b*log(c*x^n))^2*PolyLog(2, (-sqrt(-d))*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) + (6*b^2*n^2*(a + b*log(c*x^n))*PolyLog(2, sqrt(-d)*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) - (3*b*n*(a + b*log(c*x^n))^2*PolyLog(2, sqrt(-d)*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) - (6*im*b^3*n^3*PolyLog(2, (-im)*sqrt(d)*sqrt(f)*x))/(sqrt(d)*sqrt(f)) + (6*im*b^3*n^3*PolyLog(2, im*sqrt(d)*sqrt(f)*x))/(sqrt(d)*sqrt(f)) + (6*b^3*n^3*PolyLog(3, (-sqrt(-d))*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) - (6*b^2*n^2*(a + b*log(c*x^n))*PolyLog(3, (-sqrt(-d))*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) - (6*b^3*n^3*PolyLog(3, sqrt(-d)*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) + (6*b^2*n^2*(a + b*log(c*x^n))*PolyLog(3, sqrt(-d)*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) + (6*b^3*n^3*PolyLog(4, (-sqrt(-d))*sqrt(f)*x))/(sqrt(-d)*sqrt(f)) - (6*b^3*n^3*PolyLog(4, sqrt(-d)*sqrt(f)*x))/(sqrt(-d)*sqrt(f))]
    @test_int [(a + b*log(c*x^n))^3*log(d*(1/d + f*x^2))/x^2, x, 26, 12*b^3*sqrt(d)*sqrt(f)*n^3*atan(sqrt(d)*sqrt(f)*x) + 12*b^2*sqrt(d)*sqrt(f)*n^2*atan(sqrt(d)*sqrt(f)*x)*(a + b*log(c*x^n)) + 3*b*sqrt(-d)*sqrt(f)*n*(a + b*log(c*x^n))^2*log(1 - sqrt(-d)*sqrt(f)*x) + sqrt(-d)*sqrt(f)*(a + b*log(c*x^n))^3*log(1 - sqrt(-d)*sqrt(f)*x) - 3*b*sqrt(-d)*sqrt(f)*n*(a + b*log(c*x^n))^2*log(1 + sqrt(-d)*sqrt(f)*x) - sqrt(-d)*sqrt(f)*(a + b*log(c*x^n))^3*log(1 + sqrt(-d)*sqrt(f)*x) - (6*b^3*n^3*log(1 + d*f*x^2))/x - (6*b^2*n^2*(a + b*log(c*x^n))*log(1 + d*f*x^2))/x - (3*b*n*(a + b*log(c*x^n))^2*log(1 + d*f*x^2))/x - ((a + b*log(c*x^n))^3*log(1 + d*f*x^2))/x - 6*b^2*sqrt(-d)*sqrt(f)*n^2*(a + b*log(c*x^n))*PolyLog(2, (-sqrt(-d))*sqrt(f)*x) - 3*b*sqrt(-d)*sqrt(f)*n*(a + b*log(c*x^n))^2*PolyLog(2, (-sqrt(-d))*sqrt(f)*x) + 6*b^2*sqrt(-d)*sqrt(f)*n^2*(a + b*log(c*x^n))*PolyLog(2, sqrt(-d)*sqrt(f)*x) + 3*b*sqrt(-d)*sqrt(f)*n*(a + b*log(c*x^n))^2*PolyLog(2, sqrt(-d)*sqrt(f)*x) - 6*im*b^3*sqrt(d)*sqrt(f)*n^3*PolyLog(2, (-im)*sqrt(d)*sqrt(f)*x) + 6*im*b^3*sqrt(d)*sqrt(f)*n^3*PolyLog(2, im*sqrt(d)*sqrt(f)*x) + 6*b^3*sqrt(-d)*sqrt(f)*n^3*PolyLog(3, (-sqrt(-d))*sqrt(f)*x) + 6*b^2*sqrt(-d)*sqrt(f)*n^2*(a + b*log(c*x^n))*PolyLog(3, (-sqrt(-d))*sqrt(f)*x) - 6*b^3*sqrt(-d)*sqrt(f)*n^3*PolyLog(3, sqrt(-d)*sqrt(f)*x) - 6*b^2*sqrt(-d)*sqrt(f)*n^2*(a + b*log(c*x^n))*PolyLog(3, sqrt(-d)*sqrt(f)*x) - 6*b^3*sqrt(-d)*sqrt(f)*n^3*PolyLog(4, (-sqrt(-d))*sqrt(f)*x) + 6*b^3*sqrt(-d)*sqrt(f)*n^3*PolyLog(4, sqrt(-d)*sqrt(f)*x)]

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

    @test_int [x^2*log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n)), x, 7, (-7*b*n*sqrt(x))/(9*d^5*f^5) + (2*b*n*x)/(9*d^4*f^4) - (b*n*x^(3/2))/(9*d^3*f^3) + (5*b*n*x^2)/(72*d^2*f^2) - (11*b*n*x^(5/2))/(225*d*f) + (b*n*x^3)/27 + (b*n*log(1 + d*f*sqrt(x)))/(9*d^6*f^6) - (b*n*x^3*log(1 + d*f*sqrt(x)))/9 + (sqrt(x)*(a + b*log(c*x^n)))/(3*d^5*f^5) - (x*(a + b*log(c*x^n)))/(6*d^4*f^4) + (x^(3/2)*(a + b*log(c*x^n)))/(9*d^3*f^3) - (x^2*(a + b*log(c*x^n)))/(12*d^2*f^2) + (x^(5/2)*(a + b*log(c*x^n)))/(15*d*f) - (x^3*(a + b*log(c*x^n)))/18 - (log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/(3*d^6*f^6) + (x^3*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/3 - (2*b*n*PolyLog(2, -(d*f*sqrt(x))))/(3*d^6*f^6)]
    @test_int [x^1*log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n)), x, 7, (-5*b*n*sqrt(x))/(4*d^3*f^3) + (3*b*n*x)/(8*d^2*f^2) - (7*b*n*x^(3/2))/(36*d*f) + (b*n*x^2)/8 + (b*n*log(1 + d*f*sqrt(x)))/(4*d^4*f^4) - (b*n*x^2*log(1 + d*f*sqrt(x)))/4 + (sqrt(x)*(a + b*log(c*x^n)))/(2*d^3*f^3) - (x*(a + b*log(c*x^n)))/(4*d^2*f^2) + (x^(3/2)*(a + b*log(c*x^n)))/(6*d*f) - (x^2*(a + b*log(c*x^n)))/8 - (log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/(2*d^4*f^4) + (x^2*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/2 - (b*n*PolyLog(2, -(d*f*sqrt(x))))/(d^4*f^4)]
    @test_int [x^0*log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n)), x, 7, (-3*b*n*sqrt(x))/(d*f) + b*n*x - b*n*x*log(d*(1/d + f*sqrt(x))) + (b*n*log(1 + d*f*sqrt(x)))/(d^2*f^2) + (sqrt(x)*(a + b*log(c*x^n)))/(d*f) - (x*(a + b*log(c*x^n)))/2 + x*log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n)) - (log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/(d^2*f^2) - (2*b*n*PolyLog(2, -(d*f*sqrt(x))))/(d^2*f^2)]
    @test_int [log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))/x^1, x, 2, -2*(a + b*log(c*x^n))*PolyLog(2, -(d*f*sqrt(x))) + 4*b*n*PolyLog(3, -(d*f*sqrt(x)))]
    @test_int [log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))/x^2, x, 8, (-3*b*d*f*n)/sqrt(x) + b*d^2*f^2*n*log(1 + d*f*sqrt(x)) - (b*n*log(1 + d*f*sqrt(x)))/x - (b*d^2*f^2*n*log(x))/2 + (b*d^2*f^2*n*log(x)^2)/4 - (d*f*(a + b*log(c*x^n)))/sqrt(x) + d^2*f^2*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)) - (log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/x - (d^2*f^2*log(x)*(a + b*log(c*x^n)))/2 + 2*b*d^2*f^2*n*PolyLog(2, -(d*f*sqrt(x)))]
    @test_int [log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))/x^3, x, 8, (-7*b*d*f*n)/(36*x^(3/2)) + (3*b*d^2*f^2*n)/(8*x) - (5*b*d^3*f^3*n)/(4*sqrt(x)) + (b*d^4*f^4*n*log(1 + d*f*sqrt(x)))/4 - (b*n*log(1 + d*f*sqrt(x)))/(4*x^2) - (b*d^4*f^4*n*log(x))/8 + (b*d^4*f^4*n*log(x)^2)/8 - (d*f*(a + b*log(c*x^n)))/(6*x^(3/2)) + (d^2*f^2*(a + b*log(c*x^n)))/(4*x) - (d^3*f^3*(a + b*log(c*x^n)))/(2*sqrt(x)) + (d^4*f^4*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/2 - (log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/(2*x^2) - (d^4*f^4*log(x)*(a + b*log(c*x^n)))/4 + b*d^4*f^4*n*PolyLog(2, -(d*f*sqrt(x)))]
    @test_int [log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))/x^4, x, 8, (-11*b*d*f*n)/(225*x^(5/2)) + (5*b*d^2*f^2*n)/(72*x^2) - (b*d^3*f^3*n)/(9*x^(3/2)) + (2*b*d^4*f^4*n)/(9*x) - (7*b*d^5*f^5*n)/(9*sqrt(x)) + (b*d^6*f^6*n*log(1 + d*f*sqrt(x)))/9 - (b*n*log(1 + d*f*sqrt(x)))/(9*x^3) - (b*d^6*f^6*n*log(x))/18 + (b*d^6*f^6*n*log(x)^2)/12 - (d*f*(a + b*log(c*x^n)))/(15*x^(5/2)) + (d^2*f^2*(a + b*log(c*x^n)))/(12*x^2) - (d^3*f^3*(a + b*log(c*x^n)))/(9*x^(3/2)) + (d^4*f^4*(a + b*log(c*x^n)))/(6*x) - (d^5*f^5*(a + b*log(c*x^n)))/(3*sqrt(x)) + (d^6*f^6*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/3 - (log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/(3*x^3) - (d^6*f^6*log(x)*(a + b*log(c*x^n)))/6 + (2*b*d^6*f^6*n*PolyLog(2, -(d*f*sqrt(x))))/3]

    @test_int [x^2*log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))^2, x, 18, (86*b^2*n^2*sqrt(x))/(27*d^5*f^5) + (a*b*n*x)/(3*d^4*f^4) - (13*b^2*n^2*x)/(27*d^4*f^4) + (14*b^2*n^2*x^(3/2))/(81*d^3*f^3) - (19*b^2*n^2*x^2)/(216*d^2*f^2) + (182*b^2*n^2*x^(5/2))/(3375*d*f) - (1/27)*b^2*n^2*x^3 - (2*b^2*n^2*log(1 + d*f*sqrt(x)))/(27*d^6*f^6) + (2/27)*b^2*n^2*x^3*log(1 + d*f*sqrt(x)) + (b^2*n*x*log(c*x^n))/(3*d^4*f^4) - (14*b*n*sqrt(x)*(a + b*log(c*x^n)))/(9*d^5*f^5) + (b*n*x*(a + b*log(c*x^n)))/(9*d^4*f^4) - (2*b*n*x^(3/2)*(a + b*log(c*x^n)))/(9*d^3*f^3) + (5*b*n*x^2*(a + b*log(c*x^n)))/(36*d^2*f^2) - (22*b*n*x^(5/2)*(a + b*log(c*x^n)))/(225*d*f) + (2/27)*b*n*x^3*(a + b*log(c*x^n)) + (2*b*n*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/(9*d^6*f^6) - (2/9)*b*n*x^3*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)) + (sqrt(x)*(a + b*log(c*x^n))^2)/(3*d^5*f^5) - (x*(a + b*log(c*x^n))^2)/(6*d^4*f^4) + (x^(3/2)*(a + b*log(c*x^n))^2)/(9*d^3*f^3) - (x^2*(a + b*log(c*x^n))^2)/(12*d^2*f^2) + (x^(5/2)*(a + b*log(c*x^n))^2)/(15*d*f) - (1/18)*x^3*(a + b*log(c*x^n))^2 - (log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^2)/(3*d^6*f^6) + (1/3)*x^3*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^2 + (4*b^2*n^2*PolyLog(2, (-d)*f*sqrt(x)))/(9*d^6*f^6) - (4*b*n*(a + b*log(c*x^n))*PolyLog(2, (-d)*f*sqrt(x)))/(3*d^6*f^6) + (8*b^2*n^2*PolyLog(3, (-d)*f*sqrt(x)))/(3*d^6*f^6)]
    @test_int [x^1*log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))^2, x, 16, (21*b^2*n^2*sqrt(x))/(4*d^3*f^3) + (a*b*n*x)/(2*d^2*f^2) - (7*b^2*n^2*x)/(8*d^2*f^2) + (37*b^2*n^2*x^(3/2))/(108*d*f) - (3/16)*b^2*n^2*x^2 - (b^2*n^2*log(1 + d*f*sqrt(x)))/(4*d^4*f^4) + (1/4)*b^2*n^2*x^2*log(1 + d*f*sqrt(x)) + (b^2*n*x*log(c*x^n))/(2*d^2*f^2) - (5*b*n*sqrt(x)*(a + b*log(c*x^n)))/(2*d^3*f^3) + (b*n*x*(a + b*log(c*x^n)))/(4*d^2*f^2) - (7*b*n*x^(3/2)*(a + b*log(c*x^n)))/(18*d*f) + (1/4)*b*n*x^2*(a + b*log(c*x^n)) + (b*n*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/(2*d^4*f^4) - (1/2)*b*n*x^2*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)) + (sqrt(x)*(a + b*log(c*x^n))^2)/(2*d^3*f^3) - (x*(a + b*log(c*x^n))^2)/(4*d^2*f^2) + (x^(3/2)*(a + b*log(c*x^n))^2)/(6*d*f) - (1/8)*x^2*(a + b*log(c*x^n))^2 - (log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^2)/(2*d^4*f^4) + (1/2)*x^2*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^2 + (b^2*n^2*PolyLog(2, (-d)*f*sqrt(x)))/(d^4*f^4) - (2*b*n*(a + b*log(c*x^n))*PolyLog(2, (-d)*f*sqrt(x)))/(d^4*f^4) + (4*b^2*n^2*PolyLog(3, (-d)*f*sqrt(x)))/(d^4*f^4)]
    @test_int [x^0*log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))^2, x, 14, (14*b^2*n^2*sqrt(x))/(d*f) + a*b*n*x - 3*b^2*n^2*x + 2*b^2*n^2*x*log(d*(1/d + f*sqrt(x))) - (2*b^2*n^2*log(1 + d*f*sqrt(x)))/(d^2*f^2) + b^2*n*x*log(c*x^n) - (6*b*n*sqrt(x)*(a + b*log(c*x^n)))/(d*f) + b*n*x*(a + b*log(c*x^n)) - 2*b*n*x*log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n)) + (2*b*n*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/(d^2*f^2) + (sqrt(x)*(a + b*log(c*x^n))^2)/(d*f) - (x*(a + b*log(c*x^n))^2)/2 + x*log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))^2 - (log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^2)/(d^2*f^2) + (4*b^2*n^2*PolyLog(2, -(d*f*sqrt(x))))/(d^2*f^2) - (4*b*n*(a + b*log(c*x^n))*PolyLog(2, -(d*f*sqrt(x))))/(d^2*f^2) + (8*b^2*n^2*PolyLog(3, -(d*f*sqrt(x))))/(d^2*f^2)]
    @test_int [log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))^2/x^1, x, 3, -2*(a + b*log(c*x^n))^2*PolyLog(2, -(d*f*sqrt(x))) + 8*b*n*(a + b*log(c*x^n))*PolyLog(3, -(d*f*sqrt(x))) - 16*b^2*n^2*PolyLog(4, -(d*f*sqrt(x)))]
    @test_int [log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))^2/x^2, x, 17, -((14*b^2*d*f*n^2)/sqrt(x)) + 2*b^2*d^2*f^2*n^2*log(1 + d*f*sqrt(x)) - (2*b^2*n^2*log(1 + d*f*sqrt(x)))/x - b^2*d^2*f^2*n^2*log(x) + (1/2)*b^2*d^2*f^2*n^2*log(x)^2 - (6*b*d*f*n*(a + b*log(c*x^n)))/sqrt(x) + 2*b*d^2*f^2*n*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)) - (2*b*n*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/x - b*d^2*f^2*n*log(x)*(a + b*log(c*x^n)) - (d*f*(a + b*log(c*x^n))^2)/sqrt(x) + d^2*f^2*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^2 - (log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^2)/x - (d^2*f^2*(a + b*log(c*x^n))^3)/(6*b*n) + 4*b^2*d^2*f^2*n^2*PolyLog(2, (-d)*f*sqrt(x)) + 4*b*d^2*f^2*n*(a + b*log(c*x^n))*PolyLog(2, (-d)*f*sqrt(x)) - 8*b^2*d^2*f^2*n^2*PolyLog(3, (-d)*f*sqrt(x))]
    @test_int [log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))^2/x^3, x, 19, -((37*b^2*d*f*n^2)/(108*x^(3/2))) + (7*b^2*d^2*f^2*n^2)/(8*x) - (21*b^2*d^3*f^3*n^2)/(4*sqrt(x)) + (1/4)*b^2*d^4*f^4*n^2*log(1 + d*f*sqrt(x)) - (b^2*n^2*log(1 + d*f*sqrt(x)))/(4*x^2) - (1/8)*b^2*d^4*f^4*n^2*log(x) + (1/8)*b^2*d^4*f^4*n^2*log(x)^2 - (7*b*d*f*n*(a + b*log(c*x^n)))/(18*x^(3/2)) + (3*b*d^2*f^2*n*(a + b*log(c*x^n)))/(4*x) - (5*b*d^3*f^3*n*(a + b*log(c*x^n)))/(2*sqrt(x)) + (1/2)*b*d^4*f^4*n*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)) - (b*n*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/(2*x^2) - (1/4)*b*d^4*f^4*n*log(x)*(a + b*log(c*x^n)) - (d*f*(a + b*log(c*x^n))^2)/(6*x^(3/2)) + (d^2*f^2*(a + b*log(c*x^n))^2)/(4*x) - (d^3*f^3*(a + b*log(c*x^n))^2)/(2*sqrt(x)) + (1/2)*d^4*f^4*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^2 - (log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^2)/(2*x^2) - (d^4*f^4*(a + b*log(c*x^n))^3)/(12*b*n) + b^2*d^4*f^4*n^2*PolyLog(2, (-d)*f*sqrt(x)) + 2*b*d^4*f^4*n*(a + b*log(c*x^n))*PolyLog(2, (-d)*f*sqrt(x)) - 4*b^2*d^4*f^4*n^2*PolyLog(3, (-d)*f*sqrt(x))]

    @test_int [x^1*log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))^3, x, 30, -((255*b^3*n^3*sqrt(x))/(8*d^3*f^3)) - (9*a*b^2*n^2*x)/(4*d^2*f^2) + (45*b^3*n^3*x)/(16*d^2*f^2) - (175*b^3*n^3*x^(3/2))/(216*d*f) + (3/8)*b^3*n^3*x^2 + (3*b^3*n^3*log(1 + d*f*sqrt(x)))/(8*d^4*f^4) - (3/8)*b^3*n^3*x^2*log(1 + d*f*sqrt(x)) - (9*b^3*n^2*x*log(c*x^n))/(4*d^2*f^2) + (63*b^2*n^2*sqrt(x)*(a + b*log(c*x^n)))/(4*d^3*f^3) - (3*b^2*n^2*x*(a + b*log(c*x^n)))/(8*d^2*f^2) + (37*b^2*n^2*x^(3/2)*(a + b*log(c*x^n)))/(36*d*f) - (9/16)*b^2*n^2*x^2*(a + b*log(c*x^n)) - (3*b^2*n^2*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/(4*d^4*f^4) + (3/4)*b^2*n^2*x^2*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)) - (15*b*n*sqrt(x)*(a + b*log(c*x^n))^2)/(4*d^3*f^3) + (9*b*n*x*(a + b*log(c*x^n))^2)/(8*d^2*f^2) - (7*b*n*x^(3/2)*(a + b*log(c*x^n))^2)/(12*d*f) + (3/8)*b*n*x^2*(a + b*log(c*x^n))^2 + (3*b*n*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^2)/(4*d^4*f^4) - (3/4)*b*n*x^2*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^2 + (sqrt(x)*(a + b*log(c*x^n))^3)/(2*d^3*f^3) - (x*(a + b*log(c*x^n))^3)/(4*d^2*f^2) + (x^(3/2)*(a + b*log(c*x^n))^3)/(6*d*f) - (1/8)*x^2*(a + b*log(c*x^n))^3 - (log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^3)/(2*d^4*f^4) + (1/2)*x^2*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^3 - (3*b^3*n^3*PolyLog(2, (-d)*f*sqrt(x)))/(2*d^4*f^4) + (3*b^2*n^2*(a + b*log(c*x^n))*PolyLog(2, (-d)*f*sqrt(x)))/(d^4*f^4) - (3*b*n*(a + b*log(c*x^n))^2*PolyLog(2, (-d)*f*sqrt(x)))/(d^4*f^4) - (6*b^3*n^3*PolyLog(3, (-d)*f*sqrt(x)))/(d^4*f^4) + (12*b^2*n^2*(a + b*log(c*x^n))*PolyLog(3, (-d)*f*sqrt(x)))/(d^4*f^4) - (24*b^3*n^3*PolyLog(4, (-d)*f*sqrt(x)))/(d^4*f^4)]
    @test_int [x^0*log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))^3, x, 24, (-90*b^3*n^3*sqrt(x))/(d*f) - 6*a*b^2*n^2*x + 12*b^3*n^3*x - 6*b^3*n^3*x*log(d*(1/d + f*sqrt(x))) + (6*b^3*n^3*log(1 + d*f*sqrt(x)))/(d^2*f^2) - 6*b^3*n^2*x*log(c*x^n) + (42*b^2*n^2*sqrt(x)*(a + b*log(c*x^n)))/(d*f) - 3*b^2*n^2*x*(a + b*log(c*x^n)) + 6*b^2*n^2*x*log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n)) - (6*b^2*n^2*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/(d^2*f^2) - (9*b*n*sqrt(x)*(a + b*log(c*x^n))^2)/(d*f) + 3*b*n*x*(a + b*log(c*x^n))^2 - 3*b*n*x*log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))^2 + (3*b*n*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^2)/(d^2*f^2) + (sqrt(x)*(a + b*log(c*x^n))^3)/(d*f) - (x*(a + b*log(c*x^n))^3)/2 + x*log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))^3 - (log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^3)/(d^2*f^2) - (12*b^3*n^3*PolyLog(2, -(d*f*sqrt(x))))/(d^2*f^2) + (12*b^2*n^2*(a + b*log(c*x^n))*PolyLog(2, -(d*f*sqrt(x))))/(d^2*f^2) - (6*b*n*(a + b*log(c*x^n))^2*PolyLog(2, -(d*f*sqrt(x))))/(d^2*f^2) - (24*b^3*n^3*PolyLog(3, -(d*f*sqrt(x))))/(d^2*f^2) + (24*b^2*n^2*(a + b*log(c*x^n))*PolyLog(3, -(d*f*sqrt(x))))/(d^2*f^2) - (48*b^3*n^3*PolyLog(4, -(d*f*sqrt(x))))/(d^2*f^2)]
    @test_int [log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))^3/x^1, x, 4, -2*(a + b*log(c*x^n))^3*PolyLog(2, -(d*f*sqrt(x))) + 12*b*n*(a + b*log(c*x^n))^2*PolyLog(3, -(d*f*sqrt(x))) - 48*b^2*n^2*(a + b*log(c*x^n))*PolyLog(4, -(d*f*sqrt(x))) + 96*b^3*n^3*PolyLog(5, -(d*f*sqrt(x)))]
    @test_int [log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))^3/x^2, x, 28, -((90*b^3*d*f*n^3)/sqrt(x)) + 6*b^3*d^2*f^2*n^3*log(1 + d*f*sqrt(x)) - (6*b^3*n^3*log(1 + d*f*sqrt(x)))/x - 3*b^3*d^2*f^2*n^3*log(x) + (3/2)*b^3*d^2*f^2*n^3*log(x)^2 - (42*b^2*d*f*n^2*(a + b*log(c*x^n)))/sqrt(x) + 6*b^2*d^2*f^2*n^2*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)) - (6*b^2*n^2*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/x - 3*b^2*d^2*f^2*n^2*log(x)*(a + b*log(c*x^n)) - (9*b*d*f*n*(a + b*log(c*x^n))^2)/sqrt(x) + 3*b*d^2*f^2*n*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^2 - (3*b*n*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^2)/x - (1/2)*d^2*f^2*(a + b*log(c*x^n))^3 - (d*f*(a + b*log(c*x^n))^3)/sqrt(x) + d^2*f^2*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^3 - (log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^3)/x - (d^2*f^2*(a + b*log(c*x^n))^4)/(8*b*n) + 12*b^3*d^2*f^2*n^3*PolyLog(2, (-d)*f*sqrt(x)) + 12*b^2*d^2*f^2*n^2*(a + b*log(c*x^n))*PolyLog(2, (-d)*f*sqrt(x)) + 6*b*d^2*f^2*n*(a + b*log(c*x^n))^2*PolyLog(2, (-d)*f*sqrt(x)) - 24*b^3*d^2*f^2*n^3*PolyLog(3, (-d)*f*sqrt(x)) - 24*b^2*d^2*f^2*n^2*(a + b*log(c*x^n))*PolyLog(3, (-d)*f*sqrt(x)) + 48*b^3*d^2*f^2*n^3*PolyLog(4, (-d)*f*sqrt(x))]
    @test_int [log(d*(1/d + f*sqrt(x)))*(a + b*log(c*x^n))^3/x^3, x, 34, -((175*b^3*d*f*n^3)/(216*x^(3/2))) + (45*b^3*d^2*f^2*n^3)/(16*x) - (255*b^3*d^3*f^3*n^3)/(8*sqrt(x)) + (3/8)*b^3*d^4*f^4*n^3*log(1 + d*f*sqrt(x)) - (3*b^3*n^3*log(1 + d*f*sqrt(x)))/(8*x^2) - (3/16)*b^3*d^4*f^4*n^3*log(x) + (3/16)*b^3*d^4*f^4*n^3*log(x)^2 - (37*b^2*d*f*n^2*(a + b*log(c*x^n)))/(36*x^(3/2)) + (21*b^2*d^2*f^2*n^2*(a + b*log(c*x^n)))/(8*x) - (63*b^2*d^3*f^3*n^2*(a + b*log(c*x^n)))/(4*sqrt(x)) + (3/4)*b^2*d^4*f^4*n^2*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)) - (3*b^2*n^2*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n)))/(4*x^2) - (3/8)*b^2*d^4*f^4*n^2*log(x)*(a + b*log(c*x^n)) - (7*b*d*f*n*(a + b*log(c*x^n))^2)/(12*x^(3/2)) + (9*b*d^2*f^2*n*(a + b*log(c*x^n))^2)/(8*x) - (15*b*d^3*f^3*n*(a + b*log(c*x^n))^2)/(4*sqrt(x)) + (3/4)*b*d^4*f^4*n*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^2 - (3*b*n*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^2)/(4*x^2) - (1/8)*d^4*f^4*(a + b*log(c*x^n))^3 - (d*f*(a + b*log(c*x^n))^3)/(6*x^(3/2)) + (d^2*f^2*(a + b*log(c*x^n))^3)/(4*x) - (d^3*f^3*(a + b*log(c*x^n))^3)/(2*sqrt(x)) + (1/2)*d^4*f^4*log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^3 - (log(1 + d*f*sqrt(x))*(a + b*log(c*x^n))^3)/(2*x^2) - (d^4*f^4*(a + b*log(c*x^n))^4)/(16*b*n) + (3/2)*b^3*d^4*f^4*n^3*PolyLog(2, (-d)*f*sqrt(x)) + 3*b^2*d^4*f^4*n^2*(a + b*log(c*x^n))*PolyLog(2, (-d)*f*sqrt(x)) + 3*b*d^4*f^4*n*(a + b*log(c*x^n))^2*PolyLog(2, (-d)*f*sqrt(x)) - 6*b^3*d^4*f^4*n^3*PolyLog(3, (-d)*f*sqrt(x)) - 12*b^2*d^4*f^4*n^2*(a + b*log(c*x^n))*PolyLog(3, (-d)*f*sqrt(x)) + 24*b^3*d^4*f^4*n^3*PolyLog(4, (-d)*f*sqrt(x))]

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

    @test_int [log(d*(1/d + f*x^m))*(a + b*log(c*x^n))^4/x, x, 5, -(((a + b*log(c*x^n))^4*PolyLog(2, (-d)*f*x^m))/m) + (4*b*n*(a + b*log(c*x^n))^3*PolyLog(3, (-d)*f*x^m))/m^2 - (12*b^2*n^2*(a + b*log(c*x^n))^2*PolyLog(4, (-d)*f*x^m))/m^3 + (24*b^3*n^3*(a + b*log(c*x^n))*PolyLog(5, (-d)*f*x^m))/m^4 - (24*b^4*n^4*PolyLog(6, (-d)*f*x^m))/m^5]
    @test_int [log(d*(1/d + f*x^m))*(a + b*log(c*x^n))^3/x, x, 4, -(((a + b*log(c*x^n))^3*PolyLog(2, (-d)*f*x^m))/m) + (3*b*n*(a + b*log(c*x^n))^2*PolyLog(3, (-d)*f*x^m))/m^2 - (6*b^2*n^2*(a + b*log(c*x^n))*PolyLog(4, (-d)*f*x^m))/m^3 + (6*b^3*n^3*PolyLog(5, (-d)*f*x^m))/m^4]
    @test_int [log(d*(1/d + f*x^m))*(a + b*log(c*x^n))^2/x, x, 3, -(((a + b*log(c*x^n))^2*PolyLog(2, (-d)*f*x^m))/m) + (2*b*n*(a + b*log(c*x^n))*PolyLog(3, (-d)*f*x^m))/m^2 - (2*b^2*n^2*PolyLog(4, (-d)*f*x^m))/m^3]
    @test_int [log(d*(1/d + f*x^m))*(a + b*log(c*x^n))^1/x, x, 2, -(((a + b*log(c*x^n))*PolyLog(2, (-d)*f*x^m))/m) + (b*n*PolyLog(3, (-d)*f*x^m))/m^2]
    @test_int [log(d*(1/d + f*x^m))/(x*(a + b*log(c*x^n))^1), x, 0, Unintegrable(log(d*(1/d + f*x^m))/(x*(a + b*log(c*x^n))), x)]
    @test_int [log(d*(1/d + f*x^m))/(x*(a + b*log(c*x^n))^2), x, 0, Unintegrable(log(d*(1/d + f*x^m))/(x*(a + b*log(c*x^n))^2), x)]

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

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

    @test_int [x^3*log(d*(e + f*x)^m)*(a + b*log(c*x^n)), x, 7, -((5*b*e^3*m*n*x)/(16*f^3)) + (3*b*e^2*m*n*x^2)/(32*f^2) - (7*b*e*m*n*x^3)/(144*f) + (1/32)*b*m*n*x^4 + (e^3*m*x*(a + b*log(c*x^n)))/(4*f^3) - (e^2*m*x^2*(a + b*log(c*x^n)))/(8*f^2) + (e*m*x^3*(a + b*log(c*x^n)))/(12*f) - (1/16)*m*x^4*(a + b*log(c*x^n)) + (b*e^4*m*n*log(e + f*x))/(16*f^4) + (b*e^4*m*n*log(-((f*x)/e))*log(e + f*x))/(4*f^4) - (e^4*m*(a + b*log(c*x^n))*log(e + f*x))/(4*f^4) - (1/16)*b*n*x^4*log(d*(e + f*x)^m) + (1/4)*x^4*(a + b*log(c*x^n))*log(d*(e + f*x)^m) + (b*e^4*m*n*PolyLog(2, 1 + (f*x)/e))/(4*f^4)]
    @test_int [x^2*log(d*(e + f*x)^m)*(a + b*log(c*x^n)), x, 7, (4*b*e^2*m*n*x)/(9*f^2) - (5*b*e*m*n*x^2)/(36*f) + (2/27)*b*m*n*x^3 - (e^2*m*x*(a + b*log(c*x^n)))/(3*f^2) + (e*m*x^2*(a + b*log(c*x^n)))/(6*f) - (1/9)*m*x^3*(a + b*log(c*x^n)) - (b*e^3*m*n*log(e + f*x))/(9*f^3) - (b*e^3*m*n*log(-((f*x)/e))*log(e + f*x))/(3*f^3) + (e^3*m*(a + b*log(c*x^n))*log(e + f*x))/(3*f^3) - (1/9)*b*n*x^3*log(d*(e + f*x)^m) + (1/3)*x^3*(a + b*log(c*x^n))*log(d*(e + f*x)^m) - (b*e^3*m*n*PolyLog(2, 1 + (f*x)/e))/(3*f^3)]
    @test_int [x^1*log(d*(e + f*x)^m)*(a + b*log(c*x^n)), x, 7, -((3*b*e*m*n*x)/(4*f)) + (1/4)*b*m*n*x^2 + (e*m*x*(a + b*log(c*x^n)))/(2*f) - (1/4)*m*x^2*(a + b*log(c*x^n)) + (b*e^2*m*n*log(e + f*x))/(4*f^2) + (b*e^2*m*n*log(-((f*x)/e))*log(e + f*x))/(2*f^2) - (e^2*m*(a + b*log(c*x^n))*log(e + f*x))/(2*f^2) - (1/4)*b*n*x^2*log(d*(e + f*x)^m) + (1/2)*x^2*(a + b*log(c*x^n))*log(d*(e + f*x)^m) + (b*e^2*m*n*PolyLog(2, 1 + (f*x)/e))/(2*f^2)]
    @test_int [x^0*log(d*(e + f*x)^m)*(a + b*log(c*x^n)), x, 8, 2*b*m*n*x - m*x*(a + b*log(c*x^n)) - (b*n*(e + f*x)*log(d*(e + f*x)^m))/f - (b*e*n*log(-((f*x)/e))*log(d*(e + f*x)^m))/f + ((e + f*x)*(a + b*log(c*x^n))*log(d*(e + f*x)^m))/f - (b*e*m*n*PolyLog(2, 1 + (f*x)/e))/f]
    @test_int [log(d*(e + f*x)^m)*(a + b*log(c*x^n))/x^1, x, 4, ((a + b*log(c*x^n))^2*log(d*(e + f*x)^m))/(2*b*n) - (m*(a + b*log(c*x^n))^2*log(1 + (f*x)/e))/(2*b*n) - m*(a + b*log(c*x^n))*PolyLog(2, -((f*x)/e)) + b*m*n*PolyLog(3, -((f*x)/e))]
    @test_int [log(d*(e + f*x)^m)*(a + b*log(c*x^n))/x^2, x, 9, (b*f*m*n*log(x))/e - (b*f*m*n*log(x)^2)/(2*e) + (f*m*log(x)*(a + b*log(c*x^n)))/e - (b*f*m*n*log(e + f*x))/e + (b*f*m*n*log(-((f*x)/e))*log(e + f*x))/e - (f*m*(a + b*log(c*x^n))*log(e + f*x))/e - (b*n*log(d*(e + f*x)^m))/x - ((a + b*log(c*x^n))*log(d*(e + f*x)^m))/x + (b*f*m*n*PolyLog(2, 1 + (f*x)/e))/e]
    @test_int [log(d*(e + f*x)^m)*(a + b*log(c*x^n))/x^3, x, 8, -((3*b*f*m*n)/(4*e*x)) - (b*f^2*m*n*log(x))/(4*e^2) + (b*f^2*m*n*log(x)^2)/(4*e^2) - (f*m*(a + b*log(c*x^n)))/(2*e*x) - (f^2*m*log(x)*(a + b*log(c*x^n)))/(2*e^2) + (b*f^2*m*n*log(e + f*x))/(4*e^2) - (b*f^2*m*n*log(-((f*x)/e))*log(e + f*x))/(2*e^2) + (f^2*m*(a + b*log(c*x^n))*log(e + f*x))/(2*e^2) - (b*n*log(d*(e + f*x)^m))/(4*x^2) - ((a + b*log(c*x^n))*log(d*(e + f*x)^m))/(2*x^2) - (b*f^2*m*n*PolyLog(2, 1 + (f*x)/e))/(2*e^2)]
    @test_int [log(d*(e + f*x)^m)*(a + b*log(c*x^n))/x^4, x, 8, -((5*b*f*m*n)/(36*e*x^2)) + (4*b*f^2*m*n)/(9*e^2*x) + (b*f^3*m*n*log(x))/(9*e^3) - (b*f^3*m*n*log(x)^2)/(6*e^3) - (f*m*(a + b*log(c*x^n)))/(6*e*x^2) + (f^2*m*(a + b*log(c*x^n)))/(3*e^2*x) + (f^3*m*log(x)*(a + b*log(c*x^n)))/(3*e^3) - (b*f^3*m*n*log(e + f*x))/(9*e^3) + (b*f^3*m*n*log(-((f*x)/e))*log(e + f*x))/(3*e^3) - (f^3*m*(a + b*log(c*x^n))*log(e + f*x))/(3*e^3) - (b*n*log(d*(e + f*x)^m))/(9*x^3) - ((a + b*log(c*x^n))*log(d*(e + f*x)^m))/(3*x^3) + (b*f^3*m*n*PolyLog(2, 1 + (f*x)/e))/(3*e^3)]

    @test_int [x^2*log(d*(e + f*x)^m)*(a + b*log(c*x^n))^2, x, 24, (8*a*b*e^2*m*n*x)/(9*f^2) - (26*b^2*e^2*m*n^2*x)/(27*f^2) + (19*b^2*e*m*n^2*x^2)/(108*f) - (2/27)*b^2*m*n^2*x^3 + (8*b^2*e^2*m*n*x*log(c*x^n))/(9*f^2) - (5*b*e*m*n*x^2*(a + b*log(c*x^n)))/(18*f) + (4/27)*b*m*n*x^3*(a + b*log(c*x^n)) - (e^2*m*x*(a + b*log(c*x^n))^2)/(3*f^2) + (e*m*x^2*(a + b*log(c*x^n))^2)/(6*f) - (1/9)*m*x^3*(a + b*log(c*x^n))^2 + (2*b^2*e^3*m*n^2*log(e + f*x))/(27*f^3) + (2/27)*b^2*n^2*x^3*log(d*(e + f*x)^m) - (2/9)*b*n*x^3*(a + b*log(c*x^n))*log(d*(e + f*x)^m) + (1/3)*x^3*(a + b*log(c*x^n))^2*log(d*(e + f*x)^m) - (2*b*e^3*m*n*(a + b*log(c*x^n))*log(1 + (f*x)/e))/(9*f^3) + (e^3*m*(a + b*log(c*x^n))^2*log(1 + (f*x)/e))/(3*f^3) - (2*b^2*e^3*m*n^2*PolyLog(2, -((f*x)/e)))/(9*f^3) + (2*b*e^3*m*n*(a + b*log(c*x^n))*PolyLog(2, -((f*x)/e)))/(3*f^3) - (2*b^2*e^3*m*n^2*PolyLog(3, -((f*x)/e)))/(3*f^3)]
    @test_int [x^1*log(d*(e + f*x)^m)*(a + b*log(c*x^n))^2, x, 21, -((3*a*b*e*m*n*x)/(2*f)) + (7*b^2*e*m*n^2*x)/(4*f) - (3/8)*b^2*m*n^2*x^2 - (3*b^2*e*m*n*x*log(c*x^n))/(2*f) + (1/2)*b*m*n*x^2*(a + b*log(c*x^n)) + (e*m*x*(a + b*log(c*x^n))^2)/(2*f) - (1/4)*m*x^2*(a + b*log(c*x^n))^2 - (b^2*e^2*m*n^2*log(e + f*x))/(4*f^2) + (1/4)*b^2*n^2*x^2*log(d*(e + f*x)^m) - (1/2)*b*n*x^2*(a + b*log(c*x^n))*log(d*(e + f*x)^m) + (1/2)*x^2*(a + b*log(c*x^n))^2*log(d*(e + f*x)^m) + (b*e^2*m*n*(a + b*log(c*x^n))*log(1 + (f*x)/e))/(2*f^2) - (e^2*m*(a + b*log(c*x^n))^2*log(1 + (f*x)/e))/(2*f^2) + (b^2*e^2*m*n^2*PolyLog(2, -((f*x)/e)))/(2*f^2) - (b*e^2*m*n*(a + b*log(c*x^n))*PolyLog(2, -((f*x)/e)))/f^2 + (b^2*e^2*m*n^2*PolyLog(3, -((f*x)/e)))/f^2]
    @test_int [x^0*log(d*(e + f*x)^m)*(a + b*log(c*x^n))^2, x, 18, 2*a*b*m*n*x - 4*b^2*m*n^2*x + 2*b*m*n*(a - b*n)*x + 4*b^2*m*n*x*log(c*x^n) - m*x*(a + b*log(c*x^n))^2 - (2*b*e*m*n*(a - b*n)*log(e + f*x))/f - 2*a*b*n*x*log(d*(e + f*x)^m) + 2*b^2*n^2*x*log(d*(e + f*x)^m) - 2*b^2*n*x*log(c*x^n)*log(d*(e + f*x)^m) + x*(a + b*log(c*x^n))^2*log(d*(e + f*x)^m) - (2*b^2*e*m*n*log(c*x^n)*log(1 + (f*x)/e))/f + (e*m*(a + b*log(c*x^n))^2*log(1 + (f*x)/e))/f - (2*b^2*e*m*n^2*PolyLog(2, -((f*x)/e)))/f + (2*b*e*m*n*(a + b*log(c*x^n))*PolyLog(2, -((f*x)/e)))/f - (2*b^2*e*m*n^2*PolyLog(3, -((f*x)/e)))/f]
    @test_int [log(d*(e + f*x)^m)*(a + b*log(c*x^n))^2/x^1, x, 5, ((a + b*log(c*x^n))^3*log(d*(e + f*x)^m))/(3*b*n) - (m*(a + b*log(c*x^n))^3*log(1 + (f*x)/e))/(3*b*n) - m*(a + b*log(c*x^n))^2*PolyLog(2, -((f*x)/e)) + 2*b*m*n*(a + b*log(c*x^n))*PolyLog(3, -((f*x)/e)) - 2*b^2*m*n^2*PolyLog(4, -((f*x)/e))]
    @test_int [log(d*(e + f*x)^m)*(a + b*log(c*x^n))^2/x^2, x, 10, (2*b^2*f*m*n^2*log(x))/e - (2*b*f*m*n*log(1 + e/(f*x))*(a + b*log(c*x^n)))/e - (f*m*log(1 + e/(f*x))*(a + b*log(c*x^n))^2)/e - (2*b^2*f*m*n^2*log(e + f*x))/e - (2*b^2*n^2*log(d*(e + f*x)^m))/x - (2*b*n*(a + b*log(c*x^n))*log(d*(e + f*x)^m))/x - ((a + b*log(c*x^n))^2*log(d*(e + f*x)^m))/x + (2*b^2*f*m*n^2*PolyLog(2, -(e/(f*x))))/e + (2*b*f*m*n*(a + b*log(c*x^n))*PolyLog(2, -(e/(f*x))))/e + (2*b^2*f*m*n^2*PolyLog(3, -(e/(f*x))))/e]
    @test_int [log(d*(e + f*x)^m)*(a + b*log(c*x^n))^2/x^3, x, 14, -((7*b^2*f*m*n^2)/(4*e*x)) - (b^2*f^2*m*n^2*log(x))/(4*e^2) - (3*b*f*m*n*(a + b*log(c*x^n)))/(2*e*x) + (b*f^2*m*n*log(1 + e/(f*x))*(a + b*log(c*x^n)))/(2*e^2) - (f*m*(a + b*log(c*x^n))^2)/(2*e*x) + (f^2*m*log(1 + e/(f*x))*(a + b*log(c*x^n))^2)/(2*e^2) + (b^2*f^2*m*n^2*log(e + f*x))/(4*e^2) - (b^2*n^2*log(d*(e + f*x)^m))/(4*x^2) - (b*n*(a + b*log(c*x^n))*log(d*(e + f*x)^m))/(2*x^2) - ((a + b*log(c*x^n))^2*log(d*(e + f*x)^m))/(2*x^2) - (b^2*f^2*m*n^2*PolyLog(2, -(e/(f*x))))/(2*e^2) - (b*f^2*m*n*(a + b*log(c*x^n))*PolyLog(2, -(e/(f*x))))/e^2 - (b^2*f^2*m*n^2*PolyLog(3, -(e/(f*x))))/e^2]
    @test_int [log(d*(e + f*x)^m)*(a + b*log(c*x^n))^2/x^4, x, 19, -((19*b^2*f*m*n^2)/(108*e*x^2)) + (26*b^2*f^2*m*n^2)/(27*e^2*x) + (2*b^2*f^3*m*n^2*log(x))/(27*e^3) - (5*b*f*m*n*(a + b*log(c*x^n)))/(18*e*x^2) + (8*b*f^2*m*n*(a + b*log(c*x^n)))/(9*e^2*x) - (2*b*f^3*m*n*log(1 + e/(f*x))*(a + b*log(c*x^n)))/(9*e^3) - (f*m*(a + b*log(c*x^n))^2)/(6*e*x^2) + (f^2*m*(a + b*log(c*x^n))^2)/(3*e^2*x) - (f^3*m*log(1 + e/(f*x))*(a + b*log(c*x^n))^2)/(3*e^3) - (2*b^2*f^3*m*n^2*log(e + f*x))/(27*e^3) - (2*b^2*n^2*log(d*(e + f*x)^m))/(27*x^3) - (2*b*n*(a + b*log(c*x^n))*log(d*(e + f*x)^m))/(9*x^3) - ((a + b*log(c*x^n))^2*log(d*(e + f*x)^m))/(3*x^3) + (2*b^2*f^3*m*n^2*PolyLog(2, -(e/(f*x))))/(9*e^3) + (2*b*f^3*m*n*(a + b*log(c*x^n))*PolyLog(2, -(e/(f*x))))/(3*e^3) + (2*b^2*f^3*m*n^2*PolyLog(3, -(e/(f*x))))/(3*e^3)]

    @test_int [x^1*log(d*(e + f*x)^m)*(a + b*log(c*x^n))^3, x, 34, (21*a*b^2*e*m*n^2*x)/(4*f) - (45*b^3*e*m*n^3*x)/(8*f) + (3/4)*b^3*m*n^3*x^2 + (21*b^3*e*m*n^2*x*log(c*x^n))/(4*f) - (9/8)*b^2*m*n^2*x^2*(a + b*log(c*x^n)) - (9*b*e*m*n*x*(a + b*log(c*x^n))^2)/(4*f) + (3/4)*b*m*n*x^2*(a + b*log(c*x^n))^2 + (e*m*x*(a + b*log(c*x^n))^3)/(2*f) - (1/4)*m*x^2*(a + b*log(c*x^n))^3 + (3*b^3*e^2*m*n^3*log(e + f*x))/(8*f^2) - (3/8)*b^3*n^3*x^2*log(d*(e + f*x)^m) + (3/4)*b^2*n^2*x^2*(a + b*log(c*x^n))*log(d*(e + f*x)^m) - (3/4)*b*n*x^2*(a + b*log(c*x^n))^2*log(d*(e + f*x)^m) + (1/2)*x^2*(a + b*log(c*x^n))^3*log(d*(e + f*x)^m) - (3*b^2*e^2*m*n^2*(a + b*log(c*x^n))*log(1 + (f*x)/e))/(4*f^2) + (3*b*e^2*m*n*(a + b*log(c*x^n))^2*log(1 + (f*x)/e))/(4*f^2) - (e^2*m*(a + b*log(c*x^n))^3*log(1 + (f*x)/e))/(2*f^2) - (3*b^3*e^2*m*n^3*PolyLog(2, -((f*x)/e)))/(4*f^2) + (3*b^2*e^2*m*n^2*(a + b*log(c*x^n))*PolyLog(2, -((f*x)/e)))/(2*f^2) - (3*b*e^2*m*n*(a + b*log(c*x^n))^2*PolyLog(2, -((f*x)/e)))/(2*f^2) - (3*b^3*e^2*m*n^3*PolyLog(3, -((f*x)/e)))/(2*f^2) + (3*b^2*e^2*m*n^2*(a + b*log(c*x^n))*PolyLog(3, -((f*x)/e)))/f^2 - (3*b^3*e^2*m*n^3*PolyLog(4, -((f*x)/e)))/f^2]
    @test_int [x^0*log(d*(e + f*x)^m)*(a + b*log(c*x^n))^3, x, 28, -12*a*b^2*m*n^2*x + 18*b^3*m*n^3*x - 6*b^2*m*n^2*(a - b*n)*x - 18*b^3*m*n^2*x*log(c*x^n) + 6*b*m*n*x*(a + b*log(c*x^n))^2 - m*x*(a + b*log(c*x^n))^3 + (6*b^2*e*m*n^2*(a - b*n)*log(e + f*x))/f + 6*a*b^2*n^2*x*log(d*(e + f*x)^m) - 6*b^3*n^3*x*log(d*(e + f*x)^m) + 6*b^3*n^2*x*log(c*x^n)*log(d*(e + f*x)^m) - 3*b*n*x*(a + b*log(c*x^n))^2*log(d*(e + f*x)^m) + x*(a + b*log(c*x^n))^3*log(d*(e + f*x)^m) + (6*b^3*e*m*n^2*log(c*x^n)*log(1 + (f*x)/e))/f - (3*b*e*m*n*(a + b*log(c*x^n))^2*log(1 + (f*x)/e))/f + (e*m*(a + b*log(c*x^n))^3*log(1 + (f*x)/e))/f + (6*b^3*e*m*n^3*PolyLog(2, -((f*x)/e)))/f - (6*b^2*e*m*n^2*(a + b*log(c*x^n))*PolyLog(2, -((f*x)/e)))/f + (3*b*e*m*n*(a + b*log(c*x^n))^2*PolyLog(2, -((f*x)/e)))/f + (6*b^3*e*m*n^3*PolyLog(3, -((f*x)/e)))/f - (6*b^2*e*m*n^2*(a + b*log(c*x^n))*PolyLog(3, -((f*x)/e)))/f + (6*b^3*e*m*n^3*PolyLog(4, -((f*x)/e)))/f]
    @test_int [log(d*(e + f*x)^m)*(a + b*log(c*x^n))^3/x^1, x, 6, ((a + b*log(c*x^n))^4*log(d*(e + f*x)^m))/(4*b*n) - (m*(a + b*log(c*x^n))^4*log(1 + (f*x)/e))/(4*b*n) - m*(a + b*log(c*x^n))^3*PolyLog(2, -((f*x)/e)) + 3*b*m*n*(a + b*log(c*x^n))^2*PolyLog(3, -((f*x)/e)) - 6*b^2*m*n^2*(a + b*log(c*x^n))*PolyLog(4, -((f*x)/e)) + 6*b^3*m*n^3*PolyLog(5, -((f*x)/e))]
    @test_int [log(d*(e + f*x)^m)*(a + b*log(c*x^n))^3/x^2, x, 14, (6*b^3*f*m*n^3*log(x))/e - (6*b^2*f*m*n^2*log(1 + e/(f*x))*(a + b*log(c*x^n)))/e - (3*b*f*m*n*log(1 + e/(f*x))*(a + b*log(c*x^n))^2)/e - (f*m*log(1 + e/(f*x))*(a + b*log(c*x^n))^3)/e - (6*b^3*f*m*n^3*log(e + f*x))/e - (6*b^3*n^3*log(d*(e + f*x)^m))/x - (6*b^2*n^2*(a + b*log(c*x^n))*log(d*(e + f*x)^m))/x - (3*b*n*(a + b*log(c*x^n))^2*log(d*(e + f*x)^m))/x - ((a + b*log(c*x^n))^3*log(d*(e + f*x)^m))/x + (6*b^3*f*m*n^3*PolyLog(2, -(e/(f*x))))/e + (6*b^2*f*m*n^2*(a + b*log(c*x^n))*PolyLog(2, -(e/(f*x))))/e + (3*b*f*m*n*(a + b*log(c*x^n))^2*PolyLog(2, -(e/(f*x))))/e + (6*b^3*f*m*n^3*PolyLog(3, -(e/(f*x))))/e + (6*b^2*f*m*n^2*(a + b*log(c*x^n))*PolyLog(3, -(e/(f*x))))/e + (6*b^3*f*m*n^3*PolyLog(4, -(e/(f*x))))/e]
    @test_int [log(d*(e + f*x)^m)*(a + b*log(c*x^n))^3/x^3, x, 22, -((45*b^3*f*m*n^3)/(8*e*x)) - (3*b^3*f^2*m*n^3*log(x))/(8*e^2) - (21*b^2*f*m*n^2*(a + b*log(c*x^n)))/(4*e*x) + (3*b^2*f^2*m*n^2*log(1 + e/(f*x))*(a + b*log(c*x^n)))/(4*e^2) - (9*b*f*m*n*(a + b*log(c*x^n))^2)/(4*e*x) + (3*b*f^2*m*n*log(1 + e/(f*x))*(a + b*log(c*x^n))^2)/(4*e^2) - (f*m*(a + b*log(c*x^n))^3)/(2*e*x) + (f^2*m*log(1 + e/(f*x))*(a + b*log(c*x^n))^3)/(2*e^2) + (3*b^3*f^2*m*n^3*log(e + f*x))/(8*e^2) - (3*b^3*n^3*log(d*(e + f*x)^m))/(8*x^2) - (3*b^2*n^2*(a + b*log(c*x^n))*log(d*(e + f*x)^m))/(4*x^2) - (3*b*n*(a + b*log(c*x^n))^2*log(d*(e + f*x)^m))/(4*x^2) - ((a + b*log(c*x^n))^3*log(d*(e + f*x)^m))/(2*x^2) - (3*b^3*f^2*m*n^3*PolyLog(2, -(e/(f*x))))/(4*e^2) - (3*b^2*f^2*m*n^2*(a + b*log(c*x^n))*PolyLog(2, -(e/(f*x))))/(2*e^2) - (3*b*f^2*m*n*(a + b*log(c*x^n))^2*PolyLog(2, -(e/(f*x))))/(2*e^2) - (3*b^3*f^2*m*n^3*PolyLog(3, -(e/(f*x))))/(2*e^2) - (3*b^2*f^2*m*n^2*(a + b*log(c*x^n))*PolyLog(3, -(e/(f*x))))/e^2 - (3*b^3*f^2*m*n^3*PolyLog(4, -(e/(f*x))))/e^2]

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

    @test_int [x^3*log(d*(e + f*x^2)^m)*(a + b*log(c*x^n)), x, 9, -((3*b*e*m*n*x^2)/(16*f)) + (1/16)*b*m*n*x^4 + (e*m*x^2*(a + b*log(c*x^n)))/(4*f) - (1/8)*m*x^4*(a + b*log(c*x^n)) + (b*e^2*m*n*log(e + f*x^2))/(16*f^2) + (b*e^2*m*n*log(-((f*x^2)/e))*log(e + f*x^2))/(8*f^2) - (e^2*m*(a + b*log(c*x^n))*log(e + f*x^2))/(4*f^2) - (1/16)*b*n*x^4*log(d*(e + f*x^2)^m) + (1/4)*x^4*(a + b*log(c*x^n))*log(d*(e + f*x^2)^m) + (b*e^2*m*n*PolyLog(2, 1 + (f*x^2)/e))/(8*f^2)]
    @test_int [x^1*log(d*(e + f*x^2)^m)*(a + b*log(c*x^n)), x, 9, (1/2)*b*m*n*x^2 - (1/2)*m*x^2*(a + b*log(c*x^n)) - (b*n*(e + f*x^2)*log(d*(e + f*x^2)^m))/(4*f) - (b*e*n*log(-((f*x^2)/e))*log(d*(e + f*x^2)^m))/(4*f) + ((e + f*x^2)*(a + b*log(c*x^n))*log(d*(e + f*x^2)^m))/(2*f) - (b*e*m*n*PolyLog(2, 1 + (f*x^2)/e))/(4*f)]
    @test_int [log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))/x^1, x, 4, ((a + b*log(c*x^n))^2*log(d*(e + f*x^2)^m))/(2*b*n) - (m*(a + b*log(c*x^n))^2*log(1 + (f*x^2)/e))/(2*b*n) - (1/2)*m*(a + b*log(c*x^n))*PolyLog(2, -((f*x^2)/e)) + (1/4)*b*m*n*PolyLog(3, -((f*x^2)/e))]
    @test_int [log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))/x^3, x, 11, (b*f*m*n*log(x))/(2*e) - (b*f*m*n*log(x)^2)/(2*e) + (f*m*log(x)*(a + b*log(c*x^n)))/e - (b*f*m*n*log(e + f*x^2))/(4*e) + (b*f*m*n*log(-((f*x^2)/e))*log(e + f*x^2))/(4*e) - (f*m*(a + b*log(c*x^n))*log(e + f*x^2))/(2*e) - (b*n*log(d*(e + f*x^2)^m))/(4*x^2) - ((a + b*log(c*x^n))*log(d*(e + f*x^2)^m))/(2*x^2) + (b*f*m*n*PolyLog(2, 1 + (f*x^2)/e))/(4*e)]
    @test_int [log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))/x^5, x, 10, -((3*b*f*m*n)/(16*e*x^2)) - (b*f^2*m*n*log(x))/(8*e^2) + (b*f^2*m*n*log(x)^2)/(4*e^2) - (f*m*(a + b*log(c*x^n)))/(4*e*x^2) - (f^2*m*log(x)*(a + b*log(c*x^n)))/(2*e^2) + (b*f^2*m*n*log(e + f*x^2))/(16*e^2) - (b*f^2*m*n*log(-((f*x^2)/e))*log(e + f*x^2))/(8*e^2) + (f^2*m*(a + b*log(c*x^n))*log(e + f*x^2))/(4*e^2) - (b*n*log(d*(e + f*x^2)^m))/(16*x^4) - ((a + b*log(c*x^n))*log(d*(e + f*x^2)^m))/(4*x^4) - (b*f^2*m*n*PolyLog(2, 1 + (f*x^2)/e))/(8*e^2)]

    @test_int [x^2*log(d*(e + f*x^2)^m)*(a + b*log(c*x^n)), x, 9, -((8*b*e*m*n*x)/(9*f)) + (4/27)*b*m*n*x^3 + (2*b*e^(3/2)*m*n*atan((sqrt(f)*x)/sqrt(e)))/(9*f^(3/2)) + (2*e*m*x*(a + b*log(c*x^n)))/(3*f) - (2/9)*m*x^3*(a + b*log(c*x^n)) - (2*e^(3/2)*m*atan((sqrt(f)*x)/sqrt(e))*(a + b*log(c*x^n)))/(3*f^(3/2)) - (1/9)*b*n*x^3*log(d*(e + f*x^2)^m) + (1/3)*x^3*(a + b*log(c*x^n))*log(d*(e + f*x^2)^m) + (im*b*e^(3/2)*m*n*PolyLog(2, -((im*sqrt(f)*x)/sqrt(e))))/(3*f^(3/2)) - (im*b*e^(3/2)*m*n*PolyLog(2, (im*sqrt(f)*x)/sqrt(e)))/(3*f^(3/2))]
    @test_int [x^0*log(d*(e + f*x^2)^m)*(a + b*log(c*x^n)), x, 8, 4*b*m*n*x - (2*b*sqrt(e)*m*n*atan((sqrt(f)*x)/sqrt(e)))/sqrt(f) - 2*m*x*(a + b*log(c*x^n)) + (2*sqrt(e)*m*atan((sqrt(f)*x)/sqrt(e))*(a + b*log(c*x^n)))/sqrt(f) - b*n*x*log(d*(e + f*x^2)^m) + x*(a + b*log(c*x^n))*log(d*(e + f*x^2)^m) - (im*b*sqrt(e)*m*n*PolyLog(2, -((im*sqrt(f)*x)/sqrt(e))))/sqrt(f) + (im*b*sqrt(e)*m*n*PolyLog(2, (im*sqrt(f)*x)/sqrt(e)))/sqrt(f)]
    @test_int [log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))/x^2, x, 7, (2*b*sqrt(f)*m*n*atan((sqrt(f)*x)/sqrt(e)))/sqrt(e) + (2*sqrt(f)*m*atan((sqrt(f)*x)/sqrt(e))*(a + b*log(c*x^n)))/sqrt(e) - (b*n*log(d*(e + f*x^2)^m))/x - ((a + b*log(c*x^n))*log(d*(e + f*x^2)^m))/x - (im*b*sqrt(f)*m*n*PolyLog(2, -((im*sqrt(f)*x)/sqrt(e))))/sqrt(e) + (im*b*sqrt(f)*m*n*PolyLog(2, (im*sqrt(f)*x)/sqrt(e)))/sqrt(e)]
    @test_int [log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))/x^4, x, 8, -((8*b*f*m*n)/(9*e*x)) - (2*b*f^(3/2)*m*n*atan((sqrt(f)*x)/sqrt(e)))/(9*e^(3/2)) - (2*f*m*(a + b*log(c*x^n)))/(3*e*x) - (2*f^(3/2)*m*atan((sqrt(f)*x)/sqrt(e))*(a + b*log(c*x^n)))/(3*e^(3/2)) - (b*n*log(d*(e + f*x^2)^m))/(9*x^3) - ((a + b*log(c*x^n))*log(d*(e + f*x^2)^m))/(3*x^3) + (im*b*f^(3/2)*m*n*PolyLog(2, -((im*sqrt(f)*x)/sqrt(e))))/(3*e^(3/2)) - (im*b*f^(3/2)*m*n*PolyLog(2, (im*sqrt(f)*x)/sqrt(e)))/(3*e^(3/2))]
    @test_int [log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))/x^6, x, 9, -((16*b*f*m*n)/(225*e*x^3)) + (12*b*f^2*m*n)/(25*e^2*x) + (2*b*f^(5/2)*m*n*atan((sqrt(f)*x)/sqrt(e)))/(25*e^(5/2)) - (2*f*m*(a + b*log(c*x^n)))/(15*e*x^3) + (2*f^2*m*(a + b*log(c*x^n)))/(5*e^2*x) + (2*f^(5/2)*m*atan((sqrt(f)*x)/sqrt(e))*(a + b*log(c*x^n)))/(5*e^(5/2)) - (b*n*log(d*(e + f*x^2)^m))/(25*x^5) - ((a + b*log(c*x^n))*log(d*(e + f*x^2)^m))/(5*x^5) - (im*b*f^(5/2)*m*n*PolyLog(2, -((im*sqrt(f)*x)/sqrt(e))))/(5*e^(5/2)) + (im*b*f^(5/2)*m*n*PolyLog(2, (im*sqrt(f)*x)/sqrt(e)))/(5*e^(5/2))]

    @test_int [x^1*log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))^2, x, 17, (-(3/4))*b^2*m*n^2*x^2 + b*m*n*x^2*(a + b*log(c*x^n)) - (1/2)*m*x^2*(a + b*log(c*x^n))^2 + (b^2*e*m*n^2*log(e + f*x^2))/(4*f) + (1/4)*b^2*n^2*x^2*log(d*(e + f*x^2)^m) - (1/2)*b*n*x^2*(a + b*log(c*x^n))*log(d*(e + f*x^2)^m) + (1/2)*x^2*(a + b*log(c*x^n))^2*log(d*(e + f*x^2)^m) - (b*e*m*n*(a + b*log(c*x^n))*log(1 + (f*x^2)/e))/(2*f) + (e*m*(a + b*log(c*x^n))^2*log(1 + (f*x^2)/e))/(2*f) - (b^2*e*m*n^2*PolyLog(2, -((f*x^2)/e)))/(4*f) + (b*e*m*n*(a + b*log(c*x^n))*PolyLog(2, -((f*x^2)/e)))/(2*f) - (b^2*e*m*n^2*PolyLog(3, -((f*x^2)/e)))/(4*f)]
    @test_int [log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))^2/x^1, x, 5, ((a + b*log(c*x^n))^3*log(d*(e + f*x^2)^m))/(3*b*n) - (m*(a + b*log(c*x^n))^3*log(1 + (f*x^2)/e))/(3*b*n) - (1/2)*m*(a + b*log(c*x^n))^2*PolyLog(2, -((f*x^2)/e)) + (1/2)*b*m*n*(a + b*log(c*x^n))*PolyLog(3, -((f*x^2)/e)) - (1/4)*b^2*m*n^2*PolyLog(4, -((f*x^2)/e))]
    @test_int [log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))^2/x^3, x, 11, (b^2*f*m*n^2*log(x))/(2*e) - (b*f*m*n*log(1 + e/(f*x^2))*(a + b*log(c*x^n)))/(2*e) - (f*m*log(1 + e/(f*x^2))*(a + b*log(c*x^n))^2)/(2*e) - (b^2*f*m*n^2*log(e + f*x^2))/(4*e) - (b^2*n^2*log(d*(e + f*x^2)^m))/(4*x^2) - (b*n*(a + b*log(c*x^n))*log(d*(e + f*x^2)^m))/(2*x^2) - ((a + b*log(c*x^n))^2*log(d*(e + f*x^2)^m))/(2*x^2) + (b^2*f*m*n^2*PolyLog(2, -(e/(f*x^2))))/(4*e) + (b*f*m*n*(a + b*log(c*x^n))*PolyLog(2, -(e/(f*x^2))))/(2*e) + (b^2*f*m*n^2*PolyLog(3, -(e/(f*x^2))))/(4*e)]
    @test_int [log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))^2/x^5, x, 15, -((7*b^2*f*m*n^2)/(32*e*x^2)) - (b^2*f^2*m*n^2*log(x))/(16*e^2) - (3*b*f*m*n*(a + b*log(c*x^n)))/(8*e*x^2) + (b*f^2*m*n*log(1 + e/(f*x^2))*(a + b*log(c*x^n)))/(8*e^2) - (f*m*(a + b*log(c*x^n))^2)/(4*e*x^2) + (f^2*m*log(1 + e/(f*x^2))*(a + b*log(c*x^n))^2)/(4*e^2) + (b^2*f^2*m*n^2*log(e + f*x^2))/(32*e^2) - (b^2*n^2*log(d*(e + f*x^2)^m))/(32*x^4) - (b*n*(a + b*log(c*x^n))*log(d*(e + f*x^2)^m))/(8*x^4) - ((a + b*log(c*x^n))^2*log(d*(e + f*x^2)^m))/(4*x^4) - (b^2*f^2*m*n^2*PolyLog(2, -(e/(f*x^2))))/(16*e^2) - (b*f^2*m*n*(a + b*log(c*x^n))*PolyLog(2, -(e/(f*x^2))))/(4*e^2) - (b^2*f^2*m*n^2*PolyLog(3, -(e/(f*x^2))))/(8*e^2)]

    @test_int [x^2*log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))^2, x, 30, -((16*a*b*e*m*n*x)/(9*f)) + (52*b^2*e*m*n^2*x)/(27*f) - (4/27)*b^2*m*n^2*x^3 - (4*b^2*e^(3/2)*m*n^2*atan((sqrt(f)*x)/sqrt(e)))/(27*f^(3/2)) - (16*b^2*e*m*n*x*log(c*x^n))/(9*f) + (8/27)*b*m*n*x^3*(a + b*log(c*x^n)) + (4*b*e^(3/2)*m*n*atan((sqrt(f)*x)/sqrt(e))*(a + b*log(c*x^n)))/(9*f^(3/2)) + (2*e*m*x*(a + b*log(c*x^n))^2)/(3*f) - (2/9)*m*x^3*(a + b*log(c*x^n))^2 - ((-e)^(3/2)*m*(a + b*log(c*x^n))^2*log(1 - (sqrt(f)*x)/sqrt(-e)))/(3*f^(3/2)) + ((-e)^(3/2)*m*(a + b*log(c*x^n))^2*log(1 + (sqrt(f)*x)/sqrt(-e)))/(3*f^(3/2)) + (2/27)*b^2*n^2*x^3*log(d*(e + f*x^2)^m) - (2/9)*b*n*x^3*(a + b*log(c*x^n))*log(d*(e + f*x^2)^m) + (1/3)*x^3*(a + b*log(c*x^n))^2*log(d*(e + f*x^2)^m) + (2*b*(-e)^(3/2)*m*n*(a + b*log(c*x^n))*PolyLog(2, -((sqrt(f)*x)/sqrt(-e))))/(3*f^(3/2)) - (2*b*(-e)^(3/2)*m*n*(a + b*log(c*x^n))*PolyLog(2, (sqrt(f)*x)/sqrt(-e)))/(3*f^(3/2)) - (2*im*b^2*e^(3/2)*m*n^2*PolyLog(2, -((im*sqrt(f)*x)/sqrt(e))))/(9*f^(3/2)) + (2*im*b^2*e^(3/2)*m*n^2*PolyLog(2, (im*sqrt(f)*x)/sqrt(e)))/(9*f^(3/2)) - (2*b^2*(-e)^(3/2)*m*n^2*PolyLog(3, -((sqrt(f)*x)/sqrt(-e))))/(3*f^(3/2)) + (2*b^2*(-e)^(3/2)*m*n^2*PolyLog(3, (sqrt(f)*x)/sqrt(-e)))/(3*f^(3/2))]
    @test_int [x^0*log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))^2, x, 26, 4*a*b*m*n*x - 8*b^2*m*n^2*x + 4*b*m*n*(a - b*n)*x - (4*b*sqrt(e)*m*n*(a - b*n)*atan((sqrt(f)*x)/sqrt(e)))/sqrt(f) + 8*b^2*m*n*x*log(c*x^n) - (4*b^2*sqrt(e)*m*n*atan((sqrt(f)*x)/sqrt(e))*log(c*x^n))/sqrt(f) - 2*m*x*(a + b*log(c*x^n))^2 - (sqrt(-e)*m*(a + b*log(c*x^n))^2*log(1 - (sqrt(f)*x)/sqrt(-e)))/sqrt(f) + (sqrt(-e)*m*(a + b*log(c*x^n))^2*log(1 + (sqrt(f)*x)/sqrt(-e)))/sqrt(f) - 2*a*b*n*x*log(d*(e + f*x^2)^m) + 2*b^2*n^2*x*log(d*(e + f*x^2)^m) - 2*b^2*n*x*log(c*x^n)*log(d*(e + f*x^2)^m) + x*(a + b*log(c*x^n))^2*log(d*(e + f*x^2)^m) + (2*b*sqrt(-e)*m*n*(a + b*log(c*x^n))*PolyLog(2, -((sqrt(f)*x)/sqrt(-e))))/sqrt(f) - (2*b*sqrt(-e)*m*n*(a + b*log(c*x^n))*PolyLog(2, (sqrt(f)*x)/sqrt(-e)))/sqrt(f) + (2*im*b^2*sqrt(e)*m*n^2*PolyLog(2, -((im*sqrt(f)*x)/sqrt(e))))/sqrt(f) - (2*im*b^2*sqrt(e)*m*n^2*PolyLog(2, (im*sqrt(f)*x)/sqrt(e)))/sqrt(f) - (2*b^2*sqrt(-e)*m*n^2*PolyLog(3, -((sqrt(f)*x)/sqrt(-e))))/sqrt(f) + (2*b^2*sqrt(-e)*m*n^2*PolyLog(3, (sqrt(f)*x)/sqrt(-e)))/sqrt(f)]
    @test_int [log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))^2/x^2, x, 16, (4*b^2*sqrt(f)*m*n^2*atan((sqrt(f)*x)/sqrt(e)))/sqrt(e) + (4*b*sqrt(f)*m*n*atan((sqrt(f)*x)/sqrt(e))*(a + b*log(c*x^n)))/sqrt(e) + (sqrt(f)*m*(a + b*log(c*x^n))^2*log(1 - (sqrt(f)*x)/sqrt(-e)))/sqrt(-e) - (sqrt(f)*m*(a + b*log(c*x^n))^2*log(1 + (sqrt(f)*x)/sqrt(-e)))/sqrt(-e) - (2*b^2*n^2*log(d*(e + f*x^2)^m))/x - (2*b*n*(a + b*log(c*x^n))*log(d*(e + f*x^2)^m))/x - ((a + b*log(c*x^n))^2*log(d*(e + f*x^2)^m))/x - (2*b*sqrt(f)*m*n*(a + b*log(c*x^n))*PolyLog(2, -((sqrt(f)*x)/sqrt(-e))))/sqrt(-e) + (2*b*sqrt(f)*m*n*(a + b*log(c*x^n))*PolyLog(2, (sqrt(f)*x)/sqrt(-e)))/sqrt(-e) - (2*im*b^2*sqrt(f)*m*n^2*PolyLog(2, -((im*sqrt(f)*x)/sqrt(e))))/sqrt(e) + (2*im*b^2*sqrt(f)*m*n^2*PolyLog(2, (im*sqrt(f)*x)/sqrt(e)))/sqrt(e) + (2*b^2*sqrt(f)*m*n^2*PolyLog(3, -((sqrt(f)*x)/sqrt(-e))))/sqrt(-e) - (2*b^2*sqrt(f)*m*n^2*PolyLog(3, (sqrt(f)*x)/sqrt(-e)))/sqrt(-e)]
    @test_int [log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))^2/x^4, x, 22, -((52*b^2*f*m*n^2)/(27*e*x)) - (4*b^2*f^(3/2)*m*n^2*atan((sqrt(f)*x)/sqrt(e)))/(27*e^(3/2)) - (16*b*f*m*n*(a + b*log(c*x^n)))/(9*e*x) - (4*b*f^(3/2)*m*n*atan((sqrt(f)*x)/sqrt(e))*(a + b*log(c*x^n)))/(9*e^(3/2)) - (2*f*m*(a + b*log(c*x^n))^2)/(3*e*x) + (f^(3/2)*m*(a + b*log(c*x^n))^2*log(1 - (sqrt(f)*x)/sqrt(-e)))/(3*(-e)^(3/2)) - (f^(3/2)*m*(a + b*log(c*x^n))^2*log(1 + (sqrt(f)*x)/sqrt(-e)))/(3*(-e)^(3/2)) - (2*b^2*n^2*log(d*(e + f*x^2)^m))/(27*x^3) - (2*b*n*(a + b*log(c*x^n))*log(d*(e + f*x^2)^m))/(9*x^3) - ((a + b*log(c*x^n))^2*log(d*(e + f*x^2)^m))/(3*x^3) - (2*b*f^(3/2)*m*n*(a + b*log(c*x^n))*PolyLog(2, -((sqrt(f)*x)/sqrt(-e))))/(3*(-e)^(3/2)) + (2*b*f^(3/2)*m*n*(a + b*log(c*x^n))*PolyLog(2, (sqrt(f)*x)/sqrt(-e)))/(3*(-e)^(3/2)) + (2*im*b^2*f^(3/2)*m*n^2*PolyLog(2, -((im*sqrt(f)*x)/sqrt(e))))/(9*e^(3/2)) - (2*im*b^2*f^(3/2)*m*n^2*PolyLog(2, (im*sqrt(f)*x)/sqrt(e)))/(9*e^(3/2)) + (2*b^2*f^(3/2)*m*n^2*PolyLog(3, -((sqrt(f)*x)/sqrt(-e))))/(3*(-e)^(3/2)) - (2*b^2*f^(3/2)*m*n^2*PolyLog(3, (sqrt(f)*x)/sqrt(-e)))/(3*(-e)^(3/2))]

    @test_int [x^1*log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))^3, x, 26, (3/2)*b^3*m*n^3*x^2 - (9/4)*b^2*m*n^2*x^2*(a + b*log(c*x^n)) + (3/2)*b*m*n*x^2*(a + b*log(c*x^n))^2 - (1/2)*m*x^2*(a + b*log(c*x^n))^3 - (3*b^3*e*m*n^3*log(e + f*x^2))/(8*f) - (3/8)*b^3*n^3*x^2*log(d*(e + f*x^2)^m) + (3/4)*b^2*n^2*x^2*(a + b*log(c*x^n))*log(d*(e + f*x^2)^m) - (3/4)*b*n*x^2*(a + b*log(c*x^n))^2*log(d*(e + f*x^2)^m) + (1/2)*x^2*(a + b*log(c*x^n))^3*log(d*(e + f*x^2)^m) + (3*b^2*e*m*n^2*(a + b*log(c*x^n))*log(1 + (f*x^2)/e))/(4*f) - (3*b*e*m*n*(a + b*log(c*x^n))^2*log(1 + (f*x^2)/e))/(4*f) + (e*m*(a + b*log(c*x^n))^3*log(1 + (f*x^2)/e))/(2*f) + (3*b^3*e*m*n^3*PolyLog(2, -((f*x^2)/e)))/(8*f) - (3*b^2*e*m*n^2*(a + b*log(c*x^n))*PolyLog(2, -((f*x^2)/e)))/(4*f) + (3*b*e*m*n*(a + b*log(c*x^n))^2*PolyLog(2, -((f*x^2)/e)))/(4*f) + (3*b^3*e*m*n^3*PolyLog(3, -((f*x^2)/e)))/(8*f) - (3*b^2*e*m*n^2*(a + b*log(c*x^n))*PolyLog(3, -((f*x^2)/e)))/(4*f) + (3*b^3*e*m*n^3*PolyLog(4, -((f*x^2)/e)))/(8*f)]
    @test_int [log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))^3/x^1, x, 6, ((a + b*log(c*x^n))^4*log(d*(e + f*x^2)^m))/(4*b*n) - (m*(a + b*log(c*x^n))^4*log(1 + (f*x^2)/e))/(4*b*n) - (1/2)*m*(a + b*log(c*x^n))^3*PolyLog(2, -((f*x^2)/e)) + (3/4)*b*m*n*(a + b*log(c*x^n))^2*PolyLog(3, -((f*x^2)/e)) - (3/4)*b^2*m*n^2*(a + b*log(c*x^n))*PolyLog(4, -((f*x^2)/e)) + (3/8)*b^3*m*n^3*PolyLog(5, -((f*x^2)/e))]
    @test_int [log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))^3/x^3, x, 15, (3*b^3*f*m*n^3*log(x))/(4*e) - (3*b^2*f*m*n^2*log(1 + e/(f*x^2))*(a + b*log(c*x^n)))/(4*e) - (3*b*f*m*n*log(1 + e/(f*x^2))*(a + b*log(c*x^n))^2)/(4*e) - (f*m*log(1 + e/(f*x^2))*(a + b*log(c*x^n))^3)/(2*e) - (3*b^3*f*m*n^3*log(e + f*x^2))/(8*e) - (3*b^3*n^3*log(d*(e + f*x^2)^m))/(8*x^2) - (3*b^2*n^2*(a + b*log(c*x^n))*log(d*(e + f*x^2)^m))/(4*x^2) - (3*b*n*(a + b*log(c*x^n))^2*log(d*(e + f*x^2)^m))/(4*x^2) - ((a + b*log(c*x^n))^3*log(d*(e + f*x^2)^m))/(2*x^2) + (3*b^3*f*m*n^3*PolyLog(2, -(e/(f*x^2))))/(8*e) + (3*b^2*f*m*n^2*(a + b*log(c*x^n))*PolyLog(2, -(e/(f*x^2))))/(4*e) + (3*b*f*m*n*(a + b*log(c*x^n))^2*PolyLog(2, -(e/(f*x^2))))/(4*e) + (3*b^3*f*m*n^3*PolyLog(3, -(e/(f*x^2))))/(8*e) + (3*b^2*f*m*n^2*(a + b*log(c*x^n))*PolyLog(3, -(e/(f*x^2))))/(4*e) + (3*b^3*f*m*n^3*PolyLog(4, -(e/(f*x^2))))/(8*e)]

    @test_int [x^2*log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))^3, x, 49, (52*a*b^2*e*m*n^2*x)/(9*f) - (160*b^3*e*m*n^3*x)/(27*f) + (16/81)*b^3*m*n^3*x^3 + (4*b^3*e^(3/2)*m*n^3*atan((sqrt(f)*x)/sqrt(e)))/(27*f^(3/2)) + (52*b^3*e*m*n^2*x*log(c*x^n))/(9*f) - (4/9)*b^2*m*n^2*x^3*(a + b*log(c*x^n)) - (4*b^2*e^(3/2)*m*n^2*atan((sqrt(f)*x)/sqrt(e))*(a + b*log(c*x^n)))/(9*f^(3/2)) - (8*b*e*m*n*x*(a + b*log(c*x^n))^2)/(3*f) + (4/9)*b*m*n*x^3*(a + b*log(c*x^n))^2 + (2*e*m*x*(a + b*log(c*x^n))^3)/(3*f) - (2/9)*m*x^3*(a + b*log(c*x^n))^3 + (b*(-e)^(3/2)*m*n*(a + b*log(c*x^n))^2*log(1 - (sqrt(f)*x)/sqrt(-e)))/(3*f^(3/2)) - ((-e)^(3/2)*m*(a + b*log(c*x^n))^3*log(1 - (sqrt(f)*x)/sqrt(-e)))/(3*f^(3/2)) - (b*(-e)^(3/2)*m*n*(a + b*log(c*x^n))^2*log(1 + (sqrt(f)*x)/sqrt(-e)))/(3*f^(3/2)) + ((-e)^(3/2)*m*(a + b*log(c*x^n))^3*log(1 + (sqrt(f)*x)/sqrt(-e)))/(3*f^(3/2)) - (2/27)*b^3*n^3*x^3*log(d*(e + f*x^2)^m) + (2/9)*b^2*n^2*x^3*(a + b*log(c*x^n))*log(d*(e + f*x^2)^m) - (1/3)*b*n*x^3*(a + b*log(c*x^n))^2*log(d*(e + f*x^2)^m) + (1/3)*x^3*(a + b*log(c*x^n))^3*log(d*(e + f*x^2)^m) - (2*b^2*(-e)^(3/2)*m*n^2*(a + b*log(c*x^n))*PolyLog(2, -((sqrt(f)*x)/sqrt(-e))))/(3*f^(3/2)) + (b*(-e)^(3/2)*m*n*(a + b*log(c*x^n))^2*PolyLog(2, -((sqrt(f)*x)/sqrt(-e))))/f^(3/2) + (2*b^2*(-e)^(3/2)*m*n^2*(a + b*log(c*x^n))*PolyLog(2, (sqrt(f)*x)/sqrt(-e)))/(3*f^(3/2)) - (b*(-e)^(3/2)*m*n*(a + b*log(c*x^n))^2*PolyLog(2, (sqrt(f)*x)/sqrt(-e)))/f^(3/2) + (2*im*b^3*e^(3/2)*m*n^3*PolyLog(2, -((im*sqrt(f)*x)/sqrt(e))))/(9*f^(3/2)) - (2*im*b^3*e^(3/2)*m*n^3*PolyLog(2, (im*sqrt(f)*x)/sqrt(e)))/(9*f^(3/2)) + (2*b^3*(-e)^(3/2)*m*n^3*PolyLog(3, -((sqrt(f)*x)/sqrt(-e))))/(3*f^(3/2)) - (2*b^2*(-e)^(3/2)*m*n^2*(a + b*log(c*x^n))*PolyLog(3, -((sqrt(f)*x)/sqrt(-e))))/f^(3/2) - (2*b^3*(-e)^(3/2)*m*n^3*PolyLog(3, (sqrt(f)*x)/sqrt(-e)))/(3*f^(3/2)) + (2*b^2*(-e)^(3/2)*m*n^2*(a + b*log(c*x^n))*PolyLog(3, (sqrt(f)*x)/sqrt(-e)))/f^(3/2) + (2*b^3*(-e)^(3/2)*m*n^3*PolyLog(4, -((sqrt(f)*x)/sqrt(-e))))/f^(3/2) - (2*b^3*(-e)^(3/2)*m*n^3*PolyLog(4, (sqrt(f)*x)/sqrt(-e)))/f^(3/2)]
    @test_int [x^0*log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))^3, x, 42, -24*a*b^2*m*n^2*x + 36*b^3*m*n^3*x - 12*b^2*m*n^2*(a - b*n)*x + (12*b^2*sqrt(e)*m*n^2*(a - b*n)*atan((sqrt(f)*x)/sqrt(e)))/sqrt(f) - 36*b^3*m*n^2*x*log(c*x^n) + (12*b^3*sqrt(e)*m*n^2*atan((sqrt(f)*x)/sqrt(e))*log(c*x^n))/sqrt(f) + 12*b*m*n*x*(a + b*log(c*x^n))^2 - 2*m*x*(a + b*log(c*x^n))^3 + (3*b*sqrt(-e)*m*n*(a + b*log(c*x^n))^2*log(1 - (sqrt(f)*x)/sqrt(-e)))/sqrt(f) - (sqrt(-e)*m*(a + b*log(c*x^n))^3*log(1 - (sqrt(f)*x)/sqrt(-e)))/sqrt(f) - (3*b*sqrt(-e)*m*n*(a + b*log(c*x^n))^2*log(1 + (sqrt(f)*x)/sqrt(-e)))/sqrt(f) + (sqrt(-e)*m*(a + b*log(c*x^n))^3*log(1 + (sqrt(f)*x)/sqrt(-e)))/sqrt(f) + 6*a*b^2*n^2*x*log(d*(e + f*x^2)^m) - 6*b^3*n^3*x*log(d*(e + f*x^2)^m) + 6*b^3*n^2*x*log(c*x^n)*log(d*(e + f*x^2)^m) - 3*b*n*x*(a + b*log(c*x^n))^2*log(d*(e + f*x^2)^m) + x*(a + b*log(c*x^n))^3*log(d*(e + f*x^2)^m) - (6*b^2*sqrt(-e)*m*n^2*(a + b*log(c*x^n))*PolyLog(2, -((sqrt(f)*x)/sqrt(-e))))/sqrt(f) + (3*b*sqrt(-e)*m*n*(a + b*log(c*x^n))^2*PolyLog(2, -((sqrt(f)*x)/sqrt(-e))))/sqrt(f) + (6*b^2*sqrt(-e)*m*n^2*(a + b*log(c*x^n))*PolyLog(2, (sqrt(f)*x)/sqrt(-e)))/sqrt(f) - (3*b*sqrt(-e)*m*n*(a + b*log(c*x^n))^2*PolyLog(2, (sqrt(f)*x)/sqrt(-e)))/sqrt(f) - (6*im*b^3*sqrt(e)*m*n^3*PolyLog(2, -((im*sqrt(f)*x)/sqrt(e))))/sqrt(f) + (6*im*b^3*sqrt(e)*m*n^3*PolyLog(2, (im*sqrt(f)*x)/sqrt(e)))/sqrt(f) + (6*b^3*sqrt(-e)*m*n^3*PolyLog(3, -((sqrt(f)*x)/sqrt(-e))))/sqrt(f) - (6*b^2*sqrt(-e)*m*n^2*(a + b*log(c*x^n))*PolyLog(3, -((sqrt(f)*x)/sqrt(-e))))/sqrt(f) - (6*b^3*sqrt(-e)*m*n^3*PolyLog(3, (sqrt(f)*x)/sqrt(-e)))/sqrt(f) + (6*b^2*sqrt(-e)*m*n^2*(a + b*log(c*x^n))*PolyLog(3, (sqrt(f)*x)/sqrt(-e)))/sqrt(f) + (6*b^3*sqrt(-e)*m*n^3*PolyLog(4, -((sqrt(f)*x)/sqrt(-e))))/sqrt(f) - (6*b^3*sqrt(-e)*m*n^3*PolyLog(4, (sqrt(f)*x)/sqrt(-e)))/sqrt(f)]
    @test_int [log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))^3/x^2, x, 26, (12*b^3*sqrt(f)*m*n^3*atan((sqrt(f)*x)/sqrt(e)))/sqrt(e) + (12*b^2*sqrt(f)*m*n^2*atan((sqrt(f)*x)/sqrt(e))*(a + b*log(c*x^n)))/sqrt(e) + (3*b*sqrt(f)*m*n*(a + b*log(c*x^n))^2*log(1 - (sqrt(f)*x)/sqrt(-e)))/sqrt(-e) + (sqrt(f)*m*(a + b*log(c*x^n))^3*log(1 - (sqrt(f)*x)/sqrt(-e)))/sqrt(-e) - (3*b*sqrt(f)*m*n*(a + b*log(c*x^n))^2*log(1 + (sqrt(f)*x)/sqrt(-e)))/sqrt(-e) - (sqrt(f)*m*(a + b*log(c*x^n))^3*log(1 + (sqrt(f)*x)/sqrt(-e)))/sqrt(-e) - (6*b^3*n^3*log(d*(e + f*x^2)^m))/x - (6*b^2*n^2*(a + b*log(c*x^n))*log(d*(e + f*x^2)^m))/x - (3*b*n*(a + b*log(c*x^n))^2*log(d*(e + f*x^2)^m))/x - ((a + b*log(c*x^n))^3*log(d*(e + f*x^2)^m))/x - (6*b^2*sqrt(f)*m*n^2*(a + b*log(c*x^n))*PolyLog(2, -((sqrt(f)*x)/sqrt(-e))))/sqrt(-e) - (3*b*sqrt(f)*m*n*(a + b*log(c*x^n))^2*PolyLog(2, -((sqrt(f)*x)/sqrt(-e))))/sqrt(-e) + (6*b^2*sqrt(f)*m*n^2*(a + b*log(c*x^n))*PolyLog(2, (sqrt(f)*x)/sqrt(-e)))/sqrt(-e) + (3*b*sqrt(f)*m*n*(a + b*log(c*x^n))^2*PolyLog(2, (sqrt(f)*x)/sqrt(-e)))/sqrt(-e) - (6*im*b^3*sqrt(f)*m*n^3*PolyLog(2, -((im*sqrt(f)*x)/sqrt(e))))/sqrt(e) + (6*im*b^3*sqrt(f)*m*n^3*PolyLog(2, (im*sqrt(f)*x)/sqrt(e)))/sqrt(e) + (6*b^3*sqrt(f)*m*n^3*PolyLog(3, -((sqrt(f)*x)/sqrt(-e))))/sqrt(-e) + (6*b^2*sqrt(f)*m*n^2*(a + b*log(c*x^n))*PolyLog(3, -((sqrt(f)*x)/sqrt(-e))))/sqrt(-e) - (6*b^3*sqrt(f)*m*n^3*PolyLog(3, (sqrt(f)*x)/sqrt(-e)))/sqrt(-e) - (6*b^2*sqrt(f)*m*n^2*(a + b*log(c*x^n))*PolyLog(3, (sqrt(f)*x)/sqrt(-e)))/sqrt(-e) - (6*b^3*sqrt(f)*m*n^3*PolyLog(4, -((sqrt(f)*x)/sqrt(-e))))/sqrt(-e) + (6*b^3*sqrt(f)*m*n^3*PolyLog(4, (sqrt(f)*x)/sqrt(-e)))/sqrt(-e)]
    @test_int [log(d*(e + f*x^2)^m)*(a + b*log(c*x^n))^3/x^4, x, 36, -((160*b^3*f*m*n^3)/(27*e*x)) - (4*b^3*f^(3/2)*m*n^3*atan((sqrt(f)*x)/sqrt(e)))/(27*e^(3/2)) - (52*b^2*f*m*n^2*(a + b*log(c*x^n)))/(9*e*x) - (4*b^2*f^(3/2)*m*n^2*atan((sqrt(f)*x)/sqrt(e))*(a + b*log(c*x^n)))/(9*e^(3/2)) - (8*b*f*m*n*(a + b*log(c*x^n))^2)/(3*e*x) - (2*f*m*(a + b*log(c*x^n))^3)/(3*e*x) + (b*f^(3/2)*m*n*(a + b*log(c*x^n))^2*log(1 - (sqrt(f)*x)/sqrt(-e)))/(3*(-e)^(3/2)) + (f^(3/2)*m*(a + b*log(c*x^n))^3*log(1 - (sqrt(f)*x)/sqrt(-e)))/(3*(-e)^(3/2)) - (b*f^(3/2)*m*n*(a + b*log(c*x^n))^2*log(1 + (sqrt(f)*x)/sqrt(-e)))/(3*(-e)^(3/2)) - (f^(3/2)*m*(a + b*log(c*x^n))^3*log(1 + (sqrt(f)*x)/sqrt(-e)))/(3*(-e)^(3/2)) - (2*b^3*n^3*log(d*(e + f*x^2)^m))/(27*x^3) - (2*b^2*n^2*(a + b*log(c*x^n))*log(d*(e + f*x^2)^m))/(9*x^3) - (b*n*(a + b*log(c*x^n))^2*log(d*(e + f*x^2)^m))/(3*x^3) - ((a + b*log(c*x^n))^3*log(d*(e + f*x^2)^m))/(3*x^3) - (2*b^2*f^(3/2)*m*n^2*(a + b*log(c*x^n))*PolyLog(2, -((sqrt(f)*x)/sqrt(-e))))/(3*(-e)^(3/2)) - (b*f^(3/2)*m*n*(a + b*log(c*x^n))^2*PolyLog(2, -((sqrt(f)*x)/sqrt(-e))))/(-e)^(3/2) + (2*b^2*f^(3/2)*m*n^2*(a + b*log(c*x^n))*PolyLog(2, (sqrt(f)*x)/sqrt(-e)))/(3*(-e)^(3/2)) + (b*f^(3/2)*m*n*(a + b*log(c*x^n))^2*PolyLog(2, (sqrt(f)*x)/sqrt(-e)))/(-e)^(3/2) + (2*im*b^3*f^(3/2)*m*n^3*PolyLog(2, -((im*sqrt(f)*x)/sqrt(e))))/(9*e^(3/2)) - (2*im*b^3*f^(3/2)*m*n^3*PolyLog(2, (im*sqrt(f)*x)/sqrt(e)))/(9*e^(3/2)) + (2*b^3*f^(3/2)*m*n^3*PolyLog(3, -((sqrt(f)*x)/sqrt(-e))))/(3*(-e)^(3/2)) + (2*b^2*f^(3/2)*m*n^2*(a + b*log(c*x^n))*PolyLog(3, -((sqrt(f)*x)/sqrt(-e))))/(-e)^(3/2) - (2*b^3*f^(3/2)*m*n^3*PolyLog(3, (sqrt(f)*x)/sqrt(-e)))/(3*(-e)^(3/2)) - (2*b^2*f^(3/2)*m*n^2*(a + b*log(c*x^n))*PolyLog(3, (sqrt(f)*x)/sqrt(-e)))/(-e)^(3/2) - (2*b^3*f^(3/2)*m*n^3*PolyLog(4, -((sqrt(f)*x)/sqrt(-e))))/(-e)^(3/2) + (2*b^3*f^(3/2)*m*n^3*PolyLog(4, (sqrt(f)*x)/sqrt(-e)))/(-e)^(3/2)]

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

    @test_int [x^2*log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n)), x, 9, -((7*b*e^5*k*n*sqrt(x))/(9*f^5)) + (2*b*e^4*k*n*x)/(9*f^4) - (b*e^3*k*n*x^(3/2))/(9*f^3) + (5*b*e^2*k*n*x^2)/(72*f^2) - (11*b*e*k*n*x^(5/2))/(225*f) + (1/27)*b*k*n*x^3 + (b*e^6*k*n*log(e + f*sqrt(x)))/(9*f^6) - (1/9)*b*n*x^3*log(d*(e + f*sqrt(x))^k) + (2*b*e^6*k*n*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/(3*f^6) + (e^5*k*sqrt(x)*(a + b*log(c*x^n)))/(3*f^5) - (e^4*k*x*(a + b*log(c*x^n)))/(6*f^4) + (e^3*k*x^(3/2)*(a + b*log(c*x^n)))/(9*f^3) - (e^2*k*x^2*(a + b*log(c*x^n)))/(12*f^2) + (e*k*x^(5/2)*(a + b*log(c*x^n)))/(15*f) - (1/18)*k*x^3*(a + b*log(c*x^n)) - (e^6*k*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/(3*f^6) + (1/3)*x^3*log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n)) + (2*b*e^6*k*n*PolyLog(2, 1 + (f*sqrt(x))/e))/(3*f^6)]
    @test_int [x^1*log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n)), x, 9, -((5*b*e^3*k*n*sqrt(x))/(4*f^3)) + (3*b*e^2*k*n*x)/(8*f^2) - (7*b*e*k*n*x^(3/2))/(36*f) + (1/8)*b*k*n*x^2 + (b*e^4*k*n*log(e + f*sqrt(x)))/(4*f^4) - (1/4)*b*n*x^2*log(d*(e + f*sqrt(x))^k) + (b*e^4*k*n*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/f^4 + (e^3*k*sqrt(x)*(a + b*log(c*x^n)))/(2*f^3) - (e^2*k*x*(a + b*log(c*x^n)))/(4*f^2) + (e*k*x^(3/2)*(a + b*log(c*x^n)))/(6*f) - (1/8)*k*x^2*(a + b*log(c*x^n)) - (e^4*k*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/(2*f^4) + (1/2)*x^2*log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n)) + (b*e^4*k*n*PolyLog(2, 1 + (f*sqrt(x))/e))/f^4]
    @test_int [x^0*log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n)), x, 9, -((3*b*e*k*n*sqrt(x))/f) + b*k*n*x + (b*e^2*k*n*log(e + f*sqrt(x)))/f^2 - b*n*x*log(d*(e + f*sqrt(x))^k) + (2*b*e^2*k*n*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/f^2 + (e*k*sqrt(x)*(a + b*log(c*x^n)))/f - (1/2)*k*x*(a + b*log(c*x^n)) - (e^2*k*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/f^2 + x*log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n)) + (2*b*e^2*k*n*PolyLog(2, 1 + (f*sqrt(x))/e))/f^2]
    @test_int [log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n))/x^1, x, 4, (log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n))^2)/(2*b*n) - (k*log(1 + (f*sqrt(x))/e)*(a + b*log(c*x^n))^2)/(2*b*n) - 2*k*(a + b*log(c*x^n))*PolyLog(2, -((f*sqrt(x))/e)) + 4*b*k*n*PolyLog(3, -((f*sqrt(x))/e))]
    @test_int [log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n))/x^2, x, 10, -((3*b*f*k*n)/(e*sqrt(x))) + (b*f^2*k*n*log(e + f*sqrt(x)))/e^2 - (b*n*log(d*(e + f*sqrt(x))^k))/x - (2*b*f^2*k*n*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/e^2 - (b*f^2*k*n*log(x))/(2*e^2) + (b*f^2*k*n*log(x)^2)/(4*e^2) - (f*k*(a + b*log(c*x^n)))/(e*sqrt(x)) + (f^2*k*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/e^2 - (log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n)))/x - (f^2*k*log(x)*(a + b*log(c*x^n)))/(2*e^2) - (2*b*f^2*k*n*PolyLog(2, 1 + (f*sqrt(x))/e))/e^2]
    @test_int [log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n))/x^3, x, 10, -((7*b*f*k*n)/(36*e*x^(3/2))) + (3*b*f^2*k*n)/(8*e^2*x) - (5*b*f^3*k*n)/(4*e^3*sqrt(x)) + (b*f^4*k*n*log(e + f*sqrt(x)))/(4*e^4) - (b*n*log(d*(e + f*sqrt(x))^k))/(4*x^2) - (b*f^4*k*n*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/e^4 - (b*f^4*k*n*log(x))/(8*e^4) + (b*f^4*k*n*log(x)^2)/(8*e^4) - (f*k*(a + b*log(c*x^n)))/(6*e*x^(3/2)) + (f^2*k*(a + b*log(c*x^n)))/(4*e^2*x) - (f^3*k*(a + b*log(c*x^n)))/(2*e^3*sqrt(x)) + (f^4*k*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/(2*e^4) - (log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n)))/(2*x^2) - (f^4*k*log(x)*(a + b*log(c*x^n)))/(4*e^4) - (b*f^4*k*n*PolyLog(2, 1 + (f*sqrt(x))/e))/e^4]
    @test_int [log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n))/x^4, x, 10, -((11*b*f*k*n)/(225*e*x^(5/2))) + (5*b*f^2*k*n)/(72*e^2*x^2) - (b*f^3*k*n)/(9*e^3*x^(3/2)) + (2*b*f^4*k*n)/(9*e^4*x) - (7*b*f^5*k*n)/(9*e^5*sqrt(x)) + (b*f^6*k*n*log(e + f*sqrt(x)))/(9*e^6) - (b*n*log(d*(e + f*sqrt(x))^k))/(9*x^3) - (2*b*f^6*k*n*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/(3*e^6) - (b*f^6*k*n*log(x))/(18*e^6) + (b*f^6*k*n*log(x)^2)/(12*e^6) - (f*k*(a + b*log(c*x^n)))/(15*e*x^(5/2)) + (f^2*k*(a + b*log(c*x^n)))/(12*e^2*x^2) - (f^3*k*(a + b*log(c*x^n)))/(9*e^3*x^(3/2)) + (f^4*k*(a + b*log(c*x^n)))/(6*e^4*x) - (f^5*k*(a + b*log(c*x^n)))/(3*e^5*sqrt(x)) + (f^6*k*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/(3*e^6) - (log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n)))/(3*x^3) - (f^6*k*log(x)*(a + b*log(c*x^n)))/(6*e^6) - (2*b*f^6*k*n*PolyLog(2, 1 + (f*sqrt(x))/e))/(3*e^6)]

    @test_int [x^2*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^2, x, 22, (86*b^2*e^5*n^2*sqrt(x))/(27*f^5) + (a*b*e^4*n*x)/(3*f^4) - (13*b^2*e^4*n^2*x)/(27*f^4) + (14*b^2*e^3*n^2*x^(3/2))/(81*f^3) - (19*b^2*e^2*n^2*x^2)/(216*f^2) + (182*b^2*e*n^2*x^(5/2))/(3375*f) - (1/27)*b^2*n^2*x^3 - (2*b^2*e^6*n^2*log(e + f*sqrt(x)))/(27*f^6) + (2/27)*b^2*n^2*x^3*log(d*(e + f*sqrt(x))) - (4*b^2*e^6*n^2*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/(9*f^6) + (b^2*e^4*n*x*log(c*x^n))/(3*f^4) - (14*b*e^5*n*sqrt(x)*(a + b*log(c*x^n)))/(9*f^5) + (b*e^4*n*x*(a + b*log(c*x^n)))/(9*f^4) - (2*b*e^3*n*x^(3/2)*(a + b*log(c*x^n)))/(9*f^3) + (5*b*e^2*n*x^2*(a + b*log(c*x^n)))/(36*f^2) - (22*b*e*n*x^(5/2)*(a + b*log(c*x^n)))/(225*f) + (2/27)*b*n*x^3*(a + b*log(c*x^n)) + (2*b*e^6*n*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/(9*f^6) - (2/9)*b*n*x^3*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n)) + (e^5*sqrt(x)*(a + b*log(c*x^n))^2)/(3*f^5) - (e^4*x*(a + b*log(c*x^n))^2)/(6*f^4) + (e^3*x^(3/2)*(a + b*log(c*x^n))^2)/(9*f^3) - (e^2*x^2*(a + b*log(c*x^n))^2)/(12*f^2) + (e*x^(5/2)*(a + b*log(c*x^n))^2)/(15*f) - (1/18)*x^3*(a + b*log(c*x^n))^2 + (1/3)*x^3*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^2 - (e^6*log(1 + (f*sqrt(x))/e)*(a + b*log(c*x^n))^2)/(3*f^6) - (4*b^2*e^6*n^2*PolyLog(2, 1 + (f*sqrt(x))/e))/(9*f^6) - (4*b*e^6*n*(a + b*log(c*x^n))*PolyLog(2, -((f*sqrt(x))/e)))/(3*f^6) + (8*b^2*e^6*n^2*PolyLog(3, -((f*sqrt(x))/e)))/(3*f^6)]
    @test_int [x^1*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^2, x, 20, (21*b^2*e^3*n^2*sqrt(x))/(4*f^3) + (a*b*e^2*n*x)/(2*f^2) - (7*b^2*e^2*n^2*x)/(8*f^2) + (37*b^2*e*n^2*x^(3/2))/(108*f) - (3/16)*b^2*n^2*x^2 - (b^2*e^4*n^2*log(e + f*sqrt(x)))/(4*f^4) + (1/4)*b^2*n^2*x^2*log(d*(e + f*sqrt(x))) - (b^2*e^4*n^2*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/f^4 + (b^2*e^2*n*x*log(c*x^n))/(2*f^2) - (5*b*e^3*n*sqrt(x)*(a + b*log(c*x^n)))/(2*f^3) + (b*e^2*n*x*(a + b*log(c*x^n)))/(4*f^2) - (7*b*e*n*x^(3/2)*(a + b*log(c*x^n)))/(18*f) + (1/4)*b*n*x^2*(a + b*log(c*x^n)) + (b*e^4*n*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/(2*f^4) - (1/2)*b*n*x^2*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n)) + (e^3*sqrt(x)*(a + b*log(c*x^n))^2)/(2*f^3) - (e^2*x*(a + b*log(c*x^n))^2)/(4*f^2) + (e*x^(3/2)*(a + b*log(c*x^n))^2)/(6*f) - (1/8)*x^2*(a + b*log(c*x^n))^2 + (1/2)*x^2*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^2 - (e^4*log(1 + (f*sqrt(x))/e)*(a + b*log(c*x^n))^2)/(2*f^4) - (b^2*e^4*n^2*PolyLog(2, 1 + (f*sqrt(x))/e))/f^4 - (2*b*e^4*n*(a + b*log(c*x^n))*PolyLog(2, -((f*sqrt(x))/e)))/f^4 + (4*b^2*e^4*n^2*PolyLog(3, -((f*sqrt(x))/e)))/f^4]
    @test_int [x^0*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^2, x, 18, (14*b^2*e*n^2*sqrt(x))/f + a*b*n*x - 3*b^2*n^2*x - (2*b^2*e^2*n^2*log(e + f*sqrt(x)))/f^2 + 2*b^2*n^2*x*log(d*(e + f*sqrt(x))) - (4*b^2*e^2*n^2*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/f^2 + b^2*n*x*log(c*x^n) - (6*b*e*n*sqrt(x)*(a + b*log(c*x^n)))/f + b*n*x*(a + b*log(c*x^n)) + (2*b*e^2*n*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/f^2 - 2*b*n*x*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n)) + (e*sqrt(x)*(a + b*log(c*x^n))^2)/f - (1/2)*x*(a + b*log(c*x^n))^2 + x*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^2 - (e^2*log(1 + (f*sqrt(x))/e)*(a + b*log(c*x^n))^2)/f^2 - (4*b^2*e^2*n^2*PolyLog(2, 1 + (f*sqrt(x))/e))/f^2 - (4*b*e^2*n*(a + b*log(c*x^n))*PolyLog(2, -((f*sqrt(x))/e)))/f^2 + (8*b^2*e^2*n^2*PolyLog(3, -((f*sqrt(x))/e)))/f^2]
    @test_int [log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^2/x^1, x, 5, (log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^3)/(3*b*n) - (log(1 + (f*sqrt(x))/e)*(a + b*log(c*x^n))^3)/(3*b*n) - 2*(a + b*log(c*x^n))^2*PolyLog(2, -((f*sqrt(x))/e)) + 8*b*n*(a + b*log(c*x^n))*PolyLog(3, -((f*sqrt(x))/e)) - 16*b^2*n^2*PolyLog(4, -((f*sqrt(x))/e))]
    @test_int [log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^2/x^2, x, 21, -((14*b^2*f*n^2)/(e*sqrt(x))) + (2*b^2*f^2*n^2*log(e + f*sqrt(x)))/e^2 - (2*b^2*n^2*log(d*(e + f*sqrt(x))))/x - (4*b^2*f^2*n^2*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/e^2 - (b^2*f^2*n^2*log(x))/e^2 + (b^2*f^2*n^2*log(x)^2)/(2*e^2) - (6*b*f*n*(a + b*log(c*x^n)))/(e*sqrt(x)) + (2*b*f^2*n*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/e^2 - (2*b*n*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n)))/x - (b*f^2*n*log(x)*(a + b*log(c*x^n)))/e^2 - (f*(a + b*log(c*x^n))^2)/(e*sqrt(x)) - (log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^2)/x + (f^2*log(1 + (f*sqrt(x))/e)*(a + b*log(c*x^n))^2)/e^2 - (f^2*(a + b*log(c*x^n))^3)/(6*b*e^2*n) - (4*b^2*f^2*n^2*PolyLog(2, 1 + (f*sqrt(x))/e))/e^2 + (4*b*f^2*n*(a + b*log(c*x^n))*PolyLog(2, -((f*sqrt(x))/e)))/e^2 - (8*b^2*f^2*n^2*PolyLog(3, -((f*sqrt(x))/e)))/e^2]
    @test_int [log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^2/x^3, x, 23, -((37*b^2*f*n^2)/(108*e*x^(3/2))) + (7*b^2*f^2*n^2)/(8*e^2*x) - (21*b^2*f^3*n^2)/(4*e^3*sqrt(x)) + (b^2*f^4*n^2*log(e + f*sqrt(x)))/(4*e^4) - (b^2*n^2*log(d*(e + f*sqrt(x))))/(4*x^2) - (b^2*f^4*n^2*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/e^4 - (b^2*f^4*n^2*log(x))/(8*e^4) + (b^2*f^4*n^2*log(x)^2)/(8*e^4) - (7*b*f*n*(a + b*log(c*x^n)))/(18*e*x^(3/2)) + (3*b*f^2*n*(a + b*log(c*x^n)))/(4*e^2*x) - (5*b*f^3*n*(a + b*log(c*x^n)))/(2*e^3*sqrt(x)) + (b*f^4*n*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/(2*e^4) - (b*n*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n)))/(2*x^2) - (b*f^4*n*log(x)*(a + b*log(c*x^n)))/(4*e^4) - (f*(a + b*log(c*x^n))^2)/(6*e*x^(3/2)) + (f^2*(a + b*log(c*x^n))^2)/(4*e^2*x) - (f^3*(a + b*log(c*x^n))^2)/(2*e^3*sqrt(x)) - (log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^2)/(2*x^2) + (f^4*log(1 + (f*sqrt(x))/e)*(a + b*log(c*x^n))^2)/(2*e^4) - (f^4*(a + b*log(c*x^n))^3)/(12*b*e^4*n) - (b^2*f^4*n^2*PolyLog(2, 1 + (f*sqrt(x))/e))/e^4 + (2*b*f^4*n*(a + b*log(c*x^n))*PolyLog(2, -((f*sqrt(x))/e)))/e^4 - (4*b^2*f^4*n^2*PolyLog(3, -((f*sqrt(x))/e)))/e^4]

    @test_int [x^1*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^3, x, 36, -((255*b^3*e^3*n^3*sqrt(x))/(8*f^3)) - (9*a*b^2*e^2*n^2*x)/(4*f^2) + (45*b^3*e^2*n^3*x)/(16*f^2) - (175*b^3*e*n^3*x^(3/2))/(216*f) + (3/8)*b^3*n^3*x^2 + (3*b^3*e^4*n^3*log(e + f*sqrt(x)))/(8*f^4) - (3/8)*b^3*n^3*x^2*log(d*(e + f*sqrt(x))) + (3*b^3*e^4*n^3*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/(2*f^4) - (9*b^3*e^2*n^2*x*log(c*x^n))/(4*f^2) + (63*b^2*e^3*n^2*sqrt(x)*(a + b*log(c*x^n)))/(4*f^3) - (3*b^2*e^2*n^2*x*(a + b*log(c*x^n)))/(8*f^2) + (37*b^2*e*n^2*x^(3/2)*(a + b*log(c*x^n)))/(36*f) - (9/16)*b^2*n^2*x^2*(a + b*log(c*x^n)) - (3*b^2*e^4*n^2*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/(4*f^4) + (3/4)*b^2*n^2*x^2*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n)) - (15*b*e^3*n*sqrt(x)*(a + b*log(c*x^n))^2)/(4*f^3) + (9*b*e^2*n*x*(a + b*log(c*x^n))^2)/(8*f^2) - (7*b*e*n*x^(3/2)*(a + b*log(c*x^n))^2)/(12*f) + (3/8)*b*n*x^2*(a + b*log(c*x^n))^2 - (3/4)*b*n*x^2*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^2 + (3*b*e^4*n*log(1 + (f*sqrt(x))/e)*(a + b*log(c*x^n))^2)/(4*f^4) + (e^3*sqrt(x)*(a + b*log(c*x^n))^3)/(2*f^3) - (e^2*x*(a + b*log(c*x^n))^3)/(4*f^2) + (e*x^(3/2)*(a + b*log(c*x^n))^3)/(6*f) - (1/8)*x^2*(a + b*log(c*x^n))^3 + (1/2)*x^2*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^3 - (e^4*log(1 + (f*sqrt(x))/e)*(a + b*log(c*x^n))^3)/(2*f^4) + (3*b^3*e^4*n^3*PolyLog(2, 1 + (f*sqrt(x))/e))/(2*f^4) + (3*b^2*e^4*n^2*(a + b*log(c*x^n))*PolyLog(2, -((f*sqrt(x))/e)))/f^4 - (3*b*e^4*n*(a + b*log(c*x^n))^2*PolyLog(2, -((f*sqrt(x))/e)))/f^4 - (6*b^3*e^4*n^3*PolyLog(3, -((f*sqrt(x))/e)))/f^4 + (12*b^2*e^4*n^2*(a + b*log(c*x^n))*PolyLog(3, -((f*sqrt(x))/e)))/f^4 - (24*b^3*e^4*n^3*PolyLog(4, -((f*sqrt(x))/e)))/f^4]
    @test_int [x^0*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^3, x, 30, -((90*b^3*e*n^3*sqrt(x))/f) - 6*a*b^2*n^2*x + 12*b^3*n^3*x + (6*b^3*e^2*n^3*log(e + f*sqrt(x)))/f^2 - 6*b^3*n^3*x*log(d*(e + f*sqrt(x))) + (12*b^3*e^2*n^3*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/f^2 - 6*b^3*n^2*x*log(c*x^n) + (42*b^2*e*n^2*sqrt(x)*(a + b*log(c*x^n)))/f - 3*b^2*n^2*x*(a + b*log(c*x^n)) - (6*b^2*e^2*n^2*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/f^2 + 6*b^2*n^2*x*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n)) - (9*b*e*n*sqrt(x)*(a + b*log(c*x^n))^2)/f + 3*b*n*x*(a + b*log(c*x^n))^2 - 3*b*n*x*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^2 + (3*b*e^2*n*log(1 + (f*sqrt(x))/e)*(a + b*log(c*x^n))^2)/f^2 + (e*sqrt(x)*(a + b*log(c*x^n))^3)/f - (1/2)*x*(a + b*log(c*x^n))^3 + x*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^3 - (e^2*log(1 + (f*sqrt(x))/e)*(a + b*log(c*x^n))^3)/f^2 + (12*b^3*e^2*n^3*PolyLog(2, 1 + (f*sqrt(x))/e))/f^2 + (12*b^2*e^2*n^2*(a + b*log(c*x^n))*PolyLog(2, -((f*sqrt(x))/e)))/f^2 - (6*b*e^2*n*(a + b*log(c*x^n))^2*PolyLog(2, -((f*sqrt(x))/e)))/f^2 - (24*b^3*e^2*n^3*PolyLog(3, -((f*sqrt(x))/e)))/f^2 + (24*b^2*e^2*n^2*(a + b*log(c*x^n))*PolyLog(3, -((f*sqrt(x))/e)))/f^2 - (48*b^3*e^2*n^3*PolyLog(4, -((f*sqrt(x))/e)))/f^2]
    @test_int [log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^3/x^1, x, 6, (log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^4)/(4*b*n) - (log(1 + (f*sqrt(x))/e)*(a + b*log(c*x^n))^4)/(4*b*n) - 2*(a + b*log(c*x^n))^3*PolyLog(2, -((f*sqrt(x))/e)) + 12*b*n*(a + b*log(c*x^n))^2*PolyLog(3, -((f*sqrt(x))/e)) - 48*b^2*n^2*(a + b*log(c*x^n))*PolyLog(4, -((f*sqrt(x))/e)) + 96*b^3*n^3*PolyLog(5, -((f*sqrt(x))/e))]
    @test_int [log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^3/x^2, x, 34, -((90*b^3*f*n^3)/(e*sqrt(x))) + (6*b^3*f^2*n^3*log(e + f*sqrt(x)))/e^2 - (6*b^3*n^3*log(d*(e + f*sqrt(x))))/x - (12*b^3*f^2*n^3*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/e^2 - (3*b^3*f^2*n^3*log(x))/e^2 + (3*b^3*f^2*n^3*log(x)^2)/(2*e^2) - (42*b^2*f*n^2*(a + b*log(c*x^n)))/(e*sqrt(x)) + (6*b^2*f^2*n^2*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/e^2 - (6*b^2*n^2*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n)))/x - (3*b^2*f^2*n^2*log(x)*(a + b*log(c*x^n)))/e^2 - (9*b*f*n*(a + b*log(c*x^n))^2)/(e*sqrt(x)) - (3*b*n*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^2)/x + (3*b*f^2*n*log(1 + (f*sqrt(x))/e)*(a + b*log(c*x^n))^2)/e^2 - (f^2*(a + b*log(c*x^n))^3)/(2*e^2) - (f*(a + b*log(c*x^n))^3)/(e*sqrt(x)) - (log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^3)/x + (f^2*log(1 + (f*sqrt(x))/e)*(a + b*log(c*x^n))^3)/e^2 - (f^2*(a + b*log(c*x^n))^4)/(8*b*e^2*n) - (12*b^3*f^2*n^3*PolyLog(2, 1 + (f*sqrt(x))/e))/e^2 + (12*b^2*f^2*n^2*(a + b*log(c*x^n))*PolyLog(2, -((f*sqrt(x))/e)))/e^2 + (6*b*f^2*n*(a + b*log(c*x^n))^2*PolyLog(2, -((f*sqrt(x))/e)))/e^2 - (24*b^3*f^2*n^3*PolyLog(3, -((f*sqrt(x))/e)))/e^2 - (24*b^2*f^2*n^2*(a + b*log(c*x^n))*PolyLog(3, -((f*sqrt(x))/e)))/e^2 + (48*b^3*f^2*n^3*PolyLog(4, -((f*sqrt(x))/e)))/e^2]
    @test_int [log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^3/x^3, x, 40, -((175*b^3*f*n^3)/(216*e*x^(3/2))) + (45*b^3*f^2*n^3)/(16*e^2*x) - (255*b^3*f^3*n^3)/(8*e^3*sqrt(x)) + (3*b^3*f^4*n^3*log(e + f*sqrt(x)))/(8*e^4) - (3*b^3*n^3*log(d*(e + f*sqrt(x))))/(8*x^2) - (3*b^3*f^4*n^3*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/(2*e^4) - (3*b^3*f^4*n^3*log(x))/(16*e^4) + (3*b^3*f^4*n^3*log(x)^2)/(16*e^4) - (37*b^2*f*n^2*(a + b*log(c*x^n)))/(36*e*x^(3/2)) + (21*b^2*f^2*n^2*(a + b*log(c*x^n)))/(8*e^2*x) - (63*b^2*f^3*n^2*(a + b*log(c*x^n)))/(4*e^3*sqrt(x)) + (3*b^2*f^4*n^2*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/(4*e^4) - (3*b^2*n^2*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n)))/(4*x^2) - (3*b^2*f^4*n^2*log(x)*(a + b*log(c*x^n)))/(8*e^4) - (7*b*f*n*(a + b*log(c*x^n))^2)/(12*e*x^(3/2)) + (9*b*f^2*n*(a + b*log(c*x^n))^2)/(8*e^2*x) - (15*b*f^3*n*(a + b*log(c*x^n))^2)/(4*e^3*sqrt(x)) - (3*b*n*log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^2)/(4*x^2) + (3*b*f^4*n*log(1 + (f*sqrt(x))/e)*(a + b*log(c*x^n))^2)/(4*e^4) - (f^4*(a + b*log(c*x^n))^3)/(8*e^4) - (f*(a + b*log(c*x^n))^3)/(6*e*x^(3/2)) + (f^2*(a + b*log(c*x^n))^3)/(4*e^2*x) - (f^3*(a + b*log(c*x^n))^3)/(2*e^3*sqrt(x)) - (log(d*(e + f*sqrt(x)))*(a + b*log(c*x^n))^3)/(2*x^2) + (f^4*log(1 + (f*sqrt(x))/e)*(a + b*log(c*x^n))^3)/(2*e^4) - (f^4*(a + b*log(c*x^n))^4)/(16*b*e^4*n) - (3*b^3*f^4*n^3*PolyLog(2, 1 + (f*sqrt(x))/e))/(2*e^4) + (3*b^2*f^4*n^2*(a + b*log(c*x^n))*PolyLog(2, -((f*sqrt(x))/e)))/e^4 + (3*b*f^4*n*(a + b*log(c*x^n))^2*PolyLog(2, -((f*sqrt(x))/e)))/e^4 - (6*b^3*f^4*n^3*PolyLog(3, -((f*sqrt(x))/e)))/e^4 - (12*b^2*f^4*n^2*(a + b*log(c*x^n))*PolyLog(3, -((f*sqrt(x))/e)))/e^4 + (24*b^3*f^4*n^3*PolyLog(4, -((f*sqrt(x))/e)))/e^4]

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

    @test_int [x^(3/2)*log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n)), x, 9, (24*b*e^4*k*n*sqrt(x))/(25*f^4) - (7*b*e^3*k*n*x)/(25*f^3) + (32*b*e^2*k*n*x^(3/2))/(225*f^2) - (9*b*e*k*n*x^2)/(100*f) + (8/125)*b*k*n*x^(5/2) - (4*b*e^5*k*n*log(e + f*sqrt(x)))/(25*f^5) - (4/25)*b*n*x^(5/2)*log(d*(e + f*sqrt(x))^k) - (4*b*e^5*k*n*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/(5*f^5) - (2*e^4*k*sqrt(x)*(a + b*log(c*x^n)))/(5*f^4) + (e^3*k*x*(a + b*log(c*x^n)))/(5*f^3) - (2*e^2*k*x^(3/2)*(a + b*log(c*x^n)))/(15*f^2) + (e*k*x^2*(a + b*log(c*x^n)))/(10*f) - (2/25)*k*x^(5/2)*(a + b*log(c*x^n)) + (2*e^5*k*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/(5*f^5) + (2/5)*x^(5/2)*log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n)) - (4*b*e^5*k*n*PolyLog(2, 1 + (f*sqrt(x))/e))/(5*f^5)]
    @test_int [x^(1/2)*log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n)), x, 9, (16*b*e^2*k*n*sqrt(x))/(9*f^2) - (5*b*e*k*n*x)/(9*f) + (8/27)*b*k*n*x^(3/2) - (4*b*e^3*k*n*log(e + f*sqrt(x)))/(9*f^3) - (4/9)*b*n*x^(3/2)*log(d*(e + f*sqrt(x))^k) - (4*b*e^3*k*n*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/(3*f^3) - (2*e^2*k*sqrt(x)*(a + b*log(c*x^n)))/(3*f^2) + (e*k*x*(a + b*log(c*x^n)))/(3*f) - (2/9)*k*x^(3/2)*(a + b*log(c*x^n)) + (2*e^3*k*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/(3*f^3) + (2/3)*x^(3/2)*log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n)) - (4*b*e^3*k*n*PolyLog(2, 1 + (f*sqrt(x))/e))/(3*f^3)]
    @test_int [log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n))/x^(3/2), x, 11, -((4*b*f*k*n*log(e + f*sqrt(x)))/e) - (4*b*n*log(d*(e + f*sqrt(x))^k))/sqrt(x) + (4*b*f*k*n*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/e + (2*b*f*k*n*log(x))/e - (b*f*k*n*log(x)^2)/(2*e) - (2*f*k*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/e - (2*log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n)))/sqrt(x) + (f*k*log(x)*(a + b*log(c*x^n)))/e + (4*b*f*k*n*PolyLog(2, 1 + (f*sqrt(x))/e))/e]
    @test_int [log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n))/x^(5/2), x, 10, -((5*b*f*k*n)/(9*e*x)) + (16*b*f^2*k*n)/(9*e^2*sqrt(x)) - (4*b*f^3*k*n*log(e + f*sqrt(x)))/(9*e^3) - (4*b*n*log(d*(e + f*sqrt(x))^k))/(9*x^(3/2)) + (4*b*f^3*k*n*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/(3*e^3) + (2*b*f^3*k*n*log(x))/(9*e^3) - (b*f^3*k*n*log(x)^2)/(6*e^3) - (f*k*(a + b*log(c*x^n)))/(3*e*x) + (2*f^2*k*(a + b*log(c*x^n)))/(3*e^2*sqrt(x)) - (2*f^3*k*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/(3*e^3) - (2*log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n)))/(3*x^(3/2)) + (f^3*k*log(x)*(a + b*log(c*x^n)))/(3*e^3) + (4*b*f^3*k*n*PolyLog(2, 1 + (f*sqrt(x))/e))/(3*e^3)]
    @test_int [log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n))/x^(7/2), x, 10, -((9*b*f*k*n)/(100*e*x^2)) + (32*b*f^2*k*n)/(225*e^2*x^(3/2)) - (7*b*f^3*k*n)/(25*e^3*x) + (24*b*f^4*k*n)/(25*e^4*sqrt(x)) - (4*b*f^5*k*n*log(e + f*sqrt(x)))/(25*e^5) - (4*b*n*log(d*(e + f*sqrt(x))^k))/(25*x^(5/2)) + (4*b*f^5*k*n*log(e + f*sqrt(x))*log(-((f*sqrt(x))/e)))/(5*e^5) + (2*b*f^5*k*n*log(x))/(25*e^5) - (b*f^5*k*n*log(x)^2)/(10*e^5) - (f*k*(a + b*log(c*x^n)))/(10*e*x^2) + (2*f^2*k*(a + b*log(c*x^n)))/(15*e^2*x^(3/2)) - (f^3*k*(a + b*log(c*x^n)))/(5*e^3*x) + (2*f^4*k*(a + b*log(c*x^n)))/(5*e^4*sqrt(x)) - (2*f^5*k*log(e + f*sqrt(x))*(a + b*log(c*x^n)))/(5*e^5) - (2*log(d*(e + f*sqrt(x))^k)*(a + b*log(c*x^n)))/(5*x^(5/2)) + (f^5*k*log(x)*(a + b*log(c*x^n)))/(5*e^5) + (4*b*f^5*k*n*PolyLog(2, 1 + (f*sqrt(x))/e))/(5*e^5)]

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

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

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

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

    @test_int [(g*x)^(3*m - 1)*log(d*(e + f*x^m)^k)*(a + b*log(c*x^n)), x, 18, (2*b*k*n*(g*x)^(3*m))/(27*g*m^2) + (4*b*e^2*k*n*(g*x)^(3*m))/(x^(2*m)*(9*f^2*g*m^2)) - (5*b*e*k*n*(g*x)^(3*m))/(x^m*(36*f*g*m^2)) - (k*(g*x)^(3*m)*(a + b*log(c*x^n)))/(9*g*m) - (e^2*k*(g*x)^(3*m)*(a + b*log(c*x^n)))/(x^(2*m)*(3*f^2*g*m)) + (e*k*(g*x)^(3*m)*(a + b*log(c*x^n)))/(x^m*(6*f*g*m)) - (b*e^3*k*n*(g*x)^(3*m)*log(e + f*x^m))/(x^(3*m)*(9*f^3*g*m^2)) - (b*e^3*k*n*(g*x)^(3*m)*log(-((f*x^m)/e))*log(e + f*x^m))/(x^(3*m)*(3*f^3*g*m^2)) + (e^3*k*(g*x)^(3*m)*(a + b*log(c*x^n))*log(e + f*x^m))/(x^(3*m)*(3*f^3*g*m)) - (b*n*(g*x)^(3*m)*log(d*(e + f*x^m)^k))/(9*g*m^2) + ((g*x)^(3*m)*(a + b*log(c*x^n))*log(d*(e + f*x^m)^k))/(3*g*m) - (b*e^3*k*n*(g*x)^(3*m)*PolyLog(2, 1 + (f*x^m)/e))/(x^(3*m)*(3*f^3*g*m^2))]
    @test_int [(g*x)^(2*m - 1)*log(d*(e + f*x^m)^k)*(a + b*log(c*x^n)), x, 16, (b*k*n*(g*x)^(2*m))/(4*g*m^2) - (3*b*e*k*n*(g*x)^(2*m))/(x^m*(4*f*g*m^2)) - (k*(g*x)^(2*m)*(a + b*log(c*x^n)))/(4*g*m) + (e*k*(g*x)^(2*m)*(a + b*log(c*x^n)))/(x^m*(2*f*g*m)) + (b*e^2*k*n*(g*x)^(2*m)*log(e + f*x^m))/(x^(2*m)*(4*f^2*g*m^2)) + (b*e^2*k*n*(g*x)^(2*m)*log(-((f*x^m)/e))*log(e + f*x^m))/(x^(2*m)*(2*f^2*g*m^2)) - (e^2*k*(g*x)^(2*m)*(a + b*log(c*x^n))*log(e + f*x^m))/(x^(2*m)*(2*f^2*g*m)) - (b*n*(g*x)^(2*m)*log(d*(e + f*x^m)^k))/(4*g*m^2) + ((g*x)^(2*m)*(a + b*log(c*x^n))*log(d*(e + f*x^m)^k))/(2*g*m) + (b*e^2*k*n*(g*x)^(2*m)*PolyLog(2, 1 + (f*x^m)/e))/(x^(2*m)*(2*f^2*g*m^2))]
    @test_int [(g*x)^(1*m - 1)*log(d*(e + f*x^m)^k)*(a + b*log(c*x^n)), x, 14, (2*b*k*n*(g*x)^m)/(g*m^2) - (k*(g*x)^m*(a + b*log(c*x^n)))/(g*m) - (b*e*k*n*(g*x)^m*log(e + f*x^m))/(x^m*(f*g*m^2)) - (b*e*k*n*(g*x)^m*log(-((f*x^m)/e))*log(e + f*x^m))/(x^m*(f*g*m^2)) + (e*k*(g*x)^m*(a + b*log(c*x^n))*log(e + f*x^m))/(x^m*(f*g*m)) - (b*n*(g*x)^m*log(d*(e + f*x^m)^k))/(g*m^2) + ((g*x)^m*(a + b*log(c*x^n))*log(d*(e + f*x^m)^k))/(g*m) - (b*e*k*n*(g*x)^m*PolyLog(2, 1 + (f*x^m)/e))/(x^m*(f*g*m^2))]
    @test_int [(g*x)^(-1*m - 1)*log(d*(e + f*x^m)^k)*(a + b*log(c*x^n)), x, 15, (b*f*k*n*x^m*log(x))/((g*x)^m*(e*g*m)) - (b*f*k*n*x^m*log(x)^2)/((g*x)^m*(2*e*g)) + (f*k*x^m*log(x)*(a + b*log(c*x^n)))/((g*x)^m*(e*g)) - (b*f*k*n*x^m*log(e + f*x^m))/((g*x)^m*(e*g*m^2)) + (b*f*k*n*x^m*log(-((f*x^m)/e))*log(e + f*x^m))/((g*x)^m*(e*g*m^2)) - (f*k*x^m*(a + b*log(c*x^n))*log(e + f*x^m))/((g*x)^m*(e*g*m)) - (b*n*log(d*(e + f*x^m)^k))/((g*x)^m*(g*m^2)) - ((a + b*log(c*x^n))*log(d*(e + f*x^m)^k))/((g*x)^m*(g*m)) + (b*f*k*n*x^m*PolyLog(2, 1 + (f*x^m)/e))/((g*x)^m*(e*g*m^2))]
    @test_int [(g*x)^(-2*m - 1)*log(d*(e + f*x^m)^k)*(a + b*log(c*x^n)), x, 16, -((3*b*f*k*n*x^m)/((g*x)^(2*m)*(4*e*g*m^2))) - (b*f^2*k*n*x^(2*m)*log(x))/((g*x)^(2*m)*(4*e^2*g*m)) + (b*f^2*k*n*x^(2*m)*log(x)^2)/((g*x)^(2*m)*(4*e^2*g)) - (f*k*x^m*(a + b*log(c*x^n)))/((g*x)^(2*m)*(2*e*g*m)) - (f^2*k*x^(2*m)*log(x)*(a + b*log(c*x^n)))/((g*x)^(2*m)*(2*e^2*g)) + (b*f^2*k*n*x^(2*m)*log(e + f*x^m))/((g*x)^(2*m)*(4*e^2*g*m^2)) - (b*f^2*k*n*x^(2*m)*log(-((f*x^m)/e))*log(e + f*x^m))/((g*x)^(2*m)*(2*e^2*g*m^2)) + (f^2*k*x^(2*m)*(a + b*log(c*x^n))*log(e + f*x^m))/((g*x)^(2*m)*(2*e^2*g*m)) - (b*n*log(d*(e + f*x^m)^k))/((g*x)^(2*m)*(4*g*m^2)) - ((a + b*log(c*x^n))*log(d*(e + f*x^m)^k))/((g*x)^(2*m)*(2*g*m)) - (b*f^2*k*n*x^(2*m)*PolyLog(2, 1 + (f*x^m)/e))/((g*x)^(2*m)*(2*e^2*g*m^2))]
    @test_int [(g*x)^(-3*m - 1)*log(d*(e + f*x^m)^k)*(a + b*log(c*x^n)), x, 18, -((5*b*f*k*n*x^m)/((g*x)^(3*m)*(36*e*g*m^2))) + (4*b*f^2*k*n*x^(2*m))/((g*x)^(3*m)*(9*e^2*g*m^2)) + (b*f^3*k*n*x^(3*m)*log(x))/((g*x)^(3*m)*(9*e^3*g*m)) - (b*f^3*k*n*x^(3*m)*log(x)^2)/((g*x)^(3*m)*(6*e^3*g)) - (f*k*x^m*(a + b*log(c*x^n)))/((g*x)^(3*m)*(6*e*g*m)) + (f^2*k*x^(2*m)*(a + b*log(c*x^n)))/((g*x)^(3*m)*(3*e^2*g*m)) + (f^3*k*x^(3*m)*log(x)*(a + b*log(c*x^n)))/((g*x)^(3*m)*(3*e^3*g)) - (b*f^3*k*n*x^(3*m)*log(e + f*x^m))/((g*x)^(3*m)*(9*e^3*g*m^2)) + (b*f^3*k*n*x^(3*m)*log(-((f*x^m)/e))*log(e + f*x^m))/((g*x)^(3*m)*(3*e^3*g*m^2)) - (f^3*k*x^(3*m)*(a + b*log(c*x^n))*log(e + f*x^m))/((g*x)^(3*m)*(3*e^3*g*m)) - (b*n*log(d*(e + f*x^m)^k))/((g*x)^(3*m)*(9*g*m^2)) - ((a + b*log(c*x^n))*log(d*(e + f*x^m)^k))/((g*x)^(3*m)*(3*g*m)) + (b*f^3*k*n*x^(3*m)*PolyLog(2, 1 + (f*x^m)/e))/((g*x)^(3*m)*(3*e^3*g*m^2))]

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

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

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

    @test_int [x^2*(a + b*log(c*x^n))*(d + e*log(f*x^r)), x, 3, (1/27)*b*e*n*r*x^3 - (1/27)*e*r*x^3*(3*a - b*n + 3*b*log(c*x^n)) - (1/9)*b*n*x^3*(d + e*log(f*x^r)) + (1/3)*x^3*(a + b*log(c*x^n))*(d + e*log(f*x^r))]
    @test_int [x^1*(a + b*log(c*x^n))*(d + e*log(f*x^r)), x, 3, (1/8)*b*e*n*r*x^2 - (1/8)*e*r*x^2*(2*a - b*n + 2*b*log(c*x^n)) - (1/4)*b*n*x^2*(d + e*log(f*x^r)) + (1/2)*x^2*(a + b*log(c*x^n))*(d + e*log(f*x^r))]
    @test_int [x^0*(a + b*log(c*x^n))*(d + e*log(f*x^r)), x, 3, b*e*n*r*x - e*(a - b*n)*r*x - b*e*r*x*log(c*x^n) + a*x*(d + e*log(f*x^r)) - b*n*x*(d + e*log(f*x^r)) + b*x*log(c*x^n)*(d + e*log(f*x^r))]
    @test_int [(a + b*log(c*x^n))*(d + e*log(f*x^r))/x^1, x, 4, -((e*r*(a + b*log(c*x^n))^3)/(6*b^2*n^2)) + ((a + b*log(c*x^n))^2*(d + e*log(f*x^r)))/(2*b*n)]
    @test_int [(a + b*log(c*x^n))*(d + e*log(f*x^r))/x^2, x, 2, -((b*e*n*r)/x) - (e*r*(a + b*n + b*log(c*x^n)))/x - (b*n*(d + e*log(f*x^r)))/x - ((a + b*log(c*x^n))*(d + e*log(f*x^r)))/x]
    @test_int [(a + b*log(c*x^n))*(d + e*log(f*x^r))/x^3, x, 3, -((b*e*n*r)/(8*x^2)) - (e*r*(2*a + b*n + 2*b*log(c*x^n)))/(8*x^2) - (b*n*(d + e*log(f*x^r)))/(4*x^2) - ((a + b*log(c*x^n))*(d + e*log(f*x^r)))/(2*x^2)]
    @test_int [(a + b*log(c*x^n))*(d + e*log(f*x^r))/x^4, x, 3, -((b*e*n*r)/(27*x^3)) - (e*r*(3*a + b*n + 3*b*log(c*x^n)))/(27*x^3) - (b*n*(d + e*log(f*x^r)))/(9*x^3) - ((a + b*log(c*x^n))*(d + e*log(f*x^r)))/(3*x^3)]

    @test_int [x^2*(a + b*log(c*x^n))^2*(d + e*log(f*x^r)), x, 7, (-(2/81))*b^2*e*n^2*r*x^3 + (2/81)*b*e*n*(3*a - b*n)*r*x^3 - (1/81)*e*(9*a^2 - 6*a*b*n + 2*b^2*n^2)*r*x^3 + (2/27)*b^2*e*n*r*x^3*log(c*x^n) - (2/27)*b*e*(3*a - b*n)*r*x^3*log(c*x^n) - (1/9)*b^2*e*r*x^3*log(c*x^n)^2 + (2/27)*b^2*n^2*x^3*(d + e*log(f*x^r)) - (2/9)*b*n*x^3*(a + b*log(c*x^n))*(d + e*log(f*x^r)) + (1/3)*x^3*(a + b*log(c*x^n))^2*(d + e*log(f*x^r))]
    @test_int [x^1*(a + b*log(c*x^n))^2*(d + e*log(f*x^r)), x, 7, (-(1/8))*b^2*e*n^2*r*x^2 + (1/8)*b*e*n*(2*a - b*n)*r*x^2 - (1/8)*e*(2*a^2 - 2*a*b*n + b^2*n^2)*r*x^2 + (1/4)*b^2*e*n*r*x^2*log(c*x^n) - (1/4)*b*e*(2*a - b*n)*r*x^2*log(c*x^n) - (1/4)*b^2*e*r*x^2*log(c*x^n)^2 + (1/4)*b^2*n^2*x^2*(d + e*log(f*x^r)) - (1/2)*b*n*x^2*(a + b*log(c*x^n))*(d + e*log(f*x^r)) + (1/2)*x^2*(a + b*log(c*x^n))^2*(d + e*log(f*x^r))]
    @test_int [x^0*(a + b*log(c*x^n))^2*(d + e*log(f*x^r)), x, 6, 2*a*b*e*n*r*x - 4*b^2*e*n^2*r*x + 2*b*e*n*(a - b*n)*r*x + 4*b^2*e*n*r*x*log(c*x^n) - e*r*x*(a + b*log(c*x^n))^2 - 2*a*b*n*x*(d + e*log(f*x^r)) + 2*b^2*n^2*x*(d + e*log(f*x^r)) - 2*b^2*n*x*log(c*x^n)*(d + e*log(f*x^r)) + x*(a + b*log(c*x^n))^2*(d + e*log(f*x^r))]
    @test_int [(a + b*log(c*x^n))^2*(d + e*log(f*x^r))/x^1, x, 4, -((e*r*(a + b*log(c*x^n))^4)/(12*b^2*n^2)) + ((a + b*log(c*x^n))^3*(d + e*log(f*x^r)))/(3*b*n)]
    @test_int [(a + b*log(c*x^n))^2*(d + e*log(f*x^r))/x^2, x, 6, -((2*b^2*e*n^2*r)/x) - (2*b*e*n*(a + b*n)*r)/x - (e*(a^2 + 2*a*b*n + 2*b^2*n^2)*r)/x - (2*b^2*e*n*r*log(c*x^n))/x - (2*b*e*(a + b*n)*r*log(c*x^n))/x - (b^2*e*r*log(c*x^n)^2)/x - (2*b^2*n^2*(d + e*log(f*x^r)))/x - (2*b*n*(a + b*log(c*x^n))*(d + e*log(f*x^r)))/x - ((a + b*log(c*x^n))^2*(d + e*log(f*x^r)))/x]
    @test_int [(a + b*log(c*x^n))^2*(d + e*log(f*x^r))/x^3, x, 7, -((b^2*e*n^2*r)/(8*x^2)) - (b*e*n*(2*a + b*n)*r)/(8*x^2) - (e*(2*a^2 + 2*a*b*n + b^2*n^2)*r)/(8*x^2) - (b^2*e*n*r*log(c*x^n))/(4*x^2) - (b*e*(2*a + b*n)*r*log(c*x^n))/(4*x^2) - (b^2*e*r*log(c*x^n)^2)/(4*x^2) - (b^2*n^2*(d + e*log(f*x^r)))/(4*x^2) - (b*n*(a + b*log(c*x^n))*(d + e*log(f*x^r)))/(2*x^2) - ((a + b*log(c*x^n))^2*(d + e*log(f*x^r)))/(2*x^2)]
    @test_int [(a + b*log(c*x^n))^2*(d + e*log(f*x^r))/x^4, x, 7, -((2*b^2*e*n^2*r)/(81*x^3)) - (2*b*e*n*(3*a + b*n)*r)/(81*x^3) - (e*(9*a^2 + 6*a*b*n + 2*b^2*n^2)*r)/(81*x^3) - (2*b^2*e*n*r*log(c*x^n))/(27*x^3) - (2*b*e*(3*a + b*n)*r*log(c*x^n))/(27*x^3) - (b^2*e*r*log(c*x^n)^2)/(9*x^3) - (2*b^2*n^2*(d + e*log(f*x^r)))/(27*x^3) - (2*b*n*(a + b*log(c*x^n))*(d + e*log(f*x^r)))/(9*x^3) - ((a + b*log(c*x^n))^2*(d + e*log(f*x^r)))/(3*x^3)]

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

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

    @test_int [(a + b*log(c*x^n))/(d + e*log(c*x^n))^2, x, 7, (((-b)*d + a*e + b*e*n)*x*ExpIntegralEi((d + e*log(c*x^n))/(e*n)))/(ℯ^(d/(e*n))*(c*x^n)^n^(-1)*(e^3*n^2)) + ((b*d - a*e)*x)/(e^2*n*(d + e*log(c*x^n))), -(((b*d - a*e)*x*ExpIntegralEi((d + e*log(c*x^n))/(e*n)))/(ℯ^(d/(e*n))*(c*x^n)^n^(-1)*(e^3*n^2))) + (b*x*ExpIntegralEi((d + e*log(c*x^n))/(e*n)))/(ℯ^(d/(e*n))*(c*x^n)^n^(-1)*(e^2*n)) + ((b*d - a*e)*x)/(e^2*n*(d + e*log(c*x^n)))]

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

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

    @test_int [(g*x)^m*(a + b*log(c*x^n))^p*(d + e*log(f*x^r)), x, 8, -((e*r*x*(g*x)^m*Gamma(2 + p, -((a*(1 + m))/(b*n)) - ((1 + m)*log(c*x^n))/n)*(a + b*log(c*x^n))^p)/(ℯ^((a*(1 + m))/(b*n))*(c*x^n)^((1 + m)/n)*(-(((1 + m)*(a + b*log(c*x^n)))/(b*n)))^p*(1 + m)^2)) - (e*r*x*(g*x)^m*Gamma(1 + p, -((a*(1 + m))/(b*n)) - ((1 + m)*log(c*x^n))/n)*(a + b*log(c*x^n))^(1 + p))/(ℯ^((a*(1 + m))/(b*n))*(c*x^n)^((1 + m)/n)*(-(((1 + m)*(a + b*log(c*x^n)))/(b*n)))^p*(b*(1 + m)*n)) + ((g*x)^(1 + m)*Gamma(1 + p, -(((1 + m)*(a + b*log(c*x^n)))/(b*n)))*(a + b*log(c*x^n))^p*(d + e*log(f*x^r)))/(ℯ^((a*(1 + m))/(b*n))*(c*x^n)^((1 + m)/n)*(-(((1 + m)*(a + b*log(c*x^n)))/(b*n)))^p*(g*(1 + m)))]

    @test_int [x^2*(a + b*log(c*x^n))^p*(d + e*log(f*x^r)), x, 7, ((-3^(-2 - p))*e*r*x^3*Gamma(2 + p, -((3*a)/(b*n)) - (3*log(c*x^n))/n)*(a + b*log(c*x^n))^p)/(ℯ^((3*a)/(b*n))*(c*x^n)^(3/n)*(-((a + b*log(c*x^n))/(b*n)))^p) - (3^(-1 - p)*e*r*x^3*Gamma(1 + p, -((3*a)/(b*n)) - (3*log(c*x^n))/n)*(a + b*log(c*x^n))^(1 + p))/(ℯ^((3*a)/(b*n))*(c*x^n)^(3/n)*(-((a + b*log(c*x^n))/(b*n)))^p*(b*n)) + (3^(-1 - p)*x^3*Gamma(1 + p, -((3*(a + b*log(c*x^n)))/(b*n)))*(a + b*log(c*x^n))^p*(d + e*log(f*x^r)))/(ℯ^((3*a)/(b*n))*(c*x^n)^(3/n)*(-((a + b*log(c*x^n))/(b*n)))^p)]
    @test_int [x^1*(a + b*log(c*x^n))^p*(d + e*log(f*x^r)), x, 7, ((-2^(-2 - p))*e*r*x^2*Gamma(2 + p, -((2*a)/(b*n)) - (2*log(c*x^n))/n)*(a + b*log(c*x^n))^p)/(ℯ^((2*a)/(b*n))*(c*x^n)^(2/n)*(-((a + b*log(c*x^n))/(b*n)))^p) - (2^(-1 - p)*e*r*x^2*Gamma(1 + p, -((2*a)/(b*n)) - (2*log(c*x^n))/n)*(a + b*log(c*x^n))^(1 + p))/(ℯ^((2*a)/(b*n))*(c*x^n)^(2/n)*(-((a + b*log(c*x^n))/(b*n)))^p*(b*n)) + (2^(-1 - p)*x^2*Gamma(1 + p, -((2*(a + b*log(c*x^n)))/(b*n)))*(a + b*log(c*x^n))^p*(d + e*log(f*x^r)))/(ℯ^((2*a)/(b*n))*(c*x^n)^(2/n)*(-((a + b*log(c*x^n))/(b*n)))^p)]
    @test_int [x^0*(a + b*log(c*x^n))^p*(d + e*log(f*x^r)), x, 7, ((-e)*r*x*Gamma(2 + p, -(a/(b*n)) - log(c*x^n)/n)*(a + b*log(c*x^n))^p)/(ℯ^(a/(b*n))*(c*x^n)^n^(-1)*(-((a + b*log(c*x^n))/(b*n)))^p) - (e*r*x*Gamma(1 + p, -(a/(b*n)) - log(c*x^n)/n)*(a + b*log(c*x^n))^(1 + p))/(ℯ^(a/(b*n))*(c*x^n)^n^(-1)*(-((a + b*log(c*x^n))/(b*n)))^p*(b*n)) + (x*Gamma(1 + p, -((a + b*log(c*x^n))/(b*n)))*(a + b*log(c*x^n))^p*(d + e*log(f*x^r)))/(ℯ^(a/(b*n))*(c*x^n)^n^(-1)*(-((a + b*log(c*x^n))/(b*n)))^p)]
    @test_int [(a + b*log(c*x^n))^p*(d + e*log(f*x^r))/x^1, x, 4, -((e*r*(a + b*log(c*x^n))^(2 + p))/(b^2*n^2*(1 + p)*(2 + p))) + ((a + b*log(c*x^n))^(1 + p)*(d + e*log(f*x^r)))/(b*n*(1 + p))]
    @test_int [(a + b*log(c*x^n))^p*(d + e*log(f*x^r))/x^2, x, 7, -((e*ℯ^(a/(b*n))*r*(c*x^n)^(1/n)*Gamma(2 + p, a/(b*n) + log(c*x^n)/n)*(a + b*log(c*x^n))^p)/(((a + b*log(c*x^n))/(b*n))^p*x)) + (e*ℯ^(a/(b*n))*r*(c*x^n)^(1/n)*Gamma(1 + p, a/(b*n) + log(c*x^n)/n)*(a + b*log(c*x^n))^(1 + p))/(((a + b*log(c*x^n))/(b*n))^p*(b*n*x)) - (ℯ^(a/(b*n))*(c*x^n)^(1/n)*Gamma(1 + p, (a + b*log(c*x^n))/(b*n))*(a + b*log(c*x^n))^p*(d + e*log(f*x^r)))/(((a + b*log(c*x^n))/(b*n))^p*x)]
    @test_int [(a + b*log(c*x^n))^p*(d + e*log(f*x^r))/x^3, x, 7, -((2^(-2 - p)*e*ℯ^((2*a)/(b*n))*r*(c*x^n)^(2/n)*Gamma(2 + p, (2*a)/(b*n) + (2*log(c*x^n))/n)*(a + b*log(c*x^n))^p)/(((a + b*log(c*x^n))/(b*n))^p*x^2)) + (2^(-1 - p)*e*ℯ^((2*a)/(b*n))*r*(c*x^n)^(2/n)*Gamma(1 + p, (2*a)/(b*n) + (2*log(c*x^n))/n)*(a + b*log(c*x^n))^(1 + p))/(((a + b*log(c*x^n))/(b*n))^p*(b*n*x^2)) - (2^(-1 - p)*ℯ^((2*a)/(b*n))*(c*x^n)^(2/n)*Gamma(1 + p, (2*(a + b*log(c*x^n)))/(b*n))*(a + b*log(c*x^n))^p*(d + e*log(f*x^r)))/(((a + b*log(c*x^n))/(b*n))^p*x^2)]
    @test_int [(a + b*log(c*x^n))^p*(d + e*log(f*x^r))/x^4, x, 7, -((3^(-2 - p)*e*ℯ^((3*a)/(b*n))*r*(c*x^n)^(3/n)*Gamma(2 + p, (3*a)/(b*n) + (3*log(c*x^n))/n)*(a + b*log(c*x^n))^p)/(((a + b*log(c*x^n))/(b*n))^p*x^3)) + (3^(-1 - p)*e*ℯ^((3*a)/(b*n))*r*(c*x^n)^(3/n)*Gamma(1 + p, (3*a)/(b*n) + (3*log(c*x^n))/n)*(a + b*log(c*x^n))^(1 + p))/(((a + b*log(c*x^n))/(b*n))^p*(b*n*x^3)) - (3^(-1 - p)*ℯ^((3*a)/(b*n))*(c*x^n)^(3/n)*Gamma(1 + p, (3*(a + b*log(c*x^n)))/(b*n))*(a + b*log(c*x^n))^p*(d + e*log(f*x^r)))/(((a + b*log(c*x^n))/(b*n))^p*x^3)]

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

    @test_int [(d + e*x^2)*asin(a*x)*log(c*x^n), x, 17, -((d*n*sqrt(1 - a^2*x^2))/a) - ((3*a^2*d + e)*n*sqrt(1 - a^2*x^2))/(3*a^3) + (2*e*n*(1 - a^2*x^2)^(3/2))/(27*a^3) - d*n*x*asin(a*x) - (1/9)*e*n*x^3*asin(a*x) - (e*n*atanh(sqrt(1 - a^2*x^2)))/(9*a^3) + ((3*a^2*d + e)*n*atanh(sqrt(1 - a^2*x^2)))/(3*a^3) + ((3*a^2*d + e)*sqrt(1 - a^2*x^2)*log(c*x^n))/(3*a^3) - (e*(1 - a^2*x^2)^(3/2)*log(c*x^n))/(9*a^3) + d*x*asin(a*x)*log(c*x^n) + (1/3)*e*x^3*asin(a*x)*log(c*x^n)]
    @test_int [(d + e*x^2)*acos(a*x)*log(c*x^n), x, 17, (d*n*sqrt(1 - a^2*x^2))/a + ((3*a^2*d + e)*n*sqrt(1 - a^2*x^2))/(3*a^3) - (2*e*n*(1 - a^2*x^2)^(3/2))/(27*a^3) - d*n*x*acos(a*x) - (1/9)*e*n*x^3*acos(a*x) + (e*n*atanh(sqrt(1 - a^2*x^2)))/(9*a^3) - ((3*a^2*d + e)*n*atanh(sqrt(1 - a^2*x^2)))/(3*a^3) - ((3*a^2*d + e)*sqrt(1 - a^2*x^2)*log(c*x^n))/(3*a^3) + (e*(1 - a^2*x^2)^(3/2)*log(c*x^n))/(9*a^3) + d*x*acos(a*x)*log(c*x^n) + (1/3)*e*x^3*acos(a*x)*log(c*x^n)]
    @test_int [(d + e*x^2)*atan(a*x)*log(c*x^n), x, 9, (5*e*n*x^2)/(36*a) - d*n*x*atan(a*x) - (1/9)*e*n*x^3*atan(a*x) - (e*x^2*log(c*x^n))/(6*a) + d*x*atan(a*x)*log(c*x^n) + (1/3)*e*x^3*atan(a*x)*log(c*x^n) + (d*n*log(1 + a^2*x^2))/(2*a) - (e*n*log(1 + a^2*x^2))/(18*a^3) - ((3*a^2*d - e)*log(c*x^n)*log(1 + a^2*x^2))/(6*a^3) - ((3*a^2*d - e)*n*PolyLog(2, (-a^2)*x^2))/(12*a^3)]
    @test_int [(d + e*x^2)*acot(a*x)*log(c*x^n), x, 9, -((5*e*n*x^2)/(36*a)) - d*n*x*acot(a*x) - (1/9)*e*n*x^3*acot(a*x) + (e*x^2*log(c*x^n))/(6*a) + d*x*acot(a*x)*log(c*x^n) + (1/3)*e*x^3*acot(a*x)*log(c*x^n) - (d*n*log(1 + a^2*x^2))/(2*a) + (e*n*log(1 + a^2*x^2))/(18*a^3) + ((3*a^2*d - e)*log(c*x^n)*log(1 + a^2*x^2))/(6*a^3) + ((3*a^2*d - e)*n*PolyLog(2, (-a^2)*x^2))/(12*a^3)]

    @test_int [(d + e*x^2)*asinh(a*x)*log(c*x^n), x, 17, (d*n*sqrt(1 + a^2*x^2))/a + ((3*a^2*d - e)*n*sqrt(1 + a^2*x^2))/(3*a^3) + (2*e*n*(1 + a^2*x^2)^(3/2))/(27*a^3) - d*n*x*asinh(a*x) - (1/9)*e*n*x^3*asinh(a*x) - ((3*a^2*d - e)*n*atanh(sqrt(1 + a^2*x^2)))/(3*a^3) - (e*n*atanh(sqrt(1 + a^2*x^2)))/(9*a^3) - ((3*a^2*d - e)*sqrt(1 + a^2*x^2)*log(c*x^n))/(3*a^3) - (e*(1 + a^2*x^2)^(3/2)*log(c*x^n))/(9*a^3) + d*x*asinh(a*x)*log(c*x^n) + (1/3)*e*x^3*asinh(a*x)*log(c*x^n)]
    @test_int [(d + e*x^2)*acosh(a*x)*log(c*x^n), x, 12, (d*n*sqrt(-1 + a*x)*sqrt(1 + a*x))/a + (2*e*n*sqrt(-1 + a*x)*sqrt(1 + a*x))/(27*a^3) + ((9*a^2*d + 2*e)*n*sqrt(-1 + a*x)*sqrt(1 + a*x))/(9*a^3) + (e*n*x^2*sqrt(-1 + a*x)*sqrt(1 + a*x))/(27*a) + (e*n*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2))/(27*a^3) - d*n*x*acosh(a*x) - (1/9)*e*n*x^3*acosh(a*x) - ((9*a^2*d + 2*e)*n*atan(sqrt(-1 + a*x)*sqrt(1 + a*x)))/(9*a^3) - ((9*a^2*d + 2*e)*sqrt(-1 + a*x)*sqrt(1 + a*x)*log(c*x^n))/(9*a^3) - (e*x^2*sqrt(-1 + a*x)*sqrt(1 + a*x)*log(c*x^n))/(9*a) + d*x*acosh(a*x)*log(c*x^n) + (1/3)*e*x^3*acosh(a*x)*log(c*x^n)]
    @test_int [(d + e*x^2)*atanh(a*x)*log(c*x^n), x, 9, -((5*e*n*x^2)/(36*a)) - d*n*x*atanh(a*x) - (1/9)*e*n*x^3*atanh(a*x) + (e*x^2*log(c*x^n))/(6*a) + d*x*atanh(a*x)*log(c*x^n) + (1/3)*e*x^3*atanh(a*x)*log(c*x^n) - (d*n*log(1 - a^2*x^2))/(2*a) - (e*n*log(1 - a^2*x^2))/(18*a^3) + ((3*a^2*d + e)*log(c*x^n)*log(1 - a^2*x^2))/(6*a^3) + ((3*a^2*d + e)*n*PolyLog(2, a^2*x^2))/(12*a^3)]
    @test_int [(d + e*x^2)*acoth(a*x)*log(c*x^n), x, 9, -((5*e*n*x^2)/(36*a)) - d*n*x*acoth(a*x) - (1/9)*e*n*x^3*acoth(a*x) + (e*x^2*log(c*x^n))/(6*a) + d*x*acoth(a*x)*log(c*x^n) + (1/3)*e*x^3*acoth(a*x)*log(c*x^n) - (d*n*log(1 - a^2*x^2))/(2*a) - (e*n*log(1 - a^2*x^2))/(18*a^3) + ((3*a^2*d + e)*log(c*x^n)*log(1 - a^2*x^2))/(6*a^3) + ((3*a^2*d + e)*n*PolyLog(2, a^2*x^2))/(12*a^3)]

    @test_int [(d + e*x^2)*asin(a*x)^2*log(c*x^n), x, 21, 2*d*n*x + (2*e*n*x)/(27*a^2) + (4/9)*(9*d + (2*e)/a^2)*n*x + (2/27)*e*n*x^3 - (2*d*n*sqrt(1 - a^2*x^2)*asin(a*x))/a - (4*e*n*sqrt(1 - a^2*x^2)*asin(a*x))/(27*a^3) - (2*(9*a^2*d + 2*e)*n*sqrt(1 - a^2*x^2)*asin(a*x))/(9*a^3) - (2*e*n*x^2*sqrt(1 - a^2*x^2)*asin(a*x))/(27*a) + (2*e*n*(1 - a^2*x^2)^(3/2)*asin(a*x))/(27*a^3) - d*n*x*asin(a*x)^2 - (1/9)*e*n*x^3*asin(a*x)^2 + (4*(9*a^2*d + 2*e)*n*asin(a*x)*atanh(ℯ^(im*asin(a*x))))/(9*a^3) - 2*d*x*log(c*x^n) - (4*e*x*log(c*x^n))/(9*a^2) - (2/27)*e*x^3*log(c*x^n) + (2*d*sqrt(1 - a^2*x^2)*asin(a*x)*log(c*x^n))/a + (4*e*sqrt(1 - a^2*x^2)*asin(a*x)*log(c*x^n))/(9*a^3) + (2*e*x^2*sqrt(1 - a^2*x^2)*asin(a*x)*log(c*x^n))/(9*a) + d*x*asin(a*x)^2*log(c*x^n) + (1/3)*e*x^3*asin(a*x)^2*log(c*x^n) - (2*im*(9*a^2*d + 2*e)*n*PolyLog(2, -ℯ^(im*asin(a*x))))/(9*a^3) + (2*im*(9*a^2*d + 2*e)*n*PolyLog(2, ℯ^(im*asin(a*x))))/(9*a^3)]
    @test_int [(d + e*x^2)*acos(a*x)^2*log(c*x^n), x, 21, 2*d*n*x + (2*e*n*x)/(27*a^2) + (4/9)*(9*d + (2*e)/a^2)*n*x + (2/27)*e*n*x^3 + (2*d*n*sqrt(1 - a^2*x^2)*acos(a*x))/a + (4*e*n*sqrt(1 - a^2*x^2)*acos(a*x))/(27*a^3) + (2*(9*a^2*d + 2*e)*n*sqrt(1 - a^2*x^2)*acos(a*x))/(9*a^3) + (2*e*n*x^2*sqrt(1 - a^2*x^2)*acos(a*x))/(27*a) - (2*e*n*(1 - a^2*x^2)^(3/2)*acos(a*x))/(27*a^3) - d*n*x*acos(a*x)^2 - (1/9)*e*n*x^3*acos(a*x)^2 + (4*im*(9*a^2*d + 2*e)*n*acos(a*x)*atan(ℯ^(im*acos(a*x))))/(9*a^3) - 2*d*x*log(c*x^n) - (4*e*x*log(c*x^n))/(9*a^2) - (2/27)*e*x^3*log(c*x^n) - (2*d*sqrt(1 - a^2*x^2)*acos(a*x)*log(c*x^n))/a - (4*e*sqrt(1 - a^2*x^2)*acos(a*x)*log(c*x^n))/(9*a^3) - (2*e*x^2*sqrt(1 - a^2*x^2)*acos(a*x)*log(c*x^n))/(9*a) + d*x*acos(a*x)^2*log(c*x^n) + (1/3)*e*x^3*acos(a*x)^2*log(c*x^n) - (2*im*(9*a^2*d + 2*e)*n*PolyLog(2, (-im)*ℯ^(im*acos(a*x))))/(9*a^3) + (2*im*(9*a^2*d + 2*e)*n*PolyLog(2, im*ℯ^(im*acos(a*x))))/(9*a^3)]

    @test_int [(d + e*x^2)*asinh(a*x)^2*log(c*x^n), x, 21, -2*d*n*x + (2*e*n*x)/(27*a^2) - (4/9)*(9*d - (2*e)/a^2)*n*x - (2/27)*e*n*x^3 + (2*d*n*sqrt(1 + a^2*x^2)*asinh(a*x))/a + (2*(9*a^2*d - 2*e)*n*sqrt(1 + a^2*x^2)*asinh(a*x))/(9*a^3) - (4*e*n*sqrt(1 + a^2*x^2)*asinh(a*x))/(27*a^3) + (2*e*n*x^2*sqrt(1 + a^2*x^2)*asinh(a*x))/(27*a) + (2*e*n*(1 + a^2*x^2)^(3/2)*asinh(a*x))/(27*a^3) - d*n*x*asinh(a*x)^2 - (1/9)*e*n*x^3*asinh(a*x)^2 - (4*(9*a^2*d - 2*e)*n*asinh(a*x)*atanh(ℯ^asinh(a*x)))/(9*a^3) + 2*d*x*log(c*x^n) - (4*e*x*log(c*x^n))/(9*a^2) + (2/27)*e*x^3*log(c*x^n) - (2*d*sqrt(1 + a^2*x^2)*asinh(a*x)*log(c*x^n))/a + (4*e*sqrt(1 + a^2*x^2)*asinh(a*x)*log(c*x^n))/(9*a^3) - (2*e*x^2*sqrt(1 + a^2*x^2)*asinh(a*x)*log(c*x^n))/(9*a) + d*x*asinh(a*x)^2*log(c*x^n) + (1/3)*e*x^3*asinh(a*x)^2*log(c*x^n) - (2*(9*a^2*d - 2*e)*n*PolyLog(2, -ℯ^asinh(a*x)))/(9*a^3) + (2*(9*a^2*d - 2*e)*n*PolyLog(2, ℯ^asinh(a*x)))/(9*a^3)]
    @test_int [(d + e*x^2)*acosh(a*x)^2*log(c*x^n), x, 22, -2*d*n*x - (2*e*n*x)/(27*a^2) - (4/9)*(9*d + (2*e)/a^2)*n*x - (2/27)*e*n*x^3 + (2*d*n*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x))/a + (4*e*n*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x))/(27*a^3) + (2*(9*a^2*d + 2*e)*n*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x))/(9*a^3) + (2*e*n*x^2*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x))/(27*a) + (2*e*n*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*acosh(a*x))/(27*a^3) - d*n*x*acosh(a*x)^2 - (1/9)*e*n*x^3*acosh(a*x)^2 - (4*(9*a^2*d + 2*e)*n*acosh(a*x)*atan(ℯ^acosh(a*x)))/(9*a^3) + 2*d*x*log(c*x^n) + (4*e*x*log(c*x^n))/(9*a^2) + (2/27)*e*x^3*log(c*x^n) - (2*d*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)*log(c*x^n))/a - (4*e*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)*log(c*x^n))/(9*a^3) - (2*e*x^2*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)*log(c*x^n))/(9*a) + d*x*acosh(a*x)^2*log(c*x^n) + (1/3)*e*x^3*acosh(a*x)^2*log(c*x^n) + (2*im*(9*a^2*d + 2*e)*n*PolyLog(2, (-im)*ℯ^acosh(a*x)))/(9*a^3) - (2*im*(9*a^2*d + 2*e)*n*PolyLog(2, im*ℯ^acosh(a*x)))/(9*a^3)]

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*PolyLog(k, e*x^q)*(a+b*log(c*x^n))^p / x=#

    @test_int [PolyLog(k, e*x^q)*(a + b*log(c*x^n))^p/x, x, 0, Unintegrable(((a + b*log(c*x^n))^p*PolyLog(k, e*x^q))/x, x)]

    @test_int [PolyLog(k, e*x^q)*(a + b*log(c*x^n))^3/x, x, 4, ((a + b*log(c*x^n))^3*PolyLog(1 + k, e*x^q))/q - (3*b*n*(a + b*log(c*x^n))^2*PolyLog(2 + k, e*x^q))/q^2 + (6*b^2*n^2*(a + b*log(c*x^n))*PolyLog(3 + k, e*x^q))/q^3 - (6*b^3*n^3*PolyLog(4 + k, e*x^q))/q^4]
    @test_int [PolyLog(k, e*x^q)*(a + b*log(c*x^n))^2/x, x, 3, ((a + b*log(c*x^n))^2*PolyLog(1 + k, e*x^q))/q - (2*b*n*(a + b*log(c*x^n))*PolyLog(2 + k, e*x^q))/q^2 + (2*b^2*n^2*PolyLog(3 + k, e*x^q))/q^3]
    @test_int [PolyLog(k, e*x^q)*(a + b*log(c*x^n))^1/x, x, 2, ((a + b*log(c*x^n))*PolyLog(1 + k, e*x^q))/q - (b*n*PolyLog(2 + k, e*x^q))/q^2]
    @test_int [PolyLog(k, e*x^q)/(x*(a + b*log(c*x^n))^1), x, 0, Unintegrable(PolyLog(k, e*x^q)/(x*(a + b*log(c*x^n))), x)]
    @test_int [PolyLog(k, e*x^q)/(x*(a + b*log(c*x^n))^2), x, 1, -(PolyLog(k, e*x^q)/(b*n*(a + b*log(c*x^n)))) + (q*Unintegrable(PolyLog(-1 + k, e*x^q)/(x*(a + b*log(c*x^n))), x))/(b*n)]
    @test_int [PolyLog(k, e*x^q)/(x*(a + b*log(c*x^n))^3), x, 2, -((q*PolyLog(-1 + k, e*x^q))/(2*b^2*n^2*(a + b*log(c*x^n)))) - PolyLog(k, e*x^q)/(2*b*n*(a + b*log(c*x^n))^2) + (q^2*Unintegrable(PolyLog(-2 + k, e*x^q)/(x*(a + b*log(c*x^n))), x))/(2*b^2*n^2)]

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

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

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

    @test_int [x^2*PolyLog(2, e*x)*(a + b*log(c*x^n)), x, 10, (5*b*n*x)/(27*e^2) + (7*b*n*x^2)/(108*e) + (1/27)*b*n*x^3 - (x*(a + b*log(c*x^n)))/(9*e^2) - (x^2*(a + b*log(c*x^n)))/(18*e) - (1/27)*x^3*(a + b*log(c*x^n)) + (2*b*n*log(1 - e*x))/(27*e^3) - (2/27)*b*n*x^3*log(1 - e*x) - ((a + b*log(c*x^n))*log(1 - e*x))/(9*e^3) + (1/9)*x^3*(a + b*log(c*x^n))*log(1 - e*x) - (b*n*PolyLog(2, e*x))/(9*e^3) - (1/9)*b*n*x^3*PolyLog(2, e*x) + (1/3)*x^3*(a + b*log(c*x^n))*PolyLog(2, e*x)]
    @test_int [x^1*PolyLog(2, e*x)*(a + b*log(c*x^n)), x, 10, (b*n*x)/(2*e) + (3/16)*b*n*x^2 - (x*(a + b*log(c*x^n)))/(4*e) - (1/8)*x^2*(a + b*log(c*x^n)) + (b*n*log(1 - e*x))/(4*e^2) - (1/4)*b*n*x^2*log(1 - e*x) - ((a + b*log(c*x^n))*log(1 - e*x))/(4*e^2) + (1/4)*x^2*(a + b*log(c*x^n))*log(1 - e*x) - (b*n*PolyLog(2, e*x))/(4*e^2) - (1/4)*b*n*x^2*PolyLog(2, e*x) + (1/2)*x^2*(a + b*log(c*x^n))*PolyLog(2, e*x)]
    @test_int [x^0*PolyLog(2, e*x)*(a + b*log(c*x^n)), x, 10, 3*b*n*x - x*(a + b*log(c*x^n)) + (2*b*n*(1 - e*x)*log(1 - e*x))/e - ((1 - e*x)*(a + b*log(c*x^n))*log(1 - e*x))/e - (b*n*PolyLog(2, e*x))/e - b*n*x*PolyLog(2, e*x) + x*(a + b*log(c*x^n))*PolyLog(2, e*x)]
    @test_int [PolyLog(2, e*x)*(a + b*log(c*x^n))/x^1, x, 2, (a + b*log(c*x^n))*PolyLog(3, e*x) - b*n*PolyLog(4, e*x)]
    @test_int [PolyLog(2, e*x)*(a + b*log(c*x^n))/x^2, x, 13, 2*b*e*n*log(x) - (1/2)*b*e*n*log(x)^2 + e*log(x)*(a + b*log(c*x^n)) - 2*b*e*n*log(1 - e*x) + (2*b*n*log(1 - e*x))/x - e*(a + b*log(c*x^n))*log(1 - e*x) + ((a + b*log(c*x^n))*log(1 - e*x))/x - b*e*n*PolyLog(2, e*x) - (b*n*PolyLog(2, e*x))/x - ((a + b*log(c*x^n))*PolyLog(2, e*x))/x]
    @test_int [PolyLog(2, e*x)*(a + b*log(c*x^n))/x^3, x, 11, -((b*e*n)/(2*x)) + (1/4)*b*e^2*n*log(x) - (1/8)*b*e^2*n*log(x)^2 - (e*(a + b*log(c*x^n)))/(4*x) + (1/4)*e^2*log(x)*(a + b*log(c*x^n)) - (1/4)*b*e^2*n*log(1 - e*x) + (b*n*log(1 - e*x))/(4*x^2) - (1/4)*e^2*(a + b*log(c*x^n))*log(1 - e*x) + ((a + b*log(c*x^n))*log(1 - e*x))/(4*x^2) - (1/4)*b*e^2*n*PolyLog(2, e*x) - (b*n*PolyLog(2, e*x))/(4*x^2) - ((a + b*log(c*x^n))*PolyLog(2, e*x))/(2*x^2)]

    @test_int [x^2*PolyLog(3, e*x)*(a + b*log(c*x^n)), x, 15, -((2*b*n*x)/(27*e^2)) - (b*n*x^2)/(36*e) - (4/243)*b*n*x^3 + (x*(a + b*log(c*x^n)))/(27*e^2) + (x^2*(a + b*log(c*x^n)))/(54*e) + (1/81)*x^3*(a + b*log(c*x^n)) - (b*n*log(1 - e*x))/(27*e^3) + (1/27)*b*n*x^3*log(1 - e*x) + ((a + b*log(c*x^n))*log(1 - e*x))/(27*e^3) - (1/27)*x^3*(a + b*log(c*x^n))*log(1 - e*x) + (b*n*PolyLog(2, e*x))/(27*e^3) + (2/27)*b*n*x^3*PolyLog(2, e*x) - (1/9)*x^3*(a + b*log(c*x^n))*PolyLog(2, e*x) - (1/9)*b*n*x^3*PolyLog(3, e*x) + (1/3)*x^3*(a + b*log(c*x^n))*PolyLog(3, e*x)]
    @test_int [x^1*PolyLog(3, e*x)*(a + b*log(c*x^n)), x, 15, -((5*b*n*x)/(16*e)) - (1/8)*b*n*x^2 + (x*(a + b*log(c*x^n)))/(8*e) + (1/16)*x^2*(a + b*log(c*x^n)) - (3*b*n*log(1 - e*x))/(16*e^2) + (3/16)*b*n*x^2*log(1 - e*x) + ((a + b*log(c*x^n))*log(1 - e*x))/(8*e^2) - (1/8)*x^2*(a + b*log(c*x^n))*log(1 - e*x) + (b*n*PolyLog(2, e*x))/(8*e^2) + (1/4)*b*n*x^2*PolyLog(2, e*x) - (1/4)*x^2*(a + b*log(c*x^n))*PolyLog(2, e*x) - (1/4)*b*n*x^2*PolyLog(3, e*x) + (1/2)*x^2*(a + b*log(c*x^n))*PolyLog(3, e*x)]
    @test_int [x^0*PolyLog(3, e*x)*(a + b*log(c*x^n)), x, 14, -4*b*n*x + x*(a + b*log(c*x^n)) - (3*b*n*(1 - e*x)*log(1 - e*x))/e + ((1 - e*x)*(a + b*log(c*x^n))*log(1 - e*x))/e + (b*n*PolyLog(2, e*x))/e + 2*b*n*x*PolyLog(2, e*x) - x*(a + b*log(c*x^n))*PolyLog(2, e*x) - b*n*x*PolyLog(3, e*x) + x*(a + b*log(c*x^n))*PolyLog(3, e*x)]
    @test_int [PolyLog(3, e*x)*(a + b*log(c*x^n))/x^1, x, 2, (a + b*log(c*x^n))*PolyLog(4, e*x) - b*n*PolyLog(5, e*x)]
    @test_int [PolyLog(3, e*x)*(a + b*log(c*x^n))/x^2, x, 19, 3*b*e*n*log(x) - (1/2)*b*e*n*log(x)^2 + e*log(x)*(a + b*log(c*x^n)) - 3*b*e*n*log(1 - e*x) + (3*b*n*log(1 - e*x))/x - e*(a + b*log(c*x^n))*log(1 - e*x) + ((a + b*log(c*x^n))*log(1 - e*x))/x - b*e*n*PolyLog(2, e*x) - (2*b*n*PolyLog(2, e*x))/x - ((a + b*log(c*x^n))*PolyLog(2, e*x))/x - (b*n*PolyLog(3, e*x))/x - ((a + b*log(c*x^n))*PolyLog(3, e*x))/x]
    @test_int [PolyLog(3, e*x)*(a + b*log(c*x^n))/x^3, x, 16, -((5*b*e*n)/(16*x)) + (3/16)*b*e^2*n*log(x) - (1/16)*b*e^2*n*log(x)^2 - (e*(a + b*log(c*x^n)))/(8*x) + (1/8)*e^2*log(x)*(a + b*log(c*x^n)) - (3/16)*b*e^2*n*log(1 - e*x) + (3*b*n*log(1 - e*x))/(16*x^2) - (1/8)*e^2*(a + b*log(c*x^n))*log(1 - e*x) + ((a + b*log(c*x^n))*log(1 - e*x))/(8*x^2) - (1/8)*b*e^2*n*PolyLog(2, e*x) - (b*n*PolyLog(2, e*x))/(4*x^2) - ((a + b*log(c*x^n))*PolyLog(2, e*x))/(4*x^2) - (b*n*PolyLog(3, e*x))/(4*x^2) - ((a + b*log(c*x^n))*PolyLog(3, e*x))/(2*x^2)]

    @test_int [(d*x)^m*PolyLog(1, e*x^q)*(a + b*log(c*x^n)), x, 0, -Unintegrable((d*x)^m*(a + b*log(c*x^n))*log(1 - e*x^q), x)]
    @test_int [(d*x)^m*PolyLog(2, e*x^q)*(a + b*log(c*x^n)), x, 4, -((b*e*n*q^2*x^(1 + q)*(d*x)^m*HypergeometricFunctions._₂F₁(1, (1 + m + q)/q, (1 + m + 2*q)/q, e*x^q))/((1 + m)^3*(1 + m + q))) - (b*n*q*(d*x)^(1 + m)*log(1 - e*x^q))/(d*(1 + m)^3) - (b*n*(d*x)^(1 + m)*PolyLog(2, e*x^q))/(d*(1 + m)^2) + ((d*x)^(1 + m)*(a + b*log(c*x^n))*PolyLog(2, e*x^q))/(d*(1 + m)) + (q*Unintegrable((d*x)^m*(a + b*log(c*x^n))*log(1 - e*x^q), x))/(1 + m)]
    @test_int [(d*x)^m*PolyLog(3, e*x^q)*(a + b*log(c*x^n)), x, 9, (2*b*e*n*q^3*x^(1 + q)*(d*x)^m*HypergeometricFunctions._₂F₁(1, (1 + m + q)/q, (1 + m + 2*q)/q, e*x^q))/((1 + m)^4*(1 + m + q)) + (2*b*n*q^2*(d*x)^(1 + m)*log(1 - e*x^q))/(d*(1 + m)^4) + (2*b*n*q*(d*x)^(1 + m)*PolyLog(2, e*x^q))/(d*(1 + m)^3) - (q*(d*x)^(1 + m)*(a + b*log(c*x^n))*PolyLog(2, e*x^q))/(d*(1 + m)^2) - (b*n*(d*x)^(1 + m)*PolyLog(3, e*x^q))/(d*(1 + m)^2) + ((d*x)^(1 + m)*(a + b*log(c*x^n))*PolyLog(3, e*x^q))/(d*(1 + m)) - (q^2*Unintegrable((d*x)^m*(a + b*log(c*x^n))*log(1 - e*x^q), x))/(1 + m)^2]

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

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

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

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

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

    @test_int [log(c*(b*x^n)^p)^2*x^2, x, 3, (2/27)*n^2*p^2*x^3 - (2/9)*n*p*x^3*log(c*(b*x^n)^p) + (1/3)*x^3*log(c*(b*x^n)^p)^2]
    @test_int [log(c*(b*x^n)^p)^2*x^1, x, 3, (1/4)*n^2*p^2*x^2 - (1/2)*n*p*x^2*log(c*(b*x^n)^p) + (1/2)*x^2*log(c*(b*x^n)^p)^2]
    @test_int [log(c*(b*x^n)^p)^2*x^0, x, 3, 2*n^2*p^2*x - 2*n*p*x*log(c*(b*x^n)^p) + x*log(c*(b*x^n)^p)^2]
    @test_int [log(c*(b*x^n)^p)^2/x^1, x, 3, log(c*(b*x^n)^p)^3/(3*n*p)]
    @test_int [log(c*(b*x^n)^p)^2/x^2, x, 3, -((2*n^2*p^2)/x) - (2*n*p*log(c*(b*x^n)^p))/x - log(c*(b*x^n)^p)^2/x]
    @test_int [log(c*(b*x^n)^p)^2/x^3, x, 3, -((n^2*p^2)/(4*x^2)) - (n*p*log(c*(b*x^n)^p))/(2*x^2) - log(c*(b*x^n)^p)^2/(2*x^2)]
    @test_int [log(c*(b*x^n)^p)^2/x^4, x, 3, -((2*n^2*p^2)/(27*x^3)) - (2*n*p*log(c*(b*x^n)^p))/(9*x^3) - log(c*(b*x^n)^p)^2/(3*x^3)]

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

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

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

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

    @test_int [(e*x)^q*(a + b*log(c*(d*x^m)^n))^p, x, 3, ((e*x)^(1 + q)*Gamma(1 + p, -(((1 + q)*(a + b*log(c*(d*x^m)^n)))/(b*m*n)))*(a + b*log(c*(d*x^m)^n))^p)/(ℯ^((a*(1 + q))/(b*m*n))*(c*(d*x^m)^n)^((1 + q)/(m*n))*(-(((1 + q)*(a + b*log(c*(d*x^m)^n)))/(b*m*n)))^p*(e*(1 + q)))]

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

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

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

max_stars_repo_path: test/3 Logarithms/3.1.5 u (a+b log(c x^n))^p.jl