@testset "7.3.5 u (a+b arctanh(c+d x))^p" begin
    (a, b, c, d, e, f, m, x, ) = @variables a b c d e f m x

    #= ::Package:: =#

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


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


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


    @test_int [x^3*atanh(a + b*x)^2, x, 19, -((a*x)/b^3) + (a + b*x)^2/(12*b^4) + (a*atanh(a + b*x))/b^4 + ((1 + 6*a^2)*(a + b*x)*atanh(a + b*x))/(2*b^4) - (a*(a + b*x)^2*atanh(a + b*x))/b^4 + ((a + b*x)^3*atanh(a + b*x))/(6*b^4) - (a*(1 + a^2)*atanh(a + b*x)^2)/b^4 - ((1 + 6*a^2 + a^4)*atanh(a + b*x)^2)/(4*b^4) + (1/4)*x^4*atanh(a + b*x)^2 + (2*a*(1 + a^2)*atanh(a + b*x)*log(2/(1 - a - b*x)))/b^4 + log(1 - (a + b*x)^2)/(12*b^4) + ((1 + 6*a^2)*log(1 - (a + b*x)^2))/(4*b^4) + (a*(1 + a^2)*PolyLog(2, -((1 + a + b*x)/(1 - a - b*x))))/b^4]
    @test_int [x^2*atanh(a + b*x)^2, x, 15, x/(3*b^2) - atanh(a + b*x)/(3*b^3) - (2*a*(a + b*x)*atanh(a + b*x))/b^3 + ((a + b*x)^2*atanh(a + b*x))/(3*b^3) + (a*(3 + a^2)*atanh(a + b*x)^2)/(3*b^3) + ((1 + 3*a^2)*atanh(a + b*x)^2)/(3*b^3) + (1/3)*x^3*atanh(a + b*x)^2 - (2*(1 + 3*a^2)*atanh(a + b*x)*log(2/(1 - a - b*x)))/(3*b^3) - (a*log(1 - (a + b*x)^2))/b^3 - ((1 + 3*a^2)*PolyLog(2, -((1 + a + b*x)/(1 - a - b*x))))/(3*b^3)]
    @test_int [x^1*atanh(a + b*x)^2, x, 12, ((a + b*x)*atanh(a + b*x))/b^2 - (a*atanh(a + b*x)^2)/b^2 - ((1 + a^2)*atanh(a + b*x)^2)/(2*b^2) + (1/2)*x^2*atanh(a + b*x)^2 + (2*a*atanh(a + b*x)*log(2/(1 - a - b*x)))/b^2 + log(1 - (a + b*x)^2)/(2*b^2) + (a*PolyLog(2, -((1 + a + b*x)/(1 - a - b*x))))/b^2]
    @test_int [x^0*atanh(a + b*x)^2, x, 6, atanh(a + b*x)^2/b + ((a + b*x)*atanh(a + b*x)^2)/b - (2*atanh(a + b*x)*log(2/(1 - a - b*x)))/b - PolyLog(2, -((1 + a + b*x)/(1 - a - b*x)))/b]
    @test_int [atanh(a + b*x)^2/x^1, x, 2, (-atanh(a + b*x)^2)*log(2/(1 + a + b*x)) + atanh(a + b*x)^2*log((2*b*x)/((1 - a)*(1 + a + b*x))) + atanh(a + b*x)*PolyLog(2, 1 - 2/(1 + a + b*x)) - atanh(a + b*x)*PolyLog(2, 1 - (2*b*x)/((1 - a)*(1 + a + b*x))) + (1/2)*PolyLog(3, 1 - 2/(1 + a + b*x)) - (1/2)*PolyLog(3, 1 - (2*b*x)/((1 - a)*(1 + a + b*x)))]
    @test_int [atanh(a + b*x)^2/x^2, x, 17, -(atanh(a + b*x)^2/x) + (b*atanh(a + b*x)*log(2/(1 - a - b*x)))/(1 - a) + (b*atanh(a + b*x)*log(2/(1 + a + b*x)))/(1 + a) - (2*b*atanh(a + b*x)*log(2/(1 + a + b*x)))/(1 - a^2) + (2*b*atanh(a + b*x)*log((2*b*x)/((1 - a)*(1 + a + b*x))))/(1 - a^2) + (b*PolyLog(2, -((1 + a + b*x)/(1 - a - b*x))))/(2*(1 - a)) - (b*PolyLog(2, 1 - 2/(1 + a + b*x)))/(2*(1 + a)) + (b*PolyLog(2, 1 - 2/(1 + a + b*x)))/(1 - a^2) - (b*PolyLog(2, 1 - (2*b*x)/((1 - a)*(1 + a + b*x))))/(1 - a^2)]
    @test_int [atanh(a + b*x)^2/x^3, x, 21, -((b*atanh(a + b*x))/((1 - a^2)*x)) - atanh(a + b*x)^2/(2*x^2) + (b^2*log(x))/(1 - a^2)^2 + (b^2*atanh(a + b*x)*log(2/(1 - a - b*x)))/(2*(1 - a)^2) - (b^2*log(1 - a - b*x))/(2*(1 - a)^2*(1 + a)) - (b^2*atanh(a + b*x)*log(2/(1 + a + b*x)))/(2*(1 + a)^2) - (2*a*b^2*atanh(a + b*x)*log(2/(1 + a + b*x)))/(1 - a^2)^2 + (2*a*b^2*atanh(a + b*x)*log((2*b*x)/((1 - a)*(1 + a + b*x))))/(1 - a^2)^2 - (b^2*log(1 + a + b*x))/(2*(1 - a)*(1 + a)^2) + (b^2*PolyLog(2, -((1 + a + b*x)/(1 - a - b*x))))/(4*(1 - a)^2) + (b^2*PolyLog(2, 1 - 2/(1 + a + b*x)))/(4*(1 + a)^2) + (a*b^2*PolyLog(2, 1 - 2/(1 + a + b*x)))/(1 - a^2)^2 - (a*b^2*PolyLog(2, 1 - (2*b*x)/((1 - a)*(1 + a + b*x))))/(1 - a^2)^2]


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


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


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


    @test_int [(c*e + d*e*x)^3*(a + b*atanh(c + d*x))^2, x, 13, (a*b*e^3*x)/2 + (b^2*e^3*(c + d*x)^2)/(12*d) + (b^2*e^3*(c + d*x)*atanh(c + d*x))/(2*d) + (b*e^3*(c + d*x)^3*(a + b*atanh(c + d*x)))/(6*d) - (e^3*(a + b*atanh(c + d*x))^2)/(4*d) + (e^3*(c + d*x)^4*(a + b*atanh(c + d*x))^2)/(4*d) + (b^2*e^3*log(1 - (c + d*x)^2))/(3*d)]
    @test_int [(c*e + d*e*x)^2*(a + b*atanh(c + d*x))^2, x, 11, (1/3)*b^2*e^2*x - (b^2*e^2*atanh(c + d*x))/(3*d) + (b*e^2*(c + d*x)^2*(a + b*atanh(c + d*x)))/(3*d) + (e^2*(a + b*atanh(c + d*x))^2)/(3*d) + (e^2*(c + d*x)^3*(a + b*atanh(c + d*x))^2)/(3*d) - (2*b*e^2*(a + b*atanh(c + d*x))*log(2/(1 - c - d*x)))/(3*d) - (b^2*e^2*PolyLog(2, -((1 + c + d*x)/(1 - c - d*x))))/(3*d)]
    @test_int [(c*e + d*e*x)^1*(a + b*atanh(c + d*x))^2, x, 8, a*b*e*x + (b^2*e*(c + d*x)*atanh(c + d*x))/d - (e*(a + b*atanh(c + d*x))^2)/(2*d) + (e*(c + d*x)^2*(a + b*atanh(c + d*x))^2)/(2*d) + (b^2*e*log(1 - (c + d*x)^2))/(2*d)]
    @test_int [(a + b*atanh(c + d*x))^2/(c*e + d*e*x)^1, x, 8, (2*(a + b*atanh(c + d*x))^2*atanh(1 - 2/(1 - c - d*x)))/(d*e) - (b*(a + b*atanh(c + d*x))*PolyLog(2, 1 - 2/(1 - c - d*x)))/(d*e) + (b*(a + b*atanh(c + d*x))*PolyLog(2, -1 + 2/(1 - c - d*x)))/(d*e) + (b^2*PolyLog(3, 1 - 2/(1 - c - d*x)))/(2*d*e) - (b^2*PolyLog(3, -1 + 2/(1 - c - d*x)))/(2*d*e)]
    @test_int [(a + b*atanh(c + d*x))^2/(c*e + d*e*x)^2, x, 6, (a + b*atanh(c + d*x))^2/(d*e^2) - (a + b*atanh(c + d*x))^2/(d*e^2*(c + d*x)) + (2*b*(a + b*atanh(c + d*x))*log(2 - 2/(1 + c + d*x)))/(d*e^2) - (b^2*PolyLog(2, -1 + 2/(1 + c + d*x)))/(d*e^2)]
    @test_int [(a + b*atanh(c + d*x))^2/(c*e + d*e*x)^3, x, 10, -((b*(a + b*atanh(c + d*x)))/(d*e^3*(c + d*x))) + (a + b*atanh(c + d*x))^2/(2*d*e^3) - (a + b*atanh(c + d*x))^2/(2*d*e^3*(c + d*x)^2) + (b^2*log(c + d*x))/(d*e^3) - (b^2*log(1 - (c + d*x)^2))/(2*d*e^3)]
    @test_int [(a + b*atanh(c + d*x))^2/(c*e + d*e*x)^4, x, 10, -(b^2/(3*d*e^4*(c + d*x))) + (b^2*atanh(c + d*x))/(3*d*e^4) - (b*(a + b*atanh(c + d*x)))/(3*d*e^4*(c + d*x)^2) + (a + b*atanh(c + d*x))^2/(3*d*e^4) - (a + b*atanh(c + d*x))^2/(3*d*e^4*(c + d*x)^3) + (2*b*(a + b*atanh(c + d*x))*log(2 - 2/(1 + c + d*x)))/(3*d*e^4) - (b^2*PolyLog(2, -1 + 2/(1 + c + d*x)))/(3*d*e^4)]
    @test_int [(a + b*atanh(c + d*x))^2/(c*e + d*e*x)^5, x, 15, -(b^2/(12*d*e^5*(c + d*x)^2)) - (b*(a + b*atanh(c + d*x)))/(6*d*e^5*(c + d*x)^3) - (b*(a + b*atanh(c + d*x)))/(2*d*e^5*(c + d*x)) + (a + b*atanh(c + d*x))^2/(4*d*e^5) - (a + b*atanh(c + d*x))^2/(4*d*e^5*(c + d*x)^4) + (2*b^2*log(c + d*x))/(3*d*e^5) - (b^2*log(1 - (c + d*x)^2))/(3*d*e^5)]


    @test_int [(c*e + d*e*x)^2*(a + b*atanh(c + d*x))^3, x, 14, a*b^2*e^2*x + (b^3*e^2*(c + d*x)*atanh(c + d*x))/d - (b*e^2*(a + b*atanh(c + d*x))^2)/(2*d) + (b*e^2*(c + d*x)^2*(a + b*atanh(c + d*x))^2)/(2*d) + (e^2*(a + b*atanh(c + d*x))^3)/(3*d) + (e^2*(c + d*x)^3*(a + b*atanh(c + d*x))^3)/(3*d) - (b*e^2*(a + b*atanh(c + d*x))^2*log(2/(1 - c - d*x)))/d + (b^3*e^2*log(1 - (c + d*x)^2))/(2*d) - (b^2*e^2*(a + b*atanh(c + d*x))*PolyLog(2, 1 - 2/(1 - c - d*x)))/d + (b^3*e^2*PolyLog(3, 1 - 2/(1 - c - d*x)))/(2*d)]
    @test_int [(c*e + d*e*x)^1*(a + b*atanh(c + d*x))^3, x, 10, (3*b*e*(a + b*atanh(c + d*x))^2)/(2*d) + (3*b*e*(c + d*x)*(a + b*atanh(c + d*x))^2)/(2*d) - (e*(a + b*atanh(c + d*x))^3)/(2*d) + (e*(c + d*x)^2*(a + b*atanh(c + d*x))^3)/(2*d) - (3*b^2*e*(a + b*atanh(c + d*x))*log(2/(1 - c - d*x)))/d - (3*b^3*e*PolyLog(2, -((1 + c + d*x)/(1 - c - d*x))))/(2*d)]
    @test_int [(a + b*atanh(c + d*x))^3/(c*e + d*e*x)^1, x, 10, (2*(a + b*atanh(c + d*x))^3*atanh(1 - 2/(1 - c - d*x)))/(d*e) - (3*b*(a + b*atanh(c + d*x))^2*PolyLog(2, 1 - 2/(1 - c - d*x)))/(2*d*e) + (3*b*(a + b*atanh(c + d*x))^2*PolyLog(2, -1 + 2/(1 - c - d*x)))/(2*d*e) + (3*b^2*(a + b*atanh(c + d*x))*PolyLog(3, 1 - 2/(1 - c - d*x)))/(2*d*e) - (3*b^2*(a + b*atanh(c + d*x))*PolyLog(3, -1 + 2/(1 - c - d*x)))/(2*d*e) - (3*b^3*PolyLog(4, 1 - 2/(1 - c - d*x)))/(4*d*e) + (3*b^3*PolyLog(4, -1 + 2/(1 - c - d*x)))/(4*d*e)]
    @test_int [(a + b*atanh(c + d*x))^3/(c*e + d*e*x)^2, x, 7, (a + b*atanh(c + d*x))^3/(d*e^2) - (a + b*atanh(c + d*x))^3/(d*e^2*(c + d*x)) + (3*b*(a + b*atanh(c + d*x))^2*log(2 - 2/(1 + c + d*x)))/(d*e^2) - (3*b^2*(a + b*atanh(c + d*x))*PolyLog(2, -1 + 2/(1 + c + d*x)))/(d*e^2) - (3*b^3*PolyLog(3, -1 + 2/(1 + c + d*x)))/(2*d*e^2)]
    @test_int [(a + b*atanh(c + d*x))^3/(c*e + d*e*x)^3, x, 9, (3*b*(a + b*atanh(c + d*x))^2)/(2*d*e^3) - (3*b*(a + b*atanh(c + d*x))^2)/(2*d*e^3*(c + d*x)) + (a + b*atanh(c + d*x))^3/(2*d*e^3) - (a + b*atanh(c + d*x))^3/(2*d*e^3*(c + d*x)^2) + (3*b^2*(a + b*atanh(c + d*x))*log(2 - 2/(1 + c + d*x)))/(d*e^3) - (3*b^3*PolyLog(2, -1 + 2/(1 + c + d*x)))/(2*d*e^3)]
    @test_int [(a + b*atanh(c + d*x))^3/(c*e + d*e*x)^4, x, 16, -((b^2*(a + b*atanh(c + d*x)))/(d*e^4*(c + d*x))) + (b*(a + b*atanh(c + d*x))^2)/(2*d*e^4) - (b*(a + b*atanh(c + d*x))^2)/(2*d*e^4*(c + d*x)^2) + (a + b*atanh(c + d*x))^3/(3*d*e^4) - (a + b*atanh(c + d*x))^3/(3*d*e^4*(c + d*x)^3) + (b^3*log(c + d*x))/(d*e^4) - (b^3*log(1 - (c + d*x)^2))/(2*d*e^4) + (b*(a + b*atanh(c + d*x))^2*log(2 - 2/(1 + c + d*x)))/(d*e^4) - (b^2*(a + b*atanh(c + d*x))*PolyLog(2, -1 + 2/(1 + c + d*x)))/(d*e^4) - (b^3*PolyLog(3, -1 + 2/(1 + c + d*x)))/(2*d*e^4)]


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


    @test_int [atanh(a + b*x)/((a*d)/b + d*x), x, 3, -(PolyLog(2, -a - b*x)/(2*d)) + PolyLog(2, a + b*x)/(2*d)]


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


    @test_int [(e + f*x)^3*(a + b*atanh(c + d*x)), x, 7, (b*f*(6*d^2*e^2 - 12*c*d*e*f + (1 + 6*c^2)*f^2)*x)/(4*d^3) + (b*f^2*(d*e - c*f)*(c + d*x)^2)/(2*d^4) + (b*f^3*(c + d*x)^3)/(12*d^4) + ((e + f*x)^4*(a + b*atanh(c + d*x)))/(4*f) + (b*(d*e + f - c*f)^4*log(1 - c - d*x))/(8*d^4*f) - (b*(d*e - f - c*f)^4*log(1 + c + d*x))/(8*d^4*f)]
    @test_int [(e + f*x)^2*(a + b*atanh(c + d*x)), x, 7, (b*f*(d*e - c*f)*x)/d^2 + (b*f^2*(c + d*x)^2)/(6*d^3) + ((e + f*x)^3*(a + b*atanh(c + d*x)))/(3*f) + (b*(d*e + f - c*f)^3*log(1 - c - d*x))/(6*d^3*f) - (b*(d*e - (1 + c)*f)^3*log(1 + c + d*x))/(6*d^3*f)]
    @test_int [(e + f*x)^1*(a + b*atanh(c + d*x)), x, 7, (b*f*x)/(2*d) + ((e + f*x)^2*(a + b*atanh(c + d*x)))/(2*f) + (b*(d*e + f - c*f)^2*log(1 - c - d*x))/(4*d^2*f) - (b*(d*e - (1 + c)*f)^2*log(1 + c + d*x))/(4*d^2*f)]
    @test_int [(e + f*x)^0*(a + b*atanh(c + d*x)), x, 4, a*x + (b*(c + d*x)*atanh(c + d*x))/d + (b*log(1 - (c + d*x)^2))/(2*d)]
    @test_int [(a + b*atanh(c + d*x))/(e + f*x)^1, x, 5, -(((a + b*atanh(c + d*x))*log(2/(1 + c + d*x)))/f) + ((a + b*atanh(c + d*x))*log((2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/f + (b*PolyLog(2, 1 - 2/(1 + c + d*x)))/(2*f) - (b*PolyLog(2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/(2*f)]
    @test_int [(a + b*atanh(c + d*x))/(e + f*x)^2, x, 7, If(13>=8, -((a + b*atanh(c + d*x))/(f*(e + f*x))) - (b*d*log(1 - c - d*x))/(2*f*(d*e + f - c*f)) + (b*d*log(1 + c + d*x))/(2*f*(d*e - f - c*f)) - (b*d*log(e + f*x))/((d*e + f - c*f)*(d*e - (1 + c)*f)), -((a + b*atanh(c + d*x))/(f*(e + f*x))) - (b*d*log(1 - c - d*x))/(2*f*(d*e + f - c*f)) + (b*d*log(1 + c + d*x))/(2*f*(d*e - f - c*f)) - (b*d*log(e + f*x))/((d*e - f - c*f)*(d*e + f - c*f)))]
    @test_int [(a + b*atanh(c + d*x))/(e + f*x)^3, x, 5, If(13>=8, (b*d)/(2*(d*e + f - c*f)*(d*e - (1 + c)*f)*(e + f*x)) - (a + b*atanh(c + d*x))/(2*f*(e + f*x)^2) - (b*d^2*log(1 - c - d*x))/(4*f*(d*e + f - c*f)^2) + (b*d^2*log(1 + c + d*x))/(4*f*(d*e - f - c*f)^2) - (b*d^2*(d*e - c*f)*log(e + f*x))/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2), (b*d)/(2*(d*e - f - c*f)*(d*e + f - c*f)*(e + f*x)) - (a + b*atanh(c + d*x))/(2*f*(e + f*x)^2) - (b*d^2*log(1 - c - d*x))/(4*f*(d*e + f - c*f)^2) + (b*d^2*log(1 + c + d*x))/(4*f*(d*e - f - c*f)^2) - (b*d^2*(d*e - c*f)*log(e + f*x))/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2))]


    @test_int [(e + f*x)^3*(a + b*atanh(c + d*x))^2, x, 20, (b^2*f^2*(d*e - c*f)*x)/d^3 + (a*b*f*(6*d^2*e^2 - 12*c*d*e*f + (1 + 6*c^2)*f^2)*x)/(2*d^3) + (b^2*f^3*(c + d*x)^2)/(12*d^4) - (b^2*f^2*(d*e - c*f)*atanh(c + d*x))/d^4 + (b^2*f*(6*d^2*e^2 - 12*c*d*e*f + (1 + 6*c^2)*f^2)*(c + d*x)*atanh(c + d*x))/(2*d^4) + (b*f^2*(d*e - c*f)*(c + d*x)^2*(a + b*atanh(c + d*x)))/d^4 + (b*f^3*(c + d*x)^3*(a + b*atanh(c + d*x)))/(6*d^4) + ((d*e - c*f)*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)*(a + b*atanh(c + d*x))^2)/d^4 - ((d^4*e^4 - 4*c*d^3*e^3*f + 6*(1 + c^2)*d^2*e^2*f^2 - 4*c*(3 + c^2)*d*e*f^3 + (1 + 6*c^2 + c^4)*f^4)*(a + b*atanh(c + d*x))^2)/(4*d^4*f) + ((e + f*x)^4*(a + b*atanh(c + d*x))^2)/(4*f) - (2*b*(d*e - c*f)*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)*(a + b*atanh(c + d*x))*log(2/(1 - c - d*x)))/d^4 + (b^2*f^3*log(1 - (c + d*x)^2))/(12*d^4) + (b^2*f*(6*d^2*e^2 - 12*c*d*e*f + (1 + 6*c^2)*f^2)*log(1 - (c + d*x)^2))/(4*d^4) - (b^2*(d*e - c*f)*(d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)*PolyLog(2, -((1 + c + d*x)/(1 - c - d*x))))/d^4]
    @test_int [(e + f*x)^2*(a + b*atanh(c + d*x))^2, x, 16, (b^2*f^2*x)/(3*d^2) + (2*a*b*f*(d*e - c*f)*x)/d^2 - (b^2*f^2*atanh(c + d*x))/(3*d^3) + (2*b^2*f*(d*e - c*f)*(c + d*x)*atanh(c + d*x))/d^3 + (b*f^2*(c + d*x)^2*(a + b*atanh(c + d*x)))/(3*d^3) - ((d*e - c*f)*(d^2*e^2 - 2*c*d*e*f + (3 + c^2)*f^2)*(a + b*atanh(c + d*x))^2)/(3*d^3*f) + ((3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*(a + b*atanh(c + d*x))^2)/(3*d^3) + ((e + f*x)^3*(a + b*atanh(c + d*x))^2)/(3*f) - (2*b*(3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*(a + b*atanh(c + d*x))*log(2/(1 - c - d*x)))/(3*d^3) + (b^2*f*(d*e - c*f)*log(1 - (c + d*x)^2))/d^3 - (b^2*(3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*PolyLog(2, -((1 + c + d*x)/(1 - c - d*x))))/(3*d^3)]
    @test_int [(e + f*x)^1*(a + b*atanh(c + d*x))^2, x, 13, (a*b*f*x)/d + (b^2*f*(c + d*x)*atanh(c + d*x))/d^2 + ((d*e - c*f)*(a + b*atanh(c + d*x))^2)/d^2 - ((d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)*(a + b*atanh(c + d*x))^2)/(2*d^2*f) + ((e + f*x)^2*(a + b*atanh(c + d*x))^2)/(2*f) - (2*b*(d*e - c*f)*(a + b*atanh(c + d*x))*log(2/(1 - c - d*x)))/d^2 + (b^2*f*log(1 - (c + d*x)^2))/(2*d^2) - (b^2*(d*e - c*f)*PolyLog(2, -((1 + c + d*x)/(1 - c - d*x))))/d^2]
    @test_int [(e + f*x)^0*(a + b*atanh(c + d*x))^2, x, 6, (a + b*atanh(c + d*x))^2/d + ((c + d*x)*(a + b*atanh(c + d*x))^2)/d - (2*b*(a + b*atanh(c + d*x))*log(2/(1 - c - d*x)))/d - (b^2*PolyLog(2, -((1 + c + d*x)/(1 - c - d*x))))/d]
    @test_int [(a + b*atanh(c + d*x))^2/(e + f*x)^1, x, 2, -(((a + b*atanh(c + d*x))^2*log(2/(1 + c + d*x)))/f) + ((a + b*atanh(c + d*x))^2*log((2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/f + (b*(a + b*atanh(c + d*x))*PolyLog(2, 1 - 2/(1 + c + d*x)))/f - (b*(a + b*atanh(c + d*x))*PolyLog(2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/f + (b^2*PolyLog(3, 1 - 2/(1 + c + d*x)))/(2*f) - (b^2*PolyLog(3, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/(2*f)]
    @test_int [(a + b*atanh(c + d*x))^2/(e + f*x)^2, x, 24, If(13>=8, -((a + b*atanh(c + d*x))^2/(f*(e + f*x))) + (b^2*d*atanh(c + d*x)*log(2/(1 - c - d*x)))/(f*(d*e + f - c*f)) - (a*b*d*log(1 - c - d*x))/(f*(d*e + f - c*f)) - (b^2*d*atanh(c + d*x)*log(2/(1 + c + d*x)))/(f*(d*e - f - c*f)) + (2*b^2*d*atanh(c + d*x)*log(2/(1 + c + d*x)))/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (a*b*d*log(1 + c + d*x))/(f*(d*e - f - c*f)) + (2*a*b*d*log(e + f*x))/(f^2 - (d*e - c*f)^2) - (2*b^2*d*atanh(c + d*x)*log((2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (b^2*d*PolyLog(2, -((1 + c + d*x)/(1 - c - d*x))))/(2*f*(d*e + f - c*f)) + (b^2*d*PolyLog(2, 1 - 2/(1 + c + d*x)))/(2*f*(d*e - f - c*f)) - (b^2*d*PolyLog(2, 1 - 2/(1 + c + d*x)))/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (b^2*d*PolyLog(2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/((d*e + f - c*f)*(d*e - (1 + c)*f)), -((a + b*atanh(c + d*x))^2/(f*(e + f*x))) + (b^2*d*atanh(c + d*x)*log(2/(1 - c - d*x)))/(f*(d*e + f - c*f)) - (a*b*d*log(1 - c - d*x))/(f*(d*e + f - c*f)) - (b^2*d*atanh(c + d*x)*log(2/(1 + c + d*x)))/(f*(d*e - f - c*f)) + (2*b^2*d*atanh(c + d*x)*log(2/(1 + c + d*x)))/((d*e - f - c*f)*(d*e + f - c*f)) + (a*b*d*log(1 + c + d*x))/(f*(d*e - f - c*f)) + (2*a*b*d*log(e + f*x))/(f^2 - (d*e - c*f)^2) - (2*b^2*d*atanh(c + d*x)*log((2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/((d*e - f - c*f)*(d*e + f - c*f)) + (b^2*d*PolyLog(2, -((1 + c + d*x)/(1 - c - d*x))))/(2*f*(d*e + f - c*f)) + (b^2*d*PolyLog(2, 1 - 2/(1 + c + d*x)))/(2*f*(d*e - f - c*f)) - (b^2*d*PolyLog(2, 1 - 2/(1 + c + d*x)))/((d*e - f - c*f)*(d*e + f - c*f)) + (b^2*d*PolyLog(2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/((d*e - f - c*f)*(d*e + f - c*f)))]
    @test_int [(a + b*atanh(c + d*x))^2/(e + f*x)^3, x, 26, If(13>=8, -((a*b*d)/((f^2 - (d*e - c*f)^2)*(e + f*x))) + (b^2*d*atanh(c + d*x))/((d*e + f - c*f)*(d*e - (1 + c)*f)*(e + f*x)) - (a + b*atanh(c + d*x))^2/(2*f*(e + f*x)^2) + (b^2*d^2*atanh(c + d*x)*log(2/(1 - c - d*x)))/(2*f*(d*e + f - c*f)^2) - (a*b*d^2*log(1 - c - d*x))/(2*f*(d*e + f - c*f)^2) + (b^2*d^2*log(1 - c - d*x))/(2*(d*e + f - c*f)^2*(d*e - (1 + c)*f)) - (b^2*d^2*atanh(c + d*x)*log(2/(1 + c + d*x)))/(2*f*(d*e - f - c*f)^2) + (2*b^2*d^2*(d*e - c*f)*atanh(c + d*x)*log(2/(1 + c + d*x)))/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2) + (a*b*d^2*log(1 + c + d*x))/(2*f*(d*e - f - c*f)^2) - (b^2*d^2*log(1 + c + d*x))/(2*(d*e + f - c*f)*(d*e - (1 + c)*f)^2) + (b^2*d^2*f*log(e + f*x))/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2) - (2*a*b*d^2*(d*e - c*f)*log(e + f*x))/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2) - (2*b^2*d^2*(d*e - c*f)*atanh(c + d*x)*log((2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2) + (b^2*d^2*PolyLog(2, -((1 + c + d*x)/(1 - c - d*x))))/(4*f*(d*e + f - c*f)^2) + (b^2*d^2*PolyLog(2, 1 - 2/(1 + c + d*x)))/(4*f*(d*e - f - c*f)^2) - (b^2*d^2*(d*e - c*f)*PolyLog(2, 1 - 2/(1 + c + d*x)))/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2) + (b^2*d^2*(d*e - c*f)*PolyLog(2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2), -((a*b*d)/((f^2 - (d*e - c*f)^2)*(e + f*x))) + (b^2*d*atanh(c + d*x))/((d*e - f - c*f)*(d*e + f - c*f)*(e + f*x)) - (a + b*atanh(c + d*x))^2/(2*f*(e + f*x)^2) + (b^2*d^2*atanh(c + d*x)*log(2/(1 - c - d*x)))/(2*f*(d*e + f - c*f)^2) - (a*b*d^2*log(1 - c - d*x))/(2*f*(d*e + f - c*f)^2) + (b^2*d^2*log(1 - c - d*x))/(2*(d*e + f - c*f)^2*(d*e - (1 + c)*f)) - (b^2*d^2*atanh(c + d*x)*log(2/(1 + c + d*x)))/(2*f*(d*e - f - c*f)^2) + (2*b^2*d^2*(d*e - c*f)*atanh(c + d*x)*log(2/(1 + c + d*x)))/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2) + (a*b*d^2*log(1 + c + d*x))/(2*f*(d*e - f - c*f)^2) - (b^2*d^2*log(1 + c + d*x))/(2*(d*e + f - c*f)*(d*e - (1 + c)*f)^2) + (b^2*d^2*f*log(e + f*x))/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2) - (2*a*b*d^2*(d*e - c*f)*log(e + f*x))/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2) - (2*b^2*d^2*(d*e - c*f)*atanh(c + d*x)*log((2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2) + (b^2*d^2*PolyLog(2, -((1 + c + d*x)/(1 - c - d*x))))/(4*f*(d*e + f - c*f)^2) + (b^2*d^2*PolyLog(2, 1 - 2/(1 + c + d*x)))/(4*f*(d*e - f - c*f)^2) - (b^2*d^2*(d*e - c*f)*PolyLog(2, 1 - 2/(1 + c + d*x)))/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2) + (b^2*d^2*(d*e - c*f)*PolyLog(2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2))]


    @test_int [(e + f*x)^2*(a + b*atanh(c + d*x))^3, x, 21, (a*b^2*f^2*x)/d^2 + (b^3*f^2*(c + d*x)*atanh(c + d*x))/d^3 - (b*f^2*(a + b*atanh(c + d*x))^2)/(2*d^3) + (3*b*f*(d*e - c*f)*(a + b*atanh(c + d*x))^2)/d^3 + (3*b*f*(d*e - c*f)*(c + d*x)*(a + b*atanh(c + d*x))^2)/d^3 + (b*f^2*(c + d*x)^2*(a + b*atanh(c + d*x))^2)/(2*d^3) - ((d*e - c*f)*(d^2*e^2 - 2*c*d*e*f + (3 + c^2)*f^2)*(a + b*atanh(c + d*x))^3)/(3*d^3*f) + ((3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*(a + b*atanh(c + d*x))^3)/(3*d^3) + ((e + f*x)^3*(a + b*atanh(c + d*x))^3)/(3*f) - (6*b^2*f*(d*e - c*f)*(a + b*atanh(c + d*x))*log(2/(1 - c - d*x)))/d^3 - (b*(3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*(a + b*atanh(c + d*x))^2*log(2/(1 - c - d*x)))/d^3 + (b^3*f^2*log(1 - (c + d*x)^2))/(2*d^3) - (3*b^3*f*(d*e - c*f)*PolyLog(2, -((1 + c + d*x)/(1 - c - d*x))))/d^3 - (b^2*(3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*(a + b*atanh(c + d*x))*PolyLog(2, 1 - 2/(1 - c - d*x)))/d^3 + (b^3*(3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*PolyLog(3, 1 - 2/(1 - c - d*x)))/(2*d^3)]
    @test_int [(e + f*x)^1*(a + b*atanh(c + d*x))^3, x, 15, (3*b*f*(a + b*atanh(c + d*x))^2)/(2*d^2) + (3*b*f*(c + d*x)*(a + b*atanh(c + d*x))^2)/(2*d^2) + ((d*e - c*f)*(a + b*atanh(c + d*x))^3)/d^2 - ((d^2*e^2 - 2*c*d*e*f + (1 + c^2)*f^2)*(a + b*atanh(c + d*x))^3)/(2*d^2*f) + ((e + f*x)^2*(a + b*atanh(c + d*x))^3)/(2*f) - (3*b^2*f*(a + b*atanh(c + d*x))*log(2/(1 - c - d*x)))/d^2 - (3*b*(d*e - c*f)*(a + b*atanh(c + d*x))^2*log(2/(1 - c - d*x)))/d^2 - (3*b^3*f*PolyLog(2, -((1 + c + d*x)/(1 - c - d*x))))/(2*d^2) - (3*b^2*(d*e - c*f)*(a + b*atanh(c + d*x))*PolyLog(2, 1 - 2/(1 - c - d*x)))/d^2 + (3*b^3*(d*e - c*f)*PolyLog(3, 1 - 2/(1 - c - d*x)))/(2*d^2)]
    @test_int [(e + f*x)^0*(a + b*atanh(c + d*x))^3, x, 6, (a + b*atanh(c + d*x))^3/d + ((c + d*x)*(a + b*atanh(c + d*x))^3)/d - (3*b*(a + b*atanh(c + d*x))^2*log(2/(1 - c - d*x)))/d - (3*b^2*(a + b*atanh(c + d*x))*PolyLog(2, 1 - 2/(1 - c - d*x)))/d + (3*b^3*PolyLog(3, 1 - 2/(1 - c - d*x)))/(2*d)]
    @test_int [(a + b*atanh(c + d*x))^3/(e + f*x)^1, x, 2, -(((a + b*atanh(c + d*x))^3*log(2/(1 + c + d*x)))/f) + ((a + b*atanh(c + d*x))^3*log((2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/f + (3*b*(a + b*atanh(c + d*x))^2*PolyLog(2, 1 - 2/(1 + c + d*x)))/(2*f) - (3*b*(a + b*atanh(c + d*x))^2*PolyLog(2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/(2*f) + (3*b^2*(a + b*atanh(c + d*x))*PolyLog(3, 1 - 2/(1 + c + d*x)))/(2*f) - (3*b^2*(a + b*atanh(c + d*x))*PolyLog(3, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/(2*f) + (3*b^3*PolyLog(4, 1 - 2/(1 + c + d*x)))/(4*f) - (3*b^3*PolyLog(4, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/(4*f)]
    @test_int [(a + b*atanh(c + d*x))^3/(e + f*x)^2, x, 33, If(13>=8, -((a + b*atanh(c + d*x))^3/(f*(e + f*x))) + (3*a*b^2*d*atanh(c + d*x)*log(2/(1 - c - d*x)))/(f*(d*e + f - c*f)) + (3*b^3*d*atanh(c + d*x)^2*log(2/(1 - c - d*x)))/(2*f*(d*e + f - c*f)) - (3*a^2*b*d*log(1 - c - d*x))/(2*f*(d*e + f - c*f)) - (3*a*b^2*d*atanh(c + d*x)*log(2/(1 + c + d*x)))/(f*(d*e - f - c*f)) + (6*a*b^2*d*atanh(c + d*x)*log(2/(1 + c + d*x)))/((d*e + f - c*f)*(d*e - (1 + c)*f)) - (3*b^3*d*atanh(c + d*x)^2*log(2/(1 + c + d*x)))/(2*f*(d*e - f - c*f)) + (3*b^3*d*atanh(c + d*x)^2*log(2/(1 + c + d*x)))/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*a^2*b*d*log(1 + c + d*x))/(2*f*(d*e - f - c*f)) + (3*a^2*b*d*log(e + f*x))/(f^2 - (d*e - c*f)^2) - (6*a*b^2*d*atanh(c + d*x)*log((2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/((d*e + f - c*f)*(d*e - (1 + c)*f)) - (3*b^3*d*atanh(c + d*x)^2*log((2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*a*b^2*d*PolyLog(2, -((1 + c + d*x)/(1 - c - d*x))))/(2*f*(d*e + f - c*f)) + (3*b^3*d*atanh(c + d*x)*PolyLog(2, 1 - 2/(1 - c - d*x)))/(2*f*(d*e + f - c*f)) + (3*a*b^2*d*PolyLog(2, 1 - 2/(1 + c + d*x)))/(2*f*(d*e - f - c*f)) - (3*a*b^2*d*PolyLog(2, 1 - 2/(1 + c + d*x)))/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*b^3*d*atanh(c + d*x)*PolyLog(2, 1 - 2/(1 + c + d*x)))/(2*f*(d*e - f - c*f)) - (3*b^3*d*atanh(c + d*x)*PolyLog(2, 1 - 2/(1 + c + d*x)))/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*a*b^2*d*PolyLog(2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*b^3*d*atanh(c + d*x)*PolyLog(2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/((d*e + f - c*f)*(d*e - (1 + c)*f)) - (3*b^3*d*PolyLog(3, 1 - 2/(1 - c - d*x)))/(4*f*(d*e + f - c*f)) + (3*b^3*d*PolyLog(3, 1 - 2/(1 + c + d*x)))/(4*f*(d*e - f - c*f)) - (3*b^3*d*PolyLog(3, 1 - 2/(1 + c + d*x)))/(2*(d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*b^3*d*PolyLog(3, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/(2*(d*e + f - c*f)*(d*e - (1 + c)*f)), -((a + b*atanh(c + d*x))^3/(f*(e + f*x))) + (3*a*b^2*d*atanh(c + d*x)*log(2/(1 - c - d*x)))/(f*(d*e + f - c*f)) + (3*b^3*d*atanh(c + d*x)^2*log(2/(1 - c - d*x)))/(2*f*(d*e + f - c*f)) - (3*a^2*b*d*log(1 - c - d*x))/(2*f*(d*e + f - c*f)) - (3*a*b^2*d*atanh(c + d*x)*log(2/(1 + c + d*x)))/(f*(d*e - f - c*f)) + (6*a*b^2*d*atanh(c + d*x)*log(2/(1 + c + d*x)))/((d*e - f - c*f)*(d*e + f - c*f)) - (3*b^3*d*atanh(c + d*x)^2*log(2/(1 + c + d*x)))/(2*f*(d*e - f - c*f)) + (3*b^3*d*atanh(c + d*x)^2*log(2/(1 + c + d*x)))/((d*e - f - c*f)*(d*e + f - c*f)) + (3*a^2*b*d*log(1 + c + d*x))/(2*f*(d*e - f - c*f)) + (3*a^2*b*d*log(e + f*x))/(f^2 - (d*e - c*f)^2) - (6*a*b^2*d*atanh(c + d*x)*log((2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/((d*e - f - c*f)*(d*e + f - c*f)) - (3*b^3*d*atanh(c + d*x)^2*log((2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/((d*e - f - c*f)*(d*e + f - c*f)) + (3*a*b^2*d*PolyLog(2, -((1 + c + d*x)/(1 - c - d*x))))/(2*f*(d*e + f - c*f)) + (3*b^3*d*atanh(c + d*x)*PolyLog(2, 1 - 2/(1 - c - d*x)))/(2*f*(d*e + f - c*f)) + (3*a*b^2*d*PolyLog(2, 1 - 2/(1 + c + d*x)))/(2*f*(d*e - f - c*f)) - (3*a*b^2*d*PolyLog(2, 1 - 2/(1 + c + d*x)))/((d*e - f - c*f)*(d*e + f - c*f)) + (3*b^3*d*atanh(c + d*x)*PolyLog(2, 1 - 2/(1 + c + d*x)))/(2*f*(d*e - f - c*f)) - (3*b^3*d*atanh(c + d*x)*PolyLog(2, 1 - 2/(1 + c + d*x)))/((d*e - f - c*f)*(d*e + f - c*f)) + (3*a*b^2*d*PolyLog(2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/((d*e - f - c*f)*(d*e + f - c*f)) + (3*b^3*d*atanh(c + d*x)*PolyLog(2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/((d*e - f - c*f)*(d*e + f - c*f)) - (3*b^3*d*PolyLog(3, 1 - 2/(1 - c - d*x)))/(4*f*(d*e + f - c*f)) + (3*b^3*d*PolyLog(3, 1 - 2/(1 + c + d*x)))/(4*f*(d*e - f - c*f)) - (3*b^3*d*PolyLog(3, 1 - 2/(1 + c + d*x)))/(2*(d*e - f - c*f)*(d*e + f - c*f)) + (3*b^3*d*PolyLog(3, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))))/(2*(d*e - f - c*f)*(d*e + f - c*f)))]


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


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


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


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


    @test_int [atanh(a + b*x)/(c + d*x^3), x, 23, -((log(1 - a - b*x)*log((b*(c^(1/3) + d^(1/3)*x))/(b*c^(1/3) + (1 - a)*d^(1/3))))/(6*c^(2/3)*d^(1/3))) + (log(1 + a + b*x)*log((b*(c^(1/3) + d^(1/3)*x))/(b*c^(1/3) - (1 + a)*d^(1/3))))/(6*c^(2/3)*d^(1/3)) - ((-1)^(2/3)*log(1 - a - b*x)*log((b*(c^(1/3) - (-1)^(1/3)*d^(1/3)*x))/(b*c^(1/3) - (-1)^(1/3)*(1 - a)*d^(1/3))))/(6*c^(2/3)*d^(1/3)) + ((-1)^(2/3)*log(1 + a + b*x)*log((b*(c^(1/3) - (-1)^(1/3)*d^(1/3)*x))/(b*c^(1/3) + (-1)^(1/3)*(1 + a)*d^(1/3))))/(6*c^(2/3)*d^(1/3)) + ((-1)^(1/3)*log(1 - a - b*x)*log((b*(c^(1/3) + (-1)^(2/3)*d^(1/3)*x))/(b*c^(1/3) + (-1)^(2/3)*(1 - a)*d^(1/3))))/(6*c^(2/3)*d^(1/3)) - ((-1)^(1/3)*log(1 + a + b*x)*log((b*(c^(1/3) + (-1)^(2/3)*d^(1/3)*x))/(b*c^(1/3) - (-1)^(2/3)*(1 + a)*d^(1/3))))/(6*c^(2/3)*d^(1/3)) - PolyLog(2, (d^(1/3)*(1 - a - b*x))/(b*c^(1/3) + (1 - a)*d^(1/3)))/(6*c^(2/3)*d^(1/3)) - ((-1)^(2/3)*PolyLog(2, -(((-1)^(1/3)*d^(1/3)*(1 - a - b*x))/(b*c^(1/3) - (-1)^(1/3)*(1 - a)*d^(1/3)))))/(6*c^(2/3)*d^(1/3)) + ((-1)^(1/3)*PolyLog(2, ((-1)^(2/3)*d^(1/3)*(1 - a - b*x))/(b*c^(1/3) + (-1)^(2/3)*(1 - a)*d^(1/3))))/(6*c^(2/3)*d^(1/3)) + PolyLog(2, -((d^(1/3)*(1 + a + b*x))/(b*c^(1/3) - (1 + a)*d^(1/3))))/(6*c^(2/3)*d^(1/3)) + ((-1)^(2/3)*PolyLog(2, ((-1)^(1/3)*d^(1/3)*(1 + a + b*x))/(b*c^(1/3) + (-1)^(1/3)*(1 + a)*d^(1/3))))/(6*c^(2/3)*d^(1/3)) - ((-1)^(1/3)*PolyLog(2, -(((-1)^(2/3)*d^(1/3)*(1 + a + b*x))/(b*c^(1/3) - (-1)^(2/3)*(1 + a)*d^(1/3)))))/(6*c^(2/3)*d^(1/3))]
    @test_int [atanh(a + b*x)/(c + d*x^2), x, 17, -(log(1 - a - b*x)*log((b*(sqrt(-c) - sqrt(d)*x))/(b*sqrt(-c) - (1 - a)*sqrt(d))))/(4*sqrt(-c)*sqrt(d)) + (log(1 + a + b*x)*log((b*(sqrt(-c) - sqrt(d)*x))/(b*sqrt(-c) + (1 + a)*sqrt(d))))/(4*sqrt(-c)*sqrt(d)) + (log(1 - a - b*x)*log((b*(sqrt(-c) + sqrt(d)*x))/(b*sqrt(-c) + (1 - a)*sqrt(d))))/(4*sqrt(-c)*sqrt(d)) - (log(1 + a + b*x)*log((b*(sqrt(-c) + sqrt(d)*x))/(b*sqrt(-c) - (1 + a)*sqrt(d))))/(4*sqrt(-c)*sqrt(d)) - PolyLog(2, -((sqrt(d)*(1 - a - b*x))/(b*sqrt(-c) - (1 - a)*sqrt(d))))/(4*sqrt(-c)*sqrt(d)) + PolyLog(2, (sqrt(d)*(1 - a - b*x))/(b*sqrt(-c) + (1 - a)*sqrt(d)))/(4*sqrt(-c)*sqrt(d)) - PolyLog(2, -((sqrt(d)*(1 + a + b*x))/(b*sqrt(-c) - (1 + a)*sqrt(d))))/(4*sqrt(-c)*sqrt(d)) + PolyLog(2, (sqrt(d)*(1 + a + b*x))/(b*sqrt(-c) + (1 + a)*sqrt(d)))/(4*sqrt(-c)*sqrt(d))]
    @test_int [atanh(a + b*x)/(c + d*x^1), x, 5, -((atanh(a + b*x)*log(2/(1 + a + b*x)))/d) + (atanh(a + b*x)*log((2*b*(c + d*x))/((b*c + d - a*d)*(1 + a + b*x))))/d + PolyLog(2, 1 - 2/(1 + a + b*x))/(2*d) - PolyLog(2, 1 - (2*b*(c + d*x))/((b*c + d - a*d)*(1 + a + b*x)))/(2*d)]
    @test_int [atanh(a + b*x)/(c + d/x^1), x, 15, ((1 - a - b*x)*log(1 - a - b*x))/(2*b*c) + ((1 + a + b*x)*log(1 + a + b*x))/(2*b*c) - (d*log(1 + a + b*x)*log(-((b*(d + c*x))/(c + a*c - b*d))))/(2*c^2) + (d*log(1 - a - b*x)*log((b*(d + c*x))/(c - a*c + b*d)))/(2*c^2) + (d*PolyLog(2, (c*(1 - a - b*x))/(c - a*c + b*d)))/(2*c^2) - (d*PolyLog(2, (c*(1 + a + b*x))/(c + a*c - b*d)))/(2*c^2)]
    @test_int [atanh(a + b*x)/(c + d/x^2), x, 25, ((1 - a - b*x)*log(1 - a - b*x))/(2*b*c) + ((1 + a + b*x)*log(1 + a + b*x))/(2*b*c) + (sqrt(d)*log(1 - a - b*x)*log(-((b*(sqrt(d) - sqrt(-c)*x))/((1 - a)*sqrt(-c) - b*sqrt(d)))))/(4*(-c)^(3/2)) - (sqrt(d)*log(1 + a + b*x)*log((b*(sqrt(d) - sqrt(-c)*x))/((1 + a)*sqrt(-c) + b*sqrt(d))))/(4*(-c)^(3/2)) + (sqrt(d)*log(1 + a + b*x)*log(-((b*(sqrt(d) + sqrt(-c)*x))/((1 + a)*sqrt(-c) - b*sqrt(d)))))/(4*(-c)^(3/2)) - (sqrt(d)*log(1 - a - b*x)*log((b*(sqrt(d) + sqrt(-c)*x))/((1 - a)*sqrt(-c) + b*sqrt(d))))/(4*(-c)^(3/2)) + (sqrt(d)*PolyLog(2, (sqrt(-c)*(1 - a - b*x))/(sqrt(-c) - a*sqrt(-c) - b*sqrt(d))))/(4*(-c)^(3/2)) - (sqrt(d)*PolyLog(2, (sqrt(-c)*(1 - a - b*x))/((1 - a)*sqrt(-c) + b*sqrt(d))))/(4*(-c)^(3/2)) + (sqrt(d)*PolyLog(2, (sqrt(-c)*(1 + a + b*x))/((1 + a)*sqrt(-c) - b*sqrt(d))))/(4*(-c)^(3/2)) - (sqrt(d)*PolyLog(2, (sqrt(-c)*(1 + a + b*x))/((1 + a)*sqrt(-c) + b*sqrt(d))))/(4*(-c)^(3/2))]
    @test_int [atanh(a + b*x)/(c + d/x^3), x, 31, ((1 - a - b*x)*log(1 - a - b*x))/(2*b*c) + ((1 + a + b*x)*log(1 + a + b*x))/(2*b*c) - (d^(1/3)*log(1 + a + b*x)*log(-((b*(d^(1/3) + c^(1/3)*x))/((1 + a)*c^(1/3) - b*d^(1/3)))))/(6*c^(4/3)) + (d^(1/3)*log(1 - a - b*x)*log((b*(d^(1/3) + c^(1/3)*x))/((1 - a)*c^(1/3) + b*d^(1/3))))/(6*c^(4/3)) + ((-1)^(2/3)*d^(1/3)*log(1 - a - b*x)*log(-((b*(d^(1/3) - (-1)^(1/3)*c^(1/3)*x))/((-1)^(1/3)*(1 - a)*c^(1/3) - b*d^(1/3)))))/(6*c^(4/3)) - ((-1)^(2/3)*d^(1/3)*log(1 + a + b*x)*log((b*(d^(1/3) - (-1)^(1/3)*c^(1/3)*x))/((-1)^(1/3)*(1 + a)*c^(1/3) + b*d^(1/3))))/(6*c^(4/3)) + ((-1)^(1/3)*d^(1/3)*log(1 + a + b*x)*log(-((b*(d^(1/3) + (-1)^(2/3)*c^(1/3)*x))/((-1)^(2/3)*(1 + a)*c^(1/3) - b*d^(1/3)))))/(6*c^(4/3)) - ((-1)^(1/3)*d^(1/3)*log(1 - a - b*x)*log((b*(d^(1/3) + (-1)^(2/3)*c^(1/3)*x))/((-1)^(2/3)*(1 - a)*c^(1/3) + b*d^(1/3))))/(6*c^(4/3)) + ((-1)^(2/3)*d^(1/3)*PolyLog(2, ((-1)^(1/3)*c^(1/3)*(1 - a - b*x))/((-1)^(1/3)*(1 - a)*c^(1/3) - b*d^(1/3))))/(6*c^(4/3)) + (d^(1/3)*PolyLog(2, (c^(1/3)*(1 - a - b*x))/((1 - a)*c^(1/3) + b*d^(1/3))))/(6*c^(4/3)) - ((-1)^(1/3)*d^(1/3)*PolyLog(2, ((-1)^(2/3)*c^(1/3)*(1 - a - b*x))/((-1)^(2/3)*(1 - a)*c^(1/3) + b*d^(1/3))))/(6*c^(4/3)) - (d^(1/3)*PolyLog(2, (c^(1/3)*(1 + a + b*x))/((1 + a)*c^(1/3) - b*d^(1/3))))/(6*c^(4/3)) + ((-1)^(1/3)*d^(1/3)*PolyLog(2, ((-1)^(2/3)*c^(1/3)*(1 + a + b*x))/((-1)^(2/3)*(1 + a)*c^(1/3) - b*d^(1/3))))/(6*c^(4/3)) - ((-1)^(2/3)*d^(1/3)*PolyLog(2, ((-1)^(1/3)*c^(1/3)*(1 + a + b*x))/((-1)^(1/3)*(1 + a)*c^(1/3) + b*d^(1/3))))/(6*c^(4/3))]


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


    #= [atanh(a + b*x)/(a + b*x^(3/2)), x, 41, (log(-a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) - sqrt(b)*sqrt(x))/(sqrt(-1 - a) + a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) - sqrt(b)*sqrt(x))/(sqrt(-1 - a) - (-1)^(1/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) - sqrt(b)*sqrt(x))/(sqrt(-1 - a) + (-1)^(2/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - (log(-a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(1 - a) - sqrt(b)*sqrt(x))/(sqrt(1 - a) + a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(1 - a) - sqrt(b)*sqrt(x))/(sqrt(1 - a) - (-1)^(1/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log((sqrt(1 - a) - sqrt(b)*sqrt(x))/(sqrt(1 - a) + (-1)^(2/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) + (log(-a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) + sqrt(b)*sqrt(x))/(sqrt(-1 - a) - a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) + sqrt(b)*sqrt(x))/(sqrt(-1 - a) + (-1)^(1/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) + sqrt(b)*sqrt(x))/(sqrt(-1 - a) - (-1)^(2/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - (log(-a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(1 - a) + sqrt(b)*sqrt(x))/(sqrt(1 - a) - a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(1 - a) + sqrt(b)*sqrt(x))/(sqrt(1 - a) + (-1)^(1/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log((sqrt(1 - a) + sqrt(b)*sqrt(x))/(sqrt(1 - a) - (-1)^(2/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) + (log(-a^(1/3) - b^(1/3)*sqrt(x))*log(1 - a - b*x))/(3*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log(1 - a - b*x))/(3*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log(1 - a - b*x))/(3*a^(1/3)*b^(2/3)) - (log(-a^(1/3) - b^(1/3)*sqrt(x))*log(1 + a + b*x))/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log(1 + a + b*x))/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log(1 + a + b*x))/(3*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*PolyLog(2, -((b^(1/6)*((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x)))/(sqrt(-1 - a) - (-1)^(1/3)*a^(1/3)*b^(1/6)))))/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*PolyLog(2, -((b^(1/6)*((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x)))/(sqrt(1 - a) - (-1)^(1/3)*a^(1/3)*b^(1/6)))))/(3*a^(1/3)*b^(2/3)) + PolyLog(2, -((b^(1/6)*(a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-1 - a) - a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - PolyLog(2, -((b^(1/6)*(a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(1 - a) - a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) + PolyLog(2, (b^(1/6)*(a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-1 - a) + a^(1/3)*b^(1/6)))/(3*a^(1/3)*b^(2/3)) - PolyLog(2, (b^(1/6)*(a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(1 - a) + a^(1/3)*b^(1/6)))/(3*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*PolyLog(2, -((b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-1 - a) - (-1)^(2/3)*a^(1/3)*b^(1/6)))))/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*PolyLog(2, -((b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(1 - a) - (-1)^(2/3)*a^(1/3)*b^(1/6)))))/(3*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*PolyLog(2, (b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-1 - a) + (-1)^(2/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*PolyLog(2, (b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(1 - a) + (-1)^(2/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*PolyLog(2, ((-1)^(1/3)*b^(1/6)*(a^(1/3) + (-1)^(2/3)*b^(1/3)*sqrt(x)))/(sqrt(-1 - a) + (-1)^(1/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*PolyLog(2, ((-1)^(1/3)*b^(1/6)*(a^(1/3) + (-1)^(2/3)*b^(1/3)*sqrt(x)))/(sqrt(1 - a) + (-1)^(1/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3))] =#
    @test_int [atanh(a + b*x)/(c + d*sqrt(x)), x, 31, (2*sqrt(1 + a)*atan((sqrt(b)*sqrt(x))/sqrt(1 + a)))/(sqrt(b)*d) - (2*sqrt(1 - a)*atanh((sqrt(b)*sqrt(x))/sqrt(1 - a)))/(sqrt(b)*d) + (c*log((d*(sqrt(-1 - a) - sqrt(b)*sqrt(x)))/(sqrt(b)*c + sqrt(-1 - a)*d))*log(c + d*sqrt(x)))/d^2 - (c*log((d*(sqrt(1 - a) - sqrt(b)*sqrt(x)))/(sqrt(b)*c + sqrt(1 - a)*d))*log(c + d*sqrt(x)))/d^2 + (c*log(-((d*(sqrt(-1 - a) + sqrt(b)*sqrt(x)))/(sqrt(b)*c - sqrt(-1 - a)*d)))*log(c + d*sqrt(x)))/d^2 - (c*log(-((d*(sqrt(1 - a) + sqrt(b)*sqrt(x)))/(sqrt(b)*c - sqrt(1 - a)*d)))*log(c + d*sqrt(x)))/d^2 - (sqrt(x)*log(1 - a - b*x))/d + (c*log(c + d*sqrt(x))*log(1 - a - b*x))/d^2 + (sqrt(x)*log(1 + a + b*x))/d - (c*log(c + d*sqrt(x))*log(1 + a + b*x))/d^2 + (c*PolyLog(2, (sqrt(b)*(c + d*sqrt(x)))/(sqrt(b)*c - sqrt(-1 - a)*d)))/d^2 + (c*PolyLog(2, (sqrt(b)*(c + d*sqrt(x)))/(sqrt(b)*c + sqrt(-1 - a)*d)))/d^2 - (c*PolyLog(2, (sqrt(b)*(c + d*sqrt(x)))/(sqrt(b)*c - sqrt(1 - a)*d)))/d^2 - (c*PolyLog(2, (sqrt(b)*(c + d*sqrt(x)))/(sqrt(b)*c + sqrt(1 - a)*d)))/d^2]
    @test_int [atanh(a + b*x)/(c + d/sqrt(x)), x, 37, (-2*sqrt(1 + a)*d*atan((sqrt(b)*sqrt(x))/sqrt(1 + a)))/(sqrt(b)*c^2) + (2*sqrt(1 - a)*d*atanh((sqrt(b)*sqrt(x))/sqrt(1 - a)))/(sqrt(b)*c^2) - (d^2*log((c*(sqrt(-1 - a) - sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*c + sqrt(b)*d))*log(d + c*sqrt(x)))/c^3 + (d^2*log((c*(sqrt(1 - a) - sqrt(b)*sqrt(x)))/(sqrt(1 - a)*c + sqrt(b)*d))*log(d + c*sqrt(x)))/c^3 - (d^2*log((c*(sqrt(-1 - a) + sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*c - sqrt(b)*d))*log(d + c*sqrt(x)))/c^3 + (d^2*log((c*(sqrt(1 - a) + sqrt(b)*sqrt(x)))/(sqrt(1 - a)*c - sqrt(b)*d))*log(d + c*sqrt(x)))/c^3 + (d*sqrt(x)*log(1 - a - b*x))/c^2 + ((1 - a - b*x)*log(1 - a - b*x))/(2*b*c) - (d^2*log(d + c*sqrt(x))*log(1 - a - b*x))/c^3 - (d*sqrt(x)*log(1 + a + b*x))/c^2 + ((1 + a + b*x)*log(1 + a + b*x))/(2*b*c) + (d^2*log(d + c*sqrt(x))*log(1 + a + b*x))/c^3 - (d^2*PolyLog(2, -((sqrt(b)*(d + c*sqrt(x)))/(sqrt(-1 - a)*c - sqrt(b)*d))))/c^3 + (d^2*PolyLog(2, -((sqrt(b)*(d + c*sqrt(x)))/(sqrt(1 - a)*c - sqrt(b)*d))))/c^3 - (d^2*PolyLog(2, (sqrt(b)*(d + c*sqrt(x)))/(sqrt(-1 - a)*c + sqrt(b)*d)))/c^3 + (d^2*PolyLog(2, (sqrt(b)*(d + c*sqrt(x)))/(sqrt(1 - a)*c + sqrt(b)*d)))/c^3]
    #= [atanh(a + b*x)/(a + b/x^(3/2)), x, 49, -(b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) - sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + b^(5/6))))/(3*a^(5/3)) - ((-1)^(2/3)*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) - sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - (-1)^(1/3)*b^(5/6))))/(3*a^(5/3)) + ((-1)^(1/3)*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) - sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + (-1)^(2/3)*b^(5/6))))/(3*a^(5/3)) + (b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(1 - a) - sqrt(b)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) + b^(5/6))))/(3*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(1 - a) - sqrt(b)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) - (-1)^(1/3)*b^(5/6))))/(3*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(1 - a) - sqrt(b)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) + (-1)^(2/3)*b^(5/6))))/(3*a^(5/3)) - (b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) + sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - b^(5/6))))/(3*a^(5/3)) - ((-1)^(2/3)*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) + sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + (-1)^(1/3)*b^(5/6))))/(3*a^(5/3)) + ((-1)^(1/3)*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) + sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - (-1)^(2/3)*b^(5/6))))/(3*a^(5/3)) + (b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(1 - a) + sqrt(b)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) - b^(5/6))))/(3*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(1 - a) + sqrt(b)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) + (-1)^(1/3)*b^(5/6))))/(3*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(1 - a) + sqrt(b)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) - (-1)^(2/3)*b^(5/6))))/(3*a^(5/3)) + ((1 - a - b*x)*log(1 - a - b*x))/(2*a*b) - (b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log(1 - a - b*x))/(3*a^(5/3)) - ((-1)^(2/3)*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log(1 - a - b*x))/(3*a^(5/3)) + ((-1)^(1/3)*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log(1 - a - b*x))/(3*a^(5/3)) + ((1 + a + b*x)*log(1 + a + b*x))/(2*a*b) + (b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log(1 + a + b*x))/(3*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log(1 + a + b*x))/(3*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log(1 + a + b*x))/(3*a^(5/3)) - ((-1)^(2/3)*b^(2/3)*PolyLog(2, -((sqrt(b)*((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - (-1)^(1/3)*b^(5/6)))))/(3*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*PolyLog(2, -((sqrt(b)*((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) - (-1)^(1/3)*b^(5/6)))))/(3*a^(5/3)) - (b^(2/3)*PolyLog(2, -((sqrt(b)*(b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - b^(5/6)))))/(3*a^(5/3)) + (b^(2/3)*PolyLog(2, -((sqrt(b)*(b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) - b^(5/6)))))/(3*a^(5/3)) - (b^(2/3)*PolyLog(2, (sqrt(b)*(b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + b^(5/6))))/(3*a^(5/3)) + (b^(2/3)*PolyLog(2, (sqrt(b)*(b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) + b^(5/6))))/(3*a^(5/3)) + ((-1)^(1/3)*b^(2/3)*PolyLog(2, -((sqrt(b)*((-1)^(2/3)*b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - (-1)^(2/3)*b^(5/6)))))/(3*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*PolyLog(2, -((sqrt(b)*((-1)^(2/3)*b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) - (-1)^(2/3)*b^(5/6)))))/(3*a^(5/3)) + ((-1)^(1/3)*b^(2/3)*PolyLog(2, (sqrt(b)*((-1)^(2/3)*b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + (-1)^(2/3)*b^(5/6))))/(3*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*PolyLog(2, (sqrt(b)*((-1)^(2/3)*b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) + (-1)^(2/3)*b^(5/6))))/(3*a^(5/3)) - ((-1)^(2/3)*b^(2/3)*PolyLog(2, ((-1)^(1/3)*sqrt(b)*(b^(1/3) + (-1)^(2/3)*a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + (-1)^(1/3)*b^(5/6))))/(3*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*PolyLog(2, ((-1)^(1/3)*sqrt(b)*(b^(1/3) + (-1)^(2/3)*a^(1/3)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) + (-1)^(1/3)*b^(5/6))))/(3*a^(5/3))] =#


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


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


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


    @test_int [(c*e + d*e*x)*(a + b*atanh(c + d*x))/(1 - (c + d*x)^2), x, 6, -((e*(a + b*atanh(c + d*x))^2)/(2*b*d)) + (e*(a + b*atanh(c + d*x))*log(2/(1 - c - d*x)))/d + (b*e*PolyLog(2, -((1 + c + d*x)/(1 - c - d*x))))/(2*d)]
    end
