text:
@testset "7.3.2 (d x)^m (a+b arctanh(c x^n))^p" begin
    (a, b, c, d, m, n, p, x, ) = @variables a b c d m n p x

    #= ::Package:: =#

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

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

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

    @test_int [x^5*(a + b*atanh(c*x)), x, 4, (b*x)/(6*c^5) + (b*x^3)/(18*c^3) + (b*x^5)/(30*c) - (b*atanh(c*x))/(6*c^6) + (1/6)*x^6*(a + b*atanh(c*x))]
    @test_int [x^4*(a + b*atanh(c*x)), x, 4, (b*x^2)/(10*c^3) + (b*x^4)/(20*c) + (1/5)*x^5*(a + b*atanh(c*x)) + (b*log(1 - c^2*x^2))/(10*c^5)]
    @test_int [x^3*(a + b*atanh(c*x)), x, 4, (b*x)/(4*c^3) + (b*x^3)/(12*c) - (b*atanh(c*x))/(4*c^4) + (1/4)*x^4*(a + b*atanh(c*x))]
    @test_int [x^2*(a + b*atanh(c*x)), x, 4, (b*x^2)/(6*c) + (1/3)*x^3*(a + b*atanh(c*x)) + (b*log(1 - c^2*x^2))/(6*c^3)]
    @test_int [x^1*(a + b*atanh(c*x)), x, 3, (b*x)/(2*c) - (b*atanh(c*x))/(2*c^2) + (1/2)*x^2*(a + b*atanh(c*x))]
    @test_int [x^0*(a + b*atanh(c*x)), x, 3, a*x + b*x*atanh(c*x) + (b*log(1 - c^2*x^2))/(2*c)]
    @test_int [(a + b*atanh(c*x))/x^1, x, 1, a*log(x) - (1/2)*b*PolyLog(2, (-c)*x) + (1/2)*b*PolyLog(2, c*x)]
    @test_int [(a + b*atanh(c*x))/x^2, x, 5, -((a + b*atanh(c*x))/x) + b*c*log(x) - (1/2)*b*c*log(1 - c^2*x^2)]
    @test_int [(a + b*atanh(c*x))/x^3, x, 3, -((b*c)/(2*x)) + (1/2)*b*c^2*atanh(c*x) - (a + b*atanh(c*x))/(2*x^2)]
    @test_int [(a + b*atanh(c*x))/x^4, x, 4, -((b*c)/(6*x^2)) - (a + b*atanh(c*x))/(3*x^3) + (1/3)*b*c^3*log(x) - (1/6)*b*c^3*log(1 - c^2*x^2)]
    @test_int [(a + b*atanh(c*x))/x^5, x, 4, -((b*c)/(12*x^3)) - (b*c^3)/(4*x) + (1/4)*b*c^4*atanh(c*x) - (a + b*atanh(c*x))/(4*x^4)]
    @test_int [(a + b*atanh(c*x))/x^6, x, 4, -((b*c)/(20*x^4)) - (b*c^3)/(10*x^2) - (a + b*atanh(c*x))/(5*x^5) + (1/5)*b*c^5*log(x) - (1/10)*b*c^5*log(1 - c^2*x^2)]

    @test_int [x^5*(a + b*atanh(c*x))^2, x, 16, (a*b*x)/(3*c^5) + (4*b^2*x^2)/(45*c^4) + (b^2*x^4)/(60*c^2) + (b^2*x*atanh(c*x))/(3*c^5) + (b*x^3*(a + b*atanh(c*x)))/(9*c^3) + (b*x^5*(a + b*atanh(c*x)))/(15*c) - (a + b*atanh(c*x))^2/(6*c^6) + (1/6)*x^6*(a + b*atanh(c*x))^2 + (23*b^2*log(1 - c^2*x^2))/(90*c^6)]
    @test_int [x^4*(a + b*atanh(c*x))^2, x, 14, (3*b^2*x)/(10*c^4) + (b^2*x^3)/(30*c^2) - (3*b^2*atanh(c*x))/(10*c^5) + (b*x^2*(a + b*atanh(c*x)))/(5*c^3) + (b*x^4*(a + b*atanh(c*x)))/(10*c) + (a + b*atanh(c*x))^2/(5*c^5) + (1/5)*x^5*(a + b*atanh(c*x))^2 - (2*b*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(5*c^5) - (b^2*PolyLog(2, 1 - 2/(1 - c*x)))/(5*c^5)]
    @test_int [x^3*(a + b*atanh(c*x))^2, x, 11, (a*b*x)/(2*c^3) + (b^2*x^2)/(12*c^2) + (b^2*x*atanh(c*x))/(2*c^3) + (b*x^3*(a + b*atanh(c*x)))/(6*c) - (a + b*atanh(c*x))^2/(4*c^4) + (1/4)*x^4*(a + b*atanh(c*x))^2 + (b^2*log(1 - c^2*x^2))/(3*c^4)]
    @test_int [x^2*(a + b*atanh(c*x))^2, x, 9, (b^2*x)/(3*c^2) - (b^2*atanh(c*x))/(3*c^3) + (b*x^2*(a + b*atanh(c*x)))/(3*c) + (a + b*atanh(c*x))^2/(3*c^3) + (1/3)*x^3*(a + b*atanh(c*x))^2 - (2*b*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(3*c^3) - (b^2*PolyLog(2, 1 - 2/(1 - c*x)))/(3*c^3)]
    @test_int [x^1*(a + b*atanh(c*x))^2, x, 6, (a*b*x)/c + (b^2*x*atanh(c*x))/c - (a + b*atanh(c*x))^2/(2*c^2) + (1/2)*x^2*(a + b*atanh(c*x))^2 + (b^2*log(1 - c^2*x^2))/(2*c^2)]
    @test_int [x^0*(a + b*atanh(c*x))^2, x, 5, (a + b*atanh(c*x))^2/c + x*(a + b*atanh(c*x))^2 - (2*b*(a + b*atanh(c*x))*log(2/(1 - c*x)))/c - (b^2*PolyLog(2, 1 - 2/(1 - c*x)))/c]
    @test_int [(a + b*atanh(c*x))^2/x^1, x, 6, 2*(a + b*atanh(c*x))^2*atanh(1 - 2/(1 - c*x)) - b*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)) + b*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 - c*x)) + (1/2)*b^2*PolyLog(3, 1 - 2/(1 - c*x)) - (1/2)*b^2*PolyLog(3, -1 + 2/(1 - c*x))]
    @test_int [(a + b*atanh(c*x))^2/x^2, x, 4, c*(a + b*atanh(c*x))^2 - (a + b*atanh(c*x))^2/x + 2*b*c*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)) - b^2*c*PolyLog(2, -1 + 2/(1 + c*x))]
    @test_int [(a + b*atanh(c*x))^2/x^3, x, 8, -((b*c*(a + b*atanh(c*x)))/x) + (1/2)*c^2*(a + b*atanh(c*x))^2 - (a + b*atanh(c*x))^2/(2*x^2) + b^2*c^2*log(x) - (1/2)*b^2*c^2*log(1 - c^2*x^2)]
    @test_int [(a + b*atanh(c*x))^2/x^4, x, 8, -((b^2*c^2)/(3*x)) + (1/3)*b^2*c^3*atanh(c*x) - (b*c*(a + b*atanh(c*x)))/(3*x^2) + (1/3)*c^3*(a + b*atanh(c*x))^2 - (a + b*atanh(c*x))^2/(3*x^3) + (2/3)*b*c^3*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)) - (1/3)*b^2*c^3*PolyLog(2, -1 + 2/(1 + c*x))]
    @test_int [(a + b*atanh(c*x))^2/x^5, x, 13, -((b^2*c^2)/(12*x^2)) - (b*c*(a + b*atanh(c*x)))/(6*x^3) - (b*c^3*(a + b*atanh(c*x)))/(2*x) + (1/4)*c^4*(a + b*atanh(c*x))^2 - (a + b*atanh(c*x))^2/(4*x^4) + (2/3)*b^2*c^4*log(x) - (1/3)*b^2*c^4*log(1 - c^2*x^2)]

    @test_int [x^5*(a + b*atanh(c*x))^3, x, 33, (19*b^3*x)/(60*c^5) + (b^3*x^3)/(60*c^3) - (19*b^3*atanh(c*x))/(60*c^6) + (4*b^2*x^2*(a + b*atanh(c*x)))/(15*c^4) + (b^2*x^4*(a + b*atanh(c*x)))/(20*c^2) + (23*b*(a + b*atanh(c*x))^2)/(30*c^6) + (b*x*(a + b*atanh(c*x))^2)/(2*c^5) + (b*x^3*(a + b*atanh(c*x))^2)/(6*c^3) + (b*x^5*(a + b*atanh(c*x))^2)/(10*c) - (a + b*atanh(c*x))^3/(6*c^6) + (1/6)*x^6*(a + b*atanh(c*x))^3 - (23*b^2*(a + b*atanh(c*x))*log(2/(1 - c*x)))/(15*c^6) - (23*b^3*PolyLog(2, 1 - 2/(1 - c*x)))/(30*c^6)]
    @test_int [x^4*(a + b*atanh(c*x))^3, x, 24, (9*a*b^2*x)/(10*c^4) + (b^3*x^2)/(20*c^3) + (9*b^3*x*atanh(c*x))/(10*c^4) + (b^2*x^3*(a + b*atanh(c*x)))/(10*c^2) - (9*b*(a + b*atanh(c*x))^2)/(20*c^5) + (3*b*x^2*(a + b*atanh(c*x))^2)/(10*c^3) + (3*b*x^4*(a + b*atanh(c*x))^2)/(20*c) + (a + b*atanh(c*x))^3/(5*c^5) + (1/5)*x^5*(a + b*atanh(c*x))^3 - (3*b*(a + b*atanh(c*x))^2*log(2/(1 - c*x)))/(5*c^5) + (b^3*log(1 - c^2*x^2))/(2*c^5) - (3*b^2*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)))/(5*c^5) + (3*b^3*PolyLog(3, 1 - 2/(1 - c*x)))/(10*c^5)]
    @test_int [x^3*(a + b*atanh(c*x))^3, x, 18, (b^3*x)/(4*c^3) - (b^3*atanh(c*x))/(4*c^4) + (b^2*x^2*(a + b*atanh(c*x)))/(4*c^2) + (b*(a + b*atanh(c*x))^2)/c^4 + (3*b*x*(a + b*atanh(c*x))^2)/(4*c^3) + (b*x^3*(a + b*atanh(c*x))^2)/(4*c) - (a + b*atanh(c*x))^3/(4*c^4) + (1/4)*x^4*(a + b*atanh(c*x))^3 - (2*b^2*(a + b*atanh(c*x))*log(2/(1 - c*x)))/c^4 - (b^3*PolyLog(2, 1 - 2/(1 - c*x)))/c^4]
    @test_int [x^2*(a + b*atanh(c*x))^3, x, 12, (a*b^2*x)/c^2 + (b^3*x*atanh(c*x))/c^2 - (b*(a + b*atanh(c*x))^2)/(2*c^3) + (b*x^2*(a + b*atanh(c*x))^2)/(2*c) + (a + b*atanh(c*x))^3/(3*c^3) + (1/3)*x^3*(a + b*atanh(c*x))^3 - (b*(a + b*atanh(c*x))^2*log(2/(1 - c*x)))/c^3 + (b^3*log(1 - c^2*x^2))/(2*c^3) - (b^2*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)))/c^3 + (b^3*PolyLog(3, 1 - 2/(1 - c*x)))/(2*c^3)]
    @test_int [x^1*(a + b*atanh(c*x))^3, x, 8, (3*b*(a + b*atanh(c*x))^2)/(2*c^2) + (3*b*x*(a + b*atanh(c*x))^2)/(2*c) - (a + b*atanh(c*x))^3/(2*c^2) + (1/2)*x^2*(a + b*atanh(c*x))^3 - (3*b^2*(a + b*atanh(c*x))*log(2/(1 - c*x)))/c^2 - (3*b^3*PolyLog(2, 1 - 2/(1 - c*x)))/(2*c^2)]
    @test_int [x^0*(a + b*atanh(c*x))^3, x, 5, (a + b*atanh(c*x))^3/c + x*(a + b*atanh(c*x))^3 - (3*b*(a + b*atanh(c*x))^2*log(2/(1 - c*x)))/c - (3*b^2*(a + b*atanh(c*x))*PolyLog(2, 1 - 2/(1 - c*x)))/c + (3*b^3*PolyLog(3, 1 - 2/(1 - c*x)))/(2*c)]
    @test_int [(a + b*atanh(c*x))^3/x^1, x, 8, 2*(a + b*atanh(c*x))^3*atanh(1 - 2/(1 - c*x)) - (3/2)*b*(a + b*atanh(c*x))^2*PolyLog(2, 1 - 2/(1 - c*x)) + (3/2)*b*(a + b*atanh(c*x))^2*PolyLog(2, -1 + 2/(1 - c*x)) + (3/2)*b^2*(a + b*atanh(c*x))*PolyLog(3, 1 - 2/(1 - c*x)) - (3/2)*b^2*(a + b*atanh(c*x))*PolyLog(3, -1 + 2/(1 - c*x)) - (3/4)*b^3*PolyLog(4, 1 - 2/(1 - c*x)) + (3/4)*b^3*PolyLog(4, -1 + 2/(1 - c*x))]
    @test_int [(a + b*atanh(c*x))^3/x^2, x, 5, c*(a + b*atanh(c*x))^3 - (a + b*atanh(c*x))^3/x + 3*b*c*(a + b*atanh(c*x))^2*log(2 - 2/(1 + c*x)) - 3*b^2*c*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 + c*x)) - (3/2)*b^3*c*PolyLog(3, -1 + 2/(1 + c*x))]
    @test_int [(a + b*atanh(c*x))^3/x^3, x, 7, (3/2)*b*c^2*(a + b*atanh(c*x))^2 - (3*b*c*(a + b*atanh(c*x))^2)/(2*x) + (1/2)*c^2*(a + b*atanh(c*x))^3 - (a + b*atanh(c*x))^3/(2*x^2) + 3*b^2*c^2*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)) - (3/2)*b^3*c^2*PolyLog(2, -1 + 2/(1 + c*x))]
    @test_int [(a + b*atanh(c*x))^3/x^4, x, 14, -((b^2*c^2*(a + b*atanh(c*x)))/x) + (1/2)*b*c^3*(a + b*atanh(c*x))^2 - (b*c*(a + b*atanh(c*x))^2)/(2*x^2) + (1/3)*c^3*(a + b*atanh(c*x))^3 - (a + b*atanh(c*x))^3/(3*x^3) + b^3*c^3*log(x) - (1/2)*b^3*c^3*log(1 - c^2*x^2) + b*c^3*(a + b*atanh(c*x))^2*log(2 - 2/(1 + c*x)) - b^2*c^3*(a + b*atanh(c*x))*PolyLog(2, -1 + 2/(1 + c*x)) - (1/2)*b^3*c^3*PolyLog(3, -1 + 2/(1 + c*x))]
    @test_int [(a + b*atanh(c*x))^3/x^5, x, 16, -((b^3*c^3)/(4*x)) + (1/4)*b^3*c^4*atanh(c*x) - (b^2*c^2*(a + b*atanh(c*x)))/(4*x^2) + b*c^4*(a + b*atanh(c*x))^2 - (b*c*(a + b*atanh(c*x))^2)/(4*x^3) - (3*b*c^3*(a + b*atanh(c*x))^2)/(4*x) + (1/4)*c^4*(a + b*atanh(c*x))^3 - (a + b*atanh(c*x))^3/(4*x^4) + 2*b^2*c^4*(a + b*atanh(c*x))*log(2 - 2/(1 + c*x)) - b^3*c^4*PolyLog(2, -1 + 2/(1 + c*x))]

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

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

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

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

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

    @test_int [(a + b*atanh(c*x))^p, x, 0, Unintegrable((a + b*atanh(c*x))^p, x)]

    @test_int [(d*x)^m*(a + b*atanh(c*x))^p, x, 0, Unintegrable((d*x)^m*(a + b* atanh(c*x))^p, x)]

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

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

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

    @test_int [x^4*(a + b*atanh(c*x^2)), x, 5, (2*b*x^3)/(15*c) + (b*atan(sqrt(c)*x))/(5*c^(5/2)) - (b*atanh(sqrt(c)*x))/(5*c^(5/2)) + (1/5)*x^5*(a + b*atanh(c*x^2))]
    @test_int [x^2*(a + b*atanh(c*x^2)), x, 5, (2*b*x)/(3*c) - (b*atan(sqrt(c)*x))/(3*c^(3/2)) - (b*atanh(sqrt(c)*x))/(3*c^(3/2)) + (1/3)*x^3*(a + b*atanh(c*x^2))]
    @test_int [x^0*(a + b*atanh(c*x^2)), x, 5, a*x + (b*atan(sqrt(c)*x))/sqrt(c) - (b*atanh(sqrt(c)*x))/sqrt(c) + b*x*atanh(c*x^2)]
    @test_int [(a + b*atanh(c*x^2))/x^2, x, 4, b*sqrt(c)*atan(sqrt(c)*x) + b*sqrt(c)*atanh(sqrt(c)*x) - (a + b*atanh(c*x^2))/x]
    @test_int [(a + b*atanh(c*x^2))/x^4, x, 5, -((2*b*c)/(3*x)) - (1/3)*b*c^(3/2)*atan(sqrt(c)*x) + (1/3)*b*c^(3/2)*atanh(sqrt(c)*x) - (a + b*atanh(c*x^2))/(3*x^3)]
    @test_int [(a + b*atanh(c*x^2))/x^6, x, 5, -((2*b*c)/(15*x^3)) + (1/5)*b*c^(5/2)*atan(sqrt(c)*x) + (1/5)*b*c^(5/2)*atanh(sqrt(c)*x) - (a + b*atanh(c*x^2))/(5*x^5)]

    @test_int [x^7*(a + b*atanh(c*x^2))^2, x, 12, (a*b*x^2)/(4*c^3) + (b^2*x^4)/(24*c^2) + (b^2*x^2*atanh(c*x^2))/(4*c^3) + (b*x^6*(a + b*atanh(c*x^2)))/(12*c) - (a + b*atanh(c*x^2))^2/(8*c^4) + (1/8)*x^8*(a + b*atanh(c*x^2))^2 + (b^2*log(1 - c^2*x^4))/(6*c^4)]
    @test_int [x^5*(a + b*atanh(c*x^2))^2, x, 10, (b^2*x^2)/(6*c^2) - (b^2*atanh(c*x^2))/(6*c^3) + (b*x^4*(a + b*atanh(c*x^2)))/(6*c) + (a + b*atanh(c*x^2))^2/(6*c^3) + (1/6)*x^6*(a + b*atanh(c*x^2))^2 - (b*(a + b*atanh(c*x^2))*log(2/(1 - c*x^2)))/(3*c^3) - (b^2*PolyLog(2, 1 - 2/(1 - c*x^2)))/(6*c^3)]
    @test_int [x^3*(a + b*atanh(c*x^2))^2, x, 7, (a*b*x^2)/(2*c) + (b^2*x^2*atanh(c*x^2))/(2*c) - (a + b*atanh(c*x^2))^2/(4*c^2) + (1/4)*x^4*(a + b*atanh(c*x^2))^2 + (b^2*log(1 - c^2*x^4))/(4*c^2)]
    @test_int [x^1*(a + b*atanh(c*x^2))^2, x, 6, (a + b*atanh(c*x^2))^2/(2*c) + (1/2)*x^2*(a + b*atanh(c*x^2))^2 - (b*(a + b*atanh(c*x^2))*log(2/(1 - c*x^2)))/c - (b^2*PolyLog(2, 1 - 2/(1 - c*x^2)))/(2*c)]
    @test_int [(a + b*atanh(c*x^2))^2/x^1, x, 7, (a + b*atanh(c*x^2))^2*atanh(1 - 2/(1 - c*x^2)) - (1/2)*b*(a + b*atanh(c*x^2))*PolyLog(2, 1 - 2/(1 - c*x^2)) + (1/2)*b*(a + b*atanh(c*x^2))*PolyLog(2, -1 + 2/(1 - c*x^2)) + (1/4)*b^2*PolyLog(3, 1 - 2/(1 - c*x^2)) - (1/4)*b^2*PolyLog(3, -1 + 2/(1 - c*x^2))]
    @test_int [(a + b*atanh(c*x^2))^2/x^3, x, 5, (1/2)*c*(a + b*atanh(c*x^2))^2 - (a + b*atanh(c*x^2))^2/(2*x^2) + b*c*(a + b*atanh(c*x^2))*log(2 - 2/(1 + c*x^2)) - (1/2)*b^2*c*PolyLog(2, -1 + 2/(1 + c*x^2))]
    @test_int [(a + b*atanh(c*x^2))^2/x^5, x, 9, -((b*c*(a + b*atanh(c*x^2)))/(2*x^2)) + (1/4)*c^2*(a + b*atanh(c*x^2))^2 - (a + b*atanh(c*x^2))^2/(4*x^4) + b^2*c^2*log(x) - (1/4)*b^2*c^2*log(1 - c^2*x^4)]

    @test_int [x^4*(a + b*atanh(c*x^2))^2, x, 102, (8*b^2*x)/(15*c^2) + (2*a*b*x^3)/(15*c) - (2/25)*a*b*x^5 + (2*a*b*atan(sqrt(c)*x))/(5*c^(5/2)) - (4*b^2*atan(sqrt(c)*x))/(15*c^(5/2)) + (im*b^2*atan(sqrt(c)*x)^2)/(5*c^(5/2)) - (4*b^2*atanh(sqrt(c)*x))/(15*c^(5/2)) - (b^2*atanh(sqrt(c)*x)^2)/(5*c^(5/2)) + (2*b^2*atanh(sqrt(c)*x)*log(2/(1 - sqrt(c)*x)))/(5*c^(5/2)) - (2*b^2*atan(sqrt(c)*x)*log(2/(1 - im*sqrt(c)*x)))/(5*c^(5/2)) + (b^2*atan(sqrt(c)*x)*log(((1 + im)*(1 - sqrt(c)*x))/(1 - im*sqrt(c)*x)))/(5*c^(5/2)) + (2*b^2*atan(sqrt(c)*x)*log(2/(1 + im*sqrt(c)*x)))/(5*c^(5/2)) - (2*b^2*atanh(sqrt(c)*x)*log(2/(1 + sqrt(c)*x)))/(5*c^(5/2)) + (b^2*atanh(sqrt(c)*x)*log(-((2*sqrt(c)*(1 - sqrt(-c)*x))/((sqrt(-c) - sqrt(c))*(1 + sqrt(c)*x)))))/(5*c^(5/2)) + (b^2*atanh(sqrt(c)*x)*log((2*sqrt(c)*(1 + sqrt(-c)*x))/((sqrt(-c) + sqrt(c))*(1 + sqrt(c)*x))))/(5*c^(5/2)) + (b^2*atan(sqrt(c)*x)*log(((1 - im)*(1 + sqrt(c)*x))/(1 - im*sqrt(c)*x)))/(5*c^(5/2)) - (b^2*x^3*log(1 - c*x^2))/(15*c) + (1/25)*b^2*x^5*log(1 - c*x^2) - (b^2*atan(sqrt(c)*x)*log(1 - c*x^2))/(5*c^(5/2)) + (b*x^3*(2*a - b*log(1 - c*x^2)))/(15*c) + (1/25)*b*x^5*(2*a - b*log(1 - c*x^2)) - (b*atanh(sqrt(c)*x)*(2*a - b*log(1 - c*x^2)))/(5*c^(5/2)) + (1/20)*x^5*(2*a - b*log(1 - c*x^2))^2 + (2*b^2*x^3*log(1 + c*x^2))/(15*c) + (1/5)*a*b*x^5*log(1 + c*x^2) + (b^2*atan(sqrt(c)*x)*log(1 + c*x^2))/(5*c^(5/2)) - (b^2*atanh(sqrt(c)*x)*log(1 + c*x^2))/(5*c^(5/2)) - (1/10)*b^2*x^5*log(1 - c*x^2)*log(1 + c*x^2) + (1/20)*b^2*x^5*log(1 + c*x^2)^2 + (b^2*PolyLog(2, 1 - 2/(1 - sqrt(c)*x)))/(5*c^(5/2)) + (im*b^2*PolyLog(2, 1 - 2/(1 - im*sqrt(c)*x)))/(5*c^(5/2)) - (im*b^2*PolyLog(2, 1 - ((1 + im)*(1 - sqrt(c)*x))/(1 - im*sqrt(c)*x)))/(10*c^(5/2)) + (im*b^2*PolyLog(2, 1 - 2/(1 + im*sqrt(c)*x)))/(5*c^(5/2)) + (b^2*PolyLog(2, 1 - 2/(1 + sqrt(c)*x)))/(5*c^(5/2)) - (b^2*PolyLog(2, 1 + (2*sqrt(c)*(1 - sqrt(-c)*x))/((sqrt(-c) - sqrt(c))*(1 + sqrt(c)*x))))/(10*c^(5/2)) - (b^2*PolyLog(2, 1 - (2*sqrt(c)*(1 + sqrt(-c)*x))/((sqrt(-c) + sqrt(c))*(1 + sqrt(c)*x))))/(10*c^(5/2)) - (im*b^2*PolyLog(2, 1 - ((1 - im)*(1 + sqrt(c)*x))/(1 - im*sqrt(c)*x)))/(10*c^(5/2))]
    @test_int [x^2*(a + b*atanh(c*x^2))^2, x, 86, (4*a*b*x)/(3*c) - (2/9)*a*b*x^3 - (2*a*b*atan(sqrt(c)*x))/(3*c^(3/2)) + (4*b^2*atan(sqrt(c)*x))/(3*c^(3/2)) - (im*b^2*atan(sqrt(c)*x)^2)/(3*c^(3/2)) - (4*b^2*atanh(sqrt(c)*x))/(3*c^(3/2)) - (b^2*atanh(sqrt(c)*x)^2)/(3*c^(3/2)) + (2*b^2*atanh(sqrt(c)*x)*log(2/(1 - sqrt(c)*x)))/(3*c^(3/2)) + (2*b^2*atan(sqrt(c)*x)*log(2/(1 - im*sqrt(c)*x)))/(3*c^(3/2)) - (b^2*atan(sqrt(c)*x)*log(((1 + im)*(1 - sqrt(c)*x))/(1 - im*sqrt(c)*x)))/(3*c^(3/2)) - (2*b^2*atan(sqrt(c)*x)*log(2/(1 + im*sqrt(c)*x)))/(3*c^(3/2)) - (2*b^2*atanh(sqrt(c)*x)*log(2/(1 + sqrt(c)*x)))/(3*c^(3/2)) + (b^2*atanh(sqrt(c)*x)*log(-((2*sqrt(c)*(1 - sqrt(-c)*x))/((sqrt(-c) - sqrt(c))*(1 + sqrt(c)*x)))))/(3*c^(3/2)) + (b^2*atanh(sqrt(c)*x)*log((2*sqrt(c)*(1 + sqrt(-c)*x))/((sqrt(-c) + sqrt(c))*(1 + sqrt(c)*x))))/(3*c^(3/2)) - (b^2*atan(sqrt(c)*x)*log(((1 - im)*(1 + sqrt(c)*x))/(1 - im*sqrt(c)*x)))/(3*c^(3/2)) - (2*b^2*x*log(1 - c*x^2))/(3*c) + (1/9)*b^2*x^3*log(1 - c*x^2) + (b^2*atan(sqrt(c)*x)*log(1 - c*x^2))/(3*c^(3/2)) + (1/9)*b*x^3*(2*a - b*log(1 - c*x^2)) - (b*atanh(sqrt(c)*x)*(2*a - b*log(1 - c*x^2)))/(3*c^(3/2)) + (1/12)*x^3*(2*a - b*log(1 - c*x^2))^2 + (2*b^2*x*log(1 + c*x^2))/(3*c) + (1/3)*a*b*x^3*log(1 + c*x^2) - (b^2*atan(sqrt(c)*x)*log(1 + c*x^2))/(3*c^(3/2)) - (b^2*atanh(sqrt(c)*x)*log(1 + c*x^2))/(3*c^(3/2)) - (1/6)*b^2*x^3*log(1 - c*x^2)*log(1 + c*x^2) + (1/12)*b^2*x^3*log(1 + c*x^2)^2 + (b^2*PolyLog(2, 1 - 2/(1 - sqrt(c)*x)))/(3*c^(3/2)) - (im*b^2*PolyLog(2, 1 - 2/(1 - im*sqrt(c)*x)))/(3*c^(3/2)) + (im*b^2*PolyLog(2, 1 - ((1 + im)*(1 - sqrt(c)*x))/(1 - im*sqrt(c)*x)))/(6*c^(3/2)) - (im*b^2*PolyLog(2, 1 - 2/(1 + im*sqrt(c)*x)))/(3*c^(3/2)) + (b^2*PolyLog(2, 1 - 2/(1 + sqrt(c)*x)))/(3*c^(3/2)) - (b^2*PolyLog(2, 1 + (2*sqrt(c)*(1 - sqrt(-c)*x))/((sqrt(-c) - sqrt(c))*(1 + sqrt(c)*x))))/(6*c^(3/2)) - (b^2*PolyLog(2, 1 - (2*sqrt(c)*(1 + sqrt(-c)*x))/((sqrt(-c) + sqrt(c))*(1 + sqrt(c)*x))))/(6*c^(3/2)) + (im*b^2*PolyLog(2, 1 - ((1 - im)*(1 + sqrt(c)*x))/(1 - im*sqrt(c)*x)))/(6*c^(3/2))]
    @test_int [x^0*(a + b*atanh(c*x^2))^2, x, 69, a^2*x + (2*a*b*atan(sqrt(c)*x))/sqrt(c) + (im*b^2*atan(sqrt(c)*x)^2)/sqrt(c) - (2*a*b*atanh(sqrt(c)*x))/sqrt(c) - (b^2*atanh(sqrt(c)*x)^2)/sqrt(c) + (2*b^2*atanh(sqrt(c)*x)*log(2/(1 - sqrt(c)*x)))/sqrt(c) - (2*b^2*atan(sqrt(c)*x)*log(2/(1 - im*sqrt(c)*x)))/sqrt(c) + (b^2*atan(sqrt(c)*x)*log(((1 + im)*(1 - sqrt(c)*x))/(1 - im*sqrt(c)*x)))/sqrt(c) + (2*b^2*atan(sqrt(c)*x)*log(2/(1 + im*sqrt(c)*x)))/sqrt(c) - (2*b^2*atanh(sqrt(c)*x)*log(2/(1 + sqrt(c)*x)))/sqrt(c) + (b^2*atanh(sqrt(c)*x)*log(-((2*sqrt(c)*(1 - sqrt(-c)*x))/((sqrt(-c) - sqrt(c))*(1 + sqrt(c)*x)))))/sqrt(c) + (b^2*atanh(sqrt(c)*x)*log((2*sqrt(c)*(1 + sqrt(-c)*x))/((sqrt(-c) + sqrt(c))*(1 + sqrt(c)*x))))/sqrt(c) + (b^2*atan(sqrt(c)*x)*log(((1 - im)*(1 + sqrt(c)*x))/(1 - im*sqrt(c)*x)))/sqrt(c) - a*b*x*log(1 - c*x^2) - (b^2*atan(sqrt(c)*x)*log(1 - c*x^2))/sqrt(c) + (b^2*atanh(sqrt(c)*x)*log(1 - c*x^2))/sqrt(c) + (1/4)*b^2*x*log(1 - c*x^2)^2 + a*b*x*log(1 + c*x^2) + (b^2*atan(sqrt(c)*x)*log(1 + c*x^2))/sqrt(c) - (b^2*atanh(sqrt(c)*x)*log(1 + c*x^2))/sqrt(c) - (1/2)*b^2*x*log(1 - c*x^2)*log(1 + c*x^2) + (1/4)*b^2*x*log(1 + c*x^2)^2 + (b^2*PolyLog(2, 1 - 2/(1 - sqrt(c)*x)))/sqrt(c) + (im*b^2*PolyLog(2, 1 - 2/(1 - im*sqrt(c)*x)))/sqrt(c) - (im*b^2*PolyLog(2, 1 - ((1 + im)*(1 - sqrt(c)*x))/(1 - im*sqrt(c)*x)))/(2*sqrt(c)) + (im*b^2*PolyLog(2, 1 - 2/(1 + im*sqrt(c)*x)))/sqrt(c) + (b^2*PolyLog(2, 1 - 2/(1 + sqrt(c)*x)))/sqrt(c) - (b^2*PolyLog(2, 1 + (2*sqrt(c)*(1 - sqrt(-c)*x))/((sqrt(-c) - sqrt(c))*(1 + sqrt(c)*x))))/(2*sqrt(c)) - (b^2*PolyLog(2, 1 - (2*sqrt(c)*(1 + sqrt(-c)*x))/((sqrt(-c) + sqrt(c))*(1 + sqrt(c)*x))))/(2*sqrt(c)) - (im*b^2*PolyLog(2, 1 - ((1 - im)*(1 + sqrt(c)*x))/(1 - im*sqrt(c)*x)))/(2*sqrt(c))]
    @test_int [(a + b*atanh(c*x^2))^2/x^2, x, 47, 2*a*b*sqrt(c)*atan(sqrt(c)*x) + im*b^2*sqrt(c)*atan(sqrt(c)*x)^2 + b^2*sqrt(c)*atanh(sqrt(c)*x)^2 - 2*b^2*sqrt(c)*atanh(sqrt(c)*x)*log(2/(1 - sqrt(c)*x)) - 2*b^2*sqrt(c)*atan(sqrt(c)*x)*log(2/(1 - im*sqrt(c)*x)) + b^2*sqrt(c)*atan(sqrt(c)*x)*log(((1 + im)*(1 - sqrt(c)*x))/(1 - im*sqrt(c)*x)) + 2*b^2*sqrt(c)*atan(sqrt(c)*x)*log(2/(1 + im*sqrt(c)*x)) + 2*b^2*sqrt(c)*atanh(sqrt(c)*x)*log(2/(1 + sqrt(c)*x)) - b^2*sqrt(c)*atanh(sqrt(c)*x)*log(-((2*sqrt(c)*(1 - sqrt(-c)*x))/((sqrt(-c) - sqrt(c))*(1 + sqrt(c)*x)))) - b^2*sqrt(c)*atanh(sqrt(c)*x)*log((2*sqrt(c)*(1 + sqrt(-c)*x))/((sqrt(-c) + sqrt(c))*(1 + sqrt(c)*x))) + b^2*sqrt(c)*atan(sqrt(c)*x)*log(((1 - im)*(1 + sqrt(c)*x))/(1 - im*sqrt(c)*x)) - b^2*sqrt(c)*atan(sqrt(c)*x)*log(1 - c*x^2) + b*sqrt(c)*atanh(sqrt(c)*x)*(2*a - b*log(1 - c*x^2)) - (2*a - b*log(1 - c*x^2))^2/(4*x) - (a*b*log(1 + c*x^2))/x + b^2*sqrt(c)*atan(sqrt(c)*x)*log(1 + c*x^2) + b^2*sqrt(c)*atanh(sqrt(c)*x)*log(1 + c*x^2) + (b^2*log(1 - c*x^2)*log(1 + c*x^2))/(2*x) - (b^2*log(1 + c*x^2)^2)/(4*x) - b^2*sqrt(c)*PolyLog(2, 1 - 2/(1 - sqrt(c)*x)) + im*b^2*sqrt(c)*PolyLog(2, 1 - 2/(1 - im*sqrt(c)*x)) - (1/2)*im*b^2*sqrt(c)*PolyLog(2, 1 - ((1 + im)*(1 - sqrt(c)*x))/(1 - im*sqrt(c)*x)) + im*b^2*sqrt(c)*PolyLog(2, 1 - 2/(1 + im*sqrt(c)*x)) - b^2*sqrt(c)*PolyLog(2, 1 - 2/(1 + sqrt(c)*x)) + (1/2)*b^2*sqrt(c)*PolyLog(2, 1 + (2*sqrt(c)*(1 - sqrt(-c)*x))/((sqrt(-c) - sqrt(c))*(1 + sqrt(c)*x))) + (1/2)*b^2*sqrt(c)*PolyLog(2, 1 - (2*sqrt(c)*(1 + sqrt(-c)*x))/((sqrt(-c) + sqrt(c))*(1 + sqrt(c)*x))) - (1/2)*im*b^2*sqrt(c)*PolyLog(2, 1 - ((1 - im)*(1 + sqrt(c)*x))/(1 - im*sqrt(c)*x))]
    @test_int [(a + b*atanh(c*x^2))^2/x^4, x, 64, -((2*a*b*c)/(3*x)) - (2/3)*a*b*c^(3/2)*atan(sqrt(c)*x) + (4/3)*b^2*c^(3/2)*atan(sqrt(c)*x) - (1/3)*im*b^2*c^(3/2)*atan(sqrt(c)*x)^2 + (4/3)*b^2*c^(3/2)*atanh(sqrt(c)*x) + (1/3)*b^2*c^(3/2)*atanh(sqrt(c)*x)^2 - (2/3)*b^2*c^(3/2)*atanh(sqrt(c)*x)*log(2/(1 - sqrt(c)*x)) + (2/3)*b^2*c^(3/2)*atan(sqrt(c)*x)*log(2/(1 - im*sqrt(c)*x)) - (1/3)*b^2*c^(3/2)*atan(sqrt(c)*x)*log(((1 + im)*(1 - sqrt(c)*x))/(1 - im*sqrt(c)*x)) - (2/3)*b^2*c^(3/2)*atan(sqrt(c)*x)*log(2/(1 + im*sqrt(c)*x)) + (2/3)*b^2*c^(3/2)*atanh(sqrt(c)*x)*log(2/(1 + sqrt(c)*x)) - (1/3)*b^2*c^(3/2)*atanh(sqrt(c)*x)*log(-((2*sqrt(c)*(1 - sqrt(-c)*x))/((sqrt(-c) - sqrt(c))*(1 + sqrt(c)*x)))) - (1/3)*b^2*c^(3/2)*atanh(sqrt(c)*x)*log((2*sqrt(c)*(1 + sqrt(-c)*x))/((sqrt(-c) + sqrt(c))*(1 + sqrt(c)*x))) - (1/3)*b^2*c^(3/2)*atan(sqrt(c)*x)*log(((1 - im)*(1 + sqrt(c)*x))/(1 - im*sqrt(c)*x)) + (b^2*c*log(1 - c*x^2))/(3*x) + (1/3)*b^2*c^(3/2)*atan(sqrt(c)*x)*log(1 - c*x^2) - (b*c*(2*a - b*log(1 - c*x^2)))/(3*x) + (1/3)*b*c^(3/2)*atanh(sqrt(c)*x)*(2*a - b*log(1 - c*x^2)) - (2*a - b*log(1 - c*x^2))^2/(12*x^3) - (a*b*log(1 + c*x^2))/(3*x^3) - (2*b^2*c*log(1 + c*x^2))/(3*x) - (1/3)*b^2*c^(3/2)*atan(sqrt(c)*x)*log(1 + c*x^2) + (1/3)*b^2*c^(3/2)*atanh(sqrt(c)*x)*log(1 + c*x^2) + (b^2*log(1 - c*x^2)*log(1 + c*x^2))/(6*x^3) - (b^2*log(1 + c*x^2)^2)/(12*x^3) - (1/3)*b^2*c^(3/2)*PolyLog(2, 1 - 2/(1 - sqrt(c)*x)) - (1/3)*im*b^2*c^(3/2)*PolyLog(2, 1 - 2/(1 - im*sqrt(c)*x)) + (1/6)*im*b^2*c^(3/2)*PolyLog(2, 1 - ((1 + im)*(1 - sqrt(c)*x))/(1 - im*sqrt(c)*x)) - (1/3)*im*b^2*c^(3/2)*PolyLog(2, 1 - 2/(1 + im*sqrt(c)*x)) - (1/3)*b^2*c^(3/2)*PolyLog(2, 1 - 2/(1 + sqrt(c)*x)) + (1/6)*b^2*c^(3/2)*PolyLog(2, 1 + (2*sqrt(c)*(1 - sqrt(-c)*x))/((sqrt(-c) - sqrt(c))*(1 + sqrt(c)*x))) + (1/6)*b^2*c^(3/2)*PolyLog(2, 1 - (2*sqrt(c)*(1 + sqrt(-c)*x))/((sqrt(-c) + sqrt(c))*(1 + sqrt(c)*x))) + (1/6)*im*b^2*c^(3/2)*PolyLog(2, 1 - ((1 - im)*(1 + sqrt(c)*x))/(1 - im*sqrt(c)*x))]
    @test_int [(a + b*atanh(c*x^2))^2/x^6, x, 77, -((2*a*b*c)/(15*x^3)) + (2*a*b*c^2)/(5*x) - (8*b^2*c^2)/(15*x) + (2/5)*a*b*c^(5/2)*atan(sqrt(c)*x) - (4/15)*b^2*c^(5/2)*atan(sqrt(c)*x) + (1/5)*im*b^2*c^(5/2)*atan(sqrt(c)*x)^2 + (4/15)*b^2*c^(5/2)*atanh(sqrt(c)*x) + (1/5)*b^2*c^(5/2)*atanh(sqrt(c)*x)^2 - (2/5)*b^2*c^(5/2)*atanh(sqrt(c)*x)*log(2/(1 - sqrt(c)*x)) - (2/5)*b^2*c^(5/2)*atan(sqrt(c)*x)*log(2/(1 - im*sqrt(c)*x)) + (1/5)*b^2*c^(5/2)*atan(sqrt(c)*x)*log(((1 + im)*(1 - sqrt(c)*x))/(1 - im*sqrt(c)*x)) + (2/5)*b^2*c^(5/2)*atan(sqrt(c)*x)*log(2/(1 + im*sqrt(c)*x)) + (2/5)*b^2*c^(5/2)*atanh(sqrt(c)*x)*log(2/(1 + sqrt(c)*x)) - (1/5)*b^2*c^(5/2)*atanh(sqrt(c)*x)*log(-((2*sqrt(c)*(1 - sqrt(-c)*x))/((sqrt(-c) - sqrt(c))*(1 + sqrt(c)*x)))) - (1/5)*b^2*c^(5/2)*atanh(sqrt(c)*x)*log((2*sqrt(c)*(1 + sqrt(-c)*x))/((sqrt(-c) + sqrt(c))*(1 + sqrt(c)*x))) + (1/5)*b^2*c^(5/2)*atan(sqrt(c)*x)*log(((1 - im)*(1 + sqrt(c)*x))/(1 - im*sqrt(c)*x)) + (b^2*c*log(1 - c*x^2))/(15*x^3) - (b^2*c^2*log(1 - c*x^2))/(5*x) - (1/5)*b^2*c^(5/2)*atan(sqrt(c)*x)*log(1 - c*x^2) - (b*c*(2*a - b*log(1 - c*x^2)))/(15*x^3) - (b*c^2*(2*a - b*log(1 - c*x^2)))/(5*x) + (1/5)*b*c^(5/2)*atanh(sqrt(c)*x)*(2*a - b*log(1 - c*x^2)) - (2*a - b*log(1 - c*x^2))^2/(20*x^5) - (a*b*log(1 + c*x^2))/(5*x^5) - (2*b^2*c*log(1 + c*x^2))/(15*x^3) + (1/5)*b^2*c^(5/2)*atan(sqrt(c)*x)*log(1 + c*x^2) + (1/5)*b^2*c^(5/2)*atanh(sqrt(c)*x)*log(1 + c*x^2) + (b^2*log(1 - c*x^2)*log(1 + c*x^2))/(10*x^5) - (b^2*log(1 + c*x^2)^2)/(20*x^5) - (1/5)*b^2*c^(5/2)*PolyLog(2, 1 - 2/(1 - sqrt(c)*x)) + (1/5)*im*b^2*c^(5/2)*PolyLog(2, 1 - 2/(1 - im*sqrt(c)*x)) - (1/10)*im*b^2*c^(5/2)*PolyLog(2, 1 - ((1 + im)*(1 - sqrt(c)*x))/(1 - im*sqrt(c)*x)) + (1/5)*im*b^2*c^(5/2)*PolyLog(2, 1 - 2/(1 + im*sqrt(c)*x)) - (1/5)*b^2*c^(5/2)*PolyLog(2, 1 - 2/(1 + sqrt(c)*x)) + (1/10)*b^2*c^(5/2)*PolyLog(2, 1 + (2*sqrt(c)*(1 - sqrt(-c)*x))/((sqrt(-c) - sqrt(c))*(1 + sqrt(c)*x))) + (1/10)*b^2*c^(5/2)*PolyLog(2, 1 - (2*sqrt(c)*(1 + sqrt(-c)*x))/((sqrt(-c) + sqrt(c))*(1 + sqrt(c)*x))) - (1/10)*im*b^2*c^(5/2)*PolyLog(2, 1 - ((1 - im)*(1 + sqrt(c)*x))/(1 - im*sqrt(c)*x))]

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

    #= [x^2*(a + b*atan(c*x^2))^3, x, 86, 0]
    @test_int [x^0*(a + b*atan(c*x^2))^3, x, 69, 0]
    @test_int [(a + b*atan(c*x^2))^3/x^2, x, 47, 0]
    @test_int [(a + b*atan(c*x^2))^3/x^4, x, 64, 0]
    @test_int [(a + b*atan(c*x^2))^3/x^6, x, 77, 0] =#

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

    @test_int [(d*x)^(5/2)*(a + b*atanh(c*x^2)), x, 16, (8*b*d*(d*x)^(3/2))/(21*c) + (2*b*d^(5/2)*atan((c^(1/4)*sqrt(d*x))/sqrt(d)))/(7*c^(7/4)) + (sqrt(2)*b*d^(5/2)*atan(1 - (sqrt(2)*c^(1/4)*sqrt(d*x))/sqrt(d)))/(7*c^(7/4)) - (sqrt(2)*b*d^(5/2)*atan(1 + (sqrt(2)*c^(1/4)*sqrt(d*x))/sqrt(d)))/(7*c^(7/4)) + (2*(d*x)^(7/2)*(a + b*atanh(c*x^2)))/(7*d) - (2*b*d^(5/2)*atanh((c^(1/4)*sqrt(d*x))/sqrt(d)))/(7*c^(7/4)) - (b*d^(5/2)*log(sqrt(d) + sqrt(c)*sqrt(d)*x - sqrt(2)*c^(1/4)*sqrt(d*x)))/(7*sqrt(2)*c^(7/4)) + (b*d^(5/2)*log(sqrt(d) + sqrt(c)*sqrt(d)*x + sqrt(2)*c^(1/4)*sqrt(d*x)))/(7*sqrt(2)*c^(7/4))]
    @test_int [(d*x)^(3/2)*(a + b*atanh(c*x^2)), x, 16, (8*b*d*sqrt(d*x))/(5*c) - (2*b*d^(3/2)*atan((c^(1/4)*sqrt(d*x))/sqrt(d)))/(5*c^(5/4)) + (sqrt(2)*b*d^(3/2)*atan(1 - (sqrt(2)*c^(1/4)*sqrt(d*x))/sqrt(d)))/(5*c^(5/4)) - (sqrt(2)*b*d^(3/2)*atan(1 + (sqrt(2)*c^(1/4)*sqrt(d*x))/sqrt(d)))/(5*c^(5/4)) + (2*(d*x)^(5/2)*(a + b*atanh(c*x^2)))/(5*d) - (2*b*d^(3/2)*atanh((c^(1/4)*sqrt(d*x))/sqrt(d)))/(5*c^(5/4)) + (b*d^(3/2)*log(sqrt(d) + sqrt(c)*sqrt(d)*x - sqrt(2)*c^(1/4)*sqrt(d*x)))/(5*sqrt(2)*c^(5/4)) - (b*d^(3/2)*log(sqrt(d) + sqrt(c)*sqrt(d)*x + sqrt(2)*c^(1/4)*sqrt(d*x)))/(5*sqrt(2)*c^(5/4))]
    @test_int [(d*x)^(1/2)*(a + b*atanh(c*x^2)), x, 15, (2*b*sqrt(d)*atan((c^(1/4)*sqrt(d*x))/sqrt(d)))/(3*c^(3/4)) - (sqrt(2)*b*sqrt(d)*atan(1 - (sqrt(2)*c^(1/4)*sqrt(d*x))/sqrt(d)))/(3*c^(3/4)) + (sqrt(2)*b*sqrt(d)*atan(1 + (sqrt(2)*c^(1/4)*sqrt(d*x))/sqrt(d)))/(3*c^(3/4)) + (2*(d*x)^(3/2)*(a + b*atanh(c*x^2)))/(3*d) - (2*b*sqrt(d)*atanh((c^(1/4)*sqrt(d*x))/sqrt(d)))/(3*c^(3/4)) + (b*sqrt(d)*log(sqrt(d) + sqrt(c)*sqrt(d)*x - sqrt(2)*c^(1/4)*sqrt(d*x)))/(3*sqrt(2)*c^(3/4)) - (b*sqrt(d)*log(sqrt(d) + sqrt(c)*sqrt(d)*x + sqrt(2)*c^(1/4)*sqrt(d*x)))/(3*sqrt(2)*c^(3/4))]
    @test_int [(a + b*atanh(c*x^2))/(d*x)^(1/2), x, 15, -((2*b*atan((c^(1/4)*sqrt(d*x))/sqrt(d)))/(c^(1/4)*sqrt(d))) - (sqrt(2)*b*atan(1 - (sqrt(2)*c^(1/4)*sqrt(d*x))/sqrt(d)))/(c^(1/4)*sqrt(d)) + (sqrt(2)*b*atan(1 + (sqrt(2)*c^(1/4)*sqrt(d*x))/sqrt(d)))/(c^(1/4)*sqrt(d)) + (2*sqrt(d*x)*(a + b*atanh(c*x^2)))/d - (2*b*atanh((c^(1/4)*sqrt(d*x))/sqrt(d)))/(c^(1/4)*sqrt(d)) - (b*log(sqrt(d) + sqrt(c)*sqrt(d)*x - sqrt(2)*c^(1/4)*sqrt(d*x)))/(sqrt(2)*c^(1/4)*sqrt(d)) + (b*log(sqrt(d) + sqrt(c)*sqrt(d)*x + sqrt(2)*c^(1/4)*sqrt(d*x)))/(sqrt(2)*c^(1/4)*sqrt(d))]
    @test_int [(a + b*atanh(c*x^2))/(d*x)^(3/2), x, 15, -((2*b*c^(1/4)*atan((c^(1/4)*sqrt(d*x))/sqrt(d)))/d^(3/2)) - (sqrt(2)*b*c^(1/4)*atan(1 - (sqrt(2)*c^(1/4)*sqrt(d*x))/sqrt(d)))/d^(3/2) + (sqrt(2)*b*c^(1/4)*atan(1 + (sqrt(2)*c^(1/4)*sqrt(d*x))/sqrt(d)))/d^(3/2) - (2*(a + b*atanh(c*x^2)))/(d*sqrt(d*x)) + (2*b*c^(1/4)*atanh((c^(1/4)*sqrt(d*x))/sqrt(d)))/d^(3/2) + (b*c^(1/4)*log(sqrt(d) + sqrt(c)*sqrt(d)*x - sqrt(2)*c^(1/4)*sqrt(d*x)))/(sqrt(2)*d^(3/2)) - (b*c^(1/4)*log(sqrt(d) + sqrt(c)*sqrt(d)*x + sqrt(2)*c^(1/4)*sqrt(d*x)))/(sqrt(2)*d^(3/2))]
    @test_int [(a + b*atanh(c*x^2))/(d*x)^(5/2), x, 15, (2*b*c^(3/4)*atan((c^(1/4)*sqrt(d*x))/sqrt(d)))/(3*d^(5/2)) - (sqrt(2)*b*c^(3/4)*atan(1 - (sqrt(2)*c^(1/4)*sqrt(d*x))/sqrt(d)))/(3*d^(5/2)) + (sqrt(2)*b*c^(3/4)*atan(1 + (sqrt(2)*c^(1/4)*sqrt(d*x))/sqrt(d)))/(3*d^(5/2)) - (2*(a + b*atanh(c*x^2)))/(3*d*(d*x)^(3/2)) + (2*b*c^(3/4)*atanh((c^(1/4)*sqrt(d*x))/sqrt(d)))/(3*d^(5/2)) - (b*c^(3/4)*log(sqrt(d) + sqrt(c)*sqrt(d)*x - sqrt(2)*c^(1/4)*sqrt(d*x)))/(3*sqrt(2)*d^(5/2)) + (b*c^(3/4)*log(sqrt(d) + sqrt(c)*sqrt(d)*x + sqrt(2)*c^(1/4)*sqrt(d*x)))/(3*sqrt(2)*d^(5/2))]
    @test_int [(a + b*atanh(c*x^2))/(d*x)^(7/2), x, 16, -((8*b*c)/(5*d^3*sqrt(d*x))) - (2*b*c^(5/4)*atan((c^(1/4)*sqrt(d*x))/sqrt(d)))/(5*d^(7/2)) + (sqrt(2)*b*c^(5/4)*atan(1 - (sqrt(2)*c^(1/4)*sqrt(d*x))/sqrt(d)))/(5*d^(7/2)) - (sqrt(2)*b*c^(5/4)*atan(1 + (sqrt(2)*c^(1/4)*sqrt(d*x))/sqrt(d)))/(5*d^(7/2)) - (2*(a + b*atanh(c*x^2)))/(5*d*(d*x)^(5/2)) + (2*b*c^(5/4)*atanh((c^(1/4)*sqrt(d*x))/sqrt(d)))/(5*d^(7/2)) - (b*c^(5/4)*log(sqrt(d) + sqrt(c)*sqrt(d)*x - sqrt(2)*c^(1/4)*sqrt(d*x)))/(5*sqrt(2)*d^(7/2)) + (b*c^(5/4)*log(sqrt(d) + sqrt(c)*sqrt(d)*x + sqrt(2)*c^(1/4)*sqrt(d*x)))/(5*sqrt(2)*d^(7/2))]
    @test_int [(a + b*atanh(c*x^2))/(d*x)^(9/2), x, 16, -((8*b*c)/(21*d^3*(d*x)^(3/2))) + (2*b*c^(7/4)*atan((c^(1/4)*sqrt(d*x))/sqrt(d)))/(7*d^(9/2)) + (sqrt(2)*b*c^(7/4)*atan(1 - (sqrt(2)*c^(1/4)*sqrt(d*x))/sqrt(d)))/(7*d^(9/2)) - (sqrt(2)*b*c^(7/4)*atan(1 + (sqrt(2)*c^(1/4)*sqrt(d*x))/sqrt(d)))/(7*d^(9/2)) - (2*(a + b*atanh(c*x^2)))/(7*d*(d*x)^(7/2)) + (2*b*c^(7/4)*atanh((c^(1/4)*sqrt(d*x))/sqrt(d)))/(7*d^(9/2)) + (b*c^(7/4)*log(sqrt(d) + sqrt(c)*sqrt(d)*x - sqrt(2)*c^(1/4)*sqrt(d*x)))/(7*sqrt(2)*d^(9/2)) - (b*c^(7/4)*log(sqrt(d) + sqrt(c)*sqrt(d)*x + sqrt(2)*c^(1/4)*sqrt(d*x)))/(7*sqrt(2)*d^(9/2))]

    @test_int [(d*x)^(1/2)*(a + b*atanh(c*x^2))^2, x, 238, (-(8/9))*a*b*x*sqrt(d*x) - (2*sqrt(2)*a*b*sqrt(d*x)*atan(1 - sqrt(2)*c^(1/4)*sqrt(x)))/(3*c^(3/4)*sqrt(x)) + (2*sqrt(2)*a*b*sqrt(d*x)*atan(1 + sqrt(2)*c^(1/4)*sqrt(x)))/(3*c^(3/4)*sqrt(x)) - (2*im*b^2*sqrt(d*x)*atan((-c)^(1/4)*sqrt(x))^2)/(3*(-c)^(3/4)*sqrt(x)) - (2*im*b^2*sqrt(d*x)*atan(c^(1/4)*sqrt(x))^2)/(3*c^(3/4)*sqrt(x)) - (2*b^2*sqrt(d*x)*atanh((-c)^(1/4)*sqrt(x))^2)/(3*(-c)^(3/4)*sqrt(x)) - (2*b^2*sqrt(d*x)*atanh(c^(1/4)*sqrt(x))^2)/(3*c^(3/4)*sqrt(x)) + (4*b^2*sqrt(d*x)*atanh((-c)^(1/4)*sqrt(x))*log(2/(1 - (-c)^(1/4)*sqrt(x))))/(3*(-c)^(3/4)*sqrt(x)) + (4*b^2*sqrt(d*x)*atan((-c)^(1/4)*sqrt(x))*log(2/(1 - im*(-c)^(1/4)*sqrt(x))))/(3*(-c)^(3/4)*sqrt(x)) - (2*b^2*sqrt(d*x)*atan((-c)^(1/4)*sqrt(x))*log(-((2*(-c)^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((im*sqrt(-sqrt(c)) - (-c)^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x))))))/(3*(-c)^(3/4)*sqrt(x)) - (2*b^2*sqrt(d*x)*atan((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((im*sqrt(-sqrt(c)) + (-c)^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(3*(-c)^(3/4)*sqrt(x)) + (2*b^2*sqrt(d*x)*atan((-c)^(1/4)*sqrt(x))*log(((1 + im)*(1 - (-c)^(1/4)*sqrt(x)))/(1 - im*(-c)^(1/4)*sqrt(x))))/(3*(-c)^(3/4)*sqrt(x)) - (4*b^2*sqrt(d*x)*atan((-c)^(1/4)*sqrt(x))*log(2/(1 + im*(-c)^(1/4)*sqrt(x))))/(3*(-c)^(3/4)*sqrt(x)) - (4*b^2*sqrt(d*x)*atanh((-c)^(1/4)*sqrt(x))*log(2/(1 + (-c)^(1/4)*sqrt(x))))/(3*(-c)^(3/4)*sqrt(x)) - (2*b^2*sqrt(d*x)*atanh((-c)^(1/4)*sqrt(x))*log(-((2*(-c)^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) - (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x))))))/(3*(-c)^(3/4)*sqrt(x)) - (2*b^2*sqrt(d*x)*atanh((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) + (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*(-c)^(3/4)*sqrt(x)) + (2*b^2*sqrt(d*x)*atanh((-c)^(1/4)*sqrt(x))*log(-((2*(-c)^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) - (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x))))))/(3*(-c)^(3/4)*sqrt(x)) + (2*b^2*sqrt(d*x)*atanh((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) + (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*(-c)^(3/4)*sqrt(x)) + (2*b^2*sqrt(d*x)*atan((-c)^(1/4)*sqrt(x))*log(((1 - im)*(1 + (-c)^(1/4)*sqrt(x)))/(1 - im*(-c)^(1/4)*sqrt(x))))/(3*(-c)^(3/4)*sqrt(x)) + (4*b^2*sqrt(d*x)*atanh(c^(1/4)*sqrt(x))*log(2/(1 - c^(1/4)*sqrt(x))))/(3*c^(3/4)*sqrt(x)) - (2*b^2*sqrt(d*x)*atan((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 - c^(1/4)*sqrt(x)))/(((-c)^(1/4) - im*c^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(3*(-c)^(3/4)*sqrt(x)) + (2*b^2*sqrt(d*x)*atanh((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 - c^(1/4)*sqrt(x)))/(((-c)^(1/4) - c^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*(-c)^(3/4)*sqrt(x)) + (4*b^2*sqrt(d*x)*atan(c^(1/4)*sqrt(x))*log(2/(1 - im*c^(1/4)*sqrt(x))))/(3*c^(3/4)*sqrt(x)) - (2*b^2*sqrt(d*x)*atan(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((im*sqrt(-sqrt(-c)) - c^(1/4))*(1 - im*c^(1/4)*sqrt(x))))))/(3*c^(3/4)*sqrt(x)) - (2*b^2*sqrt(d*x)*atan(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((im*sqrt(-sqrt(-c)) + c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(3*c^(3/4)*sqrt(x)) - (2*b^2*sqrt(d*x)*atan(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - (-c)^(1/4)*sqrt(x)))/((im*(-c)^(1/4) - c^(1/4))*(1 - im*c^(1/4)*sqrt(x))))))/(3*c^(3/4)*sqrt(x)) - (2*b^2*sqrt(d*x)*atan(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + (-c)^(1/4)*sqrt(x)))/((im*(-c)^(1/4) + c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(3*c^(3/4)*sqrt(x)) + (2*b^2*sqrt(d*x)*atan(c^(1/4)*sqrt(x))*log(((1 + im)*(1 - c^(1/4)*sqrt(x)))/(1 - im*c^(1/4)*sqrt(x))))/(3*c^(3/4)*sqrt(x)) - (4*b^2*sqrt(d*x)*atan(c^(1/4)*sqrt(x))*log(2/(1 + im*c^(1/4)*sqrt(x))))/(3*c^(3/4)*sqrt(x)) - (4*b^2*sqrt(d*x)*atanh(c^(1/4)*sqrt(x))*log(2/(1 + c^(1/4)*sqrt(x))))/(3*c^(3/4)*sqrt(x)) + (2*b^2*sqrt(d*x)*atanh(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) - c^(1/4))*(1 + c^(1/4)*sqrt(x))))))/(3*c^(3/4)*sqrt(x)) + (2*b^2*sqrt(d*x)*atanh(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*c^(3/4)*sqrt(x)) - (2*b^2*sqrt(d*x)*atanh(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) - c^(1/4))*(1 + c^(1/4)*sqrt(x))))))/(3*c^(3/4)*sqrt(x)) - (2*b^2*sqrt(d*x)*atanh(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*c^(3/4)*sqrt(x)) + (2*b^2*sqrt(d*x)*atanh(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - (-c)^(1/4)*sqrt(x)))/(((-c)^(1/4) - c^(1/4))*(1 + c^(1/4)*sqrt(x))))))/(3*c^(3/4)*sqrt(x)) + (2*b^2*sqrt(d*x)*atanh(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + (-c)^(1/4)*sqrt(x)))/(((-c)^(1/4) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*c^(3/4)*sqrt(x)) - (2*b^2*sqrt(d*x)*atan((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + c^(1/4)*sqrt(x)))/(((-c)^(1/4) + im*c^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(3*(-c)^(3/4)*sqrt(x)) + (2*b^2*sqrt(d*x)*atanh((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + c^(1/4)*sqrt(x)))/(((-c)^(1/4) + c^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*(-c)^(3/4)*sqrt(x)) + (2*b^2*sqrt(d*x)*atan(c^(1/4)*sqrt(x))*log(((1 - im)*(1 + c^(1/4)*sqrt(x)))/(1 - im*c^(1/4)*sqrt(x))))/(3*c^(3/4)*sqrt(x)) + (sqrt(2)*a*b*sqrt(d*x)*log(1 - sqrt(2)*c^(1/4)*sqrt(x) + sqrt(c)*x))/(3*c^(3/4)*sqrt(x)) - (sqrt(2)*a*b*sqrt(d*x)*log(1 + sqrt(2)*c^(1/4)*sqrt(x) + sqrt(c)*x))/(3*c^(3/4)*sqrt(x)) + (4/9)*b^2*x*sqrt(d*x)*log(1 - c*x^2) + (2*b^2*sqrt(d*x)*atan((-c)^(1/4)*sqrt(x))*log(1 - c*x^2))/(3*(-c)^(3/4)*sqrt(x)) - (2*b^2*sqrt(d*x)*atanh((-c)^(1/4)*sqrt(x))*log(1 - c*x^2))/(3*(-c)^(3/4)*sqrt(x)) + (4/9)*b*x*sqrt(d*x)*(2*a - b*log(1 - c*x^2)) + (2*b*sqrt(d*x)*atan(c^(1/4)*sqrt(x))*(2*a - b*log(1 - c*x^2)))/(3*c^(3/4)*sqrt(x)) - (2*b*sqrt(d*x)*atanh(c^(1/4)*sqrt(x))*(2*a - b*log(1 - c*x^2)))/(3*c^(3/4)*sqrt(x)) + (1/6)*x*sqrt(d*x)*(2*a - b*log(1 - c*x^2))^2 + (2/3)*a*b*x*sqrt(d*x)*log(1 + c*x^2) - (2*b^2*sqrt(d*x)*atan((-c)^(1/4)*sqrt(x))*log(1 + c*x^2))/(3*(-c)^(3/4)*sqrt(x)) + (2*b^2*sqrt(d*x)*atan(c^(1/4)*sqrt(x))*log(1 + c*x^2))/(3*c^(3/4)*sqrt(x)) + (2*b^2*sqrt(d*x)*atanh((-c)^(1/4)*sqrt(x))*log(1 + c*x^2))/(3*(-c)^(3/4)*sqrt(x)) - (2*b^2*sqrt(d*x)*atanh(c^(1/4)*sqrt(x))*log(1 + c*x^2))/(3*c^(3/4)*sqrt(x)) - (1/3)*b^2*x*sqrt(d*x)*log(1 - c*x^2)*log(1 + c*x^2) + (1/6)*b^2*x*sqrt(d*x)*log(1 + c*x^2)^2 + (2*b^2*sqrt(d*x)*PolyLog(2, 1 - 2/(1 - (-c)^(1/4)*sqrt(x))))/(3*(-c)^(3/4)*sqrt(x)) - (2*im*b^2*sqrt(d*x)*PolyLog(2, 1 - 2/(1 - im*(-c)^(1/4)*sqrt(x))))/(3*(-c)^(3/4)*sqrt(x)) + (im*b^2*sqrt(d*x)*PolyLog(2, 1 + (2*(-c)^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((im*sqrt(-sqrt(c)) - (-c)^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(3*(-c)^(3/4)*sqrt(x)) + (im*b^2*sqrt(d*x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((im*sqrt(-sqrt(c)) + (-c)^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(3*(-c)^(3/4)*sqrt(x)) - (im*b^2*sqrt(d*x)*PolyLog(2, 1 - ((1 + im)*(1 - (-c)^(1/4)*sqrt(x)))/(1 - im*(-c)^(1/4)*sqrt(x))))/(3*(-c)^(3/4)*sqrt(x)) - (2*im*b^2*sqrt(d*x)*PolyLog(2, 1 - 2/(1 + im*(-c)^(1/4)*sqrt(x))))/(3*(-c)^(3/4)*sqrt(x)) + (2*b^2*sqrt(d*x)*PolyLog(2, 1 - 2/(1 + (-c)^(1/4)*sqrt(x))))/(3*(-c)^(3/4)*sqrt(x)) + (b^2*sqrt(d*x)*PolyLog(2, 1 + (2*(-c)^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) - (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*(-c)^(3/4)*sqrt(x)) + (b^2*sqrt(d*x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) + (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*(-c)^(3/4)*sqrt(x)) - (b^2*sqrt(d*x)*PolyLog(2, 1 + (2*(-c)^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) - (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*(-c)^(3/4)*sqrt(x)) - (b^2*sqrt(d*x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) + (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*(-c)^(3/4)*sqrt(x)) - (im*b^2*sqrt(d*x)*PolyLog(2, 1 - ((1 - im)*(1 + (-c)^(1/4)*sqrt(x)))/(1 - im*(-c)^(1/4)*sqrt(x))))/(3*(-c)^(3/4)*sqrt(x)) + (2*b^2*sqrt(d*x)*PolyLog(2, 1 - 2/(1 - c^(1/4)*sqrt(x))))/(3*c^(3/4)*sqrt(x)) + (im*b^2*sqrt(d*x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 - c^(1/4)*sqrt(x)))/(((-c)^(1/4) - im*c^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(3*(-c)^(3/4)*sqrt(x)) - (b^2*sqrt(d*x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 - c^(1/4)*sqrt(x)))/(((-c)^(1/4) - c^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*(-c)^(3/4)*sqrt(x)) - (2*im*b^2*sqrt(d*x)*PolyLog(2, 1 - 2/(1 - im*c^(1/4)*sqrt(x))))/(3*c^(3/4)*sqrt(x)) + (im*b^2*sqrt(d*x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((im*sqrt(-sqrt(-c)) - c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(3*c^(3/4)*sqrt(x)) + (im*b^2*sqrt(d*x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((im*sqrt(-sqrt(-c)) + c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(3*c^(3/4)*sqrt(x)) + (im*b^2*sqrt(d*x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - (-c)^(1/4)*sqrt(x)))/((im*(-c)^(1/4) - c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(3*c^(3/4)*sqrt(x)) + (im*b^2*sqrt(d*x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + (-c)^(1/4)*sqrt(x)))/((im*(-c)^(1/4) + c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(3*c^(3/4)*sqrt(x)) - (im*b^2*sqrt(d*x)*PolyLog(2, 1 - ((1 + im)*(1 - c^(1/4)*sqrt(x)))/(1 - im*c^(1/4)*sqrt(x))))/(3*c^(3/4)*sqrt(x)) - (2*im*b^2*sqrt(d*x)*PolyLog(2, 1 - 2/(1 + im*c^(1/4)*sqrt(x))))/(3*c^(3/4)*sqrt(x)) + (2*b^2*sqrt(d*x)*PolyLog(2, 1 - 2/(1 + c^(1/4)*sqrt(x))))/(3*c^(3/4)*sqrt(x)) - (b^2*sqrt(d*x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) - c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*c^(3/4)*sqrt(x)) - (b^2*sqrt(d*x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*c^(3/4)*sqrt(x)) + (b^2*sqrt(d*x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) - c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*c^(3/4)*sqrt(x)) + (b^2*sqrt(d*x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*c^(3/4)*sqrt(x)) - (b^2*sqrt(d*x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - (-c)^(1/4)*sqrt(x)))/(((-c)^(1/4) - c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*c^(3/4)*sqrt(x)) - (b^2*sqrt(d*x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + (-c)^(1/4)*sqrt(x)))/(((-c)^(1/4) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*c^(3/4)*sqrt(x)) + (im*b^2*sqrt(d*x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + c^(1/4)*sqrt(x)))/(((-c)^(1/4) + im*c^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(3*(-c)^(3/4)*sqrt(x)) - (b^2*sqrt(d*x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + c^(1/4)*sqrt(x)))/(((-c)^(1/4) + c^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*(-c)^(3/4)*sqrt(x)) - (im*b^2*sqrt(d*x)*PolyLog(2, 1 - ((1 - im)*(1 + c^(1/4)*sqrt(x)))/(1 - im*c^(1/4)*sqrt(x))))/(3*c^(3/4)*sqrt(x))]
    @test_int [(a + b*atanh(c*x^2))^2/(d*x)^(1/2), x, 241, (2*a^2*x)/sqrt(d*x) - (2*sqrt(2)*a*b*sqrt(x)*atan(1 - sqrt(2)*c^(1/4)*sqrt(x)))/(c^(1/4)*sqrt(d*x)) + (2*sqrt(2)*a*b*sqrt(x)*atan(1 + sqrt(2)*c^(1/4)*sqrt(x)))/(c^(1/4)*sqrt(d*x)) + (2*im*b^2*sqrt(x)*atan((-c)^(1/4)*sqrt(x))^2)/((-c)^(1/4)*sqrt(d*x)) - (4*a*b*sqrt(x)*atan(c^(1/4)*sqrt(x)))/(c^(1/4)*sqrt(d*x)) + (2*im*b^2*sqrt(x)*atan(c^(1/4)*sqrt(x))^2)/(c^(1/4)*sqrt(d*x)) - (2*b^2*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))^2)/((-c)^(1/4)*sqrt(d*x)) - (4*a*b*sqrt(x)*atanh(c^(1/4)*sqrt(x)))/(c^(1/4)*sqrt(d*x)) - (2*b^2*sqrt(x)*atanh(c^(1/4)*sqrt(x))^2)/(c^(1/4)*sqrt(d*x)) + (4*b^2*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(2/(1 - (-c)^(1/4)*sqrt(x))))/((-c)^(1/4)*sqrt(d*x)) - (4*b^2*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(2/(1 - im*(-c)^(1/4)*sqrt(x))))/((-c)^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(-((2*(-c)^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((im*sqrt(-sqrt(c)) - (-c)^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x))))))/((-c)^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((im*sqrt(-sqrt(c)) + (-c)^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/((-c)^(1/4)*sqrt(d*x)) - (2*b^2*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(((1 + im)*(1 - (-c)^(1/4)*sqrt(x)))/(1 - im*(-c)^(1/4)*sqrt(x))))/((-c)^(1/4)*sqrt(d*x)) + (4*b^2*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(2/(1 + im*(-c)^(1/4)*sqrt(x))))/((-c)^(1/4)*sqrt(d*x)) - (4*b^2*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(2/(1 + (-c)^(1/4)*sqrt(x))))/((-c)^(1/4)*sqrt(d*x)) - (2*b^2*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(-((2*(-c)^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) - (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x))))))/((-c)^(1/4)*sqrt(d*x)) - (2*b^2*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) + (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/((-c)^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(-((2*(-c)^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) - (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x))))))/((-c)^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) + (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/((-c)^(1/4)*sqrt(d*x)) - (2*b^2*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(((1 - im)*(1 + (-c)^(1/4)*sqrt(x)))/(1 - im*(-c)^(1/4)*sqrt(x))))/((-c)^(1/4)*sqrt(d*x)) + (4*b^2*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(2/(1 - c^(1/4)*sqrt(x))))/(c^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 - c^(1/4)*sqrt(x)))/(((-c)^(1/4) - im*c^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/((-c)^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 - c^(1/4)*sqrt(x)))/(((-c)^(1/4) - c^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/((-c)^(1/4)*sqrt(d*x)) - (4*b^2*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(2/(1 - im*c^(1/4)*sqrt(x))))/(c^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((im*sqrt(-sqrt(-c)) - c^(1/4))*(1 - im*c^(1/4)*sqrt(x))))))/(c^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atan(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((im*sqrt(-sqrt(-c)) + c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(c^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - (-c)^(1/4)*sqrt(x)))/((im*(-c)^(1/4) - c^(1/4))*(1 - im*c^(1/4)*sqrt(x))))))/(c^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atan(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + (-c)^(1/4)*sqrt(x)))/((im*(-c)^(1/4) + c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(c^(1/4)*sqrt(d*x)) - (2*b^2*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(((1 + im)*(1 - c^(1/4)*sqrt(x)))/(1 - im*c^(1/4)*sqrt(x))))/(c^(1/4)*sqrt(d*x)) + (4*b^2*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(2/(1 + im*c^(1/4)*sqrt(x))))/(c^(1/4)*sqrt(d*x)) - (4*b^2*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(2/(1 + c^(1/4)*sqrt(x))))/(c^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) - c^(1/4))*(1 + c^(1/4)*sqrt(x))))))/(c^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(c^(1/4)*sqrt(d*x)) - (2*b^2*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) - c^(1/4))*(1 + c^(1/4)*sqrt(x))))))/(c^(1/4)*sqrt(d*x)) - (2*b^2*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(c^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - (-c)^(1/4)*sqrt(x)))/(((-c)^(1/4) - c^(1/4))*(1 + c^(1/4)*sqrt(x))))))/(c^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + (-c)^(1/4)*sqrt(x)))/(((-c)^(1/4) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(c^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + c^(1/4)*sqrt(x)))/(((-c)^(1/4) + im*c^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/((-c)^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + c^(1/4)*sqrt(x)))/(((-c)^(1/4) + c^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/((-c)^(1/4)*sqrt(d*x)) - (2*b^2*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(((1 - im)*(1 + c^(1/4)*sqrt(x)))/(1 - im*c^(1/4)*sqrt(x))))/(c^(1/4)*sqrt(d*x)) - (sqrt(2)*a*b*sqrt(x)*log(1 - sqrt(2)*c^(1/4)*sqrt(x) + sqrt(c)*x))/(c^(1/4)*sqrt(d*x)) + (sqrt(2)*a*b*sqrt(x)*log(1 + sqrt(2)*c^(1/4)*sqrt(x) + sqrt(c)*x))/(c^(1/4)*sqrt(d*x)) - (2*a*b*x*log(1 - c*x^2))/sqrt(d*x) - (2*b^2*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(1 - c*x^2))/((-c)^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(1 - c*x^2))/(c^(1/4)*sqrt(d*x)) - (2*b^2*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(1 - c*x^2))/((-c)^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(1 - c*x^2))/(c^(1/4)*sqrt(d*x)) + (b^2*x*log(1 - c*x^2)^2)/(2*sqrt(d*x)) + (2*a*b*x*log(1 + c*x^2))/sqrt(d*x) + (2*b^2*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(1 + c*x^2))/((-c)^(1/4)*sqrt(d*x)) - (2*b^2*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(1 + c*x^2))/(c^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(1 + c*x^2))/((-c)^(1/4)*sqrt(d*x)) - (2*b^2*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(1 + c*x^2))/(c^(1/4)*sqrt(d*x)) - (b^2*x*log(1 - c*x^2)*log(1 + c*x^2))/sqrt(d*x) + (b^2*x*log(1 + c*x^2)^2)/(2*sqrt(d*x)) + (2*b^2*sqrt(x)*PolyLog(2, 1 - 2/(1 - (-c)^(1/4)*sqrt(x))))/((-c)^(1/4)*sqrt(d*x)) + (2*im*b^2*sqrt(x)*PolyLog(2, 1 - 2/(1 - im*(-c)^(1/4)*sqrt(x))))/((-c)^(1/4)*sqrt(d*x)) - (im*b^2*sqrt(x)*PolyLog(2, 1 + (2*(-c)^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((im*sqrt(-sqrt(c)) - (-c)^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/((-c)^(1/4)*sqrt(d*x)) - (im*b^2*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((im*sqrt(-sqrt(c)) + (-c)^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/((-c)^(1/4)*sqrt(d*x)) + (im*b^2*sqrt(x)*PolyLog(2, 1 - ((1 + im)*(1 - (-c)^(1/4)*sqrt(x)))/(1 - im*(-c)^(1/4)*sqrt(x))))/((-c)^(1/4)*sqrt(d*x)) + (2*im*b^2*sqrt(x)*PolyLog(2, 1 - 2/(1 + im*(-c)^(1/4)*sqrt(x))))/((-c)^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*PolyLog(2, 1 - 2/(1 + (-c)^(1/4)*sqrt(x))))/((-c)^(1/4)*sqrt(d*x)) + (b^2*sqrt(x)*PolyLog(2, 1 + (2*(-c)^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) - (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/((-c)^(1/4)*sqrt(d*x)) + (b^2*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) + (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/((-c)^(1/4)*sqrt(d*x)) - (b^2*sqrt(x)*PolyLog(2, 1 + (2*(-c)^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) - (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/((-c)^(1/4)*sqrt(d*x)) - (b^2*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) + (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/((-c)^(1/4)*sqrt(d*x)) + (im*b^2*sqrt(x)*PolyLog(2, 1 - ((1 - im)*(1 + (-c)^(1/4)*sqrt(x)))/(1 - im*(-c)^(1/4)*sqrt(x))))/((-c)^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*PolyLog(2, 1 - 2/(1 - c^(1/4)*sqrt(x))))/(c^(1/4)*sqrt(d*x)) - (im*b^2*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 - c^(1/4)*sqrt(x)))/(((-c)^(1/4) - im*c^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/((-c)^(1/4)*sqrt(d*x)) - (b^2*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 - c^(1/4)*sqrt(x)))/(((-c)^(1/4) - c^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/((-c)^(1/4)*sqrt(d*x)) + (2*im*b^2*sqrt(x)*PolyLog(2, 1 - 2/(1 - im*c^(1/4)*sqrt(x))))/(c^(1/4)*sqrt(d*x)) - (im*b^2*sqrt(x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((im*sqrt(-sqrt(-c)) - c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(c^(1/4)*sqrt(d*x)) - (im*b^2*sqrt(x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((im*sqrt(-sqrt(-c)) + c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(c^(1/4)*sqrt(d*x)) - (im*b^2*sqrt(x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - (-c)^(1/4)*sqrt(x)))/((im*(-c)^(1/4) - c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(c^(1/4)*sqrt(d*x)) - (im*b^2*sqrt(x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + (-c)^(1/4)*sqrt(x)))/((im*(-c)^(1/4) + c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(c^(1/4)*sqrt(d*x)) + (im*b^2*sqrt(x)*PolyLog(2, 1 - ((1 + im)*(1 - c^(1/4)*sqrt(x)))/(1 - im*c^(1/4)*sqrt(x))))/(c^(1/4)*sqrt(d*x)) + (2*im*b^2*sqrt(x)*PolyLog(2, 1 - 2/(1 + im*c^(1/4)*sqrt(x))))/(c^(1/4)*sqrt(d*x)) + (2*b^2*sqrt(x)*PolyLog(2, 1 - 2/(1 + c^(1/4)*sqrt(x))))/(c^(1/4)*sqrt(d*x)) - (b^2*sqrt(x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) - c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(c^(1/4)*sqrt(d*x)) - (b^2*sqrt(x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(c^(1/4)*sqrt(d*x)) + (b^2*sqrt(x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) - c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(c^(1/4)*sqrt(d*x)) + (b^2*sqrt(x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(c^(1/4)*sqrt(d*x)) - (b^2*sqrt(x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - (-c)^(1/4)*sqrt(x)))/(((-c)^(1/4) - c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(c^(1/4)*sqrt(d*x)) - (b^2*sqrt(x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + (-c)^(1/4)*sqrt(x)))/(((-c)^(1/4) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(c^(1/4)*sqrt(d*x)) - (im*b^2*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + c^(1/4)*sqrt(x)))/(((-c)^(1/4) + im*c^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/((-c)^(1/4)*sqrt(d*x)) - (b^2*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + c^(1/4)*sqrt(x)))/(((-c)^(1/4) + c^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/((-c)^(1/4)*sqrt(d*x)) + (im*b^2*sqrt(x)*PolyLog(2, 1 - ((1 - im)*(1 + c^(1/4)*sqrt(x)))/(1 - im*c^(1/4)*sqrt(x))))/(c^(1/4)*sqrt(d*x))]
    @test_int [(a + b*atanh(c*x^2))^2/(d*x)^(3/2), x, 197, -((2*sqrt(2)*a*b*c^(1/4)*sqrt(x)*atan(1 - sqrt(2)*c^(1/4)*sqrt(x)))/(d*sqrt(d*x))) + (2*sqrt(2)*a*b*c^(1/4)*sqrt(x)*atan(1 + sqrt(2)*c^(1/4)*sqrt(x)))/(d*sqrt(d*x)) + (2*im*b^2*(-c)^(1/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))^2)/(d*sqrt(d*x)) + (2*im*b^2*c^(1/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))^2)/(d*sqrt(d*x)) + (2*b^2*(-c)^(1/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))^2)/(d*sqrt(d*x)) + (2*b^2*c^(1/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))^2)/(d*sqrt(d*x)) - (4*b^2*(-c)^(1/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(2/(1 - (-c)^(1/4)*sqrt(x))))/(d*sqrt(d*x)) - (4*b^2*(-c)^(1/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(2/(1 - im*(-c)^(1/4)*sqrt(x))))/(d*sqrt(d*x)) + (2*b^2*(-c)^(1/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(-((2*(-c)^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((im*sqrt(-sqrt(c)) - (-c)^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x))))))/(d*sqrt(d*x)) + (2*b^2*(-c)^(1/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((im*sqrt(-sqrt(c)) + (-c)^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) - (2*b^2*(-c)^(1/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(((1 + im)*(1 - (-c)^(1/4)*sqrt(x)))/(1 - im*(-c)^(1/4)*sqrt(x))))/(d*sqrt(d*x)) + (4*b^2*(-c)^(1/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(2/(1 + im*(-c)^(1/4)*sqrt(x))))/(d*sqrt(d*x)) + (4*b^2*(-c)^(1/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(2/(1 + (-c)^(1/4)*sqrt(x))))/(d*sqrt(d*x)) + (2*b^2*(-c)^(1/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(-((2*(-c)^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) - (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x))))))/(d*sqrt(d*x)) + (2*b^2*(-c)^(1/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) + (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) - (2*b^2*(-c)^(1/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(-((2*(-c)^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) - (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x))))))/(d*sqrt(d*x)) - (2*b^2*(-c)^(1/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) + (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) - (2*b^2*(-c)^(1/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(((1 - im)*(1 + (-c)^(1/4)*sqrt(x)))/(1 - im*(-c)^(1/4)*sqrt(x))))/(d*sqrt(d*x)) - (4*b^2*c^(1/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(2/(1 - c^(1/4)*sqrt(x))))/(d*sqrt(d*x)) + (2*b^2*(-c)^(1/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 - c^(1/4)*sqrt(x)))/(((-c)^(1/4) - im*c^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) - (2*b^2*(-c)^(1/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 - c^(1/4)*sqrt(x)))/(((-c)^(1/4) - c^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) - (4*b^2*c^(1/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(2/(1 - im*c^(1/4)*sqrt(x))))/(d*sqrt(d*x)) + (2*b^2*c^(1/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((im*sqrt(-sqrt(-c)) - c^(1/4))*(1 - im*c^(1/4)*sqrt(x))))))/(d*sqrt(d*x)) + (2*b^2*c^(1/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((im*sqrt(-sqrt(-c)) + c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) + (2*b^2*c^(1/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - (-c)^(1/4)*sqrt(x)))/((im*(-c)^(1/4) - c^(1/4))*(1 - im*c^(1/4)*sqrt(x))))))/(d*sqrt(d*x)) + (2*b^2*c^(1/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + (-c)^(1/4)*sqrt(x)))/((im*(-c)^(1/4) + c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) - (2*b^2*c^(1/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(((1 + im)*(1 - c^(1/4)*sqrt(x)))/(1 - im*c^(1/4)*sqrt(x))))/(d*sqrt(d*x)) + (4*b^2*c^(1/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(2/(1 + im*c^(1/4)*sqrt(x))))/(d*sqrt(d*x)) + (4*b^2*c^(1/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(2/(1 + c^(1/4)*sqrt(x))))/(d*sqrt(d*x)) - (2*b^2*c^(1/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) - c^(1/4))*(1 + c^(1/4)*sqrt(x))))))/(d*sqrt(d*x)) - (2*b^2*c^(1/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) + (2*b^2*c^(1/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) - c^(1/4))*(1 + c^(1/4)*sqrt(x))))))/(d*sqrt(d*x)) + (2*b^2*c^(1/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) - (2*b^2*c^(1/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - (-c)^(1/4)*sqrt(x)))/(((-c)^(1/4) - c^(1/4))*(1 + c^(1/4)*sqrt(x))))))/(d*sqrt(d*x)) - (2*b^2*c^(1/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + (-c)^(1/4)*sqrt(x)))/(((-c)^(1/4) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) + (2*b^2*(-c)^(1/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + c^(1/4)*sqrt(x)))/(((-c)^(1/4) + im*c^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) - (2*b^2*(-c)^(1/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + c^(1/4)*sqrt(x)))/(((-c)^(1/4) + c^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) - (2*b^2*c^(1/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(((1 - im)*(1 + c^(1/4)*sqrt(x)))/(1 - im*c^(1/4)*sqrt(x))))/(d*sqrt(d*x)) + (sqrt(2)*a*b*c^(1/4)*sqrt(x)*log(1 - sqrt(2)*c^(1/4)*sqrt(x) + sqrt(c)*x))/(d*sqrt(d*x)) - (sqrt(2)*a*b*c^(1/4)*sqrt(x)*log(1 + sqrt(2)*c^(1/4)*sqrt(x) + sqrt(c)*x))/(d*sqrt(d*x)) - (2*b^2*(-c)^(1/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(1 - c*x^2))/(d*sqrt(d*x)) + (2*b^2*(-c)^(1/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(1 - c*x^2))/(d*sqrt(d*x)) - (2*b*c^(1/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*(2*a - b*log(1 - c*x^2)))/(d*sqrt(d*x)) + (2*b*c^(1/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*(2*a - b*log(1 - c*x^2)))/(d*sqrt(d*x)) - (2*a - b*log(1 - c*x^2))^2/(2*d*sqrt(d*x)) - (2*a*b*log(1 + c*x^2))/(d*sqrt(d*x)) + (2*b^2*(-c)^(1/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(1 + c*x^2))/(d*sqrt(d*x)) - (2*b^2*c^(1/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(1 + c*x^2))/(d*sqrt(d*x)) - (2*b^2*(-c)^(1/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(1 + c*x^2))/(d*sqrt(d*x)) + (2*b^2*c^(1/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(1 + c*x^2))/(d*sqrt(d*x)) + (b^2*log(1 - c*x^2)*log(1 + c*x^2))/(d*sqrt(d*x)) - (b^2*log(1 + c*x^2)^2)/(2*d*sqrt(d*x)) - (2*b^2*(-c)^(1/4)*sqrt(x)*PolyLog(2, 1 - 2/(1 - (-c)^(1/4)*sqrt(x))))/(d*sqrt(d*x)) + (2*im*b^2*(-c)^(1/4)*sqrt(x)*PolyLog(2, 1 - 2/(1 - im*(-c)^(1/4)*sqrt(x))))/(d*sqrt(d*x)) - (im*b^2*(-c)^(1/4)*sqrt(x)*PolyLog(2, 1 + (2*(-c)^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((im*sqrt(-sqrt(c)) - (-c)^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) - (im*b^2*(-c)^(1/4)*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((im*sqrt(-sqrt(c)) + (-c)^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) + (im*b^2*(-c)^(1/4)*sqrt(x)*PolyLog(2, 1 - ((1 + im)*(1 - (-c)^(1/4)*sqrt(x)))/(1 - im*(-c)^(1/4)*sqrt(x))))/(d*sqrt(d*x)) + (2*im*b^2*(-c)^(1/4)*sqrt(x)*PolyLog(2, 1 - 2/(1 + im*(-c)^(1/4)*sqrt(x))))/(d*sqrt(d*x)) - (2*b^2*(-c)^(1/4)*sqrt(x)*PolyLog(2, 1 - 2/(1 + (-c)^(1/4)*sqrt(x))))/(d*sqrt(d*x)) - (b^2*(-c)^(1/4)*sqrt(x)*PolyLog(2, 1 + (2*(-c)^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) - (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) - (b^2*(-c)^(1/4)*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) + (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) + (b^2*(-c)^(1/4)*sqrt(x)*PolyLog(2, 1 + (2*(-c)^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) - (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) + (b^2*(-c)^(1/4)*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) + (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) + (im*b^2*(-c)^(1/4)*sqrt(x)*PolyLog(2, 1 - ((1 - im)*(1 + (-c)^(1/4)*sqrt(x)))/(1 - im*(-c)^(1/4)*sqrt(x))))/(d*sqrt(d*x)) - (2*b^2*c^(1/4)*sqrt(x)*PolyLog(2, 1 - 2/(1 - c^(1/4)*sqrt(x))))/(d*sqrt(d*x)) - (im*b^2*(-c)^(1/4)*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 - c^(1/4)*sqrt(x)))/(((-c)^(1/4) - im*c^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) + (b^2*(-c)^(1/4)*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 - c^(1/4)*sqrt(x)))/(((-c)^(1/4) - c^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) + (2*im*b^2*c^(1/4)*sqrt(x)*PolyLog(2, 1 - 2/(1 - im*c^(1/4)*sqrt(x))))/(d*sqrt(d*x)) - (im*b^2*c^(1/4)*sqrt(x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((im*sqrt(-sqrt(-c)) - c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) - (im*b^2*c^(1/4)*sqrt(x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((im*sqrt(-sqrt(-c)) + c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) - (im*b^2*c^(1/4)*sqrt(x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - (-c)^(1/4)*sqrt(x)))/((im*(-c)^(1/4) - c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) - (im*b^2*c^(1/4)*sqrt(x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + (-c)^(1/4)*sqrt(x)))/((im*(-c)^(1/4) + c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) + (im*b^2*c^(1/4)*sqrt(x)*PolyLog(2, 1 - ((1 + im)*(1 - c^(1/4)*sqrt(x)))/(1 - im*c^(1/4)*sqrt(x))))/(d*sqrt(d*x)) + (2*im*b^2*c^(1/4)*sqrt(x)*PolyLog(2, 1 - 2/(1 + im*c^(1/4)*sqrt(x))))/(d*sqrt(d*x)) - (2*b^2*c^(1/4)*sqrt(x)*PolyLog(2, 1 - 2/(1 + c^(1/4)*sqrt(x))))/(d*sqrt(d*x)) + (b^2*c^(1/4)*sqrt(x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) - c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) + (b^2*c^(1/4)*sqrt(x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) - (b^2*c^(1/4)*sqrt(x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) - c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) - (b^2*c^(1/4)*sqrt(x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) + (b^2*c^(1/4)*sqrt(x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - (-c)^(1/4)*sqrt(x)))/(((-c)^(1/4) - c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) + (b^2*c^(1/4)*sqrt(x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + (-c)^(1/4)*sqrt(x)))/(((-c)^(1/4) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) - (im*b^2*(-c)^(1/4)*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + c^(1/4)*sqrt(x)))/(((-c)^(1/4) + im*c^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) + (b^2*(-c)^(1/4)*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + c^(1/4)*sqrt(x)))/(((-c)^(1/4) + c^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(d*sqrt(d*x)) + (im*b^2*c^(1/4)*sqrt(x)*PolyLog(2, 1 - ((1 - im)*(1 + c^(1/4)*sqrt(x)))/(1 - im*c^(1/4)*sqrt(x))))/(d*sqrt(d*x))]
    @test_int [(a + b*atanh(c*x^2))^2/(d*x)^(5/2), x, 197, -((2*sqrt(2)*a*b*c^(3/4)*sqrt(x)*atan(1 - sqrt(2)*c^(1/4)*sqrt(x)))/(3*d^2*sqrt(d*x))) + (2*sqrt(2)*a*b*c^(3/4)*sqrt(x)*atan(1 + sqrt(2)*c^(1/4)*sqrt(x)))/(3*d^2*sqrt(d*x)) - (2*im*b^2*(-c)^(3/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))^2)/(3*d^2*sqrt(d*x)) - (2*im*b^2*c^(3/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))^2)/(3*d^2*sqrt(d*x)) + (2*b^2*(-c)^(3/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))^2)/(3*d^2*sqrt(d*x)) + (2*b^2*c^(3/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))^2)/(3*d^2*sqrt(d*x)) - (4*b^2*(-c)^(3/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(2/(1 - (-c)^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) + (4*b^2*(-c)^(3/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(2/(1 - im*(-c)^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) - (2*b^2*(-c)^(3/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(-((2*(-c)^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((im*sqrt(-sqrt(c)) - (-c)^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x))))))/(3*d^2*sqrt(d*x)) - (2*b^2*(-c)^(3/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((im*sqrt(-sqrt(c)) + (-c)^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (2*b^2*(-c)^(3/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(((1 + im)*(1 - (-c)^(1/4)*sqrt(x)))/(1 - im*(-c)^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) - (4*b^2*(-c)^(3/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(2/(1 + im*(-c)^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) + (4*b^2*(-c)^(3/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(2/(1 + (-c)^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) + (2*b^2*(-c)^(3/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(-((2*(-c)^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) - (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x))))))/(3*d^2*sqrt(d*x)) + (2*b^2*(-c)^(3/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) + (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) - (2*b^2*(-c)^(3/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(-((2*(-c)^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) - (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x))))))/(3*d^2*sqrt(d*x)) - (2*b^2*(-c)^(3/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) + (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (2*b^2*(-c)^(3/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(((1 - im)*(1 + (-c)^(1/4)*sqrt(x)))/(1 - im*(-c)^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) - (4*b^2*c^(3/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(2/(1 - c^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) - (2*b^2*(-c)^(3/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 - c^(1/4)*sqrt(x)))/(((-c)^(1/4) - im*c^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) - (2*b^2*(-c)^(3/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 - c^(1/4)*sqrt(x)))/(((-c)^(1/4) - c^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (4*b^2*c^(3/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(2/(1 - im*c^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) - (2*b^2*c^(3/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((im*sqrt(-sqrt(-c)) - c^(1/4))*(1 - im*c^(1/4)*sqrt(x))))))/(3*d^2*sqrt(d*x)) - (2*b^2*c^(3/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((im*sqrt(-sqrt(-c)) + c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) - (2*b^2*c^(3/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - (-c)^(1/4)*sqrt(x)))/((im*(-c)^(1/4) - c^(1/4))*(1 - im*c^(1/4)*sqrt(x))))))/(3*d^2*sqrt(d*x)) - (2*b^2*c^(3/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + (-c)^(1/4)*sqrt(x)))/((im*(-c)^(1/4) + c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (2*b^2*c^(3/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(((1 + im)*(1 - c^(1/4)*sqrt(x)))/(1 - im*c^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) - (4*b^2*c^(3/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(2/(1 + im*c^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) + (4*b^2*c^(3/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(2/(1 + c^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) - (2*b^2*c^(3/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) - c^(1/4))*(1 + c^(1/4)*sqrt(x))))))/(3*d^2*sqrt(d*x)) - (2*b^2*c^(3/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (2*b^2*c^(3/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) - c^(1/4))*(1 + c^(1/4)*sqrt(x))))))/(3*d^2*sqrt(d*x)) + (2*b^2*c^(3/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) - (2*b^2*c^(3/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(-((2*c^(1/4)*(1 - (-c)^(1/4)*sqrt(x)))/(((-c)^(1/4) - c^(1/4))*(1 + c^(1/4)*sqrt(x))))))/(3*d^2*sqrt(d*x)) - (2*b^2*c^(3/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log((2*c^(1/4)*(1 + (-c)^(1/4)*sqrt(x)))/(((-c)^(1/4) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) - (2*b^2*(-c)^(3/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + c^(1/4)*sqrt(x)))/(((-c)^(1/4) + im*c^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) - (2*b^2*(-c)^(3/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log((2*(-c)^(1/4)*(1 + c^(1/4)*sqrt(x)))/(((-c)^(1/4) + c^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (2*b^2*c^(3/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(((1 - im)*(1 + c^(1/4)*sqrt(x)))/(1 - im*c^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) - (sqrt(2)*a*b*c^(3/4)*sqrt(x)*log(1 - sqrt(2)*c^(1/4)*sqrt(x) + sqrt(c)*x))/(3*d^2*sqrt(d*x)) + (sqrt(2)*a*b*c^(3/4)*sqrt(x)*log(1 + sqrt(2)*c^(1/4)*sqrt(x) + sqrt(c)*x))/(3*d^2*sqrt(d*x)) + (2*b^2*(-c)^(3/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(1 - c*x^2))/(3*d^2*sqrt(d*x)) + (2*b^2*(-c)^(3/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(1 - c*x^2))/(3*d^2*sqrt(d*x)) + (2*b*c^(3/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*(2*a - b*log(1 - c*x^2)))/(3*d^2*sqrt(d*x)) + (2*b*c^(3/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*(2*a - b*log(1 - c*x^2)))/(3*d^2*sqrt(d*x)) - (2*a - b*log(1 - c*x^2))^2/(6*d^2*x*sqrt(d*x)) - (2*a*b*log(1 + c*x^2))/(3*d^2*x*sqrt(d*x)) - (2*b^2*(-c)^(3/4)*sqrt(x)*atan((-c)^(1/4)*sqrt(x))*log(1 + c*x^2))/(3*d^2*sqrt(d*x)) + (2*b^2*c^(3/4)*sqrt(x)*atan(c^(1/4)*sqrt(x))*log(1 + c*x^2))/(3*d^2*sqrt(d*x)) - (2*b^2*(-c)^(3/4)*sqrt(x)*atanh((-c)^(1/4)*sqrt(x))*log(1 + c*x^2))/(3*d^2*sqrt(d*x)) + (2*b^2*c^(3/4)*sqrt(x)*atanh(c^(1/4)*sqrt(x))*log(1 + c*x^2))/(3*d^2*sqrt(d*x)) + (b^2*log(1 - c*x^2)*log(1 + c*x^2))/(3*d^2*x*sqrt(d*x)) - (b^2*log(1 + c*x^2)^2)/(6*d^2*x*sqrt(d*x)) - (2*b^2*(-c)^(3/4)*sqrt(x)*PolyLog(2, 1 - 2/(1 - (-c)^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) - (2*im*b^2*(-c)^(3/4)*sqrt(x)*PolyLog(2, 1 - 2/(1 - im*(-c)^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) + (im*b^2*(-c)^(3/4)*sqrt(x)*PolyLog(2, 1 + (2*(-c)^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((im*sqrt(-sqrt(c)) - (-c)^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (im*b^2*(-c)^(3/4)*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((im*sqrt(-sqrt(c)) + (-c)^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) - (im*b^2*(-c)^(3/4)*sqrt(x)*PolyLog(2, 1 - ((1 + im)*(1 - (-c)^(1/4)*sqrt(x)))/(1 - im*(-c)^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) - (2*im*b^2*(-c)^(3/4)*sqrt(x)*PolyLog(2, 1 - 2/(1 + im*(-c)^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) - (2*b^2*(-c)^(3/4)*sqrt(x)*PolyLog(2, 1 - 2/(1 + (-c)^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) - (b^2*(-c)^(3/4)*sqrt(x)*PolyLog(2, 1 + (2*(-c)^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) - (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) - (b^2*(-c)^(3/4)*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) + (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (b^2*(-c)^(3/4)*sqrt(x)*PolyLog(2, 1 + (2*(-c)^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) - (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (b^2*(-c)^(3/4)*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) + (-c)^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) - (im*b^2*(-c)^(3/4)*sqrt(x)*PolyLog(2, 1 - ((1 - im)*(1 + (-c)^(1/4)*sqrt(x)))/(1 - im*(-c)^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) - (2*b^2*c^(3/4)*sqrt(x)*PolyLog(2, 1 - 2/(1 - c^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) + (im*b^2*(-c)^(3/4)*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 - c^(1/4)*sqrt(x)))/(((-c)^(1/4) - im*c^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (b^2*(-c)^(3/4)*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 - c^(1/4)*sqrt(x)))/(((-c)^(1/4) - c^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) - (2*im*b^2*c^(3/4)*sqrt(x)*PolyLog(2, 1 - 2/(1 - im*c^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) + (im*b^2*c^(3/4)*sqrt(x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((im*sqrt(-sqrt(-c)) - c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (im*b^2*c^(3/4)*sqrt(x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((im*sqrt(-sqrt(-c)) + c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (im*b^2*c^(3/4)*sqrt(x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - (-c)^(1/4)*sqrt(x)))/((im*(-c)^(1/4) - c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (im*b^2*c^(3/4)*sqrt(x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + (-c)^(1/4)*sqrt(x)))/((im*(-c)^(1/4) + c^(1/4))*(1 - im*c^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) - (im*b^2*c^(3/4)*sqrt(x)*PolyLog(2, 1 - ((1 + im)*(1 - c^(1/4)*sqrt(x)))/(1 - im*c^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) - (2*im*b^2*c^(3/4)*sqrt(x)*PolyLog(2, 1 - 2/(1 + im*c^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) - (2*b^2*c^(3/4)*sqrt(x)*PolyLog(2, 1 - 2/(1 + c^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x)) + (b^2*c^(3/4)*sqrt(x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) - c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (b^2*c^(3/4)*sqrt(x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + sqrt(-sqrt(-c))*sqrt(x)))/((sqrt(-sqrt(-c)) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) - (b^2*c^(3/4)*sqrt(x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) - c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) - (b^2*c^(3/4)*sqrt(x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + sqrt(-sqrt(c))*sqrt(x)))/((sqrt(-sqrt(c)) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (b^2*c^(3/4)*sqrt(x)*PolyLog(2, 1 + (2*c^(1/4)*(1 - (-c)^(1/4)*sqrt(x)))/(((-c)^(1/4) - c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (b^2*c^(3/4)*sqrt(x)*PolyLog(2, 1 - (2*c^(1/4)*(1 + (-c)^(1/4)*sqrt(x)))/(((-c)^(1/4) + c^(1/4))*(1 + c^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (im*b^2*(-c)^(3/4)*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + c^(1/4)*sqrt(x)))/(((-c)^(1/4) + im*c^(1/4))*(1 - im*(-c)^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) + (b^2*(-c)^(3/4)*sqrt(x)*PolyLog(2, 1 - (2*(-c)^(1/4)*(1 + c^(1/4)*sqrt(x)))/(((-c)^(1/4) + c^(1/4))*(1 + (-c)^(1/4)*sqrt(x)))))/(3*d^2*sqrt(d*x)) - (im*b^2*c^(3/4)*sqrt(x)*PolyLog(2, 1 - ((1 - im)*(1 + c^(1/4)*sqrt(x)))/(1 - im*c^(1/4)*sqrt(x))))/(3*d^2*sqrt(d*x))]

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

    @test_int [(d*x)^m*(a + b*atanh(c*x^2))^3, x, 0, Unintegrable((d*x)^m*(a + b*atanh(c*x^2))^3, x)]
    @test_int [(d*x)^m*(a + b*atanh(c*x^2))^2, x, 0, Unintegrable((d*x)^m*(a + b*atanh(c*x^2))^2, x)]
    @test_int [(d*x)^m*(a + b*atanh(c*x^2))^1, x, 2, ((d*x)^(1 + m)*(a + b*atanh(c*x^2)))/(d*(1 + m)) - (2*b*c*(d*x)^(3 + m)*HypergeometricFunctions._₂F₁(1, (3 + m)/4, (7 + m)/4, c^2*x^4))/(d^3*(1 + m)*(3 + m))]
    @test_int [(d*x)^m/(a + b*atanh(c*x^2))^1, x, 0, Unintegrable((d*x)^m/(a + b*atanh(c*x^2)), x)]
    @test_int [(d*x)^m/(a + b*atanh(c*x^2))^2, x, 0, Unintegrable((d*x)^m/(a + b*atanh(c*x^2))^2, x)]

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

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

    @test_int [x^11*(a + b*atanh(c*x^3)), x, 5, (b*x^3)/(12*c^3) + (b*x^9)/(36*c) - (b*atanh(c*x^3))/(12*c^4) + (1/12)*x^12*(a + b*atanh(c*x^3))]
    @test_int [x^8*(a + b*atanh(c*x^3)), x, 4, (b*x^6)/(18*c) + (1/9)*x^9*(a + b*atanh(c*x^3)) + (b*log(1 - c^2*x^6))/(18*c^3)]
    @test_int [x^5*(a + b*atanh(c*x^3)), x, 4, (b*x^3)/(6*c) - (b*atanh(c*x^3))/(6*c^2) + (1/6)*x^6*(a + b*atanh(c*x^3))]
    @test_int [x^2*(a + b*atanh(c*x^3)), x, 2, (1/3)*x^3*(a + b*atanh(c*x^3)) + (b*log(1 - c^2*x^6))/(6*c)]
    @test_int [(a + b*atanh(c*x^3))/x^1, x, 2, a*log(x) - (1/6)*b*PolyLog(2, (-c)*x^3) + (1/6)*b*PolyLog(2, c*x^3)]
    @test_int [(a + b*atanh(c*x^3))/x^4, x, 5, -((a + b*atanh(c*x^3))/(3*x^3)) + b*c*log(x) - (1/6)*b*c*log(1 - c^2*x^6)]
    @test_int [(a + b*atanh(c*x^3))/x^7, x, 4, -((b*c)/(6*x^3)) + (1/6)*b*c^2*atanh(c*x^3) - (a + b*atanh(c*x^3))/(6*x^6)]
    @test_int [(a + b*atanh(c*x^3))/x^10, x, 4, -((b*c)/(18*x^6)) - (a + b*atanh(c*x^3))/(9*x^9) + (1/3)*b*c^3*log(x) - (1/18)*b*c^3*log(1 - c^2*x^6)]

    @test_int [x^3*(a + b*atanh(c*x^3)), x, 12, (3*b*x)/(4*c) + (sqrt(3)*b*atan(1/sqrt(3) - (2*c^(1/3)*x)/sqrt(3)))/(8*c^(4/3)) - (sqrt(3)*b*atan(1/sqrt(3) + (2*c^(1/3)*x)/sqrt(3)))/(8*c^(4/3)) - (b*atanh(c^(1/3)*x))/(4*c^(4/3)) + (1/4)*x^4*(a + b*atanh(c*x^3)) + (b*log(1 - c^(1/3)*x + c^(2/3)*x^2))/(16*c^(4/3)) - (b*log(1 + c^(1/3)*x + c^(2/3)*x^2))/(16*c^(4/3))]
    @test_int [x^0*(a + b*atanh(c*x^3)), x, 9, a*x + (sqrt(3)*b*atan((1 + 2*c^(2/3)*x^2)/sqrt(3)))/(2*c^(1/3)) + b*x*atanh(c*x^3) + (b*log(1 - c^(2/3)*x^2))/(2*c^(1/3)) - (b*log(1 + c^(2/3)*x^2 + c^(4/3)*x^4))/(4*c^(1/3))]
    @test_int [(a + b*atanh(c*x^3))/x^3, x, 11, (-(1/4))*sqrt(3)*b*c^(2/3)*atan(1/sqrt(3) - (2*c^(1/3)*x)/sqrt(3)) + (1/4)*sqrt(3)*b*c^(2/3)*atan(1/sqrt(3) + (2*c^(1/3)*x)/sqrt(3)) + (1/2)*b*c^(2/3)*atanh(c^(1/3)*x) - (a + b*atanh(c*x^3))/(2*x^2) - (1/8)*b*c^(2/3)*log(1 - c^(1/3)*x + c^(2/3)*x^2) + (1/8)*b*c^(2/3)*log(1 + c^(1/3)*x + c^(2/3)*x^2)]
    @test_int [(a + b*atanh(c*x^3))/x^6, x, 9, -((3*b*c)/(10*x^2)) - (1/10)*sqrt(3)*b*c^(5/3)*atan((1 + 2*c^(2/3)*x^2)/sqrt(3)) - (a + b*atanh(c*x^3))/(5*x^5) - (1/10)*b*c^(5/3)*log(1 - c^(2/3)*x^2) + (1/20)*b*c^(5/3)*log(1 + c^(2/3)*x^2 + c^(4/3)*x^4)]

    @test_int [x^7*(a + b*atanh(c*x^3)), x, 12, (3*b*x^5)/(40*c) - (sqrt(3)*b*atan(1/sqrt(3) - (2*c^(1/3)*x)/sqrt(3)))/(16*c^(8/3)) + (sqrt(3)*b*atan(1/sqrt(3) + (2*c^(1/3)*x)/sqrt(3)))/(16*c^(8/3)) - (b*atanh(c^(1/3)*x))/(8*c^(8/3)) + (1/8)*x^8*(a + b*atanh(c*x^3)) + (b*log(1 - c^(1/3)*x + c^(2/3)*x^2))/(32*c^(8/3)) - (b*log(1 + c^(1/3)*x + c^(2/3)*x^2))/(32*c^(8/3))]
    @test_int [x^4*(a + b*atanh(c*x^3)), x, 9, (3*b*x^2)/(10*c) - (sqrt(3)*b*atan((1 + 2*c^(2/3)*x^2)/sqrt(3)))/(10*c^(5/3)) + (1/5)*x^5*(a + b*atanh(c*x^3)) + (b*log(1 - c^(2/3)*x^2))/(10*c^(5/3)) - (b*log(1 + c^(2/3)*x^2 + c^(4/3)*x^4))/(20*c^(5/3))]
    @test_int [x^1*(a + b*atanh(c*x^3)), x, 11, -((sqrt(3)*b*atan(1/sqrt(3) - (2*c^(1/3)*x)/sqrt(3)))/(4*c^(2/3))) + (sqrt(3)*b*atan(1/sqrt(3) + (2*c^(1/3)*x)/sqrt(3)))/(4*c^(2/3)) - (b*atanh(c^(1/3)*x))/(2*c^(2/3)) + (1/2)*x^2*(a + b*atanh(c*x^3)) + (b*log(1 - c^(1/3)*x + c^(2/3)*x^2))/(8*c^(2/3)) - (b*log(1 + c^(1/3)*x + c^(2/3)*x^2))/(8*c^(2/3))]
    @test_int [(a + b*atanh(c*x^3))/x^2, x, 8, (1/2)*sqrt(3)*b*c^(1/3)*atan((1 + 2*c^(2/3)*x^2)/sqrt(3)) - (a + b*atanh(c*x^3))/x - (1/2)*b*c^(1/3)*log(1 - c^(2/3)*x^2) + (1/4)*b*c^(1/3)*log(1 + c^(2/3)*x^2 + c^(4/3)*x^4)]
    @test_int [(a + b*atanh(c*x^3))/x^5, x, 12, -((3*b*c)/(4*x)) + (1/8)*sqrt(3)*b*c^(4/3)*atan(1/sqrt(3) - (2*c^(1/3)*x)/sqrt(3)) - (1/8)*sqrt(3)*b*c^(4/3)*atan(1/sqrt(3) + (2*c^(1/3)*x)/sqrt(3)) + (1/4)*b*c^(4/3)*atanh(c^(1/3)*x) - (a + b*atanh(c*x^3))/(4*x^4) - (1/16)*b*c^(4/3)*log(1 - c^(1/3)*x + c^(2/3)*x^2) + (1/16)*b*c^(4/3)*log(1 + c^(1/3)*x + c^(2/3)*x^2)]

    @test_int [x^11*(a + b*atanh(c*x^3))^2, x, 12, (a*b*x^3)/(6*c^3) + (b^2*x^6)/(36*c^2) + (b^2*x^3*atanh(c*x^3))/(6*c^3) + (b*x^9*(a + b*atanh(c*x^3)))/(18*c) - (a + b*atanh(c*x^3))^2/(12*c^4) + (1/12)*x^12*(a + b*atanh(c*x^3))^2 + (b^2*log(1 - c^2*x^6))/(9*c^4)]
    @test_int [x^8*(a + b*atanh(c*x^3))^2, x, 10, (b^2*x^3)/(9*c^2) - (b^2*atanh(c*x^3))/(9*c^3) + (b*x^6*(a + b*atanh(c*x^3)))/(9*c) + (a + b*atanh(c*x^3))^2/(9*c^3) + (1/9)*x^9*(a + b*atanh(c*x^3))^2 - (2*b*(a + b*atanh(c*x^3))*log(2/(1 - c*x^3)))/(9*c^3) - (b^2*PolyLog(2, 1 - 2/(1 - c*x^3)))/(9*c^3)]
    @test_int [x^5*(a + b*atanh(c*x^3))^2, x, 7, (a*b*x^3)/(3*c) + (b^2*x^3*atanh(c*x^3))/(3*c) - (a + b*atanh(c*x^3))^2/(6*c^2) + (1/6)*x^6*(a + b*atanh(c*x^3))^2 + (b^2*log(1 - c^2*x^6))/(6*c^2)]
    @test_int [x^2*(a + b*atanh(c*x^3))^2, x, 6, (a + b*atanh(c*x^3))^2/(3*c) + (1/3)*x^3*(a + b*atanh(c*x^3))^2 - (2*b*(a + b*atanh(c*x^3))*log(2/(1 - c*x^3)))/(3*c) - (b^2*PolyLog(2, 1 - 2/(1 - c*x^3)))/(3*c)]
    @test_int [(a + b*atanh(c*x^3))^2/x^1, x, 7, (2/3)*(a + b*atanh(c*x^3))^2*atanh(1 - 2/(1 - c*x^3)) - (1/3)*b*(a + b*atanh(c*x^3))*PolyLog(2, 1 - 2/(1 - c*x^3)) + (1/3)*b*(a + b*atanh(c*x^3))*PolyLog(2, -1 + 2/(1 - c*x^3)) + (1/6)*b^2*PolyLog(3, 1 - 2/(1 - c*x^3)) - (1/6)*b^2*PolyLog(3, -1 + 2/(1 - c*x^3))]
    @test_int [(a + b*atanh(c*x^3))^2/x^4, x, 5, (1/3)*c*(a + b*atanh(c*x^3))^2 - (a + b*atanh(c*x^3))^2/(3*x^3) + (2/3)*b*c*(a + b*atanh(c*x^3))*log(2 - 2/(1 + c*x^3)) - (1/3)*b^2*c*PolyLog(2, -1 + 2/(1 + c*x^3))]
    @test_int [(a + b*atanh(c*x^3))^2/x^7, x, 9, -((b*c*(a + b*atanh(c*x^3)))/(3*x^3)) + (1/6)*c^2*(a + b*atanh(c*x^3))^2 - (a + b*atanh(c*x^3))^2/(6*x^6) + b^2*c^2*log(x) - (1/6)*b^2*c^2*log(1 - c^2*x^6)]
    @test_int [(a + b*atanh(c*x^3))^2/x^10, x, 9, -((b^2*c^2)/(9*x^3)) + (1/9)*b^2*c^3*atanh(c*x^3) - (b*c*(a + b*atanh(c*x^3)))/(9*x^6) + (1/9)*c^3*(a + b*atanh(c*x^3))^2 - (a + b*atanh(c*x^3))^2/(9*x^9) + (2/9)*b*c^3*(a + b*atanh(c*x^3))*log(2 - 2/(1 + c*x^3)) - (1/9)*b^2*c^3*PolyLog(2, -1 + 2/(1 + c*x^3))]

    #= [x^3*(a + b*atanh(c*x^3))^2, x, 44, 0]
    @test_int [x^0*(a + b*atanh(c*x^3))^2, x, 69, 0]
    @test_int [(a + b*atanh(c*x^3))^2/x^3, x, 24, 0]
    @test_int [(a + b*atanh(c*x^3))^2/x^6, x, 77, 0]

    @test_int [x^1*(a + b*atanh(c*x^3))^2, x, 28, 0]
    @test_int [(a + b*atanh(c*x^3))^2/x^2, x, 47, 0]
    @test_int [(a + b*atanh(c*x^3))^2/x^5, x, 46, 0] =#

    @test_int [x^8*(a + b*atanh(c*x^3))^3, x, 13, (a*b^2*x^3)/(3*c^2) + (b^3*x^3*atanh(c*x^3))/(3*c^2) - (b*(a + b*atanh(c*x^3))^2)/(6*c^3) + (b*x^6*(a + b*atanh(c*x^3))^2)/(6*c) + (a + b*atanh(c*x^3))^3/(9*c^3) + (1/9)*x^9*(a + b*atanh(c*x^3))^3 - (b*(a + b*atanh(c*x^3))^2*log(2/(1 - c*x^3)))/(3*c^3) + (b^3*log(1 - c^2*x^6))/(6*c^3) - (b^2*(a + b*atanh(c*x^3))*PolyLog(2, 1 - 2/(1 - c*x^3)))/(3*c^3) + (b^3*PolyLog(3, 1 - 2/(1 - c*x^3)))/(6*c^3)]
    @test_int [x^5*(a + b*atanh(c*x^3))^3, x, 9, (b*(a + b*atanh(c*x^3))^2)/(2*c^2) + (b*x^3*(a + b*atanh(c*x^3))^2)/(2*c) - (a + b*atanh(c*x^3))^3/(6*c^2) + (1/6)*x^6*(a + b*atanh(c*x^3))^3 - (b^2*(a + b*atanh(c*x^3))*log(2/(1 - c*x^3)))/c^2 - (b^3*PolyLog(2, 1 - 2/(1 - c*x^3)))/(2*c^2)]
    @test_int [x^2*(a + b*atanh(c*x^3))^3, x, 6, (a + b*atanh(c*x^3))^3/(3*c) + (1/3)*x^3*(a + b*atanh(c*x^3))^3 - (b*(a + b*atanh(c*x^3))^2*log(2/(1 - c*x^3)))/c - (b^2*(a + b*atanh(c*x^3))*PolyLog(2, 1 - 2/(1 - c*x^3)))/c + (b^3*PolyLog(3, 1 - 2/(1 - c*x^3)))/(2*c)]
    @test_int [(a + b*atanh(c*x^3))^3/x^1, x, 9, (2/3)*(a + b*atanh(c*x^3))^3*atanh(1 - 2/(1 - c*x^3)) - (1/2)*b*(a + b*atanh(c*x^3))^2*PolyLog(2, 1 - 2/(1 - c*x^3)) + (1/2)*b*(a + b*atanh(c*x^3))^2*PolyLog(2, -1 + 2/(1 - c*x^3)) + (1/2)*b^2*(a + b*atanh(c*x^3))*PolyLog(3, 1 - 2/(1 - c*x^3)) - (1/2)*b^2*(a + b*atanh(c*x^3))*PolyLog(3, -1 + 2/(1 - c*x^3)) - (1/4)*b^3*PolyLog(4, 1 - 2/(1 - c*x^3)) + (1/4)*b^3*PolyLog(4, -1 + 2/(1 - c*x^3))]
    @test_int [(a + b*atanh(c*x^3))^3/x^4, x, 6, (1/3)*c*(a + b*atanh(c*x^3))^3 - (a + b*atanh(c*x^3))^3/(3*x^3) + b*c*(a + b*atanh(c*x^3))^2*log(2 - 2/(1 + c*x^3)) - b^2*c*(a + b*atanh(c*x^3))*PolyLog(2, -1 + 2/(1 + c*x^3)) - (1/2)*b^3*c*PolyLog(3, -1 + 2/(1 + c*x^3))]
    @test_int [(a + b*atanh(c*x^3))^3/x^7, x, 8, (1/2)*b*c^2*(a + b*atanh(c*x^3))^2 - (b*c*(a + b*atanh(c*x^3))^2)/(2*x^3) + (1/6)*c^2*(a + b*atanh(c*x^3))^3 - (a + b*atanh(c*x^3))^3/(6*x^6) + b^2*c^2*(a + b*atanh(c*x^3))*log(2 - 2/(1 + c*x^3)) - (1/2)*b^3*c^2*PolyLog(2, -1 + 2/(1 + c*x^3))]

    #= [x^3*(a + b*atanh(c*x^3))^3, x, 44, 0]
    @test_int [x^0*(a + b*atanh(c*x^3))^3, x, 69, 0]
    @test_int [(a + b*atanh(c*x^3))^3/x^3, x, 24, 0]
    @test_int [(a + b*atanh(c*x^3))^3/x^6, x, 77, 0]

    @test_int [x^1*(a + b*atanh(c*x^3))^3, x, 28, 0]
    @test_int [(a + b*atanh(c*x^3))^3/x^2, x, 47, 0]
    @test_int [(a + b*atanh(c*x^3))^3/x^5, x, 46, 0] =#

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

    @test_int [(d*x)^m*(a + b*atanh(c*x^3))^3, x, 0, Unintegrable((d*x)^m*(a + b*atanh(c*x^3))^3, x)]
    @test_int [(d*x)^m*(a + b*atanh(c*x^3))^2, x, 0, Unintegrable((d*x)^m*(a + b*atanh(c*x^3))^2, x)]
    @test_int [(d*x)^m*(a + b*atanh(c*x^3))^1, x, 2, ((d*x)^(1 + m)*(a + b*atanh(c*x^3)))/(d*(1 + m)) - (3*b*c*(d*x)^(4 + m)*HypergeometricFunctions._₂F₁(1, (4 + m)/6, (10 + m)/6, c^2*x^6))/(d^4*(1 + m)*(4 + m))]
    @test_int [(d*x)^m/(a + b*atanh(c*x^3))^1, x, 0, Unintegrable((d*x)^m/(a + b*atanh(c*x^3)), x)]
    @test_int [(d*x)^m/(a + b*atanh(c*x^3))^2, x, 0, Unintegrable((d*x)^m/(a + b*atanh(c*x^3))^2, x)]

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

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

    @test_int [x^3*(a + b*atanh(c/x)), x, 5, (1/4)*b*c^3*x + (1/12)*b*c*x^3 + (1/4)*x^4*(a + b*atanh(c/x)) - (1/4)*b*c^4*atanh(x/c)]
    @test_int [x^2*(a + b*atanh(c/x)), x, 5, (1/6)*b*c*x^2 + (1/3)*x^3*(a + b*atanh(c/x)) + (1/6)*b*c^3*log(c^2 - x^2)]
    @test_int [x^1*(a + b*atanh(c/x)), x, 4, (b*c*x)/2 + (1/2)*x^2*(a + b*atanh(c/x)) - (1/2)*b*c^2*atanh(x/c)]
    @test_int [x^0*(a + b*atanh(c/x)), x, 4, a*x + b*x*atanh(c/x) + (1/2)*b*c*log(c^2 - x^2)]
    @test_int [(a + b*atanh(c/x))/x^1, x, 2, a*log(x) + (1/2)*b*PolyLog(2, -(c/x)) - (1/2)*b*PolyLog(2, c/x)]
    @test_int [(a + b*atanh(c/x))/x^2, x, 2, -((a + b*atanh(c/x))/x) - (b*log(1 - c^2/x^2))/(2*c)]
    @test_int [(a + b*atanh(c/x))/x^3, x, 4, -(b/(2*c*x)) - (a + b*atanh(c/x))/(2*x^2) + (b*atanh(x/c))/(2*c^2)]
    @test_int [(a + b*atanh(c/x))/x^4, x, 5, -(b/(6*c*x^2)) - (a + b*atanh(c/x))/(3*x^3) + (b*log(x))/(3*c^3) - (b*log(c^2 - x^2))/(6*c^3)]

    @test_int [x^3*(a + b*atanh(c/x))^2, x, 14, (1/12)*b^2*c^2*x^2 + (1/2)*b*c^3*x*(a + b*acoth(x/c)) + (1/6)*b*c*x^3*(a + b*acoth(x/c)) - (1/4)*c^4*(a + b*acoth(x/c))^2 + (1/4)*x^4*(a + b*acoth(x/c))^2 + (1/3)*b^2*c^4*log(1 - c^2/x^2) + (2/3)*b^2*c^4*log(x)]
    @test_int [x^2*(a + b*atanh(c/x))^2, x, 9, (1/3)*b^2*c^2*x - (1/3)*b^2*c^3*acoth(x/c) + (1/3)*b*c*x^2*(a + b*acoth(x/c)) - (1/3)*c^3*(a + b*acoth(x/c))^2 + (1/3)*x^3*(a + b*acoth(x/c))^2 - (2/3)*b*c^3*(a + b*acoth(x/c))*log(2 - 2/(1 + c/x)) + (1/3)*b^2*c^3*PolyLog(2, -1 + 2/(1 + c/x))]
    @test_int [x^1*(a + b*atanh(c/x))^2, x, 9, b*c*x*(a + b*acoth(x/c)) - (1/2)*c^2*(a + b*acoth(x/c))^2 + (1/2)*x^2*(a + b*acoth(x/c))^2 + (1/2)*b^2*c^2*log(1 - c^2/x^2) + b^2*c^2*log(x)]
    @test_int [x^0*(a + b*atanh(c/x))^2, x, 6, c*(a + b*acoth(x/c))^2 + x*(a + b*acoth(x/c))^2 - 2*b*c*(a + b*acoth(x/c))*log((2*c)/(c - x)) - b^2*c*PolyLog(2, -((c + x)/(c - x)))]
    @test_int [(a + b*atanh(c/x))^2/x^1, x, 7, -2*(a + b*acoth(x/c))^2*atanh(1 - 2/(1 - c/x)) + b*(a + b*acoth(x/c))*PolyLog(2, 1 - 2/(1 - c/x)) - b*(a + b*acoth(x/c))*PolyLog(2, -1 + 2/(1 - c/x)) - (1/2)*b^2*PolyLog(3, 1 - 2/(1 - c/x)) + (1/2)*b^2*PolyLog(3, -1 + 2/(1 - c/x))]
    @test_int [(a + b*atanh(c/x))^2/x^2, x, 6, -((a + b*acoth(x/c))^2/c) - (a + b*acoth(x/c))^2/x + (2*b*(a + b*acoth(x/c))*log(2/(1 - c/x)))/c + (b^2*PolyLog(2, 1 - 2/(1 - c/x)))/c]
    @test_int [(a + b*atanh(c/x))^2/x^3, x, 7, -((a*b)/(c*x)) - (b^2*acoth(x/c))/(c*x) + (a + b*acoth(x/c))^2/(2*c^2) - (a + b*acoth(x/c))^2/(2*x^2) - (b^2*log(1 - c^2/x^2))/(2*c^2)]

    @test_int [x^3*(a + b*atanh(c/x))^3, x, 17, (1/4)*b^3*c^3*x - (1/4)*b^3*c^4*acoth(x/c) + (1/4)*b^2*c^2*x^2*(a + b*acoth(x/c)) - b*c^4*(a + b*acoth(x/c))^2 + (3/4)*b*c^3*x*(a + b*acoth(x/c))^2 + (1/4)*b*c*x^3*(a + b*acoth(x/c))^2 - (1/4)*c^4*(a + b*acoth(x/c))^3 + (1/4)*x^4*(a + b*acoth(x/c))^3 - 2*b^2*c^4*(a + b*acoth(x/c))*log(2 - 2/(1 + c/x)) + b^3*c^4*PolyLog(2, -1 + 2/(1 + c/x))]
    @test_int [x^2*(a + b*atanh(c/x))^3, x, 15, b^2*c^2*x*(a + b*acoth(x/c)) - (1/2)*b*c^3*(a + b*acoth(x/c))^2 + (1/2)*b*c*x^2*(a + b*acoth(x/c))^2 - (1/3)*c^3*(a + b*acoth(x/c))^3 + (1/3)*x^3*(a + b*acoth(x/c))^3 - b*c^3*(a + b*acoth(x/c))^2*log(2 - 2/(1 + c/x)) + (1/2)*b^3*c^3*log(1 - c^2/x^2) + b^3*c^3*log(x) + b^2*c^3*(a + b*acoth(x/c))*PolyLog(2, -1 + 2/(1 + c/x)) + (1/2)*b^3*c^3*PolyLog(3, -1 + 2/(1 + c/x))]
    @test_int [x^1*(a + b*atanh(c/x))^3, x, 8, (-(3/2))*b*c^2*(a + b*acoth(x/c))^2 + (3/2)*b*c*x*(a + b*acoth(x/c))^2 - (1/2)*c^2*(a + b*acoth(x/c))^3 + (1/2)*x^2*(a + b*acoth(x/c))^3 - 3*b^2*c^2*(a + b*acoth(x/c))*log(2 - 2/(1 + c/x)) + (3/2)*b^3*c^2*PolyLog(2, -1 + 2/(1 + c/x))]
    @test_int [x^0*(a + b*atanh(c/x))^3, x, 6, c*(a + b*acoth(x/c))^3 + x*(a + b*acoth(x/c))^3 - 3*b*c*(a + b*acoth(x/c))^2*log((2*c)/(c - x)) - 3*b^2*c*(a + b*acoth(x/c))*PolyLog(2, 1 - (2*c)/(c - x)) + (3/2)*b^3*c*PolyLog(3, 1 - (2*c)/(c - x))]
    @test_int [(a + b*atanh(c/x))^3/x^1, x, 9, -2*(a + b*acoth(x/c))^3*atanh(1 - 2/(1 - c/x)) + (3/2)*b*(a + b*acoth(x/c))^2*PolyLog(2, 1 - 2/(1 - c/x)) - (3/2)*b*(a + b*acoth(x/c))^2*PolyLog(2, -1 + 2/(1 - c/x)) - (3/2)*b^2*(a + b*acoth(x/c))*PolyLog(3, 1 - 2/(1 - c/x)) + (3/2)*b^2*(a + b*acoth(x/c))*PolyLog(3, -1 + 2/(1 - c/x)) + (3/4)*b^3*PolyLog(4, 1 - 2/(1 - c/x)) - (3/4)*b^3*PolyLog(4, -1 + 2/(1 - c/x))]
    @test_int [(a + b*atanh(c/x))^3/x^2, x, 6, -((a + b*acoth(x/c))^3/c) - (a + b*acoth(x/c))^3/x + (3*b*(a + b*acoth(x/c))^2*log(2/(1 - c/x)))/c + (3*b^2*(a + b*acoth(x/c))*PolyLog(2, 1 - 2/(1 - c/x)))/c - (3*b^3*PolyLog(3, 1 - 2/(1 - c/x)))/(2*c)]
    @test_int [(a + b*atanh(c/x))^3/x^3, x, 9, -((3*b*(a + b*acoth(x/c))^2)/(2*c^2)) - (3*b*(a + b*acoth(x/c))^2)/(2*c*x) + (a + b*acoth(x/c))^3/(2*c^2) - (a + b*acoth(x/c))^3/(2*x^2) + (3*b^2*(a + b*acoth(x/c))*log(2/(1 - c/x)))/c^2 + (3*b^3*PolyLog(2, 1 - 2/(1 - c/x)))/(2*c^2)]

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

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

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

    @test_int [x^4*(a + b*atanh(c/x^2)), x, 6, (2/15)*b*c*x^3 + (1/5)*b*c^(5/2)*atan(x/sqrt(c)) + (1/5)*x^5*(a + b*atanh(c/x^2)) - (1/5)*b*c^(5/2)*atanh(x/sqrt(c))]
    @test_int [x^2*(a + b*atanh(c/x^2)), x, 6, (2*b*c*x)/3 - (1/3)*b*c^(3/2)*atan(x/sqrt(c)) + (1/3)*x^3*(a + b*atanh(c/x^2)) - (1/3)*b*c^(3/2)*atanh(x/sqrt(c))]
    @test_int [x^0*(a + b*atanh(c/x^2)), x, 6, a*x + b*sqrt(c)*atan(x/sqrt(c)) + b*x*atanh(c/x^2) - b*sqrt(c)*atanh(x/sqrt(c))]
    @test_int [(a + b*atanh(c/x^2))/x^2, x, 5, (b*atan(x/sqrt(c)))/sqrt(c) - (a + b*atanh(c/x^2))/x + (b*atanh(x/sqrt(c)))/sqrt(c)]
    @test_int [(a + b*atanh(c/x^2))/x^4, x, 6, -((2*b)/(3*c*x)) - (b*atan(x/sqrt(c)))/(3*c^(3/2)) - (a + b*atanh(c/x^2))/(3*x^3) + (b*atanh(x/sqrt(c)))/(3*c^(3/2))]
    @test_int [(a + b*atanh(c/x^2))/x^6, x, 6, -((2*b)/(15*c*x^3)) + (b*atan(x/sqrt(c)))/(5*c^(5/2)) - (a + b*atanh(c/x^2))/(5*x^5) + (b*atanh(x/sqrt(c)))/(5*c^(5/2))]

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

    @test_int [x^4*(a + b*atanh(c/x^2))^2, x, 98, (8/15)*b^2*c^2*x + (2/15)*a*b*c*x^3 + (2/5)*a*b*c^(5/2)*atan(x/sqrt(c)) - (4/15)*b^2*c^(5/2)*atan(x/sqrt(c)) - (1/5)*im*b^2*c^(5/2)*atan(x/sqrt(c))^2 - (4/15)*b^2*c^(5/2)*atanh(x/sqrt(c)) + (1/5)*b^2*c^(5/2)*atanh(x/sqrt(c))^2 + (2/5)*b^2*c^(5/2)*atan(x/sqrt(c))*log(2 - (2*sqrt(c))/(sqrt(c) - im*x)) - (1/15)*b^2*c*x^3*log(1 - c/x^2) - (1/5)*b^2*c^(5/2)*atan(x/sqrt(c))*log(1 - c/x^2) + (1/15)*b*c*x^3*(2*a - b*log(1 - c/x^2)) - (1/5)*b*c^(5/2)*atanh(x/sqrt(c))*(2*a - b*log(1 - c/x^2)) + (1/20)*x^5*(2*a - b*log(1 - c/x^2))^2 + (2/15)*b^2*c*x^3*log(1 + c/x^2) + (1/5)*a*b*x^5*log(1 + c/x^2) + (1/5)*b^2*c^(5/2)*atan(x/sqrt(c))*log(1 + c/x^2) - (1/5)*b^2*c^(5/2)*atanh(x/sqrt(c))*log(1 + c/x^2) - (1/10)*b^2*x^5*log(1 - c/x^2)*log(1 + c/x^2) + (1/20)*b^2*x^5*log(1 + c/x^2)^2 - (2/5)*b^2*c^(5/2)*atan(x/sqrt(c))*log((2*sqrt(c))/(sqrt(c) - im*x)) + (1/5)*b^2*c^(5/2)*atan(x/sqrt(c))*log(((1 + im)*(sqrt(c) - x))/(sqrt(c) - im*x)) - (2/5)*b^2*c^(5/2)*atanh(x/sqrt(c))*log((2*sqrt(c))/(sqrt(c) + x)) + (1/5)*b^2*c^(5/2)*atanh(x/sqrt(c))*log((2*sqrt(c)*(sqrt(-c) - x))/((sqrt(-c) - sqrt(c))*(sqrt(c) + x))) + (1/5)*b^2*c^(5/2)*atanh(x/sqrt(c))*log((2*sqrt(c)*(sqrt(-c) + x))/((sqrt(-c) + sqrt(c))*(sqrt(c) + x))) + (1/5)*b^2*c^(5/2)*atan(x/sqrt(c))*log(((1 - im)*(sqrt(c) + x))/(sqrt(c) - im*x)) + (2/5)*b^2*c^(5/2)*atanh(x/sqrt(c))*log(2 - (2*sqrt(c))/(sqrt(c) + x)) + (1/5)*im*b^2*c^(5/2)*PolyLog(2, 1 - (2*sqrt(c))/(sqrt(c) - im*x)) - (1/5)*im*b^2*c^(5/2)*PolyLog(2, -1 + (2*sqrt(c))/(sqrt(c) - im*x)) - (1/10)*im*b^2*c^(5/2)*PolyLog(2, 1 - ((1 + im)*(sqrt(c) - x))/(sqrt(c) - im*x)) + (1/5)*b^2*c^(5/2)*PolyLog(2, -(x/sqrt(c))) - (1/5)*im*b^2*c^(5/2)*PolyLog(2, -((im*x)/sqrt(c))) + (1/5)*im*b^2*c^(5/2)*PolyLog(2, (im*x)/sqrt(c)) - (1/5)*b^2*c^(5/2)*PolyLog(2, x/sqrt(c)) + (1/5)*b^2*c^(5/2)*PolyLog(2, 1 - (2*sqrt(c))/(sqrt(c) + x)) - (1/5)*b^2*c^(5/2)*PolyLog(2, -1 + (2*sqrt(c))/(sqrt(c) + x)) - (1/10)*b^2*c^(5/2)*PolyLog(2, 1 - (2*sqrt(c)*(sqrt(-c) - x))/((sqrt(-c) - sqrt(c))*(sqrt(c) + x))) - (1/10)*b^2*c^(5/2)*PolyLog(2, 1 - (2*sqrt(c)*(sqrt(-c) + x))/((sqrt(-c) + sqrt(c))*(sqrt(c) + x))) - (1/10)*im*b^2*c^(5/2)*PolyLog(2, 1 - ((1 - im)*(sqrt(c) + x))/(sqrt(c) - im*x))]
    @test_int [x^2*(a + b*atanh(c/x^2))^2, x, 80, (4/3)*a*b*c*x - (2/3)*a*b*c^(3/2)*atan(x/sqrt(c)) + (4/3)*b^2*c^(3/2)*atan(x/sqrt(c)) + (1/3)*im*b^2*c^(3/2)*atan(x/sqrt(c))^2 - (4/3)*b^2*c^(3/2)*atanh(x/sqrt(c)) + (1/3)*b^2*c^(3/2)*atanh(x/sqrt(c))^2 - (2/3)*b^2*c^(3/2)*atan(x/sqrt(c))*log(2 - (2*sqrt(c))/(sqrt(c) - im*x)) - (2/3)*b^2*c*x*log(1 - c/x^2) + (1/3)*b^2*c^(3/2)*atan(x/sqrt(c))*log(1 - c/x^2) - (1/3)*b*c^(3/2)*atanh(x/sqrt(c))*(2*a - b*log(1 - c/x^2)) + (1/12)*x^3*(2*a - b*log(1 - c/x^2))^2 + (2/3)*b^2*c*x*log(1 + c/x^2) + (1/3)*a*b*x^3*log(1 + c/x^2) - (1/3)*b^2*c^(3/2)*atan(x/sqrt(c))*log(1 + c/x^2) - (1/3)*b^2*c^(3/2)*atanh(x/sqrt(c))*log(1 + c/x^2) - (1/6)*b^2*x^3*log(1 - c/x^2)*log(1 + c/x^2) + (1/12)*b^2*x^3*log(1 + c/x^2)^2 + (2/3)*b^2*c^(3/2)*atan(x/sqrt(c))*log((2*sqrt(c))/(sqrt(c) - im*x)) - (1/3)*b^2*c^(3/2)*atan(x/sqrt(c))*log(((1 + im)*(sqrt(c) - x))/(sqrt(c) - im*x)) - (2/3)*b^2*c^(3/2)*atanh(x/sqrt(c))*log((2*sqrt(c))/(sqrt(c) + x)) + (1/3)*b^2*c^(3/2)*atanh(x/sqrt(c))*log((2*sqrt(c)*(sqrt(-c) - x))/((sqrt(-c) - sqrt(c))*(sqrt(c) + x))) + (1/3)*b^2*c^(3/2)*atanh(x/sqrt(c))*log((2*sqrt(c)*(sqrt(-c) + x))/((sqrt(-c) + sqrt(c))*(sqrt(c) + x))) - (1/3)*b^2*c^(3/2)*atan(x/sqrt(c))*log(((1 - im)*(sqrt(c) + x))/(sqrt(c) - im*x)) + (2/3)*b^2*c^(3/2)*atanh(x/sqrt(c))*log(2 - (2*sqrt(c))/(sqrt(c) + x)) - (1/3)*im*b^2*c^(3/2)*PolyLog(2, 1 - (2*sqrt(c))/(sqrt(c) - im*x)) + (1/3)*im*b^2*c^(3/2)*PolyLog(2, -1 + (2*sqrt(c))/(sqrt(c) - im*x)) + (1/6)*im*b^2*c^(3/2)*PolyLog(2, 1 - ((1 + im)*(sqrt(c) - x))/(sqrt(c) - im*x)) + (1/3)*b^2*c^(3/2)*PolyLog(2, -(x/sqrt(c))) + (1/3)*im*b^2*c^(3/2)*PolyLog(2, -((im*x)/sqrt(c))) - (1/3)*im*b^2*c^(3/2)*PolyLog(2, (im*x)/sqrt(c)) - (1/3)*b^2*c^(3/2)*PolyLog(2, x/sqrt(c)) + (1/3)*b^2*c^(3/2)*PolyLog(2, 1 - (2*sqrt(c))/(sqrt(c) + x)) - (1/3)*b^2*c^(3/2)*PolyLog(2, -1 + (2*sqrt(c))/(sqrt(c) + x)) - (1/6)*b^2*c^(3/2)*PolyLog(2, 1 - (2*sqrt(c)*(sqrt(-c) - x))/((sqrt(-c) - sqrt(c))*(sqrt(c) + x))) - (1/6)*b^2*c^(3/2)*PolyLog(2, 1 - (2*sqrt(c)*(sqrt(-c) + x))/((sqrt(-c) + sqrt(c))*(sqrt(c) + x))) + (1/6)*im*b^2*c^(3/2)*PolyLog(2, 1 - ((1 - im)*(sqrt(c) + x))/(sqrt(c) - im*x))]
    @test_int [x^0*(a + b*atanh(c/x^2))^2, x, 100, a^2*x + 2*a*b*sqrt(c)*atan(x/sqrt(c)) - 2*a*b*sqrt(c)*atanh(x/sqrt(c)) - a*b*x*log(1 - c/x^2) - b^2*sqrt(c)*atan(x/sqrt(c))*log(1 - c/x^2) + (1/4)*b^2*x*log(1 - c/x^2)^2 + a*b*x*log(1 + c/x^2) - b^2*sqrt(c)*atanh(x/sqrt(c))*log(1 + c/x^2) - (1/2)*b^2*x*log(1 - c/x^2)*log(1 + c/x^2) + (1/4)*b^2*x*log(1 + c/x^2)^2 - (1/2)*b^2*sqrt(-c)*log(1 + c/x^2)*log(sqrt(-c) - x) + (1/4)*b^2*sqrt(-c)*log(sqrt(-c) - x)^2 - (1/2)*b^2*sqrt(c)*log(1 - c/x^2)*log(sqrt(c) - x) + (1/4)*b^2*sqrt(c)*log(sqrt(c) - x)^2 - 2*b^2*sqrt(c)*atan(x/sqrt(c))*log((2*sqrt(c))/(sqrt(c) - im*x)) + b^2*sqrt(c)*atan(x/sqrt(c))*log(((1 + im)*(sqrt(c) - x))/(sqrt(c) - im*x)) - b^2*sqrt(-c)*log(sqrt(-c) - x)*log(x/sqrt(-c)) - b^2*sqrt(c)*log(sqrt(c) - x)*log(x/sqrt(c)) + (1/2)*b^2*sqrt(-c)*log(1 + c/x^2)*log(sqrt(-c) + x) - (1/2)*b^2*sqrt(-c)*log((sqrt(-c) - x)/(2*sqrt(-c)))*log(sqrt(-c) + x) + b^2*sqrt(-c)*log(-(x/sqrt(-c)))*log(sqrt(-c) + x) - (1/4)*b^2*sqrt(-c)*log(sqrt(-c) + x)^2 + (1/2)*b^2*sqrt(-c)*log(sqrt(-c) - x)*log((sqrt(-c) + x)/(2*sqrt(-c))) - 2*b^2*sqrt(c)*atanh(x/sqrt(c))*log((2*sqrt(c))/(sqrt(c) + x)) + b^2*sqrt(c)*atanh(x/sqrt(c))*log((2*sqrt(c)*(sqrt(-c) - x))/((sqrt(-c) - sqrt(c))*(sqrt(c) + x))) + b^2*sqrt(c)*atanh(x/sqrt(c))*log((2*sqrt(c)*(sqrt(-c) + x))/((sqrt(-c) + sqrt(c))*(sqrt(c) + x))) + (1/2)*b^2*sqrt(c)*log(1 - c/x^2)*log(sqrt(c) + x) - (1/2)*b^2*sqrt(c)*log((sqrt(c) - x)/(2*sqrt(c)))*log(sqrt(c) + x) + b^2*sqrt(c)*log(-(x/sqrt(c)))*log(sqrt(c) + x) - (1/4)*b^2*sqrt(c)*log(sqrt(c) + x)^2 + (1/2)*b^2*sqrt(c)*log(sqrt(c) - x)*log((sqrt(c) + x)/(2*sqrt(c))) + b^2*sqrt(c)*atan(x/sqrt(c))*log(((1 - im)*(sqrt(c) + x))/(sqrt(c) - im*x)) + im*b^2*sqrt(c)*PolyLog(2, 1 - (2*sqrt(c))/(sqrt(c) - im*x)) - (1/2)*im*b^2*sqrt(c)*PolyLog(2, 1 - ((1 + im)*(sqrt(c) - x))/(sqrt(c) - im*x)) + b^2*sqrt(c)*PolyLog(2, -(x/sqrt(c))) - im*b^2*sqrt(c)*PolyLog(2, -((im*x)/sqrt(c))) + im*b^2*sqrt(c)*PolyLog(2, (im*x)/sqrt(c)) - b^2*sqrt(c)*PolyLog(2, x/sqrt(c)) - (1/2)*b^2*sqrt(c)*PolyLog(2, (sqrt(c) + x)/(2*sqrt(c))) + (1/2)*b^2*sqrt(-c)*PolyLog(2, (1/2)*(1 - x/sqrt(-c))) - b^2*sqrt(-c)*PolyLog(2, 1 - x/sqrt(-c)) + b^2*sqrt(-c)*PolyLog(2, 1 + x/sqrt(-c)) - (1/2)*b^2*sqrt(-c)*PolyLog(2, (c - sqrt(-c)*x)/(2*c)) - b^2*sqrt(c)*PolyLog(2, 1 - x/sqrt(c)) + (1/2)*b^2*sqrt(c)*PolyLog(2, 1/2 - x/(2*sqrt(c))) + b^2*sqrt(c)*PolyLog(2, 1 + x/sqrt(c)) + b^2*sqrt(c)*PolyLog(2, 1 - (2*sqrt(c))/(sqrt(c) + x)) - (1/2)*b^2*sqrt(c)*PolyLog(2, 1 - (2*sqrt(c)*(sqrt(-c) - x))/((sqrt(-c) - sqrt(c))*(sqrt(c) + x))) - (1/2)*b^2*sqrt(c)*PolyLog(2, 1 - (2*sqrt(c)*(sqrt(-c) + x))/((sqrt(-c) + sqrt(c))*(sqrt(c) + x))) - (1/2)*im*b^2*sqrt(c)*PolyLog(2, 1 - ((1 - im)*(sqrt(c) + x))/(sqrt(c) - im*x))]
    @test_int [(a + b*atanh(c/x^2))^2/x^2, x, 72, (2*a*b)/x - (2*a*b*acot(x/sqrt(c)))/sqrt(c) - (2*b^2*acot(x/sqrt(c)))/sqrt(c) - (2*b^2*acoth(x/sqrt(c)))/sqrt(c) - (2*b^2*atan(x/sqrt(c)))/sqrt(c) - (im*b^2*atan(x/sqrt(c))^2)/sqrt(c) + (2*b^2*atanh(x/sqrt(c)))/sqrt(c) - (b^2*atanh(x/sqrt(c))^2)/sqrt(c) + (2*b^2*atan(x/sqrt(c))*log(2 - (2*sqrt(c))/(sqrt(c) - im*x)))/sqrt(c) - (b^2*log(1 - c/x^2))/x + (b^2*acot(x/sqrt(c))*log(1 - c/x^2))/sqrt(c) - (b*(2*a - b*log(1 - c/x^2)))/x + (b*atanh(x/sqrt(c))*(2*a - b*log(1 - c/x^2)))/sqrt(c) - (2*a - b*log(1 - c/x^2))^2/(4*x) - (a*b*log(1 + c/x^2))/x + (b^2*acoth(x/sqrt(c))*log(1 + c/x^2))/sqrt(c) + (b^2*atan(x/sqrt(c))*log(1 + c/x^2))/sqrt(c) + (b^2*log(1 - c/x^2)*log(1 + c/x^2))/(2*x) - (b^2*log(1 + c/x^2)^2)/(4*x) + (2*b^2*acot(x/sqrt(c))*log(2/(1 - (im*sqrt(c))/x)))/sqrt(c) - (b^2*acot(x/sqrt(c))*log(((1 + im)*(1 - sqrt(c)/x))/(1 - (im*sqrt(c))/x)))/sqrt(c) + (2*b^2*acoth(x/sqrt(c))*log(2/(1 + sqrt(c)/x)))/sqrt(c) - (b^2*acoth(x/sqrt(c))*log(-((2*sqrt(c)*(1 - sqrt(-c)/x))/((sqrt(-c) - sqrt(c))*(1 + sqrt(c)/x)))))/sqrt(c) - (b^2*acoth(x/sqrt(c))*log((2*sqrt(c)*(1 + sqrt(-c)/x))/((sqrt(-c) + sqrt(c))*(1 + sqrt(c)/x))))/sqrt(c) - (b^2*acot(x/sqrt(c))*log(((1 - im)*(1 + sqrt(c)/x))/(1 - (im*sqrt(c))/x)))/sqrt(c) - (2*b^2*atanh(x/sqrt(c))*log(2 - (2*sqrt(c))/(sqrt(c) + x)))/sqrt(c) - (im*b^2*PolyLog(2, 1 - 2/(1 - (im*sqrt(c))/x)))/sqrt(c) + (im*b^2*PolyLog(2, 1 - ((1 + im)*(1 - sqrt(c)/x))/(1 - (im*sqrt(c))/x)))/(2*sqrt(c)) - (b^2*PolyLog(2, 1 - 2/(1 + sqrt(c)/x)))/sqrt(c) + (b^2*PolyLog(2, 1 + (2*sqrt(c)*(1 - sqrt(-c)/x))/((sqrt(-c) - sqrt(c))*(1 + sqrt(c)/x))))/(2*sqrt(c)) + (b^2*PolyLog(2, 1 - (2*sqrt(c)*(1 + sqrt(-c)/x))/((sqrt(-c) + sqrt(c))*(1 + sqrt(c)/x))))/(2*sqrt(c)) + (im*b^2*PolyLog(2, 1 - ((1 - im)*(1 + sqrt(c)/x))/(1 - (im*sqrt(c))/x)))/(2*sqrt(c)) - (im*b^2*PolyLog(2, -1 + (2*sqrt(c))/(sqrt(c) - im*x)))/sqrt(c) + (b^2*PolyLog(2, -1 + (2*sqrt(c))/(sqrt(c) + x)))/sqrt(c)]
    @test_int [(a + b*atanh(c/x^2))^2/x^4, x, 105, (2*a*b)/(9*x^3) - (2*a*b)/(3*c*x) - (2*a*b*atan(x/sqrt(c)))/(3*c^(3/2)) + (4*b^2*atan(x/sqrt(c)))/(3*c^(3/2)) + (im*b^2*atan(x/sqrt(c))^2)/(3*c^(3/2)) + (4*b^2*atanh(x/sqrt(c)))/(3*c^(3/2)) - (b^2*atanh(x/sqrt(c))^2)/(3*c^(3/2)) - (2*b^2*atan(x/sqrt(c))*log(2 - (2*sqrt(c))/(sqrt(c) - im*x)))/(3*c^(3/2)) - (b^2*log(1 - c/x^2))/(9*x^3) + (b^2*log(1 - c/x^2))/(3*c*x) + (b^2*atan(x/sqrt(c))*log(1 - c/x^2))/(3*c^(3/2)) - (b*(2*a - b*log(1 - c/x^2)))/(9*x^3) - (b*(2*a - b*log(1 - c/x^2)))/(3*c*x) + (b*atanh(x/sqrt(c))*(2*a - b*log(1 - c/x^2)))/(3*c^(3/2)) - (2*a - b*log(1 - c/x^2))^2/(12*x^3) - (a*b*log(1 + c/x^2))/(3*x^3) - (2*b^2*log(1 + c/x^2))/(3*c*x) - (b^2*atan(x/sqrt(c))*log(1 + c/x^2))/(3*c^(3/2)) + (b^2*atanh(x/sqrt(c))*log(1 + c/x^2))/(3*c^(3/2)) + (b^2*log(1 - c/x^2)*log(1 + c/x^2))/(6*x^3) - (b^2*log(1 + c/x^2)^2)/(12*x^3) + (2*b^2*atan(x/sqrt(c))*log((2*sqrt(c))/(sqrt(c) - im*x)))/(3*c^(3/2)) - (b^2*atan(x/sqrt(c))*log(((1 + im)*(sqrt(c) - x))/(sqrt(c) - im*x)))/(3*c^(3/2)) + (2*b^2*atanh(x/sqrt(c))*log((2*sqrt(c))/(sqrt(c) + x)))/(3*c^(3/2)) - (b^2*atanh(x/sqrt(c))*log((2*sqrt(c)*(sqrt(-c) - x))/((sqrt(-c) - sqrt(c))*(sqrt(c) + x))))/(3*c^(3/2)) - (b^2*atanh(x/sqrt(c))*log((2*sqrt(c)*(sqrt(-c) + x))/((sqrt(-c) + sqrt(c))*(sqrt(c) + x))))/(3*c^(3/2)) - (b^2*atan(x/sqrt(c))*log(((1 - im)*(sqrt(c) + x))/(sqrt(c) - im*x)))/(3*c^(3/2)) - (2*b^2*atanh(x/sqrt(c))*log(2 - (2*sqrt(c))/(sqrt(c) + x)))/(3*c^(3/2)) - (im*b^2*PolyLog(2, 1 - (2*sqrt(c))/(sqrt(c) - im*x)))/(3*c^(3/2)) + (im*b^2*PolyLog(2, -1 + (2*sqrt(c))/(sqrt(c) - im*x)))/(3*c^(3/2)) + (im*b^2*PolyLog(2, 1 - ((1 + im)*(sqrt(c) - x))/(sqrt(c) - im*x)))/(6*c^(3/2)) - (b^2*PolyLog(2, -(x/sqrt(c))))/(3*c^(3/2)) + (im*b^2*PolyLog(2, -((im*x)/sqrt(c))))/(3*c^(3/2)) - (im*b^2*PolyLog(2, (im*x)/sqrt(c)))/(3*c^(3/2)) + (b^2*PolyLog(2, x/sqrt(c)))/(3*c^(3/2)) - (b^2*PolyLog(2, 1 - (2*sqrt(c))/(sqrt(c) + x)))/(3*c^(3/2)) + (b^2*PolyLog(2, -1 + (2*sqrt(c))/(sqrt(c) + x)))/(3*c^(3/2)) + (b^2*PolyLog(2, 1 - (2*sqrt(c)*(sqrt(-c) - x))/((sqrt(-c) - sqrt(c))*(sqrt(c) + x))))/(6*c^(3/2)) + (b^2*PolyLog(2, 1 - (2*sqrt(c)*(sqrt(-c) + x))/((sqrt(-c) + sqrt(c))*(sqrt(c) + x))))/(6*c^(3/2)) + (im*b^2*PolyLog(2, 1 - ((1 - im)*(sqrt(c) + x))/(sqrt(c) - im*x)))/(6*c^(3/2))]
    @test_int [(a + b*atanh(c/x^2))^2/x^6, x, 130, (2*a*b)/(25*x^5) - (2*a*b)/(15*c*x^3) + (2*a*b)/(5*c^2*x) - (8*b^2)/(15*c^2*x) + (2*a*b*atan(x/sqrt(c)))/(5*c^(5/2)) - (4*b^2*atan(x/sqrt(c)))/(15*c^(5/2)) - (im*b^2*atan(x/sqrt(c))^2)/(5*c^(5/2)) + (4*b^2*atanh(x/sqrt(c)))/(15*c^(5/2)) - (b^2*atanh(x/sqrt(c))^2)/(5*c^(5/2)) + (2*b^2*atan(x/sqrt(c))*log(2 - (2*sqrt(c))/(sqrt(c) - im*x)))/(5*c^(5/2)) - (b^2*log(1 - c/x^2))/(25*x^5) + (b^2*log(1 - c/x^2))/(15*c*x^3) - (b^2*log(1 - c/x^2))/(5*c^2*x) - (b^2*atan(x/sqrt(c))*log(1 - c/x^2))/(5*c^(5/2)) - (b*(2*a - b*log(1 - c/x^2)))/(25*x^5) - (b*(2*a - b*log(1 - c/x^2)))/(15*c*x^3) - (b*(2*a - b*log(1 - c/x^2)))/(5*c^2*x) + (b*atanh(x/sqrt(c))*(2*a - b*log(1 - c/x^2)))/(5*c^(5/2)) - (2*a - b*log(1 - c/x^2))^2/(20*x^5) - (a*b*log(1 + c/x^2))/(5*x^5) - (2*b^2*log(1 + c/x^2))/(15*c*x^3) + (b^2*atan(x/sqrt(c))*log(1 + c/x^2))/(5*c^(5/2)) + (b^2*atanh(x/sqrt(c))*log(1 + c/x^2))/(5*c^(5/2)) + (b^2*log(1 - c/x^2)*log(1 + c/x^2))/(10*x^5) - (b^2*log(1 + c/x^2)^2)/(20*x^5) - (2*b^2*atan(x/sqrt(c))*log((2*sqrt(c))/(sqrt(c) - im*x)))/(5*c^(5/2)) + (b^2*atan(x/sqrt(c))*log(((1 + im)*(sqrt(c) - x))/(sqrt(c) - im*x)))/(5*c^(5/2)) + (2*b^2*atanh(x/sqrt(c))*log((2*sqrt(c))/(sqrt(c) + x)))/(5*c^(5/2)) - (b^2*atanh(x/sqrt(c))*log((2*sqrt(c)*(sqrt(-c) - x))/((sqrt(-c) - sqrt(c))*(sqrt(c) + x))))/(5*c^(5/2)) - (b^2*atanh(x/sqrt(c))*log((2*sqrt(c)*(sqrt(-c) + x))/((sqrt(-c) + sqrt(c))*(sqrt(c) + x))))/(5*c^(5/2)) + (b^2*atan(x/sqrt(c))*log(((1 - im)*(sqrt(c) + x))/(sqrt(c) - im*x)))/(5*c^(5/2)) - (2*b^2*atanh(x/sqrt(c))*log(2 - (2*sqrt(c))/(sqrt(c) + x)))/(5*c^(5/2)) + (im*b^2*PolyLog(2, 1 - (2*sqrt(c))/(sqrt(c) - im*x)))/(5*c^(5/2)) - (im*b^2*PolyLog(2, -1 + (2*sqrt(c))/(sqrt(c) - im*x)))/(5*c^(5/2)) - (im*b^2*PolyLog(2, 1 - ((1 + im)*(sqrt(c) - x))/(sqrt(c) - im*x)))/(10*c^(5/2)) - (b^2*PolyLog(2, -(x/sqrt(c))))/(5*c^(5/2)) - (im*b^2*PolyLog(2, -((im*x)/sqrt(c))))/(5*c^(5/2)) + (im*b^2*PolyLog(2, (im*x)/sqrt(c)))/(5*c^(5/2)) + (b^2*PolyLog(2, x/sqrt(c)))/(5*c^(5/2)) - (b^2*PolyLog(2, 1 - (2*sqrt(c))/(sqrt(c) + x)))/(5*c^(5/2)) + (b^2*PolyLog(2, -1 + (2*sqrt(c))/(sqrt(c) + x)))/(5*c^(5/2)) + (b^2*PolyLog(2, 1 - (2*sqrt(c)*(sqrt(-c) - x))/((sqrt(-c) - sqrt(c))*(sqrt(c) + x))))/(10*c^(5/2)) + (b^2*PolyLog(2, 1 - (2*sqrt(c)*(sqrt(-c) + x))/((sqrt(-c) + sqrt(c))*(sqrt(c) + x))))/(10*c^(5/2)) - (im*b^2*PolyLog(2, 1 - ((1 - im)*(sqrt(c) + x))/(sqrt(c) - im*x)))/(10*c^(5/2))]

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

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

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

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

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

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

    @test_int [x^3*(a + b*atanh(c*sqrt(x)))^2, x, 22, (a*b*sqrt(x))/(2*c^7) + (71*b^2*x)/(420*c^6) + (3*b^2*x^2)/(70*c^4) + (b^2*x^3)/(84*c^2) + (b^2*sqrt(x)*atanh(c*sqrt(x)))/(2*c^7) + (b*x^(3/2)*(a + b*atanh(c*sqrt(x))))/(6*c^5) + (b*x^(5/2)*(a + b*atanh(c*sqrt(x))))/(10*c^3) + (b*x^(7/2)*(a + b*atanh(c*sqrt(x))))/(14*c) - (a + b*atanh(c*sqrt(x)))^2/(4*c^8) + (1/4)*x^4*(a + b*atanh(c*sqrt(x)))^2 + (44*b^2*log(1 - c^2*x))/(105*c^8)]
    @test_int [x^2*(a + b*atanh(c*sqrt(x)))^2, x, 17, (2*a*b*sqrt(x))/(3*c^5) + (8*b^2*x)/(45*c^4) + (b^2*x^2)/(30*c^2) + (2*b^2*sqrt(x)*atanh(c*sqrt(x)))/(3*c^5) + (2*b*x^(3/2)*(a + b*atanh(c*sqrt(x))))/(9*c^3) + (2*b*x^(5/2)*(a + b*atanh(c*sqrt(x))))/(15*c) - (a + b*atanh(c*sqrt(x)))^2/(3*c^6) + (1/3)*x^3*(a + b*atanh(c*sqrt(x)))^2 + (23*b^2*log(1 - c^2*x))/(45*c^6)]
    @test_int [x^1*(a + b*atanh(c*sqrt(x)))^2, x, 12, (a*b*sqrt(x))/c^3 + (b^2*x)/(6*c^2) + (b^2*sqrt(x)*atanh(c*sqrt(x)))/c^3 + (b*x^(3/2)*(a + b*atanh(c*sqrt(x))))/(3*c) - (a + b*atanh(c*sqrt(x)))^2/(2*c^4) + (1/2)*x^2*(a + b*atanh(c*sqrt(x)))^2 + (2*b^2*log(1 - c^2*x))/(3*c^4)]
    @test_int [x^0*(a + b*atanh(c*sqrt(x)))^2, x, 7, (2*a*b*sqrt(x))/c + (2*b^2*sqrt(x)*atanh(c*sqrt(x)))/c - (a + b*atanh(c*sqrt(x)))^2/c^2 + x*(a + b*atanh(c*sqrt(x)))^2 + (b^2*log(1 - c^2*x))/c^2]
    @test_int [(a + b*atanh(c*sqrt(x)))^2/x^1, x, 7, 4*atanh(1 - 2/(1 - c*sqrt(x)))*(a + b*atanh(c*sqrt(x)))^2 - 2*b*(a + b*atanh(c*sqrt(x)))*PolyLog(2, 1 - 2/(1 - c*sqrt(x))) + 2*b*(a + b*atanh(c*sqrt(x)))*PolyLog(2, -1 + 2/(1 - c*sqrt(x))) + b^2*PolyLog(3, 1 - 2/(1 - c*sqrt(x))) - b^2*PolyLog(3, -1 + 2/(1 - c*sqrt(x)))]
    @test_int [(a + b*atanh(c*sqrt(x)))^2/x^2, x, 9, -((2*b*c*(a + b*atanh(c*sqrt(x))))/sqrt(x)) + c^2*(a + b*atanh(c*sqrt(x)))^2 - (a + b*atanh(c*sqrt(x)))^2/x + b^2*c^2*log(x) - b^2*c^2*log(1 - c^2*x)]
    @test_int [(a + b*atanh(c*sqrt(x)))^2/x^3, x, 14, -((b^2*c^2)/(6*x)) - (b*c*(a + b*atanh(c*sqrt(x))))/(3*x^(3/2)) - (b*c^3*(a + b*atanh(c*sqrt(x))))/sqrt(x) + (1/2)*c^4*(a + b*atanh(c*sqrt(x)))^2 - (a + b*atanh(c*sqrt(x)))^2/(2*x^2) + (2/3)*b^2*c^4*log(x) - (2/3)*b^2*c^4*log(1 - c^2*x)]

    @test_int [x^3*(a + b*atanh(c*sqrt(x)))^3, x, 54, (47*b^3*sqrt(x))/(70*c^7) + (23*b^3*x^(3/2))/(420*c^5) + (b^3*x^(5/2))/(140*c^3) - (47*b^3*atanh(c*sqrt(x)))/(70*c^8) + (71*b^2*x*(a + b*atanh(c*sqrt(x))))/(140*c^6) + (9*b^2*x^2*(a + b*atanh(c*sqrt(x))))/(70*c^4) + (b^2*x^3*(a + b*atanh(c*sqrt(x))))/(28*c^2) + (44*b*(a + b*atanh(c*sqrt(x)))^2)/(35*c^8) + (3*b*sqrt(x)*(a + b*atanh(c*sqrt(x)))^2)/(4*c^7) + (b*x^(3/2)*(a + b*atanh(c*sqrt(x)))^2)/(4*c^5) + (3*b*x^(5/2)*(a + b*atanh(c*sqrt(x)))^2)/(20*c^3) + (3*b*x^(7/2)*(a + b*atanh(c*sqrt(x)))^2)/(28*c) - (a + b*atanh(c*sqrt(x)))^3/(4*c^8) + (1/4)*x^4*(a + b*atanh(c*sqrt(x)))^3 - (88*b^2*(a + b*atanh(c*sqrt(x)))*log(2/(1 - c*sqrt(x))))/(35*c^8) - (44*b^3*PolyLog(2, 1 - 2/(1 - c*sqrt(x))))/(35*c^8)]
    @test_int [x^2*(a + b*atanh(c*sqrt(x)))^3, x, 34, (19*b^3*sqrt(x))/(30*c^5) + (b^3*x^(3/2))/(30*c^3) - (19*b^3*atanh(c*sqrt(x)))/(30*c^6) + (8*b^2*x*(a + b*atanh(c*sqrt(x))))/(15*c^4) + (b^2*x^2*(a + b*atanh(c*sqrt(x))))/(10*c^2) + (23*b*(a + b*atanh(c*sqrt(x)))^2)/(15*c^6) + (b*sqrt(x)*(a + b*atanh(c*sqrt(x)))^2)/c^5 + (b*x^(3/2)*(a + b*atanh(c*sqrt(x)))^2)/(3*c^3) + (b*x^(5/2)*(a + b*atanh(c*sqrt(x)))^2)/(5*c) - (a + b*atanh(c*sqrt(x)))^3/(3*c^6) + (1/3)*x^3*(a + b*atanh(c*sqrt(x)))^3 - (46*b^2*(a + b*atanh(c*sqrt(x)))*log(2/(1 - c*sqrt(x))))/(15*c^6) - (23*b^3*PolyLog(2, 1 - 2/(1 - c*sqrt(x))))/(15*c^6)]
    @test_int [x^1*(a + b*atanh(c*sqrt(x)))^3, x, 19, (b^3*sqrt(x))/(2*c^3) - (b^3*atanh(c*sqrt(x)))/(2*c^4) + (b^2*x*(a + b*atanh(c*sqrt(x))))/(2*c^2) + (2*b*(a + b*atanh(c*sqrt(x)))^2)/c^4 + (3*b*sqrt(x)*(a + b*atanh(c*sqrt(x)))^2)/(2*c^3) + (b*x^(3/2)*(a + b*atanh(c*sqrt(x)))^2)/(2*c) - (a + b*atanh(c*sqrt(x)))^3/(2*c^4) + (1/2)*x^2*(a + b*atanh(c*sqrt(x)))^3 - (4*b^2*(a + b*atanh(c*sqrt(x)))*log(2/(1 - c*sqrt(x))))/c^4 - (2*b^3*PolyLog(2, 1 - 2/(1 - c*sqrt(x))))/c^4]
    @test_int [x^0*(a + b*atanh(c*sqrt(x)))^3, x, 9, (3*b*(a + b*atanh(c*sqrt(x)))^2)/c^2 + (3*b*sqrt(x)*(a + b*atanh(c*sqrt(x)))^2)/c - (a + b*atanh(c*sqrt(x)))^3/c^2 + x*(a + b*atanh(c*sqrt(x)))^3 - (6*b^2*(a + b*atanh(c*sqrt(x)))*log(2/(1 - c*sqrt(x))))/c^2 - (3*b^3*PolyLog(2, 1 - 2/(1 - c*sqrt(x))))/c^2]
    @test_int [(a + b*atanh(c*sqrt(x)))^3/x^1, x, 9, 4*atanh(1 - 2/(1 - c*sqrt(x)))*(a + b*atanh(c*sqrt(x)))^3 - 3*b*(a + b*atanh(c*sqrt(x)))^2*PolyLog(2, 1 - 2/(1 - c*sqrt(x))) + 3*b*(a + b*atanh(c*sqrt(x)))^2*PolyLog(2, -1 + 2/(1 - c*sqrt(x))) + 3*b^2*(a + b*atanh(c*sqrt(x)))*PolyLog(3, 1 - 2/(1 - c*sqrt(x))) - 3*b^2*(a + b*atanh(c*sqrt(x)))*PolyLog(3, -1 + 2/(1 - c*sqrt(x))) - (3/2)*b^3*PolyLog(4, 1 - 2/(1 - c*sqrt(x))) + (3/2)*b^3*PolyLog(4, -1 + 2/(1 - c*sqrt(x)))]
    @test_int [(a + b*atanh(c*sqrt(x)))^3/x^2, x, 8, 3*b*c^2*(a + b*atanh(c*sqrt(x)))^2 - (3*b*c*(a + b*atanh(c*sqrt(x)))^2)/sqrt(x) + c^2*(a + b*atanh(c*sqrt(x)))^3 - (a + b*atanh(c*sqrt(x)))^3/x + 6*b^2*c^2*(a + b*atanh(c*sqrt(x)))*log(2 - 2/(1 + c*sqrt(x))) - 3*b^3*c^2*PolyLog(2, -1 + 2/(1 + c*sqrt(x)))]
    @test_int [(a + b*atanh(c*sqrt(x)))^3/x^3, x, 17, -((b^3*c^3)/(2*sqrt(x))) + (1/2)*b^3*c^4*atanh(c*sqrt(x)) - (b^2*c^2*(a + b*atanh(c*sqrt(x))))/(2*x) + 2*b*c^4*(a + b*atanh(c*sqrt(x)))^2 - (b*c*(a + b*atanh(c*sqrt(x)))^2)/(2*x^(3/2)) - (3*b*c^3*(a + b*atanh(c*sqrt(x)))^2)/(2*sqrt(x)) + (1/2)*c^4*(a + b*atanh(c*sqrt(x)))^3 - (a + b*atanh(c*sqrt(x)))^3/(2*x^2) + 4*b^2*c^4*(a + b*atanh(c*sqrt(x)))*log(2 - 2/(1 + c*sqrt(x))) - 2*b^3*c^4*PolyLog(2, -1 + 2/(1 + c*sqrt(x)))]

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

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

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

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

    @test_int [x^3*(a + b*atanh(c*x^(3/2))), x, 13, (3*b*x^(5/2))/(20*c) - (sqrt(3)*b*atan((1 - 2*c^(1/3)*sqrt(x))/sqrt(3)))/(8*c^(8/3)) + (sqrt(3)*b*atan((1 + 2*c^(1/3)*sqrt(x))/sqrt(3)))/(8*c^(8/3)) - (b*atanh(c^(1/3)*sqrt(x)))/(4*c^(8/3)) + (1/4)*x^4*(a + b*atanh(c*x^(3/2))) + (b*log(1 - c^(1/3)*sqrt(x) + c^(2/3)*x))/(16*c^(8/3)) - (b*log(1 + c^(1/3)*sqrt(x) + c^(2/3)*x))/(16*c^(8/3))]
    @test_int [x^2*(a + b*atanh(c*x^(3/2))), x, 5, (b*x^(3/2))/(3*c) - (b*atanh(c*x^(3/2)))/(3*c^2) + (1/3)*x^3*(a + b*atanh(c*x^(3/2)))]
    @test_int [x^1*(a + b*atanh(c*x^(3/2))), x, 13, (3*b*sqrt(x))/(2*c) + (sqrt(3)*b*atan((1 - 2*c^(1/3)*sqrt(x))/sqrt(3)))/(4*c^(4/3)) - (sqrt(3)*b*atan((1 + 2*c^(1/3)*sqrt(x))/sqrt(3)))/(4*c^(4/3)) - (b*atanh(c^(1/3)*sqrt(x)))/(2*c^(4/3)) + (1/2)*x^2*(a + b*atanh(c*x^(3/2))) + (b*log(1 - c^(1/3)*sqrt(x) + c^(2/3)*x))/(8*c^(4/3)) - (b*log(1 + c^(1/3)*sqrt(x) + c^(2/3)*x))/(8*c^(4/3))]
    @test_int [x^0*(a + b*atanh(c*x^(3/2))), x, 13, a*x - (sqrt(3)*b*atan((1 - 2*c^(1/3)*sqrt(x))/sqrt(3)))/(2*c^(2/3)) + (sqrt(3)*b*atan((1 + 2*c^(1/3)*sqrt(x))/sqrt(3)))/(2*c^(2/3)) - (b*atanh(c^(1/3)*sqrt(x)))/c^(2/3) + b*x*atanh(c*x^(3/2)) + (b*log(1 - c^(1/3)*sqrt(x) + c^(2/3)*x))/(4*c^(2/3)) - (b*log(1 + c^(1/3)*sqrt(x) + c^(2/3)*x))/(4*c^(2/3))]
    @test_int [(a + b*atanh(c*x^(3/2)))/x^1, x, 2, a*log(x) - (1/3)*b*PolyLog(2, (-c)*x^(3/2)) + (1/3)*b*PolyLog(2, c*x^(3/2))]
    @test_int [(a + b*atanh(c*x^(3/2)))/x^2, x, 12, (-(1/2))*sqrt(3)*b*c^(2/3)*atan((1 - 2*c^(1/3)*sqrt(x))/sqrt(3)) + (1/2)*sqrt(3)*b*c^(2/3)*atan((1 + 2*c^(1/3)*sqrt(x))/sqrt(3)) + b*c^(2/3)*atanh(c^(1/3)*sqrt(x)) - (a + b*atanh(c*x^(3/2)))/x - (1/4)*b*c^(2/3)*log(1 - c^(1/3)*sqrt(x) + c^(2/3)*x) + (1/4)*b*c^(2/3)*log(1 + c^(1/3)*sqrt(x) + c^(2/3)*x)]
    @test_int [(a + b*atanh(c*x^(3/2)))/x^3, x, 13, -((3*b*c)/(2*sqrt(x))) + (1/4)*sqrt(3)*b*c^(4/3)*atan((1 - 2*c^(1/3)*sqrt(x))/sqrt(3)) - (1/4)*sqrt(3)*b*c^(4/3)*atan((1 + 2*c^(1/3)*sqrt(x))/sqrt(3)) + (1/2)*b*c^(4/3)*atanh(c^(1/3)*sqrt(x)) - (a + b*atanh(c*x^(3/2)))/(2*x^2) - (1/8)*b*c^(4/3)*log(1 - c^(1/3)*sqrt(x) + c^(2/3)*x) + (1/8)*b*c^(4/3)*log(1 + c^(1/3)*sqrt(x) + c^(2/3)*x)]
    @test_int [(a + b*atanh(c*x^(3/2)))/x^4, x, 5, -((b*c)/(3*x^(3/2))) + (1/3)*b*c^2*atanh(c*x^(3/2)) - (a + b*atanh(c*x^(3/2)))/(3*x^3)]

    @test_int [x^2*(a + b*atanh(c*x^(3/2)))^2, x, 7, (2*a*b*x^(3/2))/(3*c) + (2*b^2*x^(3/2)*atanh(c*x^(3/2)))/(3*c) - (a + b*atanh(c*x^(3/2)))^2/(3*c^2) + (1/3)*x^3*(a + b*atanh(c*x^(3/2)))^2 + (b^2*log(1 - c^2*x^3))/(3*c^2)]
    @test_int [(a + b*atanh(c*x^(3/2)))^2/x^1, x, 7, (4/3)*(a + b*atanh(c*x^(3/2)))^2*atanh(1 - 2/(1 - c*x^(3/2))) - (2/3)*b*(a + b*atanh(c*x^(3/2)))*PolyLog(2, 1 - 2/(1 - c*x^(3/2))) + (2/3)*b*(a + b*atanh(c*x^(3/2)))*PolyLog(2, -1 + 2/(1 - c*x^(3/2))) + (1/3)*b^2*PolyLog(3, 1 - 2/(1 - c*x^(3/2))) - (1/3)*b^2*PolyLog(3, -1 + 2/(1 - c*x^(3/2)))]
    @test_int [(a + b*atanh(c*x^(3/2)))^2/x^4, x, 9, -((2*b*c*(a + b*atanh(c*x^(3/2))))/(3*x^(3/2))) + (1/3)*c^2*(a + b*atanh(c*x^(3/2)))^2 - (a + b*atanh(c*x^(3/2)))^2/(3*x^3) + b^2*c^2*log(x) - (1/3)*b^2*c^2*log(1 - c^2*x^3)]
    #=
    @test_int [x^3*atanh(c*x^(3/2))^2, x, 272, (9*x)/(20*c^2) + (3*sqrt(3)*atan((1 - 2*c^(1/3)*sqrt(x))/sqrt(3)))/(20*c^(8/3)) + (3*sqrt(3)*atan((1 + 2*c^(1/3)*sqrt(x))/sqrt(3)))/(20*c^(8/3)) + (3*log(1 - c^(1/3)*sqrt(x)))/(20*c^(8/3)) + log(1 - c^(1/3)*sqrt(x))^2/(16*c^(8/3)) - (log(1 - c^(1/3)*sqrt(x))*log(-(((-1)^(1/3) - c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))))/(8*c^(8/3)) + (log(1 - c^(1/3)*sqrt(x))*log(-(((-1)^(2/3) - c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))))/(8*c^(8/3)) - (log(1 - c^(1/3)*sqrt(x))*log((1/2)*(1 + c^(1/3)*sqrt(x))))/(8*c^(8/3)) + (3*log(1 + c^(1/3)*sqrt(x)))/(20*c^(8/3)) - (log((1/2)*(1 - c^(1/3)*sqrt(x)))*log(1 + c^(1/3)*sqrt(x)))/(8*c^(8/3)) + (log(((-1)^(1/3) - c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log(1 + c^(1/3)*sqrt(x)))/(8*c^(8/3)) - (log(((-1)^(2/3) - c^(1/3)*sqrt(x))/(1 + (-1)^(2/3)))*log(1 + c^(1/3)*sqrt(x)))/(8*c^(8/3)) + log(1 + c^(1/3)*sqrt(x))^2/(16*c^(8/3)) - (log(1 + c^(1/3)*sqrt(x))*log(-(((-1)^(1/3) + c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))))/(8*c^(8/3)) + (log(1 - c^(1/3)*sqrt(x))*log(((-1)^(1/3) + c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(8*c^(8/3)) + (log(1 + c^(1/3)*sqrt(x))*log(-(((-1)^(2/3) + c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))))/(8*c^(8/3)) - (log(1 - c^(1/3)*sqrt(x))*log(((-1)^(2/3) + c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))))/(8*c^(8/3)) + ((-1)^(1/3)*log(-(((-1)^(1/3)*(1 - c^(1/3)*sqrt(x)))/(1 - (-1)^(1/3))))*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x)))/(8*c^(8/3)) - ((-1)^(1/3)*log(((-1)^(1/3)*(1 + c^(1/3)*sqrt(x)))/(1 + (-1)^(1/3)))*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x)))/(8*c^(8/3)) + ((-1)^(1/3)*log((-1)^(1/3) + c^(1/3)*sqrt(x))*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x)))/(8*c^(8/3)) - ((-1)^(1/3)*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))^2)/(16*c^(8/3)) + ((-1)^(1/3)*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))*log((1/2)*(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))))/(8*c^(8/3)) - ((-1)^(1/3)*log(((-1)^(1/3)*(1 - c^(1/3)*sqrt(x)))/(1 + (-1)^(1/3)))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(8*c^(8/3)) + ((-1)^(1/3)*log((-1)^(1/3) - c^(1/3)*sqrt(x))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(8*c^(8/3)) + ((-1)^(1/3)*log(-(((-1)^(1/3)*(1 + c^(1/3)*sqrt(x)))/(1 - (-1)^(1/3))))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(8*c^(8/3)) - ((-1)^(1/3)*log(-(((-1)^(1/3)*((-1)^(1/3) + c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(8*c^(8/3)) + ((-1)^(1/3)*log((1/2)*(1 - (-1)^(1/3)*c^(1/3)*sqrt(x)))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(8*c^(8/3)) - ((-1)^(1/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))^2)/(16*c^(8/3)) + ((-1)^(2/3)*log(-(((-1)^(2/3)*(1 - c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(8*c^(8/3)) - ((-1)^(2/3)*log(-(-1)^(2/3) - c^(1/3)*sqrt(x))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(8*c^(8/3)) - ((-1)^(2/3)*log(((-1)^(2/3)*(1 + c^(1/3)*sqrt(x)))/(1 + (-1)^(2/3)))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(8*c^(8/3)) + ((-1)^(2/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))^2)/(16*c^(8/3)) - ((-1)^(2/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log((1/2)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))))/(8*c^(8/3)) - ((-1)^(2/3)*log(((-1)^(2/3)*(1 - c^(1/3)*sqrt(x)))/(1 + (-1)^(2/3)))*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)))/(8*c^(8/3)) + ((-1)^(2/3)*log(-(((-1)^(2/3)*(1 + c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)))/(8*c^(8/3)) - ((-1)^(2/3)*log(-(-1)^(2/3) + c^(1/3)*sqrt(x))*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)))/(8*c^(8/3)) - ((-1)^(2/3)*log((1/2)*(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)))/(8*c^(8/3)) + ((-1)^(2/3)*log(((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)))/(8*c^(8/3)) + ((-1)^(2/3)*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))^2)/(16*c^(8/3)) - ((-1)^(2/3)*log(((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log((1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(8*c^(8/3)) - ((-1)^(1/3)*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))*log(-(((-1)^(2/3)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3)))))/(8*c^(8/3)) + ((-1)^(2/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(8*c^(8/3)) - ((-1)^(2/3)*log((1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log(((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(8*c^(8/3)) - (3*log(1 - c^(1/3)*sqrt(x) + c^(2/3)*x))/(40*c^(8/3)) - (3*log(1 + c^(1/3)*sqrt(x) + c^(2/3)*x))/(40*c^(8/3)) - (3*x^(5/2)*log(1 - c*x^(3/2)))/(20*c) - (log(1 - c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(8*c^(8/3)) + (log(1 + c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(8*c^(8/3)) - ((-1)^(1/3)*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(8*c^(8/3)) + ((-1)^(1/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(8*c^(8/3)) - ((-1)^(2/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(8*c^(8/3)) + ((-1)^(2/3)*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(8*c^(8/3)) + (1/16)*x^4*log(1 - c*x^(3/2))^2 + (3*x^(5/2)*log(1 + c*x^(3/2)))/(20*c) + (log(1 - c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(8*c^(8/3)) - (log(1 + c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(8*c^(8/3)) + ((-1)^(1/3)*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(8*c^(8/3)) - ((-1)^(1/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(8*c^(8/3)) + ((-1)^(2/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(8*c^(8/3)) - ((-1)^(2/3)*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(8*c^(8/3)) - (1/8)*x^4*log(1 - c*x^(3/2))*log(1 + c*x^(3/2)) + (1/16)*x^4*log(1 + c*x^(3/2))^2 - PolyLog(2, (1/2)*(1 - c^(1/3)*sqrt(x)))/(8*c^(8/3)) - PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))/(8*c^(8/3)) + PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))/(8*c^(8/3)) + PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))/(8*c^(8/3)) - PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 + (-1)^(2/3)))/(8*c^(8/3)) + ((-1)^(1/3)*PolyLog(2, 1/(1 + (-1)^(2/3)) - c^(1/3)*sqrt(x)))/(8*c^(8/3)) - PolyLog(2, (1/2)*(1 + c^(1/3)*sqrt(x)))/(8*c^(8/3)) - PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))/(8*c^(8/3)) + PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))/(8*c^(8/3)) + PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))/(8*c^(8/3)) - PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 + (-1)^(2/3)))/(8*c^(8/3)) - ((-1)^(2/3)*PolyLog(2, 1/(1 - (-1)^(1/3)) + c^(1/3)*sqrt(x)))/(8*c^(8/3)) + ((-1)^(1/3)*PolyLog(2, 1/(1 + (-1)^(2/3)) + c^(1/3)*sqrt(x)))/(8*c^(8/3)) + ((-1)^(1/3)*PolyLog(2, (1/2)*(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))))/(8*c^(8/3)) + ((-1)^(1/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))))/(8*c^(8/3)) - ((-1)^(1/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(8*c^(8/3)) - ((-1)^(1/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))))/(8*c^(8/3)) + ((-1)^(1/3)*PolyLog(2, (1/2)*(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))))/(8*c^(8/3)) + ((-1)^(1/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))))/(8*c^(8/3)) - ((-1)^(1/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(8*c^(8/3)) - ((-1)^(1/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))))/(8*c^(8/3)) - ((-1)^(2/3)*PolyLog(2, (1/2)*(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))))/(8*c^(8/3)) + ((-1)^(2/3)*PolyLog(2, (1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))))/(8*c^(8/3)) - ((-1)^(2/3)*PolyLog(2, (1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))))/(8*c^(8/3)) - ((-1)^(2/3)*PolyLog(2, ((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(8*c^(8/3)) - ((-1)^(2/3)*PolyLog(2, (1/2)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))))/(8*c^(8/3)) - ((-1)^(2/3)*PolyLog(2, (1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))))/(8*c^(8/3)) + ((-1)^(2/3)*PolyLog(2, (1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))))/(8*c^(8/3)) - ((-1)^(2/3)*PolyLog(2, (1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))))/(8*c^(8/3)) - ((-1)^(2/3)*PolyLog(2, ((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(8*c^(8/3))]
    @test_int [x^0*atanh(c*x^(3/2))^2, x, 200, log(1 - c^(1/3)*sqrt(x))^2/(4*c^(2/3)) - (log(1 - c^(1/3)*sqrt(x))*log(-(((-1)^(1/3) - c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))))/(2*c^(2/3)) + (log(1 - c^(1/3)*sqrt(x))*log(-(((-1)^(2/3) - c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))))/(2*c^(2/3)) - (log(1 - c^(1/3)*sqrt(x))*log((1/2)*(1 + c^(1/3)*sqrt(x))))/(2*c^(2/3)) - (log((1/2)*(1 - c^(1/3)*sqrt(x)))*log(1 + c^(1/3)*sqrt(x)))/(2*c^(2/3)) + (log(((-1)^(1/3) - c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log(1 + c^(1/3)*sqrt(x)))/(2*c^(2/3)) - (log(((-1)^(2/3) - c^(1/3)*sqrt(x))/(1 + (-1)^(2/3)))*log(1 + c^(1/3)*sqrt(x)))/(2*c^(2/3)) + log(1 + c^(1/3)*sqrt(x))^2/(4*c^(2/3)) - (log(1 + c^(1/3)*sqrt(x))*log(-(((-1)^(1/3) + c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))))/(2*c^(2/3)) + (log(1 - c^(1/3)*sqrt(x))*log(((-1)^(1/3) + c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(2*c^(2/3)) + (log(1 + c^(1/3)*sqrt(x))*log(-(((-1)^(2/3) + c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))))/(2*c^(2/3)) - (log(1 - c^(1/3)*sqrt(x))*log(((-1)^(2/3) + c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))))/(2*c^(2/3)) + ((-1)^(1/3)*log(-(((-1)^(1/3)*(1 - c^(1/3)*sqrt(x)))/(1 - (-1)^(1/3))))*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x)))/(2*c^(2/3)) - ((-1)^(1/3)*log(((-1)^(1/3)*(1 + c^(1/3)*sqrt(x)))/(1 + (-1)^(1/3)))*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x)))/(2*c^(2/3)) + ((-1)^(1/3)*log((-1)^(1/3) + c^(1/3)*sqrt(x))*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x)))/(2*c^(2/3)) - ((-1)^(1/3)*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))^2)/(4*c^(2/3)) + ((-1)^(1/3)*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))*log((1/2)*(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))))/(2*c^(2/3)) - ((-1)^(1/3)*log(((-1)^(1/3)*(1 - c^(1/3)*sqrt(x)))/(1 + (-1)^(1/3)))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(2*c^(2/3)) + ((-1)^(1/3)*log((-1)^(1/3) - c^(1/3)*sqrt(x))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(2*c^(2/3)) + ((-1)^(1/3)*log(-(((-1)^(1/3)*(1 + c^(1/3)*sqrt(x)))/(1 - (-1)^(1/3))))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(2*c^(2/3)) - ((-1)^(1/3)*log(-(((-1)^(1/3)*((-1)^(1/3) + c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(2*c^(2/3)) + ((-1)^(1/3)*log((1/2)*(1 - (-1)^(1/3)*c^(1/3)*sqrt(x)))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(2*c^(2/3)) - ((-1)^(1/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))^2)/(4*c^(2/3)) + ((-1)^(2/3)*log(-(((-1)^(2/3)*(1 - c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(2*c^(2/3)) - ((-1)^(2/3)*log(-(-1)^(2/3) - c^(1/3)*sqrt(x))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(2*c^(2/3)) - ((-1)^(2/3)*log(((-1)^(2/3)*(1 + c^(1/3)*sqrt(x)))/(1 + (-1)^(2/3)))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(2*c^(2/3)) + ((-1)^(2/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))^2)/(4*c^(2/3)) - ((-1)^(2/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log((1/2)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))))/(2*c^(2/3)) - ((-1)^(2/3)*log(((-1)^(2/3)*(1 - c^(1/3)*sqrt(x)))/(1 + (-1)^(2/3)))*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)))/(2*c^(2/3)) + ((-1)^(2/3)*log(-(((-1)^(2/3)*(1 + c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)))/(2*c^(2/3)) - ((-1)^(2/3)*log(-(-1)^(2/3) + c^(1/3)*sqrt(x))*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)))/(2*c^(2/3)) - ((-1)^(2/3)*log((1/2)*(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)))/(2*c^(2/3)) + ((-1)^(2/3)*log(((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)))/(2*c^(2/3)) + ((-1)^(2/3)*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))^2)/(4*c^(2/3)) - ((-1)^(2/3)*log(((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log((1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(2*c^(2/3)) - ((-1)^(1/3)*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))*log(-(((-1)^(2/3)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3)))))/(2*c^(2/3)) + ((-1)^(2/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(2*c^(2/3)) - ((-1)^(2/3)*log((1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log(((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(2*c^(2/3)) - (log(1 - c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(2*c^(2/3)) + (log(1 + c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(2*c^(2/3)) - ((-1)^(1/3)*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(2*c^(2/3)) + ((-1)^(1/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(2*c^(2/3)) - ((-1)^(2/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(2*c^(2/3)) + ((-1)^(2/3)*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(2*c^(2/3)) + (1/4)*x*log(1 - c*x^(3/2))^2 + (log(1 - c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(2*c^(2/3)) - (log(1 + c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(2*c^(2/3)) + ((-1)^(1/3)*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(2*c^(2/3)) - ((-1)^(1/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(2*c^(2/3)) + ((-1)^(2/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(2*c^(2/3)) - ((-1)^(2/3)*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(2*c^(2/3)) - (1/2)*x*log(1 - c*x^(3/2))*log(1 + c*x^(3/2)) + (1/4)*x*log(1 + c*x^(3/2))^2 - PolyLog(2, (1/2)*(1 - c^(1/3)*sqrt(x)))/(2*c^(2/3)) - PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))/(2*c^(2/3)) + PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))/(2*c^(2/3)) + PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))/(2*c^(2/3)) - PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 + (-1)^(2/3)))/(2*c^(2/3)) + ((-1)^(1/3)*PolyLog(2, 1/(1 + (-1)^(2/3)) - c^(1/3)*sqrt(x)))/(2*c^(2/3)) - PolyLog(2, (1/2)*(1 + c^(1/3)*sqrt(x)))/(2*c^(2/3)) - PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))/(2*c^(2/3)) + PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))/(2*c^(2/3)) + PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))/(2*c^(2/3)) - PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 + (-1)^(2/3)))/(2*c^(2/3)) - ((-1)^(2/3)*PolyLog(2, 1/(1 - (-1)^(1/3)) + c^(1/3)*sqrt(x)))/(2*c^(2/3)) + ((-1)^(1/3)*PolyLog(2, 1/(1 + (-1)^(2/3)) + c^(1/3)*sqrt(x)))/(2*c^(2/3)) + ((-1)^(1/3)*PolyLog(2, (1/2)*(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))))/(2*c^(2/3)) + ((-1)^(1/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))))/(2*c^(2/3)) - ((-1)^(1/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(2*c^(2/3)) - ((-1)^(1/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))))/(2*c^(2/3)) + ((-1)^(1/3)*PolyLog(2, (1/2)*(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))))/(2*c^(2/3)) + ((-1)^(1/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))))/(2*c^(2/3)) - ((-1)^(1/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(2*c^(2/3)) - ((-1)^(1/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))))/(2*c^(2/3)) - ((-1)^(2/3)*PolyLog(2, (1/2)*(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))))/(2*c^(2/3)) + ((-1)^(2/3)*PolyLog(2, (1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))))/(2*c^(2/3)) - ((-1)^(2/3)*PolyLog(2, (1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))))/(2*c^(2/3)) - ((-1)^(2/3)*PolyLog(2, ((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(2*c^(2/3)) - ((-1)^(2/3)*PolyLog(2, (1/2)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))))/(2*c^(2/3)) - ((-1)^(2/3)*PolyLog(2, (1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))))/(2*c^(2/3)) + ((-1)^(2/3)*PolyLog(2, (1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))))/(2*c^(2/3)) - ((-1)^(2/3)*PolyLog(2, (1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))))/(2*c^(2/3)) - ((-1)^(2/3)*PolyLog(2, ((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(2*c^(2/3))]
    @test_int [atanh(c*x^(3/2))^2/x^3, x, 196, (-(3/2))*sqrt(3)*c^(4/3)*atan((1 - 2*c^(1/3)*sqrt(x))/sqrt(3)) - (3/2)*sqrt(3)*c^(4/3)*atan((1 + 2*c^(1/3)*sqrt(x))/sqrt(3)) - (3/2)*c^(4/3)*log(1 - c^(1/3)*sqrt(x)) - (1/8)*c^(4/3)*log(1 - c^(1/3)*sqrt(x))^2 + (1/4)*c^(4/3)*log(1 - c^(1/3)*sqrt(x))*log(-(((-1)^(1/3) - c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))) - (1/4)*c^(4/3)*log(1 - c^(1/3)*sqrt(x))*log(-(((-1)^(2/3) - c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))) + (1/4)*c^(4/3)*log(1 - c^(1/3)*sqrt(x))*log((1/2)*(1 + c^(1/3)*sqrt(x))) - (3/2)*c^(4/3)*log(1 + c^(1/3)*sqrt(x)) + (1/4)*c^(4/3)*log((1/2)*(1 - c^(1/3)*sqrt(x)))*log(1 + c^(1/3)*sqrt(x)) - (1/4)*c^(4/3)*log(((-1)^(1/3) - c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log(1 + c^(1/3)*sqrt(x)) + (1/4)*c^(4/3)*log(((-1)^(2/3) - c^(1/3)*sqrt(x))/(1 + (-1)^(2/3)))*log(1 + c^(1/3)*sqrt(x)) - (1/8)*c^(4/3)*log(1 + c^(1/3)*sqrt(x))^2 + (1/4)*c^(4/3)*log(1 + c^(1/3)*sqrt(x))*log(-(((-1)^(1/3) + c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))) - (1/4)*c^(4/3)*log(1 - c^(1/3)*sqrt(x))*log(((-1)^(1/3) + c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) - (1/4)*c^(4/3)*log(1 + c^(1/3)*sqrt(x))*log(-(((-1)^(2/3) + c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))) + (1/4)*c^(4/3)*log(1 - c^(1/3)*sqrt(x))*log(((-1)^(2/3) + c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))) - (1/4)*(-1)^(1/3)*c^(4/3)*log(-(((-1)^(1/3)*(1 - c^(1/3)*sqrt(x)))/(1 - (-1)^(1/3))))*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x)) + (1/4)*(-1)^(1/3)*c^(4/3)*log(((-1)^(1/3)*(1 + c^(1/3)*sqrt(x)))/(1 + (-1)^(1/3)))*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x)) - (1/4)*(-1)^(1/3)*c^(4/3)*log((-1)^(1/3) + c^(1/3)*sqrt(x))*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x)) + (1/8)*(-1)^(1/3)*c^(4/3)*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))^2 - (1/4)*(-1)^(1/3)*c^(4/3)*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))*log((1/2)*(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))) + (1/4)*(-1)^(1/3)*c^(4/3)*log(((-1)^(1/3)*(1 - c^(1/3)*sqrt(x)))/(1 + (-1)^(1/3)))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)) - (1/4)*(-1)^(1/3)*c^(4/3)*log((-1)^(1/3) - c^(1/3)*sqrt(x))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)) - (1/4)*(-1)^(1/3)*c^(4/3)*log(-(((-1)^(1/3)*(1 + c^(1/3)*sqrt(x)))/(1 - (-1)^(1/3))))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)) + (1/4)*(-1)^(1/3)*c^(4/3)*log(-(((-1)^(1/3)*((-1)^(1/3) + c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)) - (1/4)*(-1)^(1/3)*c^(4/3)*log((1/2)*(1 - (-1)^(1/3)*c^(1/3)*sqrt(x)))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)) + (1/8)*(-1)^(1/3)*c^(4/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))^2 - (1/4)*(-1)^(2/3)*c^(4/3)*log(-(((-1)^(2/3)*(1 - c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)) + (1/4)*(-1)^(2/3)*c^(4/3)*log(-(-1)^(2/3) - c^(1/3)*sqrt(x))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)) + (1/4)*(-1)^(2/3)*c^(4/3)*log(((-1)^(2/3)*(1 + c^(1/3)*sqrt(x)))/(1 + (-1)^(2/3)))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)) - (1/8)*(-1)^(2/3)*c^(4/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))^2 + (1/4)*(-1)^(2/3)*c^(4/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log((1/2)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))) + (1/4)*(-1)^(2/3)*c^(4/3)*log(((-1)^(2/3)*(1 - c^(1/3)*sqrt(x)))/(1 + (-1)^(2/3)))*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)) - (1/4)*(-1)^(2/3)*c^(4/3)*log(-(((-1)^(2/3)*(1 + c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)) + (1/4)*(-1)^(2/3)*c^(4/3)*log(-(-1)^(2/3) + c^(1/3)*sqrt(x))*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)) + (1/4)*(-1)^(2/3)*c^(4/3)*log((1/2)*(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)) - (1/4)*(-1)^(2/3)*c^(4/3)*log(((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)) - (1/8)*(-1)^(2/3)*c^(4/3)*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))^2 + (1/4)*(-1)^(2/3)*c^(4/3)*log(((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log((1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) + (1/4)*(-1)^(1/3)*c^(4/3)*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))*log(-(((-1)^(2/3)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3)))) - (1/4)*(-1)^(2/3)*c^(4/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) + (1/4)*(-1)^(2/3)*c^(4/3)*log((1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log(((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) + (3/4)*c^(4/3)*log(1 - c^(1/3)*sqrt(x) + c^(2/3)*x) + (3/4)*c^(4/3)*log(1 + c^(1/3)*sqrt(x) + c^(2/3)*x) + (3*c*log(1 - c*x^(3/2)))/(2*sqrt(x)) + (1/4)*c^(4/3)*log(1 - c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)) - (1/4)*c^(4/3)*log(1 + c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)) + (1/4)*(-1)^(1/3)*c^(4/3)*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)) - (1/4)*(-1)^(1/3)*c^(4/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)) + (1/4)*(-1)^(2/3)*c^(4/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)) - (1/4)*(-1)^(2/3)*c^(4/3)*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)) - log(1 - c*x^(3/2))^2/(8*x^2) - (3*c*log(1 + c*x^(3/2)))/(2*sqrt(x)) - (1/4)*c^(4/3)*log(1 - c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)) + (1/4)*c^(4/3)*log(1 + c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)) - (1/4)*(-1)^(1/3)*c^(4/3)*log(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)) + (1/4)*(-1)^(1/3)*c^(4/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)) - (1/4)*(-1)^(2/3)*c^(4/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)) + (1/4)*(-1)^(2/3)*c^(4/3)*log(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)) + (log(1 - c*x^(3/2))*log(1 + c*x^(3/2)))/(4*x^2) - log(1 + c*x^(3/2))^2/(8*x^2) + (1/4)*c^(4/3)*PolyLog(2, (1/2)*(1 - c^(1/3)*sqrt(x))) + (1/4)*c^(4/3)*PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))) - (1/4)*c^(4/3)*PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) - (1/4)*c^(4/3)*PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))) + (1/4)*c^(4/3)*PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))) - (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog(2, 1/(1 + (-1)^(2/3)) - c^(1/3)*sqrt(x)) + (1/4)*c^(4/3)*PolyLog(2, (1/2)*(1 + c^(1/3)*sqrt(x))) + (1/4)*c^(4/3)*PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))) - (1/4)*c^(4/3)*PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) - (1/4)*c^(4/3)*PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))) + (1/4)*c^(4/3)*PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))) + (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog(2, 1/(1 - (-1)^(1/3)) + c^(1/3)*sqrt(x)) - (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog(2, 1/(1 + (-1)^(2/3)) + c^(1/3)*sqrt(x)) - (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog(2, (1/2)*(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))) - (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))) + (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) + (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))) - (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog(2, (1/2)*(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))) - (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))) + (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) + (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))) + (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog(2, (1/2)*(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))) - (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog(2, (1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))) + (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog(2, (1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))) + (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog(2, ((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) + (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog(2, (1/2)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))) + (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog(2, (1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))) - (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog(2, (1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))) + (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog(2, (1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))) + (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog(2, ((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))]

    @test_int [x^4*atanh(c*x^(3/2))^2, x, 308, (9*x^2)/(70*c^2) - (24*sqrt(3)*atan((1 - 2*c^(1/3)*sqrt(x))/sqrt(3)))/(35*c^(10/3)) - (24*sqrt(3)*atan((1 + 2*c^(1/3)*sqrt(x))/sqrt(3)))/(35*c^(10/3)) + log(-1 - c^(1/3)*sqrt(x))^2/(20*c^(10/3)) - (log(-1 - c^(1/3)*sqrt(x))*log((1/2)*(1 - c^(1/3)*sqrt(x))))/(10*c^(10/3)) + (24*log(1 - c^(1/3)*sqrt(x)))/(35*c^(10/3)) + log(1 - c^(1/3)*sqrt(x))^2/(20*c^(10/3)) - (log(1 - c^(1/3)*sqrt(x))*log(-(((-1)^(1/3) - c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))))/(10*c^(10/3)) + (log(-1 - c^(1/3)*sqrt(x))*log(((-1)^(1/3) - c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(10*c^(10/3)) + (log(1 - c^(1/3)*sqrt(x))*log(-(((-1)^(2/3) - c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))))/(10*c^(10/3)) - (log(-1 - c^(1/3)*sqrt(x))*log(((-1)^(2/3) - c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))))/(10*c^(10/3)) - (log(1 - c^(1/3)*sqrt(x))*log((1/2)*(1 + c^(1/3)*sqrt(x))))/(10*c^(10/3)) + (24*log(1 + c^(1/3)*sqrt(x)))/(35*c^(10/3)) - (log(-1 - c^(1/3)*sqrt(x))*log(-(((-1)^(1/3) + c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))))/(10*c^(10/3)) + (log(1 - c^(1/3)*sqrt(x))*log(((-1)^(1/3) + c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(10*c^(10/3)) + (log(-1 - c^(1/3)*sqrt(x))*log(-(((-1)^(2/3) + c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))))/(10*c^(10/3)) - (log(1 - c^(1/3)*sqrt(x))*log(((-1)^(2/3) + c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))))/(10*c^(10/3)) - ((-1)^(2/3)*log(-(((-1)^(1/3)*(1 - c^(1/3)*sqrt(x)))/(1 - (-1)^(1/3))))*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(10*c^(10/3)) + ((-1)^(2/3)*log(((-1)^(1/3)*(1 + c^(1/3)*sqrt(x)))/(1 + (-1)^(1/3)))*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(10*c^(10/3)) - ((-1)^(2/3)*log((-1)^(1/3) + c^(1/3)*sqrt(x))*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(10*c^(10/3)) + ((-1)^(2/3)*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x))^2)/(20*c^(10/3)) - ((-1)^(2/3)*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log((1/2)*(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))))/(10*c^(10/3)) + ((-1)^(2/3)*log(((-1)^(1/3)*(1 - c^(1/3)*sqrt(x)))/(1 + (-1)^(1/3)))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(10*c^(10/3)) - ((-1)^(2/3)*log((-1)^(1/3) - c^(1/3)*sqrt(x))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(10*c^(10/3)) - ((-1)^(2/3)*log(-(((-1)^(1/3)*(1 + c^(1/3)*sqrt(x)))/(1 - (-1)^(1/3))))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(10*c^(10/3)) + ((-1)^(2/3)*log(-(((-1)^(1/3)*((-1)^(1/3) + c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(10*c^(10/3)) - ((-1)^(2/3)*log((1/2)*(1 - (-1)^(1/3)*c^(1/3)*sqrt(x)))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(10*c^(10/3)) + ((-1)^(2/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))^2)/(20*c^(10/3)) + ((-1)^(1/3)*log(((-1)^(2/3)*(1 - c^(1/3)*sqrt(x)))/(1 + (-1)^(2/3)))*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(10*c^(10/3)) - ((-1)^(1/3)*log(-(((-1)^(2/3)*(1 + c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(10*c^(10/3)) + ((-1)^(1/3)*log(-(-1)^(2/3) + c^(1/3)*sqrt(x))*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(10*c^(10/3)) - ((-1)^(1/3)*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x))^2)/(20*c^(10/3)) + ((-1)^(1/3)*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log((1/2)*(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))))/(10*c^(10/3)) - ((-1)^(1/3)*log(-(((-1)^(2/3)*(1 - c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(10*c^(10/3)) + ((-1)^(1/3)*log(-(-1)^(2/3) - c^(1/3)*sqrt(x))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(10*c^(10/3)) + ((-1)^(1/3)*log(((-1)^(2/3)*(1 + c^(1/3)*sqrt(x)))/(1 + (-1)^(2/3)))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(10*c^(10/3)) - ((-1)^(1/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))^2)/(20*c^(10/3)) - ((-1)^(1/3)*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(10*c^(10/3)) + ((-1)^(1/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log((1/2)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))))/(10*c^(10/3)) + ((-1)^(1/3)*log(((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log((1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(10*c^(10/3)) + ((-1)^(2/3)*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(-(((-1)^(2/3)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3)))))/(10*c^(10/3)) - ((-1)^(1/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(10*c^(10/3)) + ((-1)^(1/3)*log((1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log(((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(10*c^(10/3)) - (12*log(1 - c^(1/3)*sqrt(x) + c^(2/3)*x))/(35*c^(10/3)) - (12*log(1 + c^(1/3)*sqrt(x) + c^(2/3)*x))/(35*c^(10/3)) - (3*sqrt(x)*log(1 - c*x^(3/2)))/(5*c^3) - (3*x^(7/2)*log(1 - c*x^(3/2)))/(35*c) + (log(-1 - c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(10*c^(10/3)) - (log(1 - c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(10*c^(10/3)) + ((-1)^(2/3)*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(10*c^(10/3)) - ((-1)^(2/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(10*c^(10/3)) - ((-1)^(1/3)*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(10*c^(10/3)) + ((-1)^(1/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(10*c^(10/3)) + (1/20)*x^5*log(1 - c*x^(3/2))^2 + (3*sqrt(x)*log(1 + c*x^(3/2)))/(5*c^3) + (3*x^(7/2)*log(1 + c*x^(3/2)))/(35*c) - (log(-1 - c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(10*c^(10/3)) + (log(1 - c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(10*c^(10/3)) - ((-1)^(2/3)*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(10*c^(10/3)) + ((-1)^(2/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(10*c^(10/3)) + ((-1)^(1/3)*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(10*c^(10/3)) - ((-1)^(1/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(10*c^(10/3)) - (1/10)*x^5*log(1 - c*x^(3/2))*log(1 + c*x^(3/2)) + (1/20)*x^5*log(1 + c*x^(3/2))^2 - PolyLog(2, (1/2)*(1 - c^(1/3)*sqrt(x)))/(10*c^(10/3)) - PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))/(10*c^(10/3)) + PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))/(10*c^(10/3)) + PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))/(10*c^(10/3)) - PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 + (-1)^(2/3)))/(10*c^(10/3)) + ((-1)^(1/3)*PolyLog(2, 1/(1 - (-1)^(1/3)) - c^(1/3)*sqrt(x)))/(10*c^(10/3)) - ((-1)^(2/3)*PolyLog(2, 1/(1 + (-1)^(2/3)) - c^(1/3)*sqrt(x)))/(10*c^(10/3)) - PolyLog(2, (1/2)*(1 + c^(1/3)*sqrt(x)))/(10*c^(10/3)) - PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))/(10*c^(10/3)) + PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))/(10*c^(10/3)) + PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))/(10*c^(10/3)) - PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 + (-1)^(2/3)))/(10*c^(10/3)) + ((-1)^(1/3)*PolyLog(2, 1/(1 - (-1)^(1/3)) + c^(1/3)*sqrt(x)))/(10*c^(10/3)) - ((-1)^(2/3)*PolyLog(2, 1/(1 + (-1)^(2/3)) + c^(1/3)*sqrt(x)))/(10*c^(10/3)) - ((-1)^(2/3)*PolyLog(2, (1/2)*(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))))/(10*c^(10/3)) - ((-1)^(2/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))))/(10*c^(10/3)) + ((-1)^(2/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(10*c^(10/3)) + ((-1)^(2/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))))/(10*c^(10/3)) - ((-1)^(2/3)*PolyLog(2, (1/2)*(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))))/(10*c^(10/3)) - ((-1)^(2/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))))/(10*c^(10/3)) + ((-1)^(2/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(10*c^(10/3)) + ((-1)^(2/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))))/(10*c^(10/3)) + ((-1)^(1/3)*PolyLog(2, (1/2)*(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))))/(10*c^(10/3)) - ((-1)^(1/3)*PolyLog(2, (1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))))/(10*c^(10/3)) + ((-1)^(1/3)*PolyLog(2, (1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))))/(10*c^(10/3)) + ((-1)^(1/3)*PolyLog(2, ((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(10*c^(10/3)) + ((-1)^(1/3)*PolyLog(2, (1/2)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))))/(10*c^(10/3)) - ((-1)^(1/3)*PolyLog(2, (1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))))/(10*c^(10/3)) + ((-1)^(1/3)*PolyLog(2, (1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))))/(10*c^(10/3)) + ((-1)^(1/3)*PolyLog(2, ((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(10*c^(10/3))]
    @test_int [x^1*atanh(c*x^(3/2))^2, x, 236, -((3*sqrt(3)*atan((1 - 2*c^(1/3)*sqrt(x))/sqrt(3)))/(2*c^(4/3))) - (3*sqrt(3)*atan((1 + 2*c^(1/3)*sqrt(x))/sqrt(3)))/(2*c^(4/3)) + log(-1 - c^(1/3)*sqrt(x))^2/(8*c^(4/3)) - (log(-1 - c^(1/3)*sqrt(x))*log((1/2)*(1 - c^(1/3)*sqrt(x))))/(4*c^(4/3)) + (3*log(1 - c^(1/3)*sqrt(x)))/(2*c^(4/3)) + log(1 - c^(1/3)*sqrt(x))^2/(8*c^(4/3)) - (log(1 - c^(1/3)*sqrt(x))*log(-(((-1)^(1/3) - c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))))/(4*c^(4/3)) + (log(-1 - c^(1/3)*sqrt(x))*log(((-1)^(1/3) - c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(4*c^(4/3)) + (log(1 - c^(1/3)*sqrt(x))*log(-(((-1)^(2/3) - c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))))/(4*c^(4/3)) - (log(-1 - c^(1/3)*sqrt(x))*log(((-1)^(2/3) - c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))))/(4*c^(4/3)) - (log(1 - c^(1/3)*sqrt(x))*log((1/2)*(1 + c^(1/3)*sqrt(x))))/(4*c^(4/3)) + (3*log(1 + c^(1/3)*sqrt(x)))/(2*c^(4/3)) - (log(-1 - c^(1/3)*sqrt(x))*log(-(((-1)^(1/3) + c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))))/(4*c^(4/3)) + (log(1 - c^(1/3)*sqrt(x))*log(((-1)^(1/3) + c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(4*c^(4/3)) + (log(-1 - c^(1/3)*sqrt(x))*log(-(((-1)^(2/3) + c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))))/(4*c^(4/3)) - (log(1 - c^(1/3)*sqrt(x))*log(((-1)^(2/3) + c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))))/(4*c^(4/3)) - ((-1)^(2/3)*log(-(((-1)^(1/3)*(1 - c^(1/3)*sqrt(x)))/(1 - (-1)^(1/3))))*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(4*c^(4/3)) + ((-1)^(2/3)*log(((-1)^(1/3)*(1 + c^(1/3)*sqrt(x)))/(1 + (-1)^(1/3)))*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(4*c^(4/3)) - ((-1)^(2/3)*log((-1)^(1/3) + c^(1/3)*sqrt(x))*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(4*c^(4/3)) + ((-1)^(2/3)*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x))^2)/(8*c^(4/3)) - ((-1)^(2/3)*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log((1/2)*(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))))/(4*c^(4/3)) + ((-1)^(2/3)*log(((-1)^(1/3)*(1 - c^(1/3)*sqrt(x)))/(1 + (-1)^(1/3)))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(4*c^(4/3)) - ((-1)^(2/3)*log((-1)^(1/3) - c^(1/3)*sqrt(x))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(4*c^(4/3)) - ((-1)^(2/3)*log(-(((-1)^(1/3)*(1 + c^(1/3)*sqrt(x)))/(1 - (-1)^(1/3))))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(4*c^(4/3)) + ((-1)^(2/3)*log(-(((-1)^(1/3)*((-1)^(1/3) + c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(4*c^(4/3)) - ((-1)^(2/3)*log((1/2)*(1 - (-1)^(1/3)*c^(1/3)*sqrt(x)))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)))/(4*c^(4/3)) + ((-1)^(2/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))^2)/(8*c^(4/3)) + ((-1)^(1/3)*log(((-1)^(2/3)*(1 - c^(1/3)*sqrt(x)))/(1 + (-1)^(2/3)))*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(4*c^(4/3)) - ((-1)^(1/3)*log(-(((-1)^(2/3)*(1 + c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(4*c^(4/3)) + ((-1)^(1/3)*log(-(-1)^(2/3) + c^(1/3)*sqrt(x))*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(4*c^(4/3)) - ((-1)^(1/3)*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x))^2)/(8*c^(4/3)) + ((-1)^(1/3)*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log((1/2)*(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))))/(4*c^(4/3)) - ((-1)^(1/3)*log(-(((-1)^(2/3)*(1 - c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(4*c^(4/3)) + ((-1)^(1/3)*log(-(-1)^(2/3) - c^(1/3)*sqrt(x))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(4*c^(4/3)) + ((-1)^(1/3)*log(((-1)^(2/3)*(1 + c^(1/3)*sqrt(x)))/(1 + (-1)^(2/3)))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)))/(4*c^(4/3)) - ((-1)^(1/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))^2)/(8*c^(4/3)) - ((-1)^(1/3)*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(4*c^(4/3)) + ((-1)^(1/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log((1/2)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))))/(4*c^(4/3)) + ((-1)^(1/3)*log(((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log((1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(4*c^(4/3)) + ((-1)^(2/3)*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(-(((-1)^(2/3)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3)))))/(4*c^(4/3)) - ((-1)^(1/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(4*c^(4/3)) + ((-1)^(1/3)*log((1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log(((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(4*c^(4/3)) - (3*log(1 - c^(1/3)*sqrt(x) + c^(2/3)*x))/(4*c^(4/3)) - (3*log(1 + c^(1/3)*sqrt(x) + c^(2/3)*x))/(4*c^(4/3)) - (3*sqrt(x)*log(1 - c*x^(3/2)))/(2*c) + (log(-1 - c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(4*c^(4/3)) - (log(1 - c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(4*c^(4/3)) + ((-1)^(2/3)*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(4*c^(4/3)) - ((-1)^(2/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(4*c^(4/3)) - ((-1)^(1/3)*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(4*c^(4/3)) + ((-1)^(1/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)))/(4*c^(4/3)) + (1/8)*x^2*log(1 - c*x^(3/2))^2 + (3*sqrt(x)*log(1 + c*x^(3/2)))/(2*c) - (log(-1 - c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(4*c^(4/3)) + (log(1 - c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(4*c^(4/3)) - ((-1)^(2/3)*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(4*c^(4/3)) + ((-1)^(2/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(4*c^(4/3)) + ((-1)^(1/3)*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(4*c^(4/3)) - ((-1)^(1/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)))/(4*c^(4/3)) - (1/4)*x^2*log(1 - c*x^(3/2))*log(1 + c*x^(3/2)) + (1/8)*x^2*log(1 + c*x^(3/2))^2 - PolyLog(2, (1/2)*(1 - c^(1/3)*sqrt(x)))/(4*c^(4/3)) - PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))/(4*c^(4/3)) + PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))/(4*c^(4/3)) + PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))/(4*c^(4/3)) - PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 + (-1)^(2/3)))/(4*c^(4/3)) + ((-1)^(1/3)*PolyLog(2, 1/(1 - (-1)^(1/3)) - c^(1/3)*sqrt(x)))/(4*c^(4/3)) - ((-1)^(2/3)*PolyLog(2, 1/(1 + (-1)^(2/3)) - c^(1/3)*sqrt(x)))/(4*c^(4/3)) - PolyLog(2, (1/2)*(1 + c^(1/3)*sqrt(x)))/(4*c^(4/3)) - PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))/(4*c^(4/3)) + PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))/(4*c^(4/3)) + PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))/(4*c^(4/3)) - PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 + (-1)^(2/3)))/(4*c^(4/3)) + ((-1)^(1/3)*PolyLog(2, 1/(1 - (-1)^(1/3)) + c^(1/3)*sqrt(x)))/(4*c^(4/3)) - ((-1)^(2/3)*PolyLog(2, 1/(1 + (-1)^(2/3)) + c^(1/3)*sqrt(x)))/(4*c^(4/3)) - ((-1)^(2/3)*PolyLog(2, (1/2)*(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))))/(4*c^(4/3)) - ((-1)^(2/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))))/(4*c^(4/3)) + ((-1)^(2/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(4*c^(4/3)) + ((-1)^(2/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))))/(4*c^(4/3)) - ((-1)^(2/3)*PolyLog(2, (1/2)*(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))))/(4*c^(4/3)) - ((-1)^(2/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))))/(4*c^(4/3)) + ((-1)^(2/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(4*c^(4/3)) + ((-1)^(2/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))))/(4*c^(4/3)) + ((-1)^(1/3)*PolyLog(2, (1/2)*(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))))/(4*c^(4/3)) - ((-1)^(1/3)*PolyLog(2, (1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))))/(4*c^(4/3)) + ((-1)^(1/3)*PolyLog(2, (1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))))/(4*c^(4/3)) + ((-1)^(1/3)*PolyLog(2, ((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(4*c^(4/3)) + ((-1)^(1/3)*PolyLog(2, (1/2)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))))/(4*c^(4/3)) - ((-1)^(1/3)*PolyLog(2, (1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))))/(4*c^(4/3)) + ((-1)^(1/3)*PolyLog(2, (1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))))/(4*c^(4/3)) + ((-1)^(1/3)*PolyLog(2, ((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))))/(4*c^(4/3))]
    @test_int [atanh(c*x^(3/2))^2/x^2, x, 160, (-(1/4))*c^(2/3)*log(-1 - c^(1/3)*sqrt(x))^2 + (1/2)*c^(2/3)*log(-1 - c^(1/3)*sqrt(x))*log((1/2)*(1 - c^(1/3)*sqrt(x))) - (1/4)*c^(2/3)*log(1 - c^(1/3)*sqrt(x))^2 + (1/2)*c^(2/3)*log(1 - c^(1/3)*sqrt(x))*log(-(((-1)^(1/3) - c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))) - (1/2)*c^(2/3)*log(-1 - c^(1/3)*sqrt(x))*log(((-1)^(1/3) - c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) - (1/2)*c^(2/3)*log(1 - c^(1/3)*sqrt(x))*log(-(((-1)^(2/3) - c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))) + (1/2)*c^(2/3)*log(-1 - c^(1/3)*sqrt(x))*log(((-1)^(2/3) - c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))) + (1/2)*c^(2/3)*log(1 - c^(1/3)*sqrt(x))*log((1/2)*(1 + c^(1/3)*sqrt(x))) + (1/2)*c^(2/3)*log(-1 - c^(1/3)*sqrt(x))*log(-(((-1)^(1/3) + c^(1/3)*sqrt(x))/(1 - (-1)^(1/3)))) - (1/2)*c^(2/3)*log(1 - c^(1/3)*sqrt(x))*log(((-1)^(1/3) + c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) - (1/2)*c^(2/3)*log(-1 - c^(1/3)*sqrt(x))*log(-(((-1)^(2/3) + c^(1/3)*sqrt(x))/(1 - (-1)^(2/3)))) + (1/2)*c^(2/3)*log(1 - c^(1/3)*sqrt(x))*log(((-1)^(2/3) + c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))) + (1/2)*(-1)^(2/3)*c^(2/3)*log(-(((-1)^(1/3)*(1 - c^(1/3)*sqrt(x)))/(1 - (-1)^(1/3))))*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x)) - (1/2)*(-1)^(2/3)*c^(2/3)*log(((-1)^(1/3)*(1 + c^(1/3)*sqrt(x)))/(1 + (-1)^(1/3)))*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x)) + (1/2)*(-1)^(2/3)*c^(2/3)*log((-1)^(1/3) + c^(1/3)*sqrt(x))*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x)) - (1/4)*(-1)^(2/3)*c^(2/3)*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x))^2 + (1/2)*(-1)^(2/3)*c^(2/3)*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log((1/2)*(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))) - (1/2)*(-1)^(2/3)*c^(2/3)*log(((-1)^(1/3)*(1 - c^(1/3)*sqrt(x)))/(1 + (-1)^(1/3)))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)) + (1/2)*(-1)^(2/3)*c^(2/3)*log((-1)^(1/3) - c^(1/3)*sqrt(x))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)) + (1/2)*(-1)^(2/3)*c^(2/3)*log(-(((-1)^(1/3)*(1 + c^(1/3)*sqrt(x)))/(1 - (-1)^(1/3))))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)) - (1/2)*(-1)^(2/3)*c^(2/3)*log(-(((-1)^(1/3)*((-1)^(1/3) + c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)) + (1/2)*(-1)^(2/3)*c^(2/3)*log((1/2)*(1 - (-1)^(1/3)*c^(1/3)*sqrt(x)))*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x)) - (1/4)*(-1)^(2/3)*c^(2/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))^2 - (1/2)*(-1)^(1/3)*c^(2/3)*log(((-1)^(2/3)*(1 - c^(1/3)*sqrt(x)))/(1 + (-1)^(2/3)))*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x)) + (1/2)*(-1)^(1/3)*c^(2/3)*log(-(((-1)^(2/3)*(1 + c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x)) - (1/2)*(-1)^(1/3)*c^(2/3)*log(-(-1)^(2/3) + c^(1/3)*sqrt(x))*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x)) + (1/4)*(-1)^(1/3)*c^(2/3)*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x))^2 - (1/2)*(-1)^(1/3)*c^(2/3)*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log((1/2)*(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))) + (1/2)*(-1)^(1/3)*c^(2/3)*log(-(((-1)^(2/3)*(1 - c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3))))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)) - (1/2)*(-1)^(1/3)*c^(2/3)*log(-(-1)^(2/3) - c^(1/3)*sqrt(x))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)) - (1/2)*(-1)^(1/3)*c^(2/3)*log(((-1)^(2/3)*(1 + c^(1/3)*sqrt(x)))/(1 + (-1)^(2/3)))*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x)) + (1/4)*(-1)^(1/3)*c^(2/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))^2 + (1/2)*(-1)^(1/3)*c^(2/3)*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) - (1/2)*(-1)^(1/3)*c^(2/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log((1/2)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))) - (1/2)*(-1)^(1/3)*c^(2/3)*log(((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log((1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) - (1/2)*(-1)^(2/3)*c^(2/3)*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(-(((-1)^(2/3)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x)))/(1 - (-1)^(2/3)))) + (1/2)*(-1)^(1/3)*c^(2/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) - (1/2)*(-1)^(1/3)*c^(2/3)*log((1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))*log(((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) - (1/2)*c^(2/3)*log(-1 - c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)) + (1/2)*c^(2/3)*log(1 - c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)) - (1/2)*(-1)^(2/3)*c^(2/3)*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)) + (1/2)*(-1)^(2/3)*c^(2/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)) + (1/2)*(-1)^(1/3)*c^(2/3)*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)) - (1/2)*(-1)^(1/3)*c^(2/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 - c*x^(3/2)) - log(1 - c*x^(3/2))^2/(4*x) + (1/2)*c^(2/3)*log(-1 - c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)) - (1/2)*c^(2/3)*log(1 - c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)) + (1/2)*(-1)^(2/3)*c^(2/3)*log(-1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)) - (1/2)*(-1)^(2/3)*c^(2/3)*log(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)) - (1/2)*(-1)^(1/3)*c^(2/3)*log(-1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)) + (1/2)*(-1)^(1/3)*c^(2/3)*log(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))*log(1 + c*x^(3/2)) + (log(1 - c*x^(3/2))*log(1 + c*x^(3/2)))/(2*x) - log(1 + c*x^(3/2))^2/(4*x) + (1/2)*c^(2/3)*PolyLog(2, (1/2)*(1 - c^(1/3)*sqrt(x))) + (1/2)*c^(2/3)*PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))) - (1/2)*c^(2/3)*PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) - (1/2)*c^(2/3)*PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))) + (1/2)*c^(2/3)*PolyLog(2, (1 - c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))) - (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog(2, 1/(1 - (-1)^(1/3)) - c^(1/3)*sqrt(x)) + (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog(2, 1/(1 + (-1)^(2/3)) - c^(1/3)*sqrt(x)) + (1/2)*c^(2/3)*PolyLog(2, (1/2)*(1 + c^(1/3)*sqrt(x))) + (1/2)*c^(2/3)*PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))) - (1/2)*c^(2/3)*PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) - (1/2)*c^(2/3)*PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))) + (1/2)*c^(2/3)*PolyLog(2, (1 + c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))) - (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog(2, 1/(1 - (-1)^(1/3)) + c^(1/3)*sqrt(x)) + (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog(2, 1/(1 + (-1)^(2/3)) + c^(1/3)*sqrt(x)) + (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog(2, (1/2)*(1 - (-1)^(1/3)*c^(1/3)*sqrt(x))) + (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))) - (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) - (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog(2, (1 - (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))) + (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog(2, (1/2)*(1 + (-1)^(1/3)*c^(1/3)*sqrt(x))) + (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(1/3))) - (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) - (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog(2, (1 + (-1)^(1/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))) - (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog(2, (1/2)*(1 - (-1)^(2/3)*c^(1/3)*sqrt(x))) + (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog(2, (1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))) - (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog(2, (1 - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))) - (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog(2, ((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3))) - (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog(2, (1/2)*(1 + (-1)^(2/3)*c^(1/3)*sqrt(x))) + (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog(2, (1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 - (-1)^(2/3))) - (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog(2, (1 + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(2/3))) - (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog(2, ((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*sqrt(x))/(1 + (-1)^(1/3)))]
    =#

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

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

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

    @test_int [x^1*(a + b*atanh(c*x^n))^2, x, 0, Unintegrable(x*(a + b*atanh(c*x^n))^2, x)]
    @test_int [x^0*(a + b*atanh(c*x^n))^2, x, 0, Unintegrable((a + b*atanh(c*x^n))^2, x)]
    @test_int [(a + b*atanh(c*x^n))^2/x^1, x, 7, (2*(a + b*atanh(c*x^n))^2*atanh(1 - 2/(1 - c*x^n)))/n - (b*(a + b*atanh(c*x^n))*PolyLog(2, 1 - 2/(1 - c*x^n)))/n + (b*(a + b*atanh(c*x^n))*PolyLog(2, -1 + 2/(1 - c*x^n)))/n + (b^2*PolyLog(3, 1 - 2/(1 - c*x^n)))/(2*n) - (b^2*PolyLog(3, -1 + 2/(1 - c*x^n)))/(2*n)]
    @test_int [(a + b*atanh(c*x^n))^2/x^2, x, 0, Unintegrable((a + b*atanh(c*x^n))^2/x^2, x)]
    @test_int [(a + b*atanh(c*x^n))^2/x^3, x, 0, Unintegrable((a + b*atanh(c*x^n))^2/x^3, x)]

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

    @test_int [atanh(a*x^5)/x, x, 2, (-(1/10))*PolyLog(2, (-a)*x^5) + (1/10)*PolyLog(2, a*x^5)]

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

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

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

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

max_stars_repo_path: test/7 Inverse hyperbolic functions/7.3 Inverse hyperbolic tangent/7.3.2 (d x)^m (a+b arctanh(c x^n))^p.jl