text:
@testset "7.4.1 Inverse hyperbolic cotangent functions" begin
    (a, b, c, d, e, f, g, m, n, x, ) = @variables a b c d e f g m n x

    #= ::Package:: =#

    #= ::Title:: =#
    #=Integrands*involving*inverse*hyperbolic*cotangents=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*u*acoth(a*x)^n=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*acoth(a*x)^n=#

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

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

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

    @test_int [x^5*acoth(a*x)^3, x, 33, (19*x)/(60*a^5) + x^3/(60*a^3) + (4*x^2*acoth(a*x))/(15*a^4) + (x^4*acoth(a*x))/(20*a^2) + (23*acoth(a*x)^2)/(30*a^6) + (x*acoth(a*x)^2)/(2*a^5) + (x^3*acoth(a*x)^2)/(6*a^3) + (x^5*acoth(a*x)^2)/(10*a) - acoth(a*x)^3/(6*a^6) + (1/6)*x^6*acoth(a*x)^3 - (19*atanh(a*x))/(60*a^6) - (23*acoth(a*x)*log(2/(1 - a*x)))/(15*a^6) - (23*PolyLog(2, 1 - 2/(1 - a*x)))/(30*a^6)]
    @test_int [x^4*acoth(a*x)^3, x, 22, x^2/(20*a^3) + (9*x*acoth(a*x))/(10*a^4) + (x^3*acoth(a*x))/(10*a^2) - (9*acoth(a*x)^2)/(20*a^5) + (3*x^2*acoth(a*x)^2)/(10*a^3) + (3*x^4*acoth(a*x)^2)/(20*a) + acoth(a*x)^3/(5*a^5) + (1/5)*x^5*acoth(a*x)^3 - (3*acoth(a*x)^2*log(2/(1 - a*x)))/(5*a^5) + log(1 - a^2*x^2)/(2*a^5) - (3*acoth(a*x)*PolyLog(2, 1 - 2/(1 - a*x)))/(5*a^5) + (3*PolyLog(3, 1 - 2/(1 - a*x)))/(10*a^5)]
    @test_int [x^3*acoth(a*x)^3, x, 18, x/(4*a^3) + (x^2*acoth(a*x))/(4*a^2) + acoth(a*x)^2/a^4 + (3*x*acoth(a*x)^2)/(4*a^3) + (x^3*acoth(a*x)^2)/(4*a) - acoth(a*x)^3/(4*a^4) + (1/4)*x^4*acoth(a*x)^3 - atanh(a*x)/(4*a^4) - (2*acoth(a*x)*log(2/(1 - a*x)))/a^4 - PolyLog(2, 1 - 2/(1 - a*x))/a^4]
    @test_int [x^2*acoth(a*x)^3, x, 11, (x*acoth(a*x))/a^2 - acoth(a*x)^2/(2*a^3) + (x^2*acoth(a*x)^2)/(2*a) + acoth(a*x)^3/(3*a^3) + (1/3)*x^3*acoth(a*x)^3 - (acoth(a*x)^2*log(2/(1 - a*x)))/a^3 + log(1 - a^2*x^2)/(2*a^3) - (acoth(a*x)*PolyLog(2, 1 - 2/(1 - a*x)))/a^3 + PolyLog(3, 1 - 2/(1 - a*x))/(2*a^3)]
    @test_int [x^1*acoth(a*x)^3, x, 8, (3*acoth(a*x)^2)/(2*a^2) + (3*x*acoth(a*x)^2)/(2*a) - acoth(a*x)^3/(2*a^2) + (1/2)*x^2*acoth(a*x)^3 - (3*acoth(a*x)*log(2/(1 - a*x)))/a^2 - (3*PolyLog(2, 1 - 2/(1 - a*x)))/(2*a^2)]
    @test_int [x^0*acoth(a*x)^3, x, 5, acoth(a*x)^3/a + x*acoth(a*x)^3 - (3*acoth(a*x)^2*log(2/(1 - a*x)))/a - (3*acoth(a*x)*PolyLog(2, 1 - 2/(1 - a*x)))/a + (3*PolyLog(3, 1 - 2/(1 - a*x)))/(2*a)]
    @test_int [acoth(a*x)^3/x^1, x, 8, 2*acoth(a*x)^3*acoth(1 - 2/(1 - a*x)) + (3/2)*acoth(a*x)^2*PolyLog(2, 1 - 2/(1 + a*x)) - (3/2)*acoth(a*x)^2*PolyLog(2, 1 - (2*a*x)/(1 + a*x)) + (3/2)*acoth(a*x)*PolyLog(3, 1 - 2/(1 + a*x)) - (3/2)*acoth(a*x)*PolyLog(3, 1 - (2*a*x)/(1 + a*x)) + (3/4)*PolyLog(4, 1 - 2/(1 + a*x)) - (3/4)*PolyLog(4, 1 - (2*a*x)/(1 + a*x))]
    @test_int [acoth(a*x)^3/x^2, x, 5, a*acoth(a*x)^3 - acoth(a*x)^3/x + 3*a*acoth(a*x)^2*log(2 - 2/(1 + a*x)) - 3*a*acoth(a*x)*PolyLog(2, -1 + 2/(1 + a*x)) - (3/2)*a*PolyLog(3, -1 + 2/(1 + a*x))]
    @test_int [acoth(a*x)^3/x^3, x, 7, (3/2)*a^2*acoth(a*x)^2 - (3*a*acoth(a*x)^2)/(2*x) + (1/2)*a^2*acoth(a*x)^3 - acoth(a*x)^3/(2*x^2) + 3*a^2*acoth(a*x)*log(2 - 2/(1 + a*x)) - (3/2)*a^2*PolyLog(2, -1 + 2/(1 + a*x))]
    @test_int [acoth(a*x)^3/x^4, x, 14, -((a^2*acoth(a*x))/x) + (1/2)*a^3*acoth(a*x)^2 - (a*acoth(a*x)^2)/(2*x^2) + (1/3)*a^3*acoth(a*x)^3 - acoth(a*x)^3/(3*x^3) + a^3*log(x) - (1/2)*a^3*log(1 - a^2*x^2) + a^3*acoth(a*x)^2*log(2 - 2/(1 + a*x)) - a^3*acoth(a*x)*PolyLog(2, -1 + 2/(1 + a*x)) - (1/2)*a^3*PolyLog(3, -1 + 2/(1 + a*x))]
    @test_int [acoth(a*x)^3/x^5, x, 16, -(a^3/(4*x)) - (a^2*acoth(a*x))/(4*x^2) + a^4*acoth(a*x)^2 - (a*acoth(a*x)^2)/(4*x^3) - (3*a^3*acoth(a*x)^2)/(4*x) + (1/4)*a^4*acoth(a*x)^3 - acoth(a*x)^3/(4*x^4) + (1/4)*a^4*atanh(a*x) + 2*a^4*acoth(a*x)*log(2 - 2/(1 + a*x)) - a^4*PolyLog(2, -1 + 2/(1 + a*x))]

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

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

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

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

    @test_int [acoth(a*x)*(c + d*x^2)^4, x, 4, (d*(420*a^6*c^3 + 378*a^4*c^2*d + 180*a^2*c*d^2 + 35*d^3)*x^2)/(630*a^7) + (d^2*(378*a^4*c^2 + 180*a^2*c*d + 35*d^2)*x^4)/(1260*a^5) + (d^3*(36*a^2*c + 7*d)*x^6)/(378*a^3) + (d^4*x^8)/(72*a) + c^4*x*acoth(a*x) + (4/3)*c^3*d*x^3*acoth(a*x) + (6/5)*c^2*d^2*x^5*acoth(a*x) + (4/7)*c*d^3*x^7*acoth(a*x) + (1/9)*d^4*x^9*acoth(a*x) + ((315*a^8*c^4 + 420*a^6*c^3*d + 378*a^4*c^2*d^2 + 180*a^2*c*d^3 + 35*d^4)*log(1 - a^2*x^2))/(630*a^9)]
    @test_int [acoth(a*x)*(c + d*x^2)^3, x, 4, (d*(35*a^4*c^2 + 21*a^2*c*d + 5*d^2)*x^2)/(70*a^5) + (d^2*(21*a^2*c + 5*d)*x^4)/(140*a^3) + (d^3*x^6)/(42*a) + c^3*x*acoth(a*x) + c^2*d*x^3*acoth(a*x) + (3/5)*c*d^2*x^5*acoth(a*x) + (1/7)*d^3*x^7*acoth(a*x) + ((35*a^6*c^3 + 35*a^4*c^2*d + 21*a^2*c*d^2 + 5*d^3)*log(1 - a^2*x^2))/(70*a^7)]
    @test_int [acoth(a*x)*(c + d*x^2)^2, x, 5, (d*(10*a^2*c + 3*d)*x^2)/(30*a^3) + (d^2*x^4)/(20*a) + c^2*x*acoth(a*x) + (2/3)*c*d*x^3*acoth(a*x) + (1/5)*d^2*x^5*acoth(a*x) + ((15*a^4*c^2 + 10*a^2*c*d + 3*d^2)*log(1 - a^2*x^2))/(30*a^5)]
    @test_int [acoth(a*x)*(c + d*x^2)^1, x, 5, (d*x^2)/(6*a) + c*x*acoth(a*x) + (1/3)*d*x^3*acoth(a*x) + ((3*a^2*c + d)*log(1 - a^2*x^2))/(6*a^3)]
    @test_int [acoth(a*x)/(c + d*x^2)^1, x, 27, -((atan((sqrt(d)*x)/sqrt(c))*log(1 - 1/(a*x)))/(2*sqrt(c)*sqrt(d))) + (atan((sqrt(d)*x)/sqrt(c))*log(1 + 1/(a*x)))/(2*sqrt(c)*sqrt(d)) + (atan((sqrt(d)*x)/sqrt(c))*log(-((2*sqrt(c)*sqrt(d)*(1 - a*x))/((im*a*sqrt(c) - sqrt(d))*(sqrt(c) - im*sqrt(d)*x)))))/(2*sqrt(c)*sqrt(d)) - (atan((sqrt(d)*x)/sqrt(c))*log((2*sqrt(c)*sqrt(d)*(1 + a*x))/((im*a*sqrt(c) + sqrt(d))*(sqrt(c) - im*sqrt(d)*x))))/(2*sqrt(c)*sqrt(d)) - (im*PolyLog(2, 1 + (2*sqrt(c)*sqrt(d)*(1 - a*x))/((im*a*sqrt(c) - sqrt(d))*(sqrt(c) - im*sqrt(d)*x))))/(4*sqrt(c)*sqrt(d)) + (im*PolyLog(2, 1 - (2*sqrt(c)*sqrt(d)*(1 + a*x))/((im*a*sqrt(c) + sqrt(d))*(sqrt(c) - im*sqrt(d)*x))))/(4*sqrt(c)*sqrt(d))]
    @test_int [acoth(a*x)/(c + d*x^2)^2, x, If(13<11, 24, 25), (x*acoth(a*x))/(2*c*(c + d*x^2)) + (acoth(a*x)*atan((sqrt(d)*x)/sqrt(c)))/(2*c^(3/2)*sqrt(d)) + (im*log((sqrt(d)*(1 - a*x))/(im*a*sqrt(c) + sqrt(d)))*log(1 - (im*sqrt(d)*x)/sqrt(c)))/(8*c^(3/2)*sqrt(d)) - (im*log(-((sqrt(d)*(1 + a*x))/(im*a*sqrt(c) - sqrt(d))))*log(1 - (im*sqrt(d)*x)/sqrt(c)))/(8*c^(3/2)*sqrt(d)) - (im*log(-((sqrt(d)*(1 - a*x))/(im*a*sqrt(c) - sqrt(d))))*log(1 + (im*sqrt(d)*x)/sqrt(c)))/(8*c^(3/2)*sqrt(d)) + (im*log((sqrt(d)*(1 + a*x))/(im*a*sqrt(c) + sqrt(d)))*log(1 + (im*sqrt(d)*x)/sqrt(c)))/(8*c^(3/2)*sqrt(d)) + (a*log(1 - a^2*x^2))/(4*c*(a^2*c + d)) - (a*log(c + d*x^2))/(4*c*(a^2*c + d)) + (im*PolyLog(2, (a*(sqrt(c) - im*sqrt(d)*x))/(a*sqrt(c) - im*sqrt(d))))/(8*c^(3/2)*sqrt(d)) - (im*PolyLog(2, (a*(sqrt(c) - im*sqrt(d)*x))/(a*sqrt(c) + im*sqrt(d))))/(8*c^(3/2)*sqrt(d)) + (im*PolyLog(2, (a*(sqrt(c) + im*sqrt(d)*x))/(a*sqrt(c) - im*sqrt(d))))/(8*c^(3/2)*sqrt(d)) - (im*PolyLog(2, (a*(sqrt(c) + im*sqrt(d)*x))/(a*sqrt(c) + im*sqrt(d))))/(8*c^(3/2)*sqrt(d))]
    @test_int [acoth(a*x)/(c + d*x^2)^3, x, 23, a/(8*c*(a^2*c + d)*(c + d*x^2)) + (x*acoth(a*x))/(4*c*(c + d*x^2)^2) + (3*x*acoth(a*x))/(8*c^2*(c + d*x^2)) + (3*acoth(a*x)*atan((sqrt(d)*x)/sqrt(c)))/(8*c^(5/2)*sqrt(d)) + (3*im*log((sqrt(d)*(1 - a*x))/(im*a*sqrt(c) + sqrt(d)))*log(1 - (im*sqrt(d)*x)/sqrt(c)))/(32*c^(5/2)*sqrt(d)) - (3*im*log(-((sqrt(d)*(1 + a*x))/(im*a*sqrt(c) - sqrt(d))))*log(1 - (im*sqrt(d)*x)/sqrt(c)))/(32*c^(5/2)*sqrt(d)) - (3*im*log(-((sqrt(d)*(1 - a*x))/(im*a*sqrt(c) - sqrt(d))))*log(1 + (im*sqrt(d)*x)/sqrt(c)))/(32*c^(5/2)*sqrt(d)) + (3*im*log((sqrt(d)*(1 + a*x))/(im*a*sqrt(c) + sqrt(d)))*log(1 + (im*sqrt(d)*x)/sqrt(c)))/(32*c^(5/2)*sqrt(d)) + (a*(5*a^2*c + 3*d)*log(1 - a^2*x^2))/(16*c^2*(a^2*c + d)^2) - (a*(5*a^2*c + 3*d)*log(c + d*x^2))/(16*c^2*(a^2*c + d)^2) + (3*im*PolyLog(2, (a*(sqrt(c) - im*sqrt(d)*x))/(a*sqrt(c) - im*sqrt(d))))/(32*c^(5/2)*sqrt(d)) - (3*im*PolyLog(2, (a*(sqrt(c) - im*sqrt(d)*x))/(a*sqrt(c) + im*sqrt(d))))/(32*c^(5/2)*sqrt(d)) + (3*im*PolyLog(2, (a*(sqrt(c) + im*sqrt(d)*x))/(a*sqrt(c) - im*sqrt(d))))/(32*c^(5/2)*sqrt(d)) - (3*im*PolyLog(2, (a*(sqrt(c) + im*sqrt(d)*x))/(a*sqrt(c) + im*sqrt(d))))/(32*c^(5/2)*sqrt(d))]

    @test_int [acoth(a*x)*(c + d*x^2)^(1/2), x, 0, Unintegrable(sqrt(c + d*x^2)*acoth(a*x), x)]
    @test_int [acoth(a*x)/(c + d*x^2)^(1/2), x, 0, Unintegrable(acoth(a*x)/sqrt(c + d*x^2), x)]
    @test_int [acoth(a*x)/(c + d*x^2)^(3/2), x, 5, (x*acoth(a*x))/(c*sqrt(c + d*x^2)) - atanh((a*sqrt(c + d*x^2))/sqrt(a^2*c + d))/(c*sqrt(a^2*c + d))]
    @test_int [acoth(a*x)/(c + d*x^2)^(5/2), x, 7, a/(3*c*(a^2*c + d)*sqrt(c + d*x^2)) + (x*acoth(a*x))/(3*c*(c + d*x^2)^(3/2)) + (2*x*acoth(a*x))/(3*c^2*sqrt(c + d*x^2)) - ((3*a^2*c + 2*d)*atanh((a*sqrt(c + d*x^2))/sqrt(a^2*c + d)))/(3*c^2*(a^2*c + d)^(3/2))]
    @test_int [acoth(a*x)/(c + d*x^2)^(7/2), x, 8, a/(15*c*(a^2*c + d)*(c + d*x^2)^(3/2)) + (a*(7*a^2*c + 4*d))/(15*c^2*(a^2*c + d)^2*sqrt(c + d*x^2)) + (x*acoth(a*x))/(5*c*(c + d*x^2)^(5/2)) + (4*x*acoth(a*x))/(15*c^2*(c + d*x^2)^(3/2)) + (8*x*acoth(a*x))/(15*c^3*sqrt(c + d*x^2)) - ((15*a^4*c^2 + 20*a^2*c*d + 8*d^2)*atanh((a*sqrt(c + d*x^2))/sqrt(a^2*c + d)))/(15*c^3*(a^2*c + d)^(5/2))]
    @test_int [acoth(a*x)/(c + d*x^2)^(9/2), x, 8, a/(35*c*(a^2*c + d)*(c + d*x^2)^(5/2)) + (a*(11*a^2*c + 6*d))/(105*c^2*(a^2*c + d)^2*(c + d*x^2)^(3/2)) + (a*(19*a^4*c^2 + 22*a^2*c*d + 8*d^2))/(35*c^3*(a^2*c + d)^3*sqrt(c + d*x^2)) + (x*acoth(a*x))/(7*c*(c + d*x^2)^(7/2)) + (6*x*acoth(a*x))/(35*c^2*(c + d*x^2)^(5/2)) + (8*x*acoth(a*x))/(35*c^3*(c + d*x^2)^(3/2)) + (16*x*acoth(a*x))/(35*c^4*sqrt(c + d*x^2)) - ((35*a^6*c^3 + 70*a^4*c^2*d + 56*a^2*c*d^2 + 16*d^3)*atanh((a*sqrt(c + d*x^2))/sqrt(a^2*c + d)))/(35*c^4*(a^2*c + d)^(7/2))]

    @test_int [acoth(x)*(a - a*x^2)^(1/2), x, 3, (1/2)*sqrt(a - a*x^2) + (1/2)*x*sqrt(a - a*x^2)*acoth(x) - (a*sqrt(1 - x^2)*acoth(x)*atan(sqrt(1 - x)/sqrt(1 + x)))/sqrt(a - a*x^2) - (im*a*sqrt(1 - x^2)*PolyLog(2, -((im*sqrt(1 - x))/sqrt(1 + x))))/(2*sqrt(a - a*x^2)) + (im*a*sqrt(1 - x^2)*PolyLog(2, (im*sqrt(1 - x))/sqrt(1 + x)))/(2*sqrt(a - a*x^2))]
    @test_int [acoth(x)/(a - a*x^2)^(1/2), x, 2, -((2*sqrt(1 - x^2)*acoth(x)*atan(sqrt(1 - x)/sqrt(1 + x)))/sqrt(a - a*x^2)) - (im*sqrt(1 - x^2)*PolyLog(2, -((im*sqrt(1 - x))/sqrt(1 + x))))/sqrt(a - a*x^2) + (im*sqrt(1 - x^2)*PolyLog(2, (im*sqrt(1 - x))/sqrt(1 + x)))/sqrt(a - a*x^2)]
    @test_int [acoth(x)/(a - a*x^2)^(3/2), x, 1, -(1/(a*sqrt(a - a*x^2))) + (x*acoth(x))/(a*sqrt(a - a*x^2))]
    @test_int [acoth(x)/(a - a*x^2)^(5/2), x, 2, -(1/(9*a*(a - a*x^2)^(3/2))) - 2/(3*a^2*sqrt(a - a*x^2)) + (x*acoth(x))/(3*a*(a - a*x^2)^(3/2)) + (2*x*acoth(x))/(3*a^2*sqrt(a - a*x^2))]
    @test_int [acoth(x)/(a - a*x^2)^(7/2), x, 3, -(1/(25*a*(a - a*x^2)^(5/2))) - 4/(45*a^2*(a - a*x^2)^(3/2)) - 8/(15*a^3*sqrt(a - a*x^2)) + (x*acoth(x))/(5*a*(a - a*x^2)^(5/2)) + (4*x*acoth(x))/(15*a^2*(a - a*x^2)^(3/2)) + (8*x*acoth(x))/(15*a^3*sqrt(a - a*x^2))]

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

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

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

    @test_int [x^1*acoth(x)/(1 - x^2), x, 4, (-(1/2))*acoth(x)^2 + acoth(x)*log(2/(1 - x)) + (1/2)*PolyLog(2, (1 + x)/(-1 + x))]
    @test_int [x^0*acoth(x)/(1 - x^2), x, 1, acoth(x)^2/2]

    @test_int [x^1*acoth(x)/(1 - x^2)^2, x, 3, -(x/(4*(1 - x^2))) + acoth(x)/(2*(1 - x^2)) - atanh(x)/4]
    @test_int [x^0*acoth(x)/(1 - x^2)^2, x, 2, -(1/(4*(1 - x^2))) + (x*acoth(x))/(2*(1 - x^2)) + acoth(x)^2/4]

    @test_int [x^1*acoth(x)/(1 - x^2)^3, x, 4, -(x/(16*(1 - x^2)^2)) - (3*x)/(32*(1 - x^2)) + acoth(x)/(4*(1 - x^2)^2) - (3*atanh(x))/32]
    @test_int [x^0*acoth(x)/(1 - x^2)^3, x, 3, -(1/(16*(1 - x^2)^2)) - 3/(16*(1 - x^2)) + (x*acoth(x))/(4*(1 - x^2)^2) + (3*x*acoth(x))/(8*(1 - x^2)) + (3*acoth(x)^2)/16]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*u*acoth(a+b*x)^n=#

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

    @test_int [x^3*acoth(a + b*x), x, 7, ((1 + 6*a^2)*x)/(4*b^3) - (a*(a + b*x)^2)/(2*b^4) + (a + b*x)^3/(12*b^4) + (1/4)*x^4*acoth(a + b*x) + ((1 - a)^4*log(1 - a - b*x))/(8*b^4) - ((1 + a)^4*log(1 + a + b*x))/(8*b^4)]
    @test_int [x^2*acoth(a + b*x), x, 7, -((a*x)/b^2) + (a + b*x)^2/(6*b^3) + (1/3)*x^3*acoth(a + b*x) + ((1 - a)^3*log(1 - a - b*x))/(6*b^3) + ((1 + a)^3*log(1 + a + b*x))/(6*b^3)]
    @test_int [x^1*acoth(a + b*x), x, 7, x/(2*b) + (1/2)*x^2*acoth(a + b*x) + ((1 - a)^2*log(1 - a - b*x))/(4*b^2) - ((1 + a)^2*log(1 + a + b*x))/(4*b^2)]
    @test_int [x^0*acoth(a + b*x), x, 3, ((a + b*x)*acoth(a + b*x))/b + log(1 - (a + b*x)^2)/(2*b)]
    @test_int [acoth(a + b*x)/x^1, x, 5, (-acoth(a + b*x))*log(2/(1 + a + b*x)) + acoth(a + b*x)*log((2*b*x)/((1 - a)*(1 + a + b*x))) + (1/2)*PolyLog(2, 1 - 2/(1 + a + b*x)) - (1/2)*PolyLog(2, 1 - (2*b*x)/((1 - a)*(1 + a + b*x)))]
    @test_int [acoth(a + b*x)/x^2, x, 7, -(acoth(a + b*x)/x) + (b*log(x))/(1 - a^2) - (b*log(1 - a - b*x))/(2*(1 - a)) - (b*log(1 + a + b*x))/(2*(1 + a))]
    @test_int [acoth(a + b*x)/x^3, x, 5, -(b/(2*(1 - a^2)*x)) - acoth(a + b*x)/(2*x^2) + (a*b^2*log(x))/(1 - a^2)^2 - (b^2*log(1 - a - b*x))/(4*(1 - a)^2) + (b^2*log(1 + a + b*x))/(4*(1 + a)^2)]

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

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

    #= [acoth(a + b*x)/(c + d*x^3), x, 51, (log((d^(1/3)*(1 - a - b*x))/(b*c^(1/3) + (1 - a)*d^(1/3)))*log(-c^(1/3) - d^(1/3)*x))/(6*c^(2/3)*d^(1/3)) - (log(-((d^(1/3)*(1 + a + b*x))/(b*c^(1/3) - (1 + a)*d^(1/3))))*log(-c^(1/3) - d^(1/3)*x))/(6*c^(2/3)*d^(1/3)) - ((-1)^(1/3)*log(-((d^(1/3)*(1 - a - b*x))/((-1)^(1/3)*b*c^(1/3) - (1 - a)*d^(1/3))))*log((-1)^(1/3)*c^(1/3) - d^(1/3)*x))/(6*c^(2/3)*d^(1/3)) + ((-1)^(1/3)*log((d^(1/3)*(1 + a + b*x))/((-1)^(1/3)*b*c^(1/3) + (1 + a)*d^(1/3)))*log((-1)^(1/3)*c^(1/3) - d^(1/3)*x))/(6*c^(2/3)*d^(1/3)) + ((-1)^(2/3)*log((d^(1/3)*(1 - a - b*x))/((-1)^(2/3)*b*c^(1/3) + (1 - a)*d^(1/3)))*log((-(-1)^(2/3))*c^(1/3) - d^(1/3)*x))/(6*c^(2/3)*d^(1/3)) - ((-1)^(2/3)*log(-((d^(1/3)*(1 + a + b*x))/((-1)^(2/3)*b*c^(1/3) - (1 + a)*d^(1/3))))*log((-(-1)^(2/3))*c^(1/3) - d^(1/3)*x))/(6*c^(2/3)*d^(1/3)) - (log(-c^(1/3) - d^(1/3)*x)*log(1 - 1/(a + b*x)))/(6*c^(2/3)*d^(1/3)) + ((-1)^(1/3)*log((-1)^(1/3)*c^(1/3) - d^(1/3)*x)*log(1 - 1/(a + b*x)))/(6*c^(2/3)*d^(1/3)) - ((-1)^(2/3)*log((-(-1)^(2/3))*c^(1/3) - d^(1/3)*x)*log(1 - 1/(a + b*x)))/(6*c^(2/3)*d^(1/3)) + (log(-c^(1/3) - d^(1/3)*x)*log(1 + 1/(a + b*x)))/(6*c^(2/3)*d^(1/3)) - ((-1)^(1/3)*log((-1)^(1/3)*c^(1/3) - d^(1/3)*x)*log(1 + 1/(a + b*x)))/(6*c^(2/3)*d^(1/3)) + ((-1)^(2/3)*log((-(-1)^(2/3))*c^(1/3) - d^(1/3)*x)*log(1 + 1/(a + b*x)))/(6*c^(2/3)*d^(1/3)) + PolyLog(2, (b*(c^(1/3) + d^(1/3)*x))/(b*c^(1/3) + (1 - a)*d^(1/3)))/(6*c^(2/3)*d^(1/3)) - PolyLog(2, (b*(c^(1/3) + d^(1/3)*x))/(b*c^(1/3) - (1 + a)*d^(1/3)))/(6*c^(2/3)*d^(1/3)) + ((-1)^(2/3)*PolyLog(2, (b*((-1)^(2/3)*c^(1/3) + d^(1/3)*x))/((-1)^(2/3)*b*c^(1/3) + (1 - a)*d^(1/3))))/(6*c^(2/3)*d^(1/3)) - ((-1)^(2/3)*PolyLog(2, (b*((-1)^(2/3)*c^(1/3) + d^(1/3)*x))/((-1)^(2/3)*b*c^(1/3) - (1 + a)*d^(1/3))))/(6*c^(2/3)*d^(1/3)) - ((-1)^(1/3)*PolyLog(2, ((-1)^(1/3)*b*(c^(1/3) + (-1)^(2/3)*d^(1/3)*x))/((-1)^(1/3)*b*c^(1/3) - (1 - a)*d^(1/3))))/(6*c^(2/3)*d^(1/3)) + ((-1)^(1/3)*PolyLog(2, ((-1)^(1/3)*b*(c^(1/3) + (-1)^(2/3)*d^(1/3)*x))/((-1)^(1/3)*b*c^(1/3) + (1 + a)*d^(1/3))))/(6*c^(2/3)*d^(1/3))] =#
    @test_int [acoth(a + b*x)/(c + d*x^2), x, 15, (log(-((1 - a - b*x)/(a + b*x)))*log(1 + ((b^2*c + a^2*d)*(1 - a - b*x))/((b^2*c - b*sqrt(-c)*sqrt(d) - (1 - a)*a*d)*(a + b*x))))/(4*sqrt(-c)*sqrt(d)) - (log(-((1 - a - b*x)/(a + b*x)))*log(1 + ((b^2*c + a^2*d)*(1 - a - b*x))/((b^2*c + b*sqrt(-c)*sqrt(d) - (1 - a)*a*d)*(a + b*x))))/(4*sqrt(-c)*sqrt(d)) + (log((1 + a + b*x)/(a + b*x))*log(1 - ((b^2*c + a^2*d)*(1 + a + b*x))/((b^2*c - b*sqrt(-c)*sqrt(d) + a*(1 + a)*d)*(a + b*x))))/(4*sqrt(-c)*sqrt(d)) - (log((1 + a + b*x)/(a + b*x))*log(1 - ((b^2*c + a^2*d)*(1 + a + b*x))/((b^2*c + b*sqrt(-c)*sqrt(d) + a*(1 + a)*d)*(a + b*x))))/(4*sqrt(-c)*sqrt(d)) + PolyLog(2, -(((b^2*c + a^2*d)*(1 - a - b*x))/((b^2*c - b*sqrt(-c)*sqrt(d) - (1 - a)*a*d)*(a + b*x))))/(4*sqrt(-c)*sqrt(d)) - PolyLog(2, -(((b^2*c + a^2*d)*(1 - a - b*x))/((b^2*c + b*sqrt(-c)*sqrt(d) - (1 - a)*a*d)*(a + b*x))))/(4*sqrt(-c)*sqrt(d)) + PolyLog(2, ((b^2*c + a^2*d)*(1 + a + b*x))/((b^2*c - b*sqrt(-c)*sqrt(d) + a*(1 + a)*d)*(a + b*x)))/(4*sqrt(-c)*sqrt(d)) - PolyLog(2, ((b^2*c + a^2*d)*(1 + a + b*x))/((b^2*c + b*sqrt(-c)*sqrt(d) + a*(1 + a)*d)*(a + b*x)))/(4*sqrt(-c)*sqrt(d))]
    @test_int [acoth(a + b*x)/(c + d*x^1), x, 5, -((acoth(a + b*x)*log(2/(1 + a + b*x)))/d) + (acoth(a + b*x)*log((2*b*(c + d*x))/((b*c + d - a*d)*(1 + a + b*x))))/d + PolyLog(2, 1 - 2/(1 + a + b*x))/(2*d) - PolyLog(2, 1 - (2*b*(c + d*x))/((b*c + d - a*d)*(1 + a + b*x)))/(2*d)]
    @test_int [acoth(a + b*x)/(c + d/x^1), x, 37, ((1 - a - b*x)*log(-((1 - a - b*x)/(a + b*x))))/(2*b*c) + log(a + b*x)/(2*b*c) + log(1 + a + b*x)/(2*b*c) + ((a + b*x)*log((1 + a + b*x)/(a + b*x)))/(2*b*c) - (d*log((c*(1 - a - b*x))/(c - a*c + b*d))*log(d + c*x))/(2*c^2) + (d*log(-((1 - a - b*x)/(a + b*x)))*log(d + c*x))/(2*c^2) + (d*log((c*(1 + a + b*x))/(c + a*c - b*d))*log(d + c*x))/(2*c^2) - (d*log((1 + a + b*x)/(a + b*x))*log(d + c*x))/(2*c^2) + (d*PolyLog(2, -((b*(d + c*x))/(c + a*c - b*d))))/(2*c^2) - (d*PolyLog(2, (b*(d + c*x))/(c - a*c + b*d)))/(2*c^2), ((1 - a - b*x)*log(-1 + a + b*x))/(2*b*c) + (x*(log(-1 + a + b*x) - log(-((1 - a - b*x)/(a + b*x))) - log(a + b*x)))/(2*c) + ((1 + a + b*x)*log(1 + a + b*x))/(2*b*c) + (x*(log(a + b*x) - log(1 + a + b*x) + log((1 + a + b*x)/(a + b*x))))/(2*c) - (d*(log(-1 + a + b*x) - log(-((1 - a - b*x)/(a + b*x))) - log(a + b*x))*log(d + c*x))/(2*c^2) - (d*(log(a + b*x) - log(1 + a + b*x) + log((1 + a + b*x)/(a + b*x)))*log(d + c*x))/(2*c^2) - (d*log(1 + a + b*x)*log(-((b*(d + c*x))/(c + a*c - b*d))))/(2*c^2) + (d*log(-1 + a + b*x)*log((b*(d + c*x))/(c - a*c + b*d)))/(2*c^2) + (d*PolyLog(2, (c*(1 - a - b*x))/(c - a*c + b*d)))/(2*c^2) - (d*PolyLog(2, (c*(1 + a + b*x))/(c + a*c - b*d)))/(2*c^2)]
    @test_int [acoth(a + b*x)/(c + d/x^2), x, 57, ((1 - a - b*x)*log(-1 + a + b*x))/(2*b*c) + (x*(log(-1 + a + b*x) - log(-((1 - a - b*x)/(a + b*x))) - log(a + b*x)))/(2*c) - (sqrt(d)*atan((sqrt(c)*x)/sqrt(d))*(log(-1 + a + b*x) - log(-((1 - a - b*x)/(a + b*x))) - log(a + b*x)))/(2*c^(3/2)) + ((1 + a + b*x)*log(1 + a + b*x))/(2*b*c) + (x*(log(a + b*x) - log(1 + a + b*x) + log((1 + a + b*x)/(a + b*x))))/(2*c) - (sqrt(d)*atan((sqrt(c)*x)/sqrt(d))*(log(a + b*x) - log(1 + a + b*x) + log((1 + a + b*x)/(a + b*x))))/(2*c^(3/2)) + (sqrt(d)*log(-1 + a + b*x)*log(-((b*(sqrt(d) - sqrt(-c)*x))/((1 - a)*sqrt(-c) - b*sqrt(d)))))/(4*(-c)^(3/2)) - (sqrt(d)*log(1 + a + b*x)*log((b*(sqrt(d) - sqrt(-c)*x))/((1 + a)*sqrt(-c) + b*sqrt(d))))/(4*(-c)^(3/2)) + (sqrt(d)*log(1 + a + b*x)*log(-((b*(sqrt(d) + sqrt(-c)*x))/((1 + a)*sqrt(-c) - b*sqrt(d)))))/(4*(-c)^(3/2)) - (sqrt(d)*log(-1 + a + b*x)*log((b*(sqrt(d) + sqrt(-c)*x))/((1 - a)*sqrt(-c) + b*sqrt(d))))/(4*(-c)^(3/2)) + (sqrt(d)*PolyLog(2, (sqrt(-c)*(1 - a - b*x))/((1 - a)*sqrt(-c) - b*sqrt(d))))/(4*(-c)^(3/2)) - (sqrt(d)*PolyLog(2, (sqrt(-c)*(1 - a - b*x))/((1 - a)*sqrt(-c) + b*sqrt(d))))/(4*(-c)^(3/2)) + (sqrt(d)*PolyLog(2, (sqrt(-c)*(1 + a + b*x))/((1 + a)*sqrt(-c) - b*sqrt(d))))/(4*(-c)^(3/2)) - (sqrt(d)*PolyLog(2, (sqrt(-c)*(1 + a + b*x))/((1 + a)*sqrt(-c) + b*sqrt(d))))/(4*(-c)^(3/2))]
    #= [acoth(a + b*x)/(c + d/x^3), x, 59, log(1 - a - b*x)/(2*b*c) + log(1 + a + b*x)/(2*b*c) - (d^(1/3)*log((c^(1/3)*(1 - a - b*x))/((1 - a)*c^(1/3) + b*d^(1/3)))*log(-d^(1/3) - c^(1/3)*x))/(6*c^(4/3)) + (d^(1/3)*log((c^(1/3)*(1 + a + b*x))/((1 + a)*c^(1/3) - b*d^(1/3)))*log(-d^(1/3) - c^(1/3)*x))/(6*c^(4/3)) + ((-1)^(1/3)*d^(1/3)*log((c^(1/3)*(1 - a - b*x))/((1 - a)*c^(1/3) - (-1)^(1/3)*b*d^(1/3)))*log((-1)^(1/3)*d^(1/3) - c^(1/3)*x))/(6*c^(4/3)) - ((-1)^(1/3)*d^(1/3)*log((c^(1/3)*(1 + a + b*x))/((1 + a)*c^(1/3) + (-1)^(1/3)*b*d^(1/3)))*log((-1)^(1/3)*d^(1/3) - c^(1/3)*x))/(6*c^(4/3)) - ((-1)^(2/3)*d^(1/3)*log((c^(1/3)*(1 - a - b*x))/((1 - a)*c^(1/3) + (-1)^(2/3)*b*d^(1/3)))*log((-(-1)^(2/3))*d^(1/3) - c^(1/3)*x))/(6*c^(4/3)) + ((-1)^(2/3)*d^(1/3)*log((c^(1/3)*(1 + a + b*x))/((1 + a)*c^(1/3) - (-1)^(2/3)*b*d^(1/3)))*log((-(-1)^(2/3))*d^(1/3) - c^(1/3)*x))/(6*c^(4/3)) - ((a + b*x)*log(1 - 1/(a + b*x)))/(2*b*c) + (d^(1/3)*log(-d^(1/3) - c^(1/3)*x)*log(1 - 1/(a + b*x)))/(6*c^(4/3)) - ((-1)^(1/3)*d^(1/3)*log((-1)^(1/3)*d^(1/3) - c^(1/3)*x)*log(1 - 1/(a + b*x)))/(6*c^(4/3)) + ((-1)^(2/3)*d^(1/3)*log((-(-1)^(2/3))*d^(1/3) - c^(1/3)*x)*log(1 - 1/(a + b*x)))/(6*c^(4/3)) + ((a + b*x)*log(1 + 1/(a + b*x)))/(2*b*c) - (d^(1/3)*log(-d^(1/3) - c^(1/3)*x)*log(1 + 1/(a + b*x)))/(6*c^(4/3)) + ((-1)^(1/3)*d^(1/3)*log((-1)^(1/3)*d^(1/3) - c^(1/3)*x)*log(1 + 1/(a + b*x)))/(6*c^(4/3)) - ((-1)^(2/3)*d^(1/3)*log((-(-1)^(2/3))*d^(1/3) - c^(1/3)*x)*log(1 + 1/(a + b*x)))/(6*c^(4/3)) + (d^(1/3)*PolyLog(2, -((b*(d^(1/3) + c^(1/3)*x))/((1 + a)*c^(1/3) - b*d^(1/3)))))/(6*c^(4/3)) - (d^(1/3)*PolyLog(2, (b*(d^(1/3) + c^(1/3)*x))/((1 - a)*c^(1/3) + b*d^(1/3))))/(6*c^(4/3)) + ((-1)^(2/3)*d^(1/3)*PolyLog(2, -((b*((-1)^(2/3)*d^(1/3) + c^(1/3)*x))/((1 + a)*c^(1/3) - (-1)^(2/3)*b*d^(1/3)))))/(6*c^(4/3)) - ((-1)^(2/3)*d^(1/3)*PolyLog(2, (b*((-1)^(2/3)*d^(1/3) + c^(1/3)*x))/((1 - a)*c^(1/3) + (-1)^(2/3)*b*d^(1/3))))/(6*c^(4/3)) + ((-1)^(1/3)*d^(1/3)*PolyLog(2, -(((-1)^(1/3)*b*(d^(1/3) + (-1)^(2/3)*c^(1/3)*x))/((1 - a)*c^(1/3) - (-1)^(1/3)*b*d^(1/3)))))/(6*c^(4/3)) - ((-1)^(1/3)*d^(1/3)*PolyLog(2, ((-1)^(1/3)*b*(d^(1/3) + (-1)^(2/3)*c^(1/3)*x))/((1 + a)*c^(1/3) + (-1)^(1/3)*b*d^(1/3))))/(6*c^(4/3))] =#

    #= [acoth(a + b*x)/(a + b*x^(3/2)), x, 131, ((1 - 1/sqrt(1 + a^(-1)))*log(-a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) - sqrt(b)*sqrt(x))/(sqrt(-1 - a) + a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) + ((1 + 1/sqrt(1 + a^(-1)))*log(-a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) - sqrt(b)*sqrt(x))/(sqrt(-1 - a) + a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(1 - 1/sqrt(1 + a^(-1)))*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) - sqrt(b)*sqrt(x))/(sqrt(-1 - a) - (-1)^(1/3)*a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(1 + 1/sqrt(1 + a^(-1)))*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) - sqrt(b)*sqrt(x))/(sqrt(-1 - a) - (-1)^(1/3)*a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(1 - 1/sqrt(1 + a^(-1)))*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) - sqrt(b)*sqrt(x))/(sqrt(-1 - a) + (-1)^(2/3)*a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(1 + 1/sqrt(1 + a^(-1)))*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) - sqrt(b)*sqrt(x))/(sqrt(-1 - a) + (-1)^(2/3)*a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) - (log(-a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(1 - a) - sqrt(b)*sqrt(x))/(sqrt(1 - a) + a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(1 - a) - sqrt(b)*sqrt(x))/(sqrt(1 - a) - (-1)^(1/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log((sqrt(1 - a) - sqrt(b)*sqrt(x))/(sqrt(1 - a) + (-1)^(2/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - (log(-a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-a) - sqrt(b)*sqrt(x))/(sqrt(-a) + a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - ((sqrt(1 - a) - sqrt(-a))*log(-a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-a) - sqrt(b)*sqrt(x))/(sqrt(-a) + a^(1/3)*b^(1/6))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) - ((sqrt(1 - a) + sqrt(-a))*a^(2/3)*log(-a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-a) - sqrt(b)*sqrt(x))/(sqrt(-a) + a^(1/3)*b^(1/6))))/(6*(-a)^(3/2)*b^(2/3)) - ((-1)^(2/3)*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-a) - sqrt(b)*sqrt(x))/(sqrt(-a) - (-1)^(1/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*(sqrt(1 - a) - sqrt(-a))*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-a) - sqrt(b)*sqrt(x))/(sqrt(-a) - (-1)^(1/3)*a^(1/3)*b^(1/6))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(sqrt(1 - a) + sqrt(-a))*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-a) - sqrt(b)*sqrt(x))/(sqrt(-a) - (-1)^(1/3)*a^(1/3)*b^(1/6))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log((sqrt(-a) - sqrt(b)*sqrt(x))/(sqrt(-a) + (-1)^(2/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*(sqrt(1 - a) - sqrt(-a))*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log((sqrt(-a) - sqrt(b)*sqrt(x))/(sqrt(-a) + (-1)^(2/3)*a^(1/3)*b^(1/6))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(sqrt(1 - a) + sqrt(-a))*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log((sqrt(-a) - sqrt(b)*sqrt(x))/(sqrt(-a) + (-1)^(2/3)*a^(1/3)*b^(1/6))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) + ((1 - 1/sqrt(1 + a^(-1)))*log(-a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) + sqrt(b)*sqrt(x))/(sqrt(-1 - a) - a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) + ((1 + 1/sqrt(1 + a^(-1)))*log(-a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) + sqrt(b)*sqrt(x))/(sqrt(-1 - a) - a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(1 - 1/sqrt(1 + a^(-1)))*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) + sqrt(b)*sqrt(x))/(sqrt(-1 - a) + (-1)^(1/3)*a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(1 + 1/sqrt(1 + a^(-1)))*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) + sqrt(b)*sqrt(x))/(sqrt(-1 - a) + (-1)^(1/3)*a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(1 - 1/sqrt(1 + a^(-1)))*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) + sqrt(b)*sqrt(x))/(sqrt(-1 - a) - (-1)^(2/3)*a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(1 + 1/sqrt(1 + a^(-1)))*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log((sqrt(-1 - a) + sqrt(b)*sqrt(x))/(sqrt(-1 - a) - (-1)^(2/3)*a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) - (log(-a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(1 - a) + sqrt(b)*sqrt(x))/(sqrt(1 - a) - a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(1 - a) + sqrt(b)*sqrt(x))/(sqrt(1 - a) + (-1)^(1/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log((sqrt(1 - a) + sqrt(b)*sqrt(x))/(sqrt(1 - a) - (-1)^(2/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - (log(-a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-a) + sqrt(b)*sqrt(x))/(sqrt(-a) - a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - ((sqrt(1 - a) - sqrt(-a))*log(-a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-a) + sqrt(b)*sqrt(x))/(sqrt(-a) - a^(1/3)*b^(1/6))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) - ((sqrt(1 - a) + sqrt(-a))*a^(2/3)*log(-a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-a) + sqrt(b)*sqrt(x))/(sqrt(-a) - a^(1/3)*b^(1/6))))/(6*(-a)^(3/2)*b^(2/3)) - ((-1)^(2/3)*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-a) + sqrt(b)*sqrt(x))/(sqrt(-a) + (-1)^(1/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*(sqrt(1 - a) - sqrt(-a))*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-a) + sqrt(b)*sqrt(x))/(sqrt(-a) + (-1)^(1/3)*a^(1/3)*b^(1/6))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(sqrt(1 - a) + sqrt(-a))*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log((sqrt(-a) + sqrt(b)*sqrt(x))/(sqrt(-a) + (-1)^(1/3)*a^(1/3)*b^(1/6))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log((sqrt(-a) + sqrt(b)*sqrt(x))/(sqrt(-a) - (-1)^(2/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*(sqrt(1 - a) - sqrt(-a))*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log((sqrt(-a) + sqrt(b)*sqrt(x))/(sqrt(-a) - (-1)^(2/3)*a^(1/3)*b^(1/6))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(sqrt(1 - a) + sqrt(-a))*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log((sqrt(-a) + sqrt(b)*sqrt(x))/(sqrt(-a) - (-1)^(2/3)*a^(1/3)*b^(1/6))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) + (log(-a^(1/3) - b^(1/3)*sqrt(x))*log(1 - (a + b*x)^(-1)))/(3*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log(1 - (a + b*x)^(-1)))/(3*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log(1 - (a + b*x)^(-1)))/(3*a^(1/3)*b^(2/3)) - (log(-a^(1/3) - b^(1/3)*sqrt(x))*log(1 + (a + b*x)^(-1)))/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*log((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x))*log(1 + (a + b*x)^(-1)))/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*log(-((-1)^(2/3)*a^(1/3)) - b^(1/3)*sqrt(x))*log(1 + (a + b*x)^(-1)))/(3*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(1 - 1/sqrt(1 + a^(-1)))*PolyLog(2, -((b^(1/6)*((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x)))/(sqrt(-1 - a) - (-1)^(1/3)*a^(1/3)*b^(1/6)))))/(6*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(1 + 1/sqrt(1 + a^(-1)))*PolyLog(2, -((b^(1/6)*((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x)))/(sqrt(-1 - a) - (-1)^(1/3)*a^(1/3)*b^(1/6)))))/(6*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*PolyLog(2, -((b^(1/6)*((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x)))/(sqrt(1 - a) - (-1)^(1/3)*a^(1/3)*b^(1/6)))))/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*PolyLog(2, -((b^(1/6)*((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x)))/(sqrt(-a) - (-1)^(1/3)*a^(1/3)*b^(1/6)))))/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*(sqrt(1 - a) - sqrt(-a))*PolyLog(2, -((b^(1/6)*((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x)))/(sqrt(-a) - (-1)^(1/3)*a^(1/3)*b^(1/6)))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(sqrt(1 - a) + sqrt(-a))*PolyLog(2, -((b^(1/6)*((-1)^(1/3)*a^(1/3) - b^(1/3)*sqrt(x)))/(sqrt(-a) - (-1)^(1/3)*a^(1/3)*b^(1/6)))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) + ((1 - 1/sqrt(1 + a^(-1)))*PolyLog(2, -((b^(1/6)*(a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-1 - a) - a^(1/3)*b^(1/6)))))/(6*a^(1/3)*b^(2/3)) + ((1 + 1/sqrt(1 + a^(-1)))*PolyLog(2, -((b^(1/6)*(a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-1 - a) - a^(1/3)*b^(1/6)))))/(6*a^(1/3)*b^(2/3)) - PolyLog(2, -((b^(1/6)*(a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(1 - a) - a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - PolyLog(2, -((b^(1/6)*(a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-a) - a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - ((sqrt(1 - a) - sqrt(-a))*PolyLog(2, -((b^(1/6)*(a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-a) - a^(1/3)*b^(1/6)))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) - ((sqrt(1 - a) + sqrt(-a))*a^(2/3)*PolyLog(2, -((b^(1/6)*(a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-a) - a^(1/3)*b^(1/6)))))/(6*(-a)^(3/2)*b^(2/3)) + ((1 - 1/sqrt(1 + a^(-1)))*PolyLog(2, (b^(1/6)*(a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-1 - a) + a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) + ((1 + 1/sqrt(1 + a^(-1)))*PolyLog(2, (b^(1/6)*(a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-1 - a) + a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) - PolyLog(2, (b^(1/6)*(a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(1 - a) + a^(1/3)*b^(1/6)))/(3*a^(1/3)*b^(2/3)) - PolyLog(2, (b^(1/6)*(a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-a) + a^(1/3)*b^(1/6)))/(3*a^(1/3)*b^(2/3)) - ((sqrt(1 - a) - sqrt(-a))*PolyLog(2, (b^(1/6)*(a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-a) + a^(1/3)*b^(1/6))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) - ((sqrt(1 - a) + sqrt(-a))*a^(2/3)*PolyLog(2, (b^(1/6)*(a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-a) + a^(1/3)*b^(1/6))))/(6*(-a)^(3/2)*b^(2/3)) - ((-1)^(1/3)*(1 - 1/sqrt(1 + a^(-1)))*PolyLog(2, -((b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-1 - a) - (-1)^(2/3)*a^(1/3)*b^(1/6)))))/(6*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(1 + 1/sqrt(1 + a^(-1)))*PolyLog(2, -((b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-1 - a) - (-1)^(2/3)*a^(1/3)*b^(1/6)))))/(6*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*PolyLog(2, -((b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(1 - a) - (-1)^(2/3)*a^(1/3)*b^(1/6)))))/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*PolyLog(2, -((b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-a) - (-1)^(2/3)*a^(1/3)*b^(1/6)))))/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*(sqrt(1 - a) - sqrt(-a))*PolyLog(2, -((b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-a) - (-1)^(2/3)*a^(1/3)*b^(1/6)))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(sqrt(1 - a) + sqrt(-a))*PolyLog(2, -((b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-a) - (-1)^(2/3)*a^(1/3)*b^(1/6)))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(1 - 1/sqrt(1 + a^(-1)))*PolyLog(2, (b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-1 - a) + (-1)^(2/3)*a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(1 + 1/sqrt(1 + a^(-1)))*PolyLog(2, (b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-1 - a) + (-1)^(2/3)*a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*PolyLog(2, (b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(1 - a) + (-1)^(2/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*PolyLog(2, (b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-a) + (-1)^(2/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*(sqrt(1 - a) - sqrt(-a))*PolyLog(2, (b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-a) + (-1)^(2/3)*a^(1/3)*b^(1/6))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(sqrt(1 - a) + sqrt(-a))*PolyLog(2, (b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*sqrt(x)))/(sqrt(-a) + (-1)^(2/3)*a^(1/3)*b^(1/6))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(1 - 1/sqrt(1 + a^(-1)))*PolyLog(2, ((-1)^(1/3)*b^(1/6)*(a^(1/3) + (-1)^(2/3)*b^(1/3)*sqrt(x)))/(sqrt(-1 - a) + (-1)^(1/3)*a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(1 + 1/sqrt(1 + a^(-1)))*PolyLog(2, ((-1)^(1/3)*b^(1/6)*(a^(1/3) + (-1)^(2/3)*b^(1/3)*sqrt(x)))/(sqrt(-1 - a) + (-1)^(1/3)*a^(1/3)*b^(1/6))))/(6*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*PolyLog(2, ((-1)^(1/3)*b^(1/6)*(a^(1/3) + (-1)^(2/3)*b^(1/3)*sqrt(x)))/(sqrt(1 - a) + (-1)^(1/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*PolyLog(2, ((-1)^(1/3)*b^(1/6)*(a^(1/3) + (-1)^(2/3)*b^(1/3)*sqrt(x)))/(sqrt(-a) + (-1)^(1/3)*a^(1/3)*b^(1/6))))/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*(sqrt(1 - a) - sqrt(-a))*PolyLog(2, ((-1)^(1/3)*b^(1/6)*(a^(1/3) + (-1)^(2/3)*b^(1/3)*sqrt(x)))/(sqrt(-a) + (-1)^(1/3)*a^(1/3)*b^(1/6))))/(6*sqrt(-a)*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(sqrt(1 - a) + sqrt(-a))*PolyLog(2, ((-1)^(1/3)*b^(1/6)*(a^(1/3) + (-1)^(2/3)*b^(1/3)*sqrt(x)))/(sqrt(-a) + (-1)^(1/3)*a^(1/3)*b^(1/6))))/(6*sqrt(-a)*a^(1/3)*b^(2/3))] =#
    @test_int [acoth(a + b*x)/(c + d*sqrt(x)), x, 55, (2*sqrt(1 + a)*atan((sqrt(b)*sqrt(x))/sqrt(1 + a)))/(sqrt(b)*d) - (2*sqrt(1 - a)*atanh((sqrt(b)*sqrt(x))/sqrt(1 - a)))/(sqrt(b)*d) + (c*log((d*(sqrt(-1 - a) - sqrt(b)*sqrt(x)))/(sqrt(b)*c + sqrt(-1 - a)*d))*log(c + d*sqrt(x)))/d^2 - (c*log((d*(sqrt(1 - a) - sqrt(b)*sqrt(x)))/(sqrt(b)*c + sqrt(1 - a)*d))*log(c + d*sqrt(x)))/d^2 + (c*log(-((d*(sqrt(-1 - a) + sqrt(b)*sqrt(x)))/(sqrt(b)*c - sqrt(-1 - a)*d)))*log(c + d*sqrt(x)))/d^2 - (c*log(-((d*(sqrt(1 - a) + sqrt(b)*sqrt(x)))/(sqrt(b)*c - sqrt(1 - a)*d)))*log(c + d*sqrt(x)))/d^2 - (sqrt(x)*log(-((1 - a - b*x)/(a + b*x))))/d + (c*log(c + d*sqrt(x))*log(-((1 - a - b*x)/(a + b*x))))/d^2 + (sqrt(x)*log((1 + a + b*x)/(a + b*x)))/d - (c*log(c + d*sqrt(x))*log((1 + a + b*x)/(a + b*x)))/d^2 + (c*PolyLog(2, (sqrt(b)*(c + d*sqrt(x)))/(sqrt(b)*c - sqrt(-1 - a)*d)))/d^2 + (c*PolyLog(2, (sqrt(b)*(c + d*sqrt(x)))/(sqrt(b)*c + sqrt(-1 - a)*d)))/d^2 - (c*PolyLog(2, (sqrt(b)*(c + d*sqrt(x)))/(sqrt(b)*c - sqrt(1 - a)*d)))/d^2 - (c*PolyLog(2, (sqrt(b)*(c + d*sqrt(x)))/(sqrt(b)*c + sqrt(1 - a)*d)))/d^2]
    @test_int [acoth(a + b*x)/(c + d/sqrt(x)), x, 65, -((2*sqrt(1 + a)*d*atan((sqrt(b)*sqrt(x))/sqrt(1 + a)))/(sqrt(b)*c^2)) + (2*sqrt(1 - a)*d*atanh((sqrt(b)*sqrt(x))/sqrt(1 - a)))/(sqrt(b)*c^2) - (d^2*log((c*(sqrt(-1 - a) - sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*c + sqrt(b)*d))*log(d + c*sqrt(x)))/c^3 + (d^2*log((c*(sqrt(1 - a) - sqrt(b)*sqrt(x)))/(sqrt(1 - a)*c + sqrt(b)*d))*log(d + c*sqrt(x)))/c^3 - (d^2*log((c*(sqrt(-1 - a) + sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*c - sqrt(b)*d))*log(d + c*sqrt(x)))/c^3 + (d^2*log((c*(sqrt(1 - a) + sqrt(b)*sqrt(x)))/(sqrt(1 - a)*c - sqrt(b)*d))*log(d + c*sqrt(x)))/c^3 + ((1 - a)*log(1 - a - b*x))/(2*b*c) + (d*sqrt(x)*log(-((1 - a - b*x)/(a + b*x))))/c^2 - (x*log(-((1 - a - b*x)/(a + b*x))))/(2*c) - (d^2*log(d + c*sqrt(x))*log(-((1 - a - b*x)/(a + b*x))))/c^3 + ((1 + a)*log(1 + a + b*x))/(2*b*c) - (d*sqrt(x)*log((1 + a + b*x)/(a + b*x)))/c^2 + (x*log((1 + a + b*x)/(a + b*x)))/(2*c) + (d^2*log(d + c*sqrt(x))*log((1 + a + b*x)/(a + b*x)))/c^3 - (d^2*PolyLog(2, -((sqrt(b)*(d + c*sqrt(x)))/(sqrt(-1 - a)*c - sqrt(b)*d))))/c^3 + (d^2*PolyLog(2, -((sqrt(b)*(d + c*sqrt(x)))/(sqrt(1 - a)*c - sqrt(b)*d))))/c^3 - (d^2*PolyLog(2, (sqrt(b)*(d + c*sqrt(x)))/(sqrt(-1 - a)*c + sqrt(b)*d)))/c^3 + (d^2*PolyLog(2, (sqrt(b)*(d + c*sqrt(x)))/(sqrt(1 - a)*c + sqrt(b)*d)))/c^3]
    #= [acoth(a + b*x)/(a + b/x^(3/2)), x, 145, -((1 - 1/sqrt(1 + a^(-1)))*b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) - sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + b^(5/6))))/(6*a^(5/3)) - ((1 + 1/sqrt(1 + a^(-1)))*b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) - sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + b^(5/6))))/(6*a^(5/3)) - ((-1)^(2/3)*(1 - 1/sqrt(1 + a^(-1)))*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) - sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - (-1)^(1/3)*b^(5/6))))/(6*a^(5/3)) - ((-1)^(2/3)*(1 + 1/sqrt(1 + a^(-1)))*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) - sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - (-1)^(1/3)*b^(5/6))))/(6*a^(5/3)) + ((-1)^(1/3)*(1 - 1/sqrt(1 + a^(-1)))*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) - sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + (-1)^(2/3)*b^(5/6))))/(6*a^(5/3)) + ((-1)^(1/3)*(1 + 1/sqrt(1 + a^(-1)))*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) - sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + (-1)^(2/3)*b^(5/6))))/(6*a^(5/3)) + (b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(1 - a) - sqrt(b)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) + b^(5/6))))/(3*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(1 - a) - sqrt(b)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) - (-1)^(1/3)*b^(5/6))))/(3*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(1 - a) - sqrt(b)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) + (-1)^(2/3)*b^(5/6))))/(3*a^(5/3)) + (b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-a) - sqrt(b)*sqrt(x)))/(sqrt(-a)*a^(1/3) + b^(5/6))))/(3*a^(5/3)) + ((sqrt(1 - a) - sqrt(-a))*b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-a) - sqrt(b)*sqrt(x)))/(sqrt(-a)*a^(1/3) + b^(5/6))))/(6*sqrt(-a)*a^(5/3)) - ((sqrt(1 - a) + sqrt(-a))*b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-a) - sqrt(b)*sqrt(x)))/(sqrt(-a)*a^(1/3) + b^(5/6))))/(6*sqrt(-a)*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-a) - sqrt(b)*sqrt(x)))/(sqrt(-a)*a^(1/3) + (-1)^(2/3)*b^(5/6))))/(3*a^(5/3)) - ((-1)^(1/3)*(sqrt(1 - a) - sqrt(-a))*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-a) - sqrt(b)*sqrt(x)))/(sqrt(-a)*a^(1/3) + (-1)^(2/3)*b^(5/6))))/(6*sqrt(-a)*a^(5/3)) - ((-1)^(1/3)*(sqrt(1 - a) + sqrt(-a))*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-a) - sqrt(b)*sqrt(x)))/(sqrt(-a)*a^(1/3) + (-1)^(2/3)*b^(5/6))))/(6*(-a)^(3/2)*a^(2/3)) + ((-1)^(2/3)*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log(-((sqrt(-a)*a^(1/3)*(sqrt(-a) - sqrt(b)*sqrt(x)))/(a^(4/3) + (-1)^(1/3)*sqrt(-a)*b^(5/6)))))/(3*a^(5/3)) + ((-1)^(2/3)*(sqrt(1 - a) - sqrt(-a))*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log(-((sqrt(-a)*a^(1/3)*(sqrt(-a) - sqrt(b)*sqrt(x)))/(a^(4/3) + (-1)^(1/3)*sqrt(-a)*b^(5/6)))))/(6*sqrt(-a)*a^(5/3)) + ((-1)^(2/3)*(sqrt(1 - a) + sqrt(-a))*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log(-((sqrt(-a)*a^(1/3)*(sqrt(-a) - sqrt(b)*sqrt(x)))/(a^(4/3) + (-1)^(1/3)*sqrt(-a)*b^(5/6)))))/(6*(-a)^(3/2)*a^(2/3)) - ((1 - 1/sqrt(1 + a^(-1)))*b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) + sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - b^(5/6))))/(6*a^(5/3)) - ((1 + 1/sqrt(1 + a^(-1)))*b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) + sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - b^(5/6))))/(6*a^(5/3)) - ((-1)^(2/3)*(1 - 1/sqrt(1 + a^(-1)))*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) + sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + (-1)^(1/3)*b^(5/6))))/(6*a^(5/3)) - ((-1)^(2/3)*(1 + 1/sqrt(1 + a^(-1)))*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) + sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + (-1)^(1/3)*b^(5/6))))/(6*a^(5/3)) + ((-1)^(1/3)*(1 - 1/sqrt(1 + a^(-1)))*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) + sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - (-1)^(2/3)*b^(5/6))))/(6*a^(5/3)) + ((-1)^(1/3)*(1 + 1/sqrt(1 + a^(-1)))*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-1 - a) + sqrt(b)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - (-1)^(2/3)*b^(5/6))))/(6*a^(5/3)) + (b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(1 - a) + sqrt(b)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) - b^(5/6))))/(3*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(1 - a) + sqrt(b)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) + (-1)^(1/3)*b^(5/6))))/(3*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(1 - a) + sqrt(b)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) - (-1)^(2/3)*b^(5/6))))/(3*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-a) + sqrt(b)*sqrt(x)))/(sqrt(-a)*a^(1/3) + (-1)^(1/3)*b^(5/6))))/(3*a^(5/3)) + ((-1)^(2/3)*(sqrt(1 - a) - sqrt(-a))*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-a) + sqrt(b)*sqrt(x)))/(sqrt(-a)*a^(1/3) + (-1)^(1/3)*b^(5/6))))/(6*sqrt(-a)*a^(5/3)) + ((-1)^(2/3)*(sqrt(1 - a) + sqrt(-a))*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log((a^(1/3)*(sqrt(-a) + sqrt(b)*sqrt(x)))/(sqrt(-a)*a^(1/3) + (-1)^(1/3)*b^(5/6))))/(6*(-a)^(3/2)*a^(2/3)) + (b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log(-((sqrt(-a)*a^(1/3)*(sqrt(-a) + sqrt(b)*sqrt(x)))/(a^(4/3) + sqrt(-a)*b^(5/6)))))/(3*a^(5/3)) + ((sqrt(1 - a) - sqrt(-a))*b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log(-((sqrt(-a)*a^(1/3)*(sqrt(-a) + sqrt(b)*sqrt(x)))/(a^(4/3) + sqrt(-a)*b^(5/6)))))/(6*sqrt(-a)*a^(5/3)) - ((sqrt(1 - a) + sqrt(-a))*b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log(-((sqrt(-a)*a^(1/3)*(sqrt(-a) + sqrt(b)*sqrt(x)))/(a^(4/3) + sqrt(-a)*b^(5/6)))))/(6*sqrt(-a)*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log(-((sqrt(-a)*a^(1/3)*(sqrt(-a) + sqrt(b)*sqrt(x)))/(a^(4/3) + (-1)^(2/3)*sqrt(-a)*b^(5/6)))))/(3*a^(5/3)) - ((-1)^(1/3)*(sqrt(1 - a) - sqrt(-a))*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log(-((sqrt(-a)*a^(1/3)*(sqrt(-a) + sqrt(b)*sqrt(x)))/(a^(4/3) + (-1)^(2/3)*sqrt(-a)*b^(5/6)))))/(6*sqrt(-a)*a^(5/3)) - ((-1)^(1/3)*(sqrt(1 - a) + sqrt(-a))*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log(-((sqrt(-a)*a^(1/3)*(sqrt(-a) + sqrt(b)*sqrt(x)))/(a^(4/3) + (-1)^(2/3)*sqrt(-a)*b^(5/6)))))/(6*(-a)^(3/2)*a^(2/3)) + ((1 - a)*log(1 - a - b*x))/(2*a*b) + ((1 + a)*log(1 + a + b*x))/(2*a*b) - (x*log(1 - (a + b*x)^(-1)))/(2*a) - (b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log(1 - (a + b*x)^(-1)))/(3*a^(5/3)) - ((-1)^(2/3)*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log(1 - (a + b*x)^(-1)))/(3*a^(5/3)) + ((-1)^(1/3)*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log(1 - (a + b*x)^(-1)))/(3*a^(5/3)) + (x*log(1 + (a + b*x)^(-1)))/(2*a) + (b^(2/3)*log(-b^(1/3) - a^(1/3)*sqrt(x))*log(1 + (a + b*x)^(-1)))/(3*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*log((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x))*log(1 + (a + b*x)^(-1)))/(3*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*log(-((-1)^(2/3)*b^(1/3)) - a^(1/3)*sqrt(x))*log(1 + (a + b*x)^(-1)))/(3*a^(5/3)) - ((-1)^(2/3)*(1 - 1/sqrt(1 + a^(-1)))*b^(2/3)*PolyLog(2, -((sqrt(b)*((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - (-1)^(1/3)*b^(5/6)))))/(6*a^(5/3)) - ((-1)^(2/3)*(1 + 1/sqrt(1 + a^(-1)))*b^(2/3)*PolyLog(2, -((sqrt(b)*((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - (-1)^(1/3)*b^(5/6)))))/(6*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*PolyLog(2, -((sqrt(b)*((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) - (-1)^(1/3)*b^(5/6)))))/(3*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*PolyLog(2, -((sqrt(b)*((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x)))/(sqrt(-a)*a^(1/3) - (-1)^(1/3)*b^(5/6)))))/(3*a^(5/3)) + ((-1)^(2/3)*(sqrt(1 - a) - sqrt(-a))*b^(2/3)*PolyLog(2, -((sqrt(b)*((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x)))/(sqrt(-a)*a^(1/3) - (-1)^(1/3)*b^(5/6)))))/(6*sqrt(-a)*a^(5/3)) + ((-1)^(2/3)*(sqrt(1 - a) + sqrt(-a))*b^(2/3)*PolyLog(2, -((sqrt(b)*((-1)^(1/3)*b^(1/3) - a^(1/3)*sqrt(x)))/(sqrt(-a)*a^(1/3) - (-1)^(1/3)*b^(5/6)))))/(6*(-a)^(3/2)*a^(2/3)) - ((1 - 1/sqrt(1 + a^(-1)))*b^(2/3)*PolyLog(2, -((sqrt(b)*(b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - b^(5/6)))))/(6*a^(5/3)) - ((1 + 1/sqrt(1 + a^(-1)))*b^(2/3)*PolyLog(2, -((sqrt(b)*(b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - b^(5/6)))))/(6*a^(5/3)) + (b^(2/3)*PolyLog(2, -((sqrt(b)*(b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) - b^(5/6)))))/(3*a^(5/3)) - ((1 - 1/sqrt(1 + a^(-1)))*b^(2/3)*PolyLog(2, (sqrt(b)*(b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + b^(5/6))))/(6*a^(5/3)) - ((1 + 1/sqrt(1 + a^(-1)))*b^(2/3)*PolyLog(2, (sqrt(b)*(b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + b^(5/6))))/(6*a^(5/3)) + (b^(2/3)*PolyLog(2, (sqrt(b)*(b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) + b^(5/6))))/(3*a^(5/3)) + (b^(2/3)*PolyLog(2, (sqrt(b)*(b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-a)*a^(1/3) + b^(5/6))))/(3*a^(5/3)) + ((sqrt(1 - a) - sqrt(-a))*b^(2/3)*PolyLog(2, (sqrt(b)*(b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-a)*a^(1/3) + b^(5/6))))/(6*sqrt(-a)*a^(5/3)) - ((sqrt(1 - a) + sqrt(-a))*b^(2/3)*PolyLog(2, (sqrt(b)*(b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-a)*a^(1/3) + b^(5/6))))/(6*sqrt(-a)*a^(5/3)) + (b^(2/3)*PolyLog(2, (sqrt(b)*(b^(1/3) + a^(1/3)*sqrt(x)))/(a^(4/3)/sqrt(-a) + b^(5/6))))/(3*a^(5/3)) + ((sqrt(1 - a) - sqrt(-a))*b^(2/3)*PolyLog(2, (sqrt(b)*(b^(1/3) + a^(1/3)*sqrt(x)))/(a^(4/3)/sqrt(-a) + b^(5/6))))/(6*sqrt(-a)*a^(5/3)) - ((sqrt(1 - a) + sqrt(-a))*b^(2/3)*PolyLog(2, (sqrt(b)*(b^(1/3) + a^(1/3)*sqrt(x)))/(a^(4/3)/sqrt(-a) + b^(5/6))))/(6*sqrt(-a)*a^(5/3)) + ((-1)^(1/3)*(1 - 1/sqrt(1 + a^(-1)))*b^(2/3)*PolyLog(2, -((sqrt(b)*((-1)^(2/3)*b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - (-1)^(2/3)*b^(5/6)))))/(6*a^(5/3)) + ((-1)^(1/3)*(1 + 1/sqrt(1 + a^(-1)))*b^(2/3)*PolyLog(2, -((sqrt(b)*((-1)^(2/3)*b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) - (-1)^(2/3)*b^(5/6)))))/(6*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*PolyLog(2, -((sqrt(b)*((-1)^(2/3)*b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) - (-1)^(2/3)*b^(5/6)))))/(3*a^(5/3)) + ((-1)^(1/3)*(1 - 1/sqrt(1 + a^(-1)))*b^(2/3)*PolyLog(2, (sqrt(b)*((-1)^(2/3)*b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + (-1)^(2/3)*b^(5/6))))/(6*a^(5/3)) + ((-1)^(1/3)*(1 + 1/sqrt(1 + a^(-1)))*b^(2/3)*PolyLog(2, (sqrt(b)*((-1)^(2/3)*b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + (-1)^(2/3)*b^(5/6))))/(6*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*PolyLog(2, (sqrt(b)*((-1)^(2/3)*b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) + (-1)^(2/3)*b^(5/6))))/(3*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*PolyLog(2, (sqrt(b)*((-1)^(2/3)*b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-a)*a^(1/3) + (-1)^(2/3)*b^(5/6))))/(3*a^(5/3)) - ((-1)^(1/3)*(sqrt(1 - a) - sqrt(-a))*b^(2/3)*PolyLog(2, (sqrt(b)*((-1)^(2/3)*b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-a)*a^(1/3) + (-1)^(2/3)*b^(5/6))))/(6*sqrt(-a)*a^(5/3)) - ((-1)^(1/3)*(sqrt(1 - a) + sqrt(-a))*b^(2/3)*PolyLog(2, (sqrt(b)*((-1)^(2/3)*b^(1/3) + a^(1/3)*sqrt(x)))/(sqrt(-a)*a^(1/3) + (-1)^(2/3)*b^(5/6))))/(6*(-a)^(3/2)*a^(2/3)) - ((-1)^(1/3)*b^(2/3)*PolyLog(2, (sqrt(b)*((-1)^(2/3)*b^(1/3) + a^(1/3)*sqrt(x)))/(a^(4/3)/sqrt(-a) + (-1)^(2/3)*b^(5/6))))/(3*a^(5/3)) - ((-1)^(1/3)*(sqrt(1 - a) - sqrt(-a))*b^(2/3)*PolyLog(2, (sqrt(b)*((-1)^(2/3)*b^(1/3) + a^(1/3)*sqrt(x)))/(a^(4/3)/sqrt(-a) + (-1)^(2/3)*b^(5/6))))/(6*sqrt(-a)*a^(5/3)) - ((-1)^(1/3)*(sqrt(1 - a) + sqrt(-a))*b^(2/3)*PolyLog(2, (sqrt(b)*((-1)^(2/3)*b^(1/3) + a^(1/3)*sqrt(x)))/(a^(4/3)/sqrt(-a) + (-1)^(2/3)*b^(5/6))))/(6*(-a)^(3/2)*a^(2/3)) - ((-1)^(2/3)*(1 - 1/sqrt(1 + a^(-1)))*b^(2/3)*PolyLog(2, ((-1)^(1/3)*sqrt(b)*(b^(1/3) + (-1)^(2/3)*a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + (-1)^(1/3)*b^(5/6))))/(6*a^(5/3)) - ((-1)^(2/3)*(1 + 1/sqrt(1 + a^(-1)))*b^(2/3)*PolyLog(2, ((-1)^(1/3)*sqrt(b)*(b^(1/3) + (-1)^(2/3)*a^(1/3)*sqrt(x)))/(sqrt(-1 - a)*a^(1/3) + (-1)^(1/3)*b^(5/6))))/(6*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*PolyLog(2, ((-1)^(1/3)*sqrt(b)*(b^(1/3) + (-1)^(2/3)*a^(1/3)*sqrt(x)))/(sqrt(1 - a)*a^(1/3) + (-1)^(1/3)*b^(5/6))))/(3*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*PolyLog(2, ((-1)^(1/3)*sqrt(b)*(b^(1/3) + (-1)^(2/3)*a^(1/3)*sqrt(x)))/(sqrt(-a)*a^(1/3) + (-1)^(1/3)*b^(5/6))))/(3*a^(5/3)) + ((-1)^(2/3)*(sqrt(1 - a) - sqrt(-a))*b^(2/3)*PolyLog(2, ((-1)^(1/3)*sqrt(b)*(b^(1/3) + (-1)^(2/3)*a^(1/3)*sqrt(x)))/(sqrt(-a)*a^(1/3) + (-1)^(1/3)*b^(5/6))))/(6*sqrt(-a)*a^(5/3)) + ((-1)^(2/3)*(sqrt(1 - a) + sqrt(-a))*b^(2/3)*PolyLog(2, ((-1)^(1/3)*sqrt(b)*(b^(1/3) + (-1)^(2/3)*a^(1/3)*sqrt(x)))/(sqrt(-a)*a^(1/3) + (-1)^(1/3)*b^(5/6))))/(6*(-a)^(3/2)*a^(2/3))] =#

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

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

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*u*acoth(a*x^n)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*acoth(a*x^n)=#

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

    @test_int [x^2*acoth(sqrt(x)), x, 6, sqrt(x)/3 + x^(3/2)/9 + x^(5/2)/15 + (1/3)*x^3*acoth(sqrt(x)) - atanh(sqrt(x))/3]
    @test_int [x^1*acoth(sqrt(x)), x, 5, sqrt(x)/2 + x^(3/2)/6 + (1/2)*x^2*acoth(sqrt(x)) - atanh(sqrt(x))/2]
    @test_int [x^0*acoth(sqrt(x)), x, 4, sqrt(x) + x*acoth(sqrt(x)) - atanh(sqrt(x))]
    @test_int [acoth(sqrt(x))/x^1, x, 2, PolyLog(2, -(1/sqrt(x))) - PolyLog(2, 1/sqrt(x))]
    @test_int [acoth(sqrt(x))/x^2, x, 4, -(1/sqrt(x)) - acoth(sqrt(x))/x + atanh(sqrt(x))]
    @test_int [acoth(sqrt(x))/x^3, x, 5, -(1/(6*x^(3/2))) - 1/(2*sqrt(x)) - acoth(sqrt(x))/(2*x^2) + atanh(sqrt(x))/2]

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

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

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

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

    #= ::Subsubsection::Closed:: =#
    #=n*symbolic=#

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

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

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

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

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

    @test_int [acoth(a + b*x)/((a*d)/b + d*x), x, 3, PolyLog(2, -(1/(a + b*x)))/(2*d) - PolyLog(2, 1/(a + b*x))/(2*d)]

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

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

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

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

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

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

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*u^m*(a+b*acoth(sqrt(1-c*x)/sqrt(1+c*x)))^n=#

    @test_int [(a + b*acoth(sqrt(1 - c*x)/sqrt(1 + c*x)))^n/(1 - c^2*x^2), x, 0, Unintegrable((a + b*acoth(sqrt(1 - c*x)/sqrt(1 + c*x)))^n/(1 - c^2*x^2), x)]

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

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*x^m*acoth(tanh(a+b*x))^n=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*acoth(tanh(a+b*x))^n=#

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

    @test_int [acoth(tanh(a + b*x))*x^m, x, 2, -((b*x^(2 + m))/(2 + 3*m + m^2)) + (x^(1 + m)*acoth(tanh(a + b*x)))/(1 + m)]

    @test_int [acoth(tanh(a + b*x))*x^2, x, 2, -((b*x^4)/12) + (1/3)*x^3*acoth(tanh(a + b*x))]
    @test_int [acoth(tanh(a + b*x))*x^1, x, 2, -((b*x^3)/6) + (1/2)*x^2*acoth(tanh(a + b*x))]
    @test_int [acoth(tanh(a + b*x))*x^0, x, 2, acoth(tanh(a + b*x))^2/(2*b)]
    @test_int [acoth(tanh(a + b*x))/x^1, x, 2, b*x - (b*x - acoth(tanh(a + b*x)))*log(x)]
    @test_int [acoth(tanh(a + b*x))/x^2, x, 2, -(acoth(tanh(a + b*x))/x) + b*log(x)]
    @test_int [acoth(tanh(a + b*x))/x^3, x, 2, -(b/(2*x)) - acoth(tanh(a + b*x))/(2*x^2)]
    @test_int [acoth(tanh(a + b*x))/x^4, x, 2, -(b/(6*x^2)) - acoth(tanh(a + b*x))/(3*x^3)]

    @test_int [acoth(tanh(a + b*x))^2*x^m, x, 3, (2*b^2*x^(3 + m))/(6 + 11*m + 6*m^2 + m^3) - (2*b*x^(2 + m)*acoth(tanh(a + b*x)))/(2 + 3*m + m^2) + (x^(1 + m)*acoth(tanh(a + b*x))^2)/(1 + m)]

    @test_int [acoth(tanh(a + b*x))^2*x^3, x, 3, (b^2*x^6)/60 - (1/10)*b*x^5*acoth(tanh(a + b*x)) + (1/4)*x^4*acoth(tanh(a + b*x))^2]
    @test_int [acoth(tanh(a + b*x))^2*x^2, x, 3, (b^2*x^5)/30 - (1/6)*b*x^4*acoth(tanh(a + b*x)) + (1/3)*x^3*acoth(tanh(a + b*x))^2]
    @test_int [acoth(tanh(a + b*x))^2*x^1, x, 3, (x*acoth(tanh(a + b*x))^3)/(3*b) - acoth(tanh(a + b*x))^4/(12*b^2)]
    @test_int [acoth(tanh(a + b*x))^2*x^0, x, 2, acoth(tanh(a + b*x))^3/(3*b)]
    @test_int [acoth(tanh(a + b*x))^2/x^1, x, 3, (-b)*x*(b*x - acoth(tanh(a + b*x))) + (1/2)*acoth(tanh(a + b*x))^2 + (b*x - acoth(tanh(a + b*x)))^2*log(x)]
    @test_int [acoth(tanh(a + b*x))^2/x^2, x, 3, 2*b^2*x - acoth(tanh(a + b*x))^2/x - 2*b*(b*x - acoth(tanh(a + b*x)))*log(x)]
    @test_int [acoth(tanh(a + b*x))^2/x^3, x, 3, -((b*acoth(tanh(a + b*x)))/x) - acoth(tanh(a + b*x))^2/(2*x^2) + b^2*log(x)]
    @test_int [acoth(tanh(a + b*x))^2/x^4, x, 1, acoth(tanh(a + b*x))^3/(3*x^3*(b*x - acoth(tanh(a + b*x))))]
    @test_int [acoth(tanh(a + b*x))^2/x^5, x, 2, (b*acoth(tanh(a + b*x))^3)/(12*x^3*(b*x - acoth(tanh(a + b*x)))^2) + acoth(tanh(a + b*x))^3/(4*x^4*(b*x - acoth(tanh(a + b*x))))]

    @test_int [acoth(tanh(a + b*x))^3*x^m, x, 4, -((6*b^3*x^(4 + m))/((1 + m)*(24 + 26*m + 9*m^2 + m^3))) + (6*b^2*x^(3 + m)*acoth(tanh(a + b*x)))/(6 + 11*m + 6*m^2 + m^3) - (3*b*x^(2 + m)*acoth(tanh(a + b*x))^2)/(2 + 3*m + m^2) + (x^(1 + m)*acoth(tanh(a + b*x))^3)/(1 + m)]

    @test_int [acoth(tanh(a + b*x))^3*x^4, x, 4, (-(1/280))*b^3*x^8 + (1/35)*b^2*x^7*acoth(tanh(a + b*x)) - (1/10)*b*x^6*acoth(tanh(a + b*x))^2 + (1/5)*x^5*acoth(tanh(a + b*x))^3]
    @test_int [acoth(tanh(a + b*x))^3*x^3, x, 4, (-(1/140))*b^3*x^7 + (1/20)*b^2*x^6*acoth(tanh(a + b*x)) - (3/20)*b*x^5*acoth(tanh(a + b*x))^2 + (1/4)*x^4*acoth(tanh(a + b*x))^3]
    @test_int [acoth(tanh(a + b*x))^3*x^2, x, 4, (x^2*acoth(tanh(a + b*x))^4)/(4*b) - (x*acoth(tanh(a + b*x))^5)/(10*b^2) + acoth(tanh(a + b*x))^6/(60*b^3)]
    @test_int [acoth(tanh(a + b*x))^3*x^1, x, 3, (x*acoth(tanh(a + b*x))^4)/(4*b) - acoth(tanh(a + b*x))^5/(20*b^2)]
    @test_int [acoth(tanh(a + b*x))^3*x^0, x, 2, acoth(tanh(a + b*x))^4/(4*b)]
    @test_int [acoth(tanh(a + b*x))^3/x^1, x, 4, b*x*(b*x - acoth(tanh(a + b*x)))^2 - (1/2)*(b*x - acoth(tanh(a + b*x)))*acoth(tanh(a + b*x))^2 + (1/3)*acoth(tanh(a + b*x))^3 - (b*x - acoth(tanh(a + b*x)))^3*log(x)]
    @test_int [acoth(tanh(a + b*x))^3/x^2, x, 4, -3*b^2*x*(b*x - acoth(tanh(a + b*x))) + (3/2)*b*acoth(tanh(a + b*x))^2 - acoth(tanh(a + b*x))^3/x + 3*b*(b*x - acoth(tanh(a + b*x)))^2*log(x)]
    @test_int [acoth(tanh(a + b*x))^3/x^3, x, 4, 3*b^3*x - (3*b*acoth(tanh(a + b*x))^2)/(2*x) - acoth(tanh(a + b*x))^3/(2*x^2) - 3*b^2*(b*x - acoth(tanh(a + b*x)))*log(x)]
    @test_int [acoth(tanh(a + b*x))^3/x^4, x, 4, -((b^2*acoth(tanh(a + b*x)))/x) - (b*acoth(tanh(a + b*x))^2)/(2*x^2) - acoth(tanh(a + b*x))^3/(3*x^3) + b^3*log(x)]
    @test_int [acoth(tanh(a + b*x))^3/x^5, x, 1, acoth(tanh(a + b*x))^4/(4*x^4*(b*x - acoth(tanh(a + b*x))))]
    @test_int [acoth(tanh(a + b*x))^3/x^6, x, 2, (b*acoth(tanh(a + b*x))^4)/(20*x^4*(b*x - acoth(tanh(a + b*x)))^2) + acoth(tanh(a + b*x))^4/(5*x^5*(b*x - acoth(tanh(a + b*x))))]

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

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

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

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

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

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

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

    #= ::Subsubsection::Closed:: =#
    #=n*symbolic=#

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

    @test_int [acoth(tanh(a + b*x))^n*x^4, x, 6, If(13>=8, (x^4*acoth(tanh(a + b*x))^(1 + n))/(b*(1 + n)) - (4*x^3*acoth(tanh(a + b*x))^(2 + n))/(b^2*(1 + n)*(2 + n)) + (12*x^2*acoth(tanh(a + b*x))^(3 + n))/(b^3*(1 + n)*(2 + n)*(3 + n)) - (24*x*acoth(tanh(a + b*x))^(4 + n))/(b^4*(1 + n)*(2 + n)*(3 + n)*(4 + n)) + (24*acoth(tanh(a + b*x))^(5 + n))/(b^5*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)), (x^4*acoth(tanh(a + b*x))^(1 + n))/(b*(1 + n)) - (4*x^3*acoth(tanh(a + b*x))^(2 + n))/(b^2*(1 + n)*(2 + n)) + (12*x^2*acoth(tanh(a + b*x))^(3 + n))/(b^3*(3 + n)*(2 + 3*n + n^2)) - (24*x*acoth(tanh(a + b*x))^(4 + n))/(b^4*(4 + 5*n + n^2)*(6 + 5*n + n^2)) + (24*acoth(tanh(a + b*x))^(5 + n))/(b^5*(12 + 7*n + n^2)*(10 + 17*n + 8*n^2 + n^3)))]
    @test_int [acoth(tanh(a + b*x))^n*x^3, x, 5, If(13>=8, (x^3*acoth(tanh(a + b*x))^(1 + n))/(b*(1 + n)) - (3*x^2*acoth(tanh(a + b*x))^(2 + n))/(b^2*(1 + n)*(2 + n)) + (6*x*acoth(tanh(a + b*x))^(3 + n))/(b^3*(1 + n)*(2 + n)*(3 + n)) - (6*acoth(tanh(a + b*x))^(4 + n))/(b^4*(1 + n)*(2 + n)*(3 + n)*(4 + n)), (x^3*acoth(tanh(a + b*x))^(1 + n))/(b*(1 + n)) - (3*x^2*acoth(tanh(a + b*x))^(2 + n))/(b^2*(1 + n)*(2 + n)) + (6*x*acoth(tanh(a + b*x))^(3 + n))/(b^3*(3 + n)*(2 + 3*n + n^2)) - (6*acoth(tanh(a + b*x))^(4 + n))/(b^4*(4 + 5*n + n^2)*(6 + 5*n + n^2)))]
    @test_int [acoth(tanh(a + b*x))^n*x^2, x, 4, If(13>=8, (x^2*acoth(tanh(a + b*x))^(1 + n))/(b*(1 + n)) - (2*x*acoth(tanh(a + b*x))^(2 + n))/(b^2*(1 + n)*(2 + n)) + (2*acoth(tanh(a + b*x))^(3 + n))/(b^3*(1 + n)*(2 + n)*(3 + n)), (x^2*acoth(tanh(a + b*x))^(1 + n))/(b*(1 + n)) - (2*x*acoth(tanh(a + b*x))^(2 + n))/(b^2*(1 + n)*(2 + n)) + (2*acoth(tanh(a + b*x))^(3 + n))/(b^3*(3 + n)*(2 + 3*n + n^2)))]
    @test_int [acoth(tanh(a + b*x))^n*x^1, x, 3, (x*acoth(tanh(a + b*x))^(1 + n))/(b*(1 + n)) - acoth(tanh(a + b*x))^(2 + n)/(b^2*(1 + n)*(2 + n))]
    @test_int [acoth(tanh(a + b*x))^n*x^0, x, 2, acoth(tanh(a + b*x))^(1 + n)/(b*(1 + n))]
    @test_int [acoth(tanh(a + b*x))^n/x^1, x, 1, (acoth(tanh(a + b*x))^(1 + n)*HypergeometricFunctions._₂F₁(1, 1 + n, 2 + n, -(acoth(tanh(a + b*x))/(b*x - acoth(tanh(a + b*x))))))/((1 + n)*(b*x - acoth(tanh(a + b*x))))]
    @test_int [acoth(tanh(a + b*x))^n/x^2, x, 2, -(acoth(tanh(a + b*x))^n/x) + (b*acoth(tanh(a + b*x))^n*HypergeometricFunctions._₂F₁(1, n, 1 + n, -(acoth(tanh(a + b*x))/(b*x - acoth(tanh(a + b*x))))))/(b*x - acoth(tanh(a + b*x)))]
    @test_int [acoth(tanh(a + b*x))^n/x^3, x, 3, -((b*n*acoth(tanh(a + b*x))^(-1 + n))/(2*x)) - acoth(tanh(a + b*x))^n/(2*x^2) + (b^2*n*acoth(tanh(a + b*x))^(-1 + n)*HypergeometricFunctions._₂F₁(1, -1 + n, n, -(acoth(tanh(a + b*x))/(b*x - acoth(tanh(a + b*x))))))/(2*(b*x - acoth(tanh(a + b*x))))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*x^m*acoth(coth(a+b*x))^n=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*acoth(coth(a+b*x))^n=#

    @test_int [acoth(tanh(a + b*x))*x^m, x, 2, -((b*x^(2 + m))/(2 + 3*m + m^2)) + (x^(1 + m)*acoth(tanh(a + b*x)))/(1 + m)]

    @test_int [acoth(coth(a + b*x))*x^2, x, 2, -((b*x^4)/12) + (1/3)*x^3*acoth(coth(a + b*x))]
    @test_int [acoth(coth(a + b*x))*x^1, x, 2, -((b*x^3)/6) + (1/2)*x^2*acoth(coth(a + b*x))]
    @test_int [acoth(coth(a + b*x))*x^0, x, 2, acoth(coth(a + b*x))^2/(2*b)]
    @test_int [acoth(coth(a + b*x))/x^1, x, 2, b*x - (b*x - acoth(coth(a + b*x)))*log(x)]
    @test_int [acoth(coth(a + b*x))/x^2, x, 2, -(acoth(coth(a + b*x))/x) + b*log(x)]
    @test_int [acoth(coth(a + b*x))/x^3, x, 2, -(b/(2*x)) - acoth(coth(a + b*x))/(2*x^2)]

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

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

    #= [acoth(sinh(x)), x, 6, 0]
    @test_int [x*acoth(sinh(x)), x, 8, 0]
    @test_int [x^2*acoth(sinh(x)), x, 10, 0] =#

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

    @test_int [acoth(cosh(x)), x, 6, x*acoth(cosh(x)) - 2*x*atanh(ℯ^x) - PolyLog(2, -ℯ^x) + PolyLog(2, ℯ^x)]
    @test_int [x*acoth(cosh(x)), x, 8, (1/2)*x^2*acoth(cosh(x)) - x^2*atanh(ℯ^x) - x*PolyLog(2, -ℯ^x) + x*PolyLog(2, ℯ^x) + PolyLog(3, -ℯ^x) - PolyLog(3, ℯ^x)]
    @test_int [x^2*acoth(cosh(x)), x, 10, (1/3)*x^3*acoth(cosh(x)) - (2/3)*x^3*atanh(ℯ^x) - x^2*PolyLog(2, -ℯ^x) + x^2*PolyLog(2, ℯ^x) + 2*x*PolyLog(3, -ℯ^x) - 2*x*PolyLog(3, ℯ^x) - 2*PolyLog(4, -ℯ^x) + 2*PolyLog(4, ℯ^x)]

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

    @test_int [acoth(c + d*tanh(a + b*x))*x^2, x, 11, (1/3)*x^3*acoth(c + d*tanh(a + b*x)) + (1/6)*x^3*log(1 + ((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d)) - (1/6)*x^3*log(1 + ((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d)) + (x^2*PolyLog(2, -(((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d))))/(4*b) - (x^2*PolyLog(2, -(((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d))))/(4*b) - (x*PolyLog(3, -(((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d))))/(4*b^2) + (x*PolyLog(3, -(((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d))))/(4*b^2) + PolyLog(4, -(((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d)))/(8*b^3) - PolyLog(4, -(((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d)))/(8*b^3)]
    @test_int [acoth(c + d*tanh(a + b*x))*x^1, x, 9, (1/2)*x^2*acoth(c + d*tanh(a + b*x)) + (1/4)*x^2*log(1 + ((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d)) - (1/4)*x^2*log(1 + ((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d)) + (x*PolyLog(2, -(((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d))))/(4*b) - (x*PolyLog(2, -(((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d))))/(4*b) - PolyLog(3, -(((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d)))/(8*b^2) + PolyLog(3, -(((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d)))/(8*b^2)]
    @test_int [acoth(c + d*tanh(a + b*x))*x^0, x, 7, x*acoth(c + d*tanh(a + b*x)) + (1/2)*x*log(1 + ((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d)) - (1/2)*x*log(1 + ((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d)) + PolyLog(2, -(((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d)))/(4*b) - PolyLog(2, -(((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d)))/(4*b)]
    @test_int [acoth(c + d*tanh(a + b*x))/x^1, x, 0, CannotIntegrate(acoth(c + d*tanh(a + b*x))/x, x)]

    @test_int [acoth(1 + d + d*tanh(a + b*x))*x^3, x, 8, (b*x^5)/20 + (1/4)*x^4*acoth(1 + d + d*tanh(a + b*x)) - (1/8)*x^4*log(1 + (1 + d)*ℯ^(2*a + 2*b*x)) - (x^3*PolyLog(2, -((1 + d)*ℯ^(2*a + 2*b*x))))/(4*b) + (3*x^2*PolyLog(3, -((1 + d)*ℯ^(2*a + 2*b*x))))/(8*b^2) - (3*x*PolyLog(4, -((1 + d)*ℯ^(2*a + 2*b*x))))/(8*b^3) + (3*PolyLog(5, -((1 + d)*ℯ^(2*a + 2*b*x))))/(16*b^4)]
    @test_int [acoth(1 + d + d*tanh(a + b*x))*x^2, x, 7, (b*x^4)/12 + (1/3)*x^3*acoth(1 + d + d*tanh(a + b*x)) - (1/6)*x^3*log(1 + (1 + d)*ℯ^(2*a + 2*b*x)) - (x^2*PolyLog(2, -((1 + d)*ℯ^(2*a + 2*b*x))))/(4*b) + (x*PolyLog(3, -((1 + d)*ℯ^(2*a + 2*b*x))))/(4*b^2) - PolyLog(4, -((1 + d)*ℯ^(2*a + 2*b*x)))/(8*b^3)]
    @test_int [acoth(1 + d + d*tanh(a + b*x))*x^1, x, 6, (b*x^3)/6 + (1/2)*x^2*acoth(1 + d + d*tanh(a + b*x)) - (1/4)*x^2*log(1 + (1 + d)*ℯ^(2*a + 2*b*x)) - (x*PolyLog(2, -((1 + d)*ℯ^(2*a + 2*b*x))))/(4*b) + PolyLog(3, -((1 + d)*ℯ^(2*a + 2*b*x)))/(8*b^2)]
    @test_int [acoth(1 + d + d*tanh(a + b*x))*x^0, x, 5, (b*x^2)/2 + x*acoth(1 + d + d*tanh(a + b*x)) - (1/2)*x*log(1 + (1 + d)*ℯ^(2*a + 2*b*x)) - PolyLog(2, -((1 + d)*ℯ^(2*a + 2*b*x)))/(4*b)]
    @test_int [acoth(1 + d + d*tanh(a + b*x))/x^1, x, 0, CannotIntegrate(acoth(1 + d + d*tanh(a + b*x))/x, x)]

    @test_int [acoth(1 - d - d*tanh(a + b*x))*x^3, x, 8, (b*x^5)/20 + (1/4)*x^4*acoth(1 - d - d*tanh(a + b*x)) - (1/8)*x^4*log(1 + (1 - d)*ℯ^(2*a + 2*b*x)) - (x^3*PolyLog(2, -((1 - d)*ℯ^(2*a + 2*b*x))))/(4*b) + (3*x^2*PolyLog(3, -((1 - d)*ℯ^(2*a + 2*b*x))))/(8*b^2) - (3*x*PolyLog(4, -((1 - d)*ℯ^(2*a + 2*b*x))))/(8*b^3) + (3*PolyLog(5, -((1 - d)*ℯ^(2*a + 2*b*x))))/(16*b^4)]
    @test_int [acoth(1 - d - d*tanh(a + b*x))*x^2, x, 7, (b*x^4)/12 + (1/3)*x^3*acoth(1 - d - d*tanh(a + b*x)) - (1/6)*x^3*log(1 + (1 - d)*ℯ^(2*a + 2*b*x)) - (x^2*PolyLog(2, -((1 - d)*ℯ^(2*a + 2*b*x))))/(4*b) + (x*PolyLog(3, -((1 - d)*ℯ^(2*a + 2*b*x))))/(4*b^2) - PolyLog(4, -((1 - d)*ℯ^(2*a + 2*b*x)))/(8*b^3)]
    @test_int [acoth(1 - d - d*tanh(a + b*x))*x^1, x, 6, (b*x^3)/6 + (1/2)*x^2*acoth(1 - d - d*tanh(a + b*x)) - (1/4)*x^2*log(1 + (1 - d)*ℯ^(2*a + 2*b*x)) - (x*PolyLog(2, -((1 - d)*ℯ^(2*a + 2*b*x))))/(4*b) + PolyLog(3, -((1 - d)*ℯ^(2*a + 2*b*x)))/(8*b^2)]
    @test_int [acoth(1 - d - d*tanh(a + b*x))*x^0, x, 5, (b*x^2)/2 + x*acoth(1 - d - d*tanh(a + b*x)) - (1/2)*x*log(1 + (1 - d)*ℯ^(2*a + 2*b*x)) - PolyLog(2, -((1 - d)*ℯ^(2*a + 2*b*x)))/(4*b)]
    @test_int [acoth(1 - d - d*tanh(a + b*x))/x^1, x, 0, CannotIntegrate(acoth(1 - d - d*tanh(a + b*x))/x, x)]

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

    @test_int [acoth(c + d*coth(a + b*x))*x^2, x, 11, (1/3)*x^3*acoth(c + d*coth(a + b*x)) + (1/6)*x^3*log(1 - ((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d)) - (1/6)*x^3*log(1 - ((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d)) + (x^2*PolyLog(2, ((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d)))/(4*b) - (x^2*PolyLog(2, ((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d)))/(4*b) - (x*PolyLog(3, ((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d)))/(4*b^2) + (x*PolyLog(3, ((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d)))/(4*b^2) + PolyLog(4, ((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d))/(8*b^3) - PolyLog(4, ((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d))/(8*b^3)]
    @test_int [acoth(c + d*coth(a + b*x))*x^1, x, 9, (1/2)*x^2*acoth(c + d*coth(a + b*x)) + (1/4)*x^2*log(1 - ((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d)) - (1/4)*x^2*log(1 - ((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d)) + (x*PolyLog(2, ((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d)))/(4*b) - (x*PolyLog(2, ((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d)))/(4*b) - PolyLog(3, ((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d))/(8*b^2) + PolyLog(3, ((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d))/(8*b^2)]
    @test_int [acoth(c + d*coth(a + b*x))*x^0, x, 7, x*acoth(c + d*coth(a + b*x)) + (1/2)*x*log(1 - ((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d)) - (1/2)*x*log(1 - ((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d)) + PolyLog(2, ((1 - c - d)*ℯ^(2*a + 2*b*x))/(1 - c + d))/(4*b) - PolyLog(2, ((1 + c + d)*ℯ^(2*a + 2*b*x))/(1 + c - d))/(4*b)]
    @test_int [acoth(c + d*coth(a + b*x))/x^1, x, 0, CannotIntegrate(acoth(c + d*coth(a + b*x))/x, x)]

    @test_int [acoth(1 + d + d*coth(a + b*x))*x^3, x, 8, (b*x^5)/20 + (1/4)*x^4*acoth(1 + d + d*coth(a + b*x)) - (1/8)*x^4*log(1 - (1 + d)*ℯ^(2*a + 2*b*x)) - (x^3*PolyLog(2, (1 + d)*ℯ^(2*a + 2*b*x)))/(4*b) + (3*x^2*PolyLog(3, (1 + d)*ℯ^(2*a + 2*b*x)))/(8*b^2) - (3*x*PolyLog(4, (1 + d)*ℯ^(2*a + 2*b*x)))/(8*b^3) + (3*PolyLog(5, (1 + d)*ℯ^(2*a + 2*b*x)))/(16*b^4)]
    @test_int [acoth(1 + d + d*coth(a + b*x))*x^2, x, 7, (b*x^4)/12 + (1/3)*x^3*acoth(1 + d + d*coth(a + b*x)) - (1/6)*x^3*log(1 - (1 + d)*ℯ^(2*a + 2*b*x)) - (x^2*PolyLog(2, (1 + d)*ℯ^(2*a + 2*b*x)))/(4*b) + (x*PolyLog(3, (1 + d)*ℯ^(2*a + 2*b*x)))/(4*b^2) - PolyLog(4, (1 + d)*ℯ^(2*a + 2*b*x))/(8*b^3)]
    @test_int [acoth(1 + d + d*coth(a + b*x))*x^1, x, 6, (b*x^3)/6 + (1/2)*x^2*acoth(1 + d + d*coth(a + b*x)) - (1/4)*x^2*log(1 - (1 + d)*ℯ^(2*a + 2*b*x)) - (x*PolyLog(2, (1 + d)*ℯ^(2*a + 2*b*x)))/(4*b) + PolyLog(3, (1 + d)*ℯ^(2*a + 2*b*x))/(8*b^2)]
    @test_int [acoth(1 + d + d*coth(a + b*x))*x^0, x, 5, (b*x^2)/2 + x*acoth(1 + d + d*coth(a + b*x)) - (1/2)*x*log(1 - (1 + d)*ℯ^(2*a + 2*b*x)) - PolyLog(2, (1 + d)*ℯ^(2*a + 2*b*x))/(4*b)]
    @test_int [acoth(1 + d + d*coth(a + b*x))/x^1, x, 0, CannotIntegrate(acoth(1 + d + d*coth(a + b*x))/x, x)]

    @test_int [acoth(1 - d - d*coth(a + b*x))*x^3, x, 8, (b*x^5)/20 + (1/4)*x^4*acoth(1 - d - d*coth(a + b*x)) - (1/8)*x^4*log(1 - (1 - d)*ℯ^(2*a + 2*b*x)) - (x^3*PolyLog(2, (1 - d)*ℯ^(2*a + 2*b*x)))/(4*b) + (3*x^2*PolyLog(3, (1 - d)*ℯ^(2*a + 2*b*x)))/(8*b^2) - (3*x*PolyLog(4, (1 - d)*ℯ^(2*a + 2*b*x)))/(8*b^3) + (3*PolyLog(5, (1 - d)*ℯ^(2*a + 2*b*x)))/(16*b^4)]
    @test_int [acoth(1 - d - d*coth(a + b*x))*x^2, x, 7, (b*x^4)/12 + (1/3)*x^3*acoth(1 - d - d*coth(a + b*x)) - (1/6)*x^3*log(1 - (1 - d)*ℯ^(2*a + 2*b*x)) - (x^2*PolyLog(2, (1 - d)*ℯ^(2*a + 2*b*x)))/(4*b) + (x*PolyLog(3, (1 - d)*ℯ^(2*a + 2*b*x)))/(4*b^2) - PolyLog(4, (1 - d)*ℯ^(2*a + 2*b*x))/(8*b^3)]
    @test_int [acoth(1 - d - d*coth(a + b*x))*x^1, x, 6, (b*x^3)/6 + (1/2)*x^2*acoth(1 - d - d*coth(a + b*x)) - (1/4)*x^2*log(1 - (1 - d)*ℯ^(2*a + 2*b*x)) - (x*PolyLog(2, (1 - d)*ℯ^(2*a + 2*b*x)))/(4*b) + PolyLog(3, (1 - d)*ℯ^(2*a + 2*b*x))/(8*b^2)]
    @test_int [acoth(1 - d - d*coth(a + b*x))*x^0, x, 5, (b*x^2)/2 + x*acoth(1 - d - d*coth(a + b*x)) - (1/2)*x*log(1 - (1 - d)*ℯ^(2*a + 2*b*x)) - PolyLog(2, (1 - d)*ℯ^(2*a + 2*b*x))/(4*b)]
    @test_int [acoth(1 - d - d*coth(a + b*x))/x^1, x, 0, CannotIntegrate(acoth(1 - d - d*coth(a + b*x))/x, x)]

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

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

    @test_int [(e + f*x)^3*acoth(tan(a + b*x)), x, 12, ((e + f*x)^4*acoth(tan(a + b*x)))/(4*f) + (im*(e + f*x)^4*atan(ℯ^(2*im*(a + b*x))))/(4*f) - (im*(e + f*x)^3*PolyLog(2, (-im)*ℯ^(2*im*(a + b*x))))/(4*b) + (im*(e + f*x)^3*PolyLog(2, im*ℯ^(2*im*(a + b*x))))/(4*b) + (3*f*(e + f*x)^2*PolyLog(3, (-im)*ℯ^(2*im*(a + b*x))))/(8*b^2) - (3*f*(e + f*x)^2*PolyLog(3, im*ℯ^(2*im*(a + b*x))))/(8*b^2) + (3*im*f^2*(e + f*x)*PolyLog(4, (-im)*ℯ^(2*im*(a + b*x))))/(8*b^3) - (3*im*f^2*(e + f*x)*PolyLog(4, im*ℯ^(2*im*(a + b*x))))/(8*b^3) - (3*f^3*PolyLog(5, (-im)*ℯ^(2*im*(a + b*x))))/(16*b^4) + (3*f^3*PolyLog(5, im*ℯ^(2*im*(a + b*x))))/(16*b^4)]
    @test_int [(e + f*x)^2*acoth(tan(a + b*x)), x, 10, ((e + f*x)^3*acoth(tan(a + b*x)))/(3*f) + (im*(e + f*x)^3*atan(ℯ^(2*im*(a + b*x))))/(3*f) - (im*(e + f*x)^2*PolyLog(2, (-im)*ℯ^(2*im*(a + b*x))))/(4*b) + (im*(e + f*x)^2*PolyLog(2, im*ℯ^(2*im*(a + b*x))))/(4*b) + (f*(e + f*x)*PolyLog(3, (-im)*ℯ^(2*im*(a + b*x))))/(4*b^2) - (f*(e + f*x)*PolyLog(3, im*ℯ^(2*im*(a + b*x))))/(4*b^2) + (im*f^2*PolyLog(4, (-im)*ℯ^(2*im*(a + b*x))))/(8*b^3) - (im*f^2*PolyLog(4, im*ℯ^(2*im*(a + b*x))))/(8*b^3)]
    @test_int [(e + f*x)^1*acoth(tan(a + b*x)), x, 8, ((e + f*x)^2*acoth(tan(a + b*x)))/(2*f) + (im*(e + f*x)^2*atan(ℯ^(2*im*(a + b*x))))/(2*f) - (im*(e + f*x)*PolyLog(2, (-im)*ℯ^(2*im*(a + b*x))))/(4*b) + (im*(e + f*x)*PolyLog(2, im*ℯ^(2*im*(a + b*x))))/(4*b) + (f*PolyLog(3, (-im)*ℯ^(2*im*(a + b*x))))/(8*b^2) - (f*PolyLog(3, im*ℯ^(2*im*(a + b*x))))/(8*b^2)]
    @test_int [(e + f*x)^0*acoth(tan(a + b*x)), x, 6, x*acoth(tan(a + b*x)) + im*x*atan(ℯ^(2*im*(a + b*x))) - (im*PolyLog(2, (-im)*ℯ^(2*im*(a + b*x))))/(4*b) + (im*PolyLog(2, im*ℯ^(2*im*(a + b*x))))/(4*b)]
    @test_int [acoth(tan(a + b*x))/(e + f*x)^1, x, 0, CannotIntegrate(acoth(tan(a + b*x))/(e + f*x), x)]

    @test_int [x^2*acoth(c + d*tan(a + b*x)), x, 11, (1/3)*x^3*acoth(c + d*tan(a + b*x)) + (1/6)*x^3*log(1 + ((1 - c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c - im*d)) - (1/6)*x^3*log(1 + ((1 + c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c + im*d)) - (im*x^2*PolyLog(2, -(((1 - c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c - im*d))))/(4*b) + (im*x^2*PolyLog(2, -(((1 + c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c + im*d))))/(4*b) + (x*PolyLog(3, -(((1 - c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c - im*d))))/(4*b^2) - (x*PolyLog(3, -(((1 + c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c + im*d))))/(4*b^2) + (im*PolyLog(4, -(((1 - c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c - im*d))))/(8*b^3) - (im*PolyLog(4, -(((1 + c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c + im*d))))/(8*b^3)]
    @test_int [x^1*acoth(c + d*tan(a + b*x)), x, 9, (1/2)*x^2*acoth(c + d*tan(a + b*x)) + (1/4)*x^2*log(1 + ((1 - c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c - im*d)) - (1/4)*x^2*log(1 + ((1 + c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c + im*d)) - (im*x*PolyLog(2, -(((1 - c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c - im*d))))/(4*b) + (im*x*PolyLog(2, -(((1 + c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c + im*d))))/(4*b) + PolyLog(3, -(((1 - c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c - im*d)))/(8*b^2) - PolyLog(3, -(((1 + c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c + im*d)))/(8*b^2)]
    @test_int [x^0*acoth(c + d*tan(a + b*x)), x, 7, x*acoth(c + d*tan(a + b*x)) + (1/2)*x*log(1 + ((1 - c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c - im*d)) - (1/2)*x*log(1 + ((1 + c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c + im*d)) - (im*PolyLog(2, -(((1 - c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c - im*d))))/(4*b) + (im*PolyLog(2, -(((1 + c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c + im*d))))/(4*b)]
    @test_int [acoth(c + d*tan(a + b*x))/x^1, x, 0, CannotIntegrate(acoth(c + d*tan(a + b*x))/x, x)]

    @test_int [x^2*acoth(1 - im*d + d*tan(a + b*x)), x, 7, (1/12)*im*b*x^4 + (1/3)*x^3*acoth(1 - im*d + d*tan(a + b*x)) - (1/6)*x^3*log(1 + (1 - im*d)*ℯ^(2*im*a + 2*im*b*x)) + (im*x^2*PolyLog(2, -((1 - im*d)*ℯ^(2*im*a + 2*im*b*x))))/(4*b) - (x*PolyLog(3, -((1 - im*d)*ℯ^(2*im*a + 2*im*b*x))))/(4*b^2) - (im*PolyLog(4, -((1 - im*d)*ℯ^(2*im*a + 2*im*b*x))))/(8*b^3)]
    @test_int [x^1*acoth(1 - im*d + d*tan(a + b*x)), x, 6, (1/6)*im*b*x^3 + (1/2)*x^2*acoth(1 - im*d + d*tan(a + b*x)) - (1/4)*x^2*log(1 + (1 - im*d)*ℯ^(2*im*a + 2*im*b*x)) + (im*x*PolyLog(2, -((1 - im*d)*ℯ^(2*im*a + 2*im*b*x))))/(4*b) - PolyLog(3, -((1 - im*d)*ℯ^(2*im*a + 2*im*b*x)))/(8*b^2)]
    @test_int [x^0*acoth(1 - im*d + d*tan(a + b*x)), x, 5, (1/2)*im*b*x^2 + x*acoth(1 - im*d + d*tan(a + b*x)) - (1/2)*x*log(1 + (1 - im*d)*ℯ^(2*im*a + 2*im*b*x)) + (im*PolyLog(2, -((1 - im*d)*ℯ^(2*im*a + 2*im*b*x))))/(4*b)]
    @test_int [acoth(1 - im*d + d*tan(a + b*x))/x^1, x, 0, CannotIntegrate(acoth(1 - im*d + d*tan(a + b*x))/x, x)]

    @test_int [x^2*acoth(1 + im*d - d*tan(a + b*x)), x, 7, (1/12)*im*b*x^4 + (1/3)*x^3*acoth(1 + im*d - d*tan(a + b*x)) - (1/6)*x^3*log(1 + (1 + im*d)*ℯ^(2*im*a + 2*im*b*x)) + (im*x^2*PolyLog(2, -((1 + im*d)*ℯ^(2*im*a + 2*im*b*x))))/(4*b) - (x*PolyLog(3, -((1 + im*d)*ℯ^(2*im*a + 2*im*b*x))))/(4*b^2) - (im*PolyLog(4, -((1 + im*d)*ℯ^(2*im*a + 2*im*b*x))))/(8*b^3)]
    @test_int [x^1*acoth(1 + im*d - d*tan(a + b*x)), x, 6, (1/6)*im*b*x^3 + (1/2)*x^2*acoth(1 + im*d - d*tan(a + b*x)) - (1/4)*x^2*log(1 + (1 + im*d)*ℯ^(2*im*a + 2*im*b*x)) + (im*x*PolyLog(2, -((1 + im*d)*ℯ^(2*im*a + 2*im*b*x))))/(4*b) - PolyLog(3, -((1 + im*d)*ℯ^(2*im*a + 2*im*b*x)))/(8*b^2)]
    @test_int [x^0*acoth(1 + im*d - d*tan(a + b*x)), x, 5, (1/2)*im*b*x^2 + x*acoth(1 + im*d - d*tan(a + b*x)) - (1/2)*x*log(1 + (1 + im*d)*ℯ^(2*im*a + 2*im*b*x)) + (im*PolyLog(2, -((1 + im*d)*ℯ^(2*im*a + 2*im*b*x))))/(4*b)]
    @test_int [acoth(1 + im*d - d*tan(a + b*x))/x^1, x, 0, CannotIntegrate(acoth(1 + im*d - d*tan(a + b*x))/x, x)]

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

    @test_int [(e + f*x)^3*acoth(cot(a + b*x)), x, 12, ((e + f*x)^4*acoth(cot(a + b*x)))/(4*f) + (im*(e + f*x)^4*atan(ℯ^(2*im*(a + b*x))))/(4*f) - (im*(e + f*x)^3*PolyLog(2, (-im)*ℯ^(2*im*(a + b*x))))/(4*b) + (im*(e + f*x)^3*PolyLog(2, im*ℯ^(2*im*(a + b*x))))/(4*b) + (3*f*(e + f*x)^2*PolyLog(3, (-im)*ℯ^(2*im*(a + b*x))))/(8*b^2) - (3*f*(e + f*x)^2*PolyLog(3, im*ℯ^(2*im*(a + b*x))))/(8*b^2) + (3*im*f^2*(e + f*x)*PolyLog(4, (-im)*ℯ^(2*im*(a + b*x))))/(8*b^3) - (3*im*f^2*(e + f*x)*PolyLog(4, im*ℯ^(2*im*(a + b*x))))/(8*b^3) - (3*f^3*PolyLog(5, (-im)*ℯ^(2*im*(a + b*x))))/(16*b^4) + (3*f^3*PolyLog(5, im*ℯ^(2*im*(a + b*x))))/(16*b^4)]
    @test_int [(e + f*x)^2*acoth(cot(a + b*x)), x, 10, ((e + f*x)^3*acoth(cot(a + b*x)))/(3*f) + (im*(e + f*x)^3*atan(ℯ^(2*im*(a + b*x))))/(3*f) - (im*(e + f*x)^2*PolyLog(2, (-im)*ℯ^(2*im*(a + b*x))))/(4*b) + (im*(e + f*x)^2*PolyLog(2, im*ℯ^(2*im*(a + b*x))))/(4*b) + (f*(e + f*x)*PolyLog(3, (-im)*ℯ^(2*im*(a + b*x))))/(4*b^2) - (f*(e + f*x)*PolyLog(3, im*ℯ^(2*im*(a + b*x))))/(4*b^2) + (im*f^2*PolyLog(4, (-im)*ℯ^(2*im*(a + b*x))))/(8*b^3) - (im*f^2*PolyLog(4, im*ℯ^(2*im*(a + b*x))))/(8*b^3)]
    @test_int [(e + f*x)^1*acoth(cot(a + b*x)), x, 8, ((e + f*x)^2*acoth(cot(a + b*x)))/(2*f) + (im*(e + f*x)^2*atan(ℯ^(2*im*(a + b*x))))/(2*f) - (im*(e + f*x)*PolyLog(2, (-im)*ℯ^(2*im*(a + b*x))))/(4*b) + (im*(e + f*x)*PolyLog(2, im*ℯ^(2*im*(a + b*x))))/(4*b) + (f*PolyLog(3, (-im)*ℯ^(2*im*(a + b*x))))/(8*b^2) - (f*PolyLog(3, im*ℯ^(2*im*(a + b*x))))/(8*b^2)]
    @test_int [(e + f*x)^0*acoth(cot(a + b*x)), x, 6, x*acoth(cot(a + b*x)) + im*x*atan(ℯ^(2*im*(a + b*x))) - (im*PolyLog(2, (-im)*ℯ^(2*im*(a + b*x))))/(4*b) + (im*PolyLog(2, im*ℯ^(2*im*(a + b*x))))/(4*b)]
    @test_int [acoth(cot(a + b*x))/(e + f*x)^1, x, 0, CannotIntegrate(acoth(cot(a + b*x))/(e + f*x), x)]

    @test_int [x^2*acoth(c + d*cot(a + b*x)), x, 11, (1/3)*x^3*acoth(c + d*cot(a + b*x)) + (1/6)*x^3*log(1 - ((1 - c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c + im*d)) - (1/6)*x^3*log(1 - ((1 + c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c - im*d)) - (im*x^2*PolyLog(2, ((1 - c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c + im*d)))/(4*b) + (im*x^2*PolyLog(2, ((1 + c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c - im*d)))/(4*b) + (x*PolyLog(3, ((1 - c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c + im*d)))/(4*b^2) - (x*PolyLog(3, ((1 + c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c - im*d)))/(4*b^2) + (im*PolyLog(4, ((1 - c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c + im*d)))/(8*b^3) - (im*PolyLog(4, ((1 + c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c - im*d)))/(8*b^3)]
    @test_int [x^1*acoth(c + d*cot(a + b*x)), x, 9, (1/2)*x^2*acoth(c + d*cot(a + b*x)) + (1/4)*x^2*log(1 - ((1 - c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c + im*d)) - (1/4)*x^2*log(1 - ((1 + c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c - im*d)) - (im*x*PolyLog(2, ((1 - c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c + im*d)))/(4*b) + (im*x*PolyLog(2, ((1 + c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c - im*d)))/(4*b) + PolyLog(3, ((1 - c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c + im*d))/(8*b^2) - PolyLog(3, ((1 + c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c - im*d))/(8*b^2)]
    @test_int [x^0*acoth(c + d*cot(a + b*x)), x, 7, x*acoth(c + d*cot(a + b*x)) + (1/2)*x*log(1 - ((1 - c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c + im*d)) - (1/2)*x*log(1 - ((1 + c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c - im*d)) - (im*PolyLog(2, ((1 - c - im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 - c + im*d)))/(4*b) + (im*PolyLog(2, ((1 + c + im*d)*ℯ^(2*im*a + 2*im*b*x))/(1 + c - im*d)))/(4*b)]
    @test_int [acoth(c + d*cot(a + b*x))/x^1, x, 0, CannotIntegrate(acoth(c + d*cot(a + b*x))/x, x)]

    @test_int [x^2*acoth(1 + im*d + d*cot(a + b*x)), x, 7, (1/12)*im*b*x^4 + (1/3)*x^3*acoth(1 + im*d + d*cot(a + b*x)) - (1/6)*x^3*log(1 - (1 + im*d)*ℯ^(2*im*a + 2*im*b*x)) + (im*x^2*PolyLog(2, (1 + im*d)*ℯ^(2*im*a + 2*im*b*x)))/(4*b) - (x*PolyLog(3, (1 + im*d)*ℯ^(2*im*a + 2*im*b*x)))/(4*b^2) - (im*PolyLog(4, (1 + im*d)*ℯ^(2*im*a + 2*im*b*x)))/(8*b^3)]
    @test_int [x^1*acoth(1 + im*d + d*cot(a + b*x)), x, 6, (1/6)*im*b*x^3 + (1/2)*x^2*acoth(1 + im*d + d*cot(a + b*x)) - (1/4)*x^2*log(1 - (1 + im*d)*ℯ^(2*im*a + 2*im*b*x)) + (im*x*PolyLog(2, (1 + im*d)*ℯ^(2*im*a + 2*im*b*x)))/(4*b) - PolyLog(3, (1 + im*d)*ℯ^(2*im*a + 2*im*b*x))/(8*b^2)]
    @test_int [x^0*acoth(1 + im*d + d*cot(a + b*x)), x, 5, (1/2)*im*b*x^2 + x*acoth(1 + im*d + d*cot(a + b*x)) - (1/2)*x*log(1 - (1 + im*d)*ℯ^(2*im*a + 2*im*b*x)) + (im*PolyLog(2, (1 + im*d)*ℯ^(2*im*a + 2*im*b*x)))/(4*b)]
    @test_int [acoth(1 + im*d + d*cot(a + b*x))/x^1, x, 0, CannotIntegrate(acoth(1 + im*d + d*cot(a + b*x))/x, x)]

    @test_int [x^2*acoth(1 - im*d - d*cot(a + b*x)), x, 7, (1/12)*im*b*x^4 + (1/3)*x^3*acoth(1 - im*d - d*cot(a + b*x)) - (1/6)*x^3*log(1 - (1 - im*d)*ℯ^(2*im*a + 2*im*b*x)) + (im*x^2*PolyLog(2, (1 - im*d)*ℯ^(2*im*a + 2*im*b*x)))/(4*b) - (x*PolyLog(3, (1 - im*d)*ℯ^(2*im*a + 2*im*b*x)))/(4*b^2) - (im*PolyLog(4, (1 - im*d)*ℯ^(2*im*a + 2*im*b*x)))/(8*b^3)]
    @test_int [x^1*acoth(1 - im*d - d*cot(a + b*x)), x, 6, (1/6)*im*b*x^3 + (1/2)*x^2*acoth(1 - im*d - d*cot(a + b*x)) - (1/4)*x^2*log(1 - (1 - im*d)*ℯ^(2*im*a + 2*im*b*x)) + (im*x*PolyLog(2, (1 - im*d)*ℯ^(2*im*a + 2*im*b*x)))/(4*b) - PolyLog(3, (1 - im*d)*ℯ^(2*im*a + 2*im*b*x))/(8*b^2)]
    @test_int [x^0*acoth(1 - im*d - d*cot(a + b*x)), x, 5, (1/2)*im*b*x^2 + x*acoth(1 - im*d - d*cot(a + b*x)) - (1/2)*x*log(1 - (1 - im*d)*ℯ^(2*im*a + 2*im*b*x)) + (im*PolyLog(2, (1 - im*d)*ℯ^(2*im*a + 2*im*b*x)))/(4*b)]
    @test_int [acoth(1 - im*d - d*cot(a + b*x))/x^1, x, 0, CannotIntegrate(acoth(1 - im*d - d*cot(a + b*x))/x, x)]

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

    @test_int [((a + b*acoth(c*x^n))*(d + e*log(f*x^m)))/x, x, 11, a*d*log(x) + (a*e*log(f*x^m)^2)/(2*m) + (b*d*PolyLog(2, -(1/(x^n*c))))/(2*n) + (b*e*log(f*x^m)*PolyLog(2, -(1/(x^n*c))))/(2*n) - (b*d*PolyLog(2, 1/(x^n*c)))/(2*n) - (b*e*log(f*x^m)*PolyLog(2, 1/(x^n*c)))/(2*n) + (b*e*m*PolyLog(3, -(1/(x^n*c))))/(2*n^2) - (b*e*m*PolyLog(3, 1/(x^n*c)))/(2*n^2)]

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

    @test_int [x^5*(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2)), x, If(13<9, 18, 23), If(13<9, (b*(6*d - 11*e)*x)/(36*c^5) - (23*b*e*x)/(45*c^5) + (b*(6*d - 5*e)*x^3)/(108*c^3) - (8*b*e*x^3)/(135*c^3) + (b*(3*d - e)*x^5)/(90*c) - (b*e*x^5)/(75*c) - (e*x^2*(a + b*acoth(c*x)))/(6*c^4) - (e*x^4*(a + b*acoth(c*x)))/(12*c^2) - (1/18)*e*x^6*(a + b*acoth(c*x)) - (b*(6*d - 11*e)*atanh(c*x))/(36*c^6) + (23*b*e*atanh(c*x))/(45*c^6) + (b*e*x*log(1 - c^2*x^2))/(6*c^5) + (b*e*x^3*log(1 - c^2*x^2))/(18*c^3) + (b*e*x^5*log(1 - c^2*x^2))/(30*c) - (e*(a + b*acoth(c*x))*log(1 - c^2*x^2))/(6*c^6) + (1/6)*x^6*(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2)), (b*(3*d - e)*x)/(18*c^5) - (137*b*e*x)/(180*c^5) + (b*(3*d - e)*x^3)/(54*c^3) - (47*b*e*x^3)/(540*c^3) + (b*(3*d - e)*x^5)/(90*c) - (b*e*x^5)/(75*c) - (e*x^2*(a + b*acoth(c*x)))/(6*c^4) - (e*x^4*(a + b*acoth(c*x)))/(12*c^2) - (1/18)*e*x^6*(a + b*acoth(c*x)) - (b*(3*d - e)*atanh(c*x))/(18*c^6) + (137*b*e*atanh(c*x))/(180*c^6) + (b*e*x*log(1 - c^2*x^2))/(6*c^5) + (b*e*x^3*log(1 - c^2*x^2))/(18*c^3) + (b*e*x^5*log(1 - c^2*x^2))/(30*c) - (e*(a + b*acoth(c*x))*log(1 - c^2*x^2))/(6*c^6) + (1/6)*x^6*(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2)))]
    @test_int [x^3*(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2)), x, 14, (b*(2*d - 3*e)*x)/(8*c^3) - (2*b*e*x)/(3*c^3) + (b*(2*d - e)*x^3)/(24*c) - (b*e*x^3)/(18*c) - (e*x^2*(a + b*acoth(c*x)))/(4*c^2) - (1/8)*e*x^4*(a + b*acoth(c*x)) - (b*(2*d - 3*e)*atanh(c*x))/(8*c^4) + (2*b*e*atanh(c*x))/(3*c^4) + (b*e*x*log(1 - c^2*x^2))/(4*c^3) + (b*e*x^3*log(1 - c^2*x^2))/(12*c) - (e*(a + b*acoth(c*x))*log(1 - c^2*x^2))/(4*c^4) + (1/4)*x^4*(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2))]
    @test_int [x^1*(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2)), x, 7, (b*(d - e)*x)/(2*c) - (b*e*x)/c + (1/2)*d*x^2*(a + b*acoth(c*x)) - (1/2)*e*x^2*(a + b*acoth(c*x)) - (b*(d - e)*atanh(c*x))/(2*c^2) + (b*e*atanh(c*x))/c^2 + (b*e*x*log(1 - c^2*x^2))/(2*c) - (e*(1 - c^2*x^2)*(a + b*acoth(c*x))*log(1 - c^2*x^2))/(2*c^2)]
    @test_int [(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2))/x^1, x, 21, (-(1/2))*b*e*log(1 + 1/(c*x))^2*log(-(1/(c*x))) + (1/2)*b*e*log(1 - 1/(c*x))^2*log(1/(c*x)) + a*d*log(x) - b*e*log((c + 1/x)/c)*PolyLog(2, (c + 1/x)/c) + b*e*log(1 - 1/(c*x))*PolyLog(2, 1 - 1/(c*x)) + (1/2)*b*d*PolyLog(2, -(1/(c*x))) + (1/2)*b*e*log((-c^2)*x^2)*PolyLog(2, -(1/(c*x))) - (1/2)*b*e*(log(1 - 1/(c*x)) + log(1 + 1/(c*x)) + log((-c^2)*x^2) - log(1 - c^2*x^2))*PolyLog(2, -(1/(c*x))) - (1/2)*b*d*PolyLog(2, 1/(c*x)) - (1/2)*b*e*log((-c^2)*x^2)*PolyLog(2, 1/(c*x)) + (1/2)*b*e*(log(1 - 1/(c*x)) + log(1 + 1/(c*x)) + log((-c^2)*x^2) - log(1 - c^2*x^2))*PolyLog(2, 1/(c*x)) - (1/2)*a*e*PolyLog(2, c^2*x^2) + b*e*PolyLog(3, (c + 1/x)/c) - b*e*PolyLog(3, 1 - 1/(c*x)) + b*e*PolyLog(3, -(1/(c*x))) - b*e*PolyLog(3, 1/(c*x))]
    @test_int [(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2))/x^3, x, 13, (-(1/2))*b*c^2*e*acoth(c*x)^2 - (1/2)*b*c^2*e*atanh(c*x)^2 - a*c^2*e*log(x) + b*c^2*e*atanh(c*x)*log(2/(1 - c*x)) + (1/2)*(a + b)*c^2*e*log(1 - c*x) + (1/2)*(a - b)*c^2*e*log(1 + c*x) - (b*c*(d + e*log(1 - c^2*x^2)))/(2*x) - ((a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2)))/(2*x^2) + (1/2)*b*c^2*atanh(c*x)*(d + e*log(1 - c^2*x^2)) - b*c^2*e*acoth(c*x)*log(2 - 2/(1 + c*x)) + (1/2)*b*c^2*e*PolyLog(2, 1 - 2/(1 - c*x)) + (1/2)*b*c^2*e*PolyLog(2, -1 + 2/(1 + c*x))]
    @test_int [(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2))/x^5, x, 17, (a*c^2*e)/(4*x^2) + (5*b*c^3*e)/(12*x) + (b*c^2*e*acoth(c*x))/(4*x^2) - (1/4)*b*c^4*e*acoth(c*x)^2 - (1/4)*b*c^4*e*atanh(c*x) - (1/4)*b*c^4*e*atanh(c*x)^2 - (1/2)*a*c^4*e*log(x) + (1/2)*b*c^4*e*atanh(c*x)*log(2/(1 - c*x)) + (1/12)*(3*a + 4*b)*c^4*e*log(1 - c*x) + (1/12)*(3*a - 4*b)*c^4*e*log(1 + c*x) - (b*c*(d + e*log(1 - c^2*x^2)))/(12*x^3) - (b*c^3*(d + e*log(1 - c^2*x^2)))/(4*x) - ((a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2)))/(4*x^4) + (1/4)*b*c^4*atanh(c*x)*(d + e*log(1 - c^2*x^2)) - (1/2)*b*c^4*e*acoth(c*x)*log(2 - 2/(1 + c*x)) + (1/4)*b*c^4*e*PolyLog(2, 1 - 2/(1 - c*x)) + (1/4)*b*c^4*e*PolyLog(2, -1 + 2/(1 + c*x))]

    @test_int [x^4*(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2)), x, 26, -((2*a*e*x)/(5*c^4)) - (77*b*e*x^2)/(300*c^3) - (2*a*e*x^3)/(15*c^2) - (9*b*e*x^4)/(200*c) - (2/25)*a*e*x^5 - (2*b*e*x*acoth(c*x))/(5*c^4) - (2*b*e*x^3*acoth(c*x))/(15*c^2) - (2/25)*b*e*x^5*acoth(c*x) + (b*e*acoth(c*x)^2)/(5*c^5) - ((4*a + 3*b)*e*log(1 - c*x))/(20*c^5) + ((4*a - 3*b)*e*log(1 + c*x))/(20*c^5) - (23*b*e*log(1 - c^2*x^2))/(75*c^5) - (b*e*log(1 - c^2*x^2)^2)/(20*c^5) + (b*x^2*(d + e*log(1 - c^2*x^2)))/(10*c^3) + (b*x^4*(d + e*log(1 - c^2*x^2)))/(20*c) + (1/5)*x^5*(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2)) + (b*log(1 - c^2*x^2)*(d + e*log(1 - c^2*x^2)))/(10*c^5)]
    @test_int [x^2*(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2)), x, 21, -((2*a*e*x)/(3*c^2)) - (5*b*e*x^2)/(18*c) - (2/9)*a*e*x^3 - (2*b*e*x*acoth(c*x))/(3*c^2) - (2/9)*b*e*x^3*acoth(c*x) + (b*e*acoth(c*x)^2)/(3*c^3) - ((2*a + b)*e*log(1 - c*x))/(6*c^3) + ((2*a - b)*e*log(1 + c*x))/(6*c^3) - (4*b*e*log(1 - c^2*x^2))/(9*c^3) - (b*e*log(1 - c^2*x^2)^2)/(12*c^3) + (b*x^2*(d + e*log(1 - c^2*x^2)))/(6*c) + (1/3)*x^3*(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2)) + (b*log(1 - c^2*x^2)*(d + e*log(1 - c^2*x^2)))/(6*c^3)]
    @test_int [x^0*(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2)), x, 9, -2*a*e*x - 2*b*e*x*acoth(c*x) + (e*(a + b*acoth(c*x))^2)/(b*c) - (b*e*log(1 - c^2*x^2))/c + x*(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2)) + (b*(d + e*log(1 - c^2*x^2))^2)/(4*c*e)]
    @test_int [(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2))/x^2, x, 6, -((c*e*(a + b*acoth(c*x))^2)/b) - ((a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2)))/x + (1/2)*b*c*(d + e*log(1 - c^2*x^2))*log(1 - 1/(1 - c^2*x^2)) - (1/2)*b*c*e*PolyLog(2, 1/(1 - c^2*x^2))]
    @test_int [(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2))/x^4, x, 15, (2*c^2*e*(a + b*acoth(c*x)))/(3*x) - (c^3*e*(a + b*acoth(c*x))^2)/(3*b) - b*c^3*e*log(x) + (1/3)*b*c^3*e*log(1 - c^2*x^2) - (b*c*(1 - c^2*x^2)*(d + e*log(1 - c^2*x^2)))/(6*x^2) - ((a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2)))/(3*x^3) + (1/6)*b*c^3*(d + e*log(1 - c^2*x^2))*log(1 - 1/(1 - c^2*x^2)) - (1/6)*b*c^3*e*PolyLog(2, 1/(1 - c^2*x^2))]
    @test_int [(a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2))/x^6, x, 24, (7*b*c^3*e)/(60*x^2) + (2*c^2*e*(a + b*acoth(c*x)))/(15*x^3) + (2*c^4*e*(a + b*acoth(c*x)))/(5*x) - (c^5*e*(a + b*acoth(c*x))^2)/(5*b) - (5/6)*b*c^5*e*log(x) + (19/60)*b*c^5*e*log(1 - c^2*x^2) - (b*c*(d + e*log(1 - c^2*x^2)))/(20*x^4) - (b*c^3*(1 - c^2*x^2)*(d + e*log(1 - c^2*x^2)))/(10*x^2) - ((a + b*acoth(c*x))*(d + e*log(1 - c^2*x^2)))/(5*x^5) + (1/10)*b*c^5*(d + e*log(1 - c^2*x^2))*log(1 - 1/(1 - c^2*x^2)) - (1/10)*b*c^5*e*PolyLog(2, 1/(1 - c^2*x^2))]

    @test_int [x^1*(a + b*acoth(c*x))*(d + e*log(f + g*x^2)), x, If(13<11, 21, 22), (b*(d - e)*x)/(2*c) - (b*e*x)/c + (1/2)*d*x^2*(a + b*acoth(c*x)) - (1/2)*e*x^2*(a + b*acoth(c*x)) + (b*e*sqrt(f)*atan((sqrt(g)*x)/sqrt(f)))/(c*sqrt(g)) - (b*(d - e)*atanh(c*x))/(2*c^2) - (b*e*(c^2*f + g)*atanh(c*x)*log(2/(1 + c*x)))/(c^2*g) + (b*e*(c^2*f + g)*atanh(c*x)*log((2*c*(sqrt(-f) - sqrt(g)*x))/((c*sqrt(-f) - sqrt(g))*(1 + c*x))))/(2*c^2*g) + (b*e*(c^2*f + g)*atanh(c*x)*log((2*c*(sqrt(-f) + sqrt(g)*x))/((c*sqrt(-f) + sqrt(g))*(1 + c*x))))/(2*c^2*g) + (b*e*x*log(f + g*x^2))/(2*c) + (e*(f + g*x^2)*(a + b*acoth(c*x))*log(f + g*x^2))/(2*g) - (b*e*(c^2*f + g)*atanh(c*x)*log(f + g*x^2))/(2*c^2*g) + (b*e*(c^2*f + g)*PolyLog(2, 1 - 2/(1 + c*x)))/(2*c^2*g) - (b*e*(c^2*f + g)*PolyLog(2, 1 - (2*c*(sqrt(-f) - sqrt(g)*x))/((c*sqrt(-f) - sqrt(g))*(1 + c*x))))/(4*c^2*g) - (b*e*(c^2*f + g)*PolyLog(2, 1 - (2*c*(sqrt(-f) + sqrt(g)*x))/((c*sqrt(-f) + sqrt(g))*(1 + c*x))))/(4*c^2*g)]
    @test_int [x^0*(a + b*acoth(c*x))*(d + e*log(f + g*x^2)), x, 38, -2*a*e*x - 2*b*e*x*acoth(c*x) + (2*a*e*sqrt(f)*atan((sqrt(g)*x)/sqrt(f)))/sqrt(g) - (b*e*sqrt(f)*atan((sqrt(g)*x)/sqrt(f))*log(1 - 1/(c*x)))/sqrt(g) + (b*e*sqrt(f)*atan((sqrt(g)*x)/sqrt(f))*log(1 + 1/(c*x)))/sqrt(g) + (b*e*sqrt(f)*atan((sqrt(g)*x)/sqrt(f))*log(-((2*sqrt(f)*sqrt(g)*(1 - c*x))/((im*c*sqrt(f) - sqrt(g))*(sqrt(f) - im*sqrt(g)*x)))))/sqrt(g) - (b*e*sqrt(f)*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f)*sqrt(g)*(1 + c*x))/((im*c*sqrt(f) + sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/sqrt(g) - (b*e*log(1 - c^2*x^2))/c + x*(a + b*acoth(c*x))*(d + e*log(f + g*x^2)) + (b*log((g*(1 - c^2*x^2))/(c^2*f + g))*(d + e*log(f + g*x^2)))/(2*c) + (b*e*PolyLog(2, (c^2*(f + g*x^2))/(c^2*f + g)))/(2*c) - (im*b*e*sqrt(f)*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*(1 - c*x))/((im*c*sqrt(f) - sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*sqrt(g)) + (im*b*e*sqrt(f)*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*(1 + c*x))/((im*c*sqrt(f) + sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*sqrt(g))]
    @test_int [(a + b*acoth(c*x))*(d + e*log(f + g*x^2))/x^1, x, 6, b*e*CannotIntegrate((acoth(c*x)*log(f + g*x^2))/x, x) + a*d*log(x) + (1/2)*a*e*log(-((g*x^2)/f))*log(f + g*x^2) + (1/2)*b*d*PolyLog(2, -(1/(c*x))) - (1/2)*b*d*PolyLog(2, 1/(c*x)) + (1/2)*a*e*PolyLog(2, 1 + (g*x^2)/f)]
    @test_int [(a + b*acoth(c*x))*(d + e*log(f + g*x^2))/x^2, x, 38, (2*a*e*sqrt(g)*atan((sqrt(g)*x)/sqrt(f)))/sqrt(f) - (b*e*sqrt(g)*atan((sqrt(g)*x)/sqrt(f))*log(1 - 1/(c*x)))/sqrt(f) + (b*e*sqrt(g)*atan((sqrt(g)*x)/sqrt(f))*log(1 + 1/(c*x)))/sqrt(f) + (b*e*sqrt(g)*atan((sqrt(g)*x)/sqrt(f))*log(-((2*sqrt(f)*sqrt(g)*(1 - c*x))/((im*c*sqrt(f) - sqrt(g))*(sqrt(f) - im*sqrt(g)*x)))))/sqrt(f) - (b*e*sqrt(g)*atan((sqrt(g)*x)/sqrt(f))*log((2*sqrt(f)*sqrt(g)*(1 + c*x))/((im*c*sqrt(f) + sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/sqrt(f) - ((a + b*acoth(c*x))*(d + e*log(f + g*x^2)))/x + (1/2)*b*c*log(-((g*x^2)/f))*(d + e*log(f + g*x^2)) - (1/2)*b*c*log((g*(1 - c^2*x^2))/(c^2*f + g))*(d + e*log(f + g*x^2)) - (1/2)*b*c*e*PolyLog(2, (c^2*(f + g*x^2))/(c^2*f + g)) + (1/2)*b*c*e*PolyLog(2, 1 + (g*x^2)/f) - (im*b*e*sqrt(g)*PolyLog(2, 1 + (2*sqrt(f)*sqrt(g)*(1 - c*x))/((im*c*sqrt(f) - sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*sqrt(f)) + (im*b*e*sqrt(g)*PolyLog(2, 1 - (2*sqrt(f)*sqrt(g)*(1 + c*x))/((im*c*sqrt(f) + sqrt(g))*(sqrt(f) - im*sqrt(g)*x))))/(2*sqrt(f))]
    @test_int [(a + b*acoth(c*x))*(d + e*log(f + g*x^2))/x^3, x, 32, (b*c*e*sqrt(g)*atan((sqrt(g)*x)/sqrt(f)))/sqrt(f) + (a*e*g*log(x))/f + (b*e*g*acoth(c*x)*log(2/(1 + c*x)))/f + b*c^2*e*atanh(c*x)*log(2/(1 + c*x)) - (b*e*g*acoth(c*x)*log((2*c*(sqrt(-f) - sqrt(g)*x))/((c*sqrt(-f) - sqrt(g))*(1 + c*x))))/(2*f) - (1/2)*b*c^2*e*atanh(c*x)*log((2*c*(sqrt(-f) - sqrt(g)*x))/((c*sqrt(-f) - sqrt(g))*(1 + c*x))) - (b*e*g*acoth(c*x)*log((2*c*(sqrt(-f) + sqrt(g)*x))/((c*sqrt(-f) + sqrt(g))*(1 + c*x))))/(2*f) - (1/2)*b*c^2*e*atanh(c*x)*log((2*c*(sqrt(-f) + sqrt(g)*x))/((c*sqrt(-f) + sqrt(g))*(1 + c*x))) - (a*e*g*log(f + g*x^2))/(2*f) - (b*c*(d + e*log(f + g*x^2)))/(2*x) - ((a + b*acoth(c*x))*(d + e*log(f + g*x^2)))/(2*x^2) + (1/2)*b*c^2*atanh(c*x)*(d + e*log(f + g*x^2)) + (b*e*g*PolyLog(2, -(1/(c*x))))/(2*f) - (b*e*g*PolyLog(2, 1/(c*x)))/(2*f) - (1/2)*b*c^2*e*PolyLog(2, 1 - 2/(1 + c*x)) - (b*e*g*PolyLog(2, 1 - 2/(1 + c*x)))/(2*f) + (1/4)*b*c^2*e*PolyLog(2, 1 - (2*c*(sqrt(-f) - sqrt(g)*x))/((c*sqrt(-f) - sqrt(g))*(1 + c*x))) + (b*e*g*PolyLog(2, 1 - (2*c*(sqrt(-f) - sqrt(g)*x))/((c*sqrt(-f) - sqrt(g))*(1 + c*x))))/(4*f) + (1/4)*b*c^2*e*PolyLog(2, 1 - (2*c*(sqrt(-f) + sqrt(g)*x))/((c*sqrt(-f) + sqrt(g))*(1 + c*x))) + (b*e*g*PolyLog(2, 1 - (2*c*(sqrt(-f) + sqrt(g)*x))/((c*sqrt(-f) + sqrt(g))*(1 + c*x))))/(4*f)]

    #= ::Section::Closed:: =#
    #=Integrands*involving*inverse*hyperbolic*cotangents*of*exponentials=#

    @test_int [acoth(ℯ^x), x, 2, (1/2)*PolyLog(2, -ℯ^(-x)) - (1/2)*PolyLog(2, ℯ^(-x))]
    @test_int [x*acoth(ℯ^x), x, 7, (1/2)*x*PolyLog(2, -ℯ^(-x)) - (1/2)*x*PolyLog(2, ℯ^(-x)) + (1/2)*PolyLog(3, -ℯ^(-x)) - (1/2)*PolyLog(3, ℯ^(-x))]
    @test_int [x^2*acoth(ℯ^x), x, 9, (1/2)*x^2*PolyLog(2, -ℯ^(-x)) - (1/2)*x^2*PolyLog(2, ℯ^(-x)) + x*PolyLog(3, -ℯ^(-x)) - x*PolyLog(3, ℯ^(-x)) + PolyLog(4, -ℯ^(-x)) - PolyLog(4, ℯ^(-x))]

    @test_int [acoth(ℯ^(a + b*x)), x, 2, PolyLog(2, -ℯ^(-a - b*x))/(2*b) - PolyLog(2, ℯ^(-a - b*x))/(2*b)]
    @test_int [x*acoth(ℯ^(a + b*x)), x, 7, (x*PolyLog(2, -ℯ^(-a - b*x)))/(2*b) - (x*PolyLog(2, ℯ^(-a - b*x)))/(2*b) + PolyLog(3, -ℯ^(-a - b*x))/(2*b^2) - PolyLog(3, ℯ^(-a - b*x))/(2*b^2)]
    @test_int [x^2*acoth(ℯ^(a + b*x)), x, 9, (x^2*PolyLog(2, -ℯ^(-a - b*x)))/(2*b) - (x^2*PolyLog(2, ℯ^(-a - b*x)))/(2*b) + (x*PolyLog(3, -ℯ^(-a - b*x)))/b^2 - (x*PolyLog(3, ℯ^(-a - b*x)))/b^2 + PolyLog(4, -ℯ^(-a - b*x))/b^3 - PolyLog(4, ℯ^(-a - b*x))/b^3]

    @test_int [acoth(a + b*f^(c + d*x)), x, 6, -((acoth(a + b*f^(c + d*x))*log(2/(1 + a + b*f^(c + d*x))))/(d*log(f))) + (acoth(a + b*f^(c + d*x))*log((2*b*f^(c + d*x))/((1 - a)*(1 + a + b*f^(c + d*x)))))/(d*log(f)) + PolyLog(2, 1 - 2/(1 + a + b*f^(c + d*x)))/(2*d*log(f)) - PolyLog(2, 1 - (2*b*f^(c + d*x))/((1 - a)*(1 + a + b*f^(c + d*x))))/(2*d*log(f))]
    @test_int [x*acoth(a + b*f^(c + d*x)), x, 25, (1/4)*x^2*log(1 - (b*f^(c + d*x))/(1 - a)) - (1/4)*x^2*log(1 + (b*f^(c + d*x))/(1 + a)) - (1/4)*x^2*log(1 - 1/(a + b*f^(c + d*x))) + (1/4)*x^2*log(1 + 1/(a + b*f^(c + d*x))) + (x*PolyLog(2, (b*f^(c + d*x))/(1 - a)))/(2*d*log(f)) - (x*PolyLog(2, -((b*f^(c + d*x))/(1 + a))))/(2*d*log(f)) - PolyLog(3, (b*f^(c + d*x))/(1 - a))/(2*d^2*log(f)^2) + PolyLog(3, -((b*f^(c + d*x))/(1 + a)))/(2*d^2*log(f)^2)]
    @test_int [x^2*acoth(a + b*f^(c + d*x)), x, 29, (1/6)*x^3*log(1 - (b*f^(c + d*x))/(1 - a)) - (1/6)*x^3*log(1 + (b*f^(c + d*x))/(1 + a)) - (1/6)*x^3*log(1 - 1/(a + b*f^(c + d*x))) + (1/6)*x^3*log(1 + 1/(a + b*f^(c + d*x))) + (x^2*PolyLog(2, (b*f^(c + d*x))/(1 - a)))/(2*d*log(f)) - (x^2*PolyLog(2, -((b*f^(c + d*x))/(1 + a))))/(2*d*log(f)) - (x*PolyLog(3, (b*f^(c + d*x))/(1 - a)))/(d^2*log(f)^2) + (x*PolyLog(3, -((b*f^(c + d*x))/(1 + a))))/(d^2*log(f)^2) + PolyLog(4, (b*f^(c + d*x))/(1 - a))/(d^3*log(f)^3) - PolyLog(4, -((b*f^(c + d*x))/(1 + a)))/(d^3*log(f)^3)]

    #= ::Section::Closed:: =#
    #=Miscellaneous*integrands*involving*inverse*hyperbolic*cotangents=#

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

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

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

    @test_int [ℯ^(c*(a + b*x))*acoth(sinh(a*c + b*c*x)), x, 8, (ℯ^(a*c + b*c*x)*acoth(sinh(c*(a + b*x))))/(b*c) + ((1 - sqrt(2))*log(3 - 2*sqrt(2) - ℯ^(2*c*(a + b*x))))/(2*b*c) + ((1 + sqrt(2))*log(3 + 2*sqrt(2) - ℯ^(2*c*(a + b*x))))/(2*b*c)]
    @test_int [ℯ^(c*(a + b*x))*acoth(cosh(a*c + b*c*x)), x, 5, (ℯ^(a*c + b*c*x)*acoth(cosh(c*(a + b*x))))/(b*c) + log(1 - ℯ^(2*c*(a + b*x)))/(b*c)]
    @test_int [ℯ^(c*(a + b*x))*acoth(tanh(a*c + b*c*x)), x, 3, -(ℯ^(a*c + b*c*x)/(b*c)) + (ℯ^(a*c + b*c*x)*acoth(tanh(c*(a + b*x))))/(b*c)]
    @test_int [ℯ^(c*(a + b*x))*acoth(coth(a*c + b*c*x)), x, 3, -(ℯ^(a*c + b*c*x)/(b*c)) + (ℯ^(a*c + b*c*x)*acoth(coth(c*(a + b*x))))/(b*c)]
    @test_int [ℯ^(c*(a + b*x))*acoth(sech(a*c + b*c*x)), x, 5, (ℯ^(a*c + b*c*x)*acoth(sech(c*(a + b*x))))/(b*c) + log(1 - ℯ^(2*c*(a + b*x)))/(b*c)]
    @test_int [ℯ^(c*(a + b*x))*acoth(csch(a*c + b*c*x)), x, 8, (ℯ^(a*c + b*c*x)*acoth(csch(c*(a + b*x))))/(b*c) + ((1 - sqrt(2))*log(3 - 2*sqrt(2) - ℯ^(2*c*(a + b*x))))/(2*b*c) + ((1 + sqrt(2))*log(3 + 2*sqrt(2) - ℯ^(2*c*(a + b*x))))/(2*b*c)]
    end

max_stars_repo_path: test/7 Inverse hyperbolic functions/7.4 Inverse hyperbolic cotangent/7.4.1 Inverse hyperbolic cotangent functions.jl