text:
@testset "7.2.5 Inverse hyperbolic cosine functions" begin
    (a, b, c, d, d1, d2, e, f, g, h, m, n, x, ) = @variables a b c d d1 d2 e f g h m n x

    #= ::Package:: =#

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

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

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

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

    @test_int [(d + e*x)^3*acosh(c*x), x, 5, -((7*d*sqrt(-1 + c*x)*sqrt(1 + c*x)*(d + e*x)^2)/(48*c)) - (sqrt(-1 + c*x)*sqrt(1 + c*x)*(d + e*x)^3)/(16*c) - (sqrt(-1 + c*x)*sqrt(1 + c*x)*(4*d*(19*c^2*d^2 + 16*e^2) + e*(26*c^2*d^2 + 9*e^2)*x))/(96*c^3) - ((8*c^4*d^4 + 24*c^2*d^2*e^2 + 3*e^4)*acosh(c*x))/(32*c^4*e) + ((d + e*x)^4*acosh(c*x))/(4*e)]
    @test_int [(d + e*x)^2*acosh(c*x), x, 4, -((sqrt(-1 + c*x)*sqrt(1 + c*x)*(d + e*x)^2)/(9*c)) - (sqrt(-1 + c*x)*sqrt(1 + c*x)*(4*(4*c^2*d^2 + e^2) + 5*c^2*d*e*x))/(18*c^3) - (1/6)*d*((2*d^2)/e + (3*e)/c^2)*acosh(c*x) + ((d + e*x)^3*acosh(c*x))/(3*e)]
    @test_int [(d + e*x)^1*acosh(c*x), x, 4, -((3*d*sqrt(-1 + c*x)*sqrt(1 + c*x))/(4*c)) - (sqrt(-1 + c*x)*sqrt(1 + c*x)*(d + e*x))/(4*c) - (1/4)*((2*d^2)/e + e/c^2)*acosh(c*x) + ((d + e*x)^2*acosh(c*x))/(2*e)]
    @test_int [acosh(c*x)/(d + e*x)^1, x, 8, -(acosh(c*x)^2/(2*e)) + (acosh(c*x)*log(1 + (e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2))))/e + (acosh(c*x)*log(1 + (e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2))))/e + PolyLog(2, -((e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2))))/e + PolyLog(2, -((e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2))))/e]
    @test_int [acosh(c*x)/(d + e*x)^2, x, 3, -(acosh(c*x)/(e*(d + e*x))) + (2*c*atanh((sqrt(c*d + e)*sqrt(1 + c*x))/(sqrt(c*d - e)*sqrt(-1 + c*x))))/(sqrt(c*d - e)*e*sqrt(c*d + e))]
    @test_int [acosh(c*x)/(d + e*x)^3, x, 4, -((c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(2*(c^2*d^2 - e^2)*(d + e*x))) - acosh(c*x)/(2*e*(d + e*x)^2) + (c^3*d*atanh((sqrt(c*d + e)*sqrt(1 + c*x))/(sqrt(c*d - e)*sqrt(-1 + c*x))))/((c*d - e)^(3/2)*e*(c*d + e)^(3/2))]
    @test_int [acosh(c*x)/(d + e*x)^4, x, 6, If(13>=8, -((c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*(c^2*d^2 - e^2)*(d + e*x)^2)) - (c^3*d*sqrt(-1 + c*x)*sqrt(1 + c*x))/(2*(c*d - e)^2*(c*d + e)^2*(d + e*x)) - acosh(c*x)/(3*e*(d + e*x)^3) + (c^3*(2*c^2*d^2 + e^2)*atanh((sqrt(c*d + e)*sqrt(1 + c*x))/(sqrt(c*d - e)*sqrt(-1 + c*x))))/(3*(c*d - e)^(5/2)*e*(c*d + e)^(5/2)), -((c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*(c^2*d^2 - e^2)*(d + e*x)^2)) - (c^3*d*sqrt(-1 + c*x)*sqrt(1 + c*x))/(2*(c^2*d^2 - e^2)^2*(d + e*x)) - acosh(c*x)/(3*e*(d + e*x)^3) + (c^3*(2*c^2*d^2 + e^2)*atanh((sqrt(c*d + e)*sqrt(1 + c*x))/(sqrt(c*d - e)*sqrt(-1 + c*x))))/(3*(c*d - e)^(5/2)*e*(c*d + e)^(5/2)))]

    @test_int [(d + e*x)^3*acosh(c*x)^2, x, 18, 2*d^3*x + (4*d*e^2*x)/(3*c^2) + (3/4)*d^2*e*x^2 + (3*e^3*x^2)/(32*c^2) + (2/9)*d*e^2*x^3 + (e^3*x^4)/32 - (2*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/c - (4*d*e^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(3*c^3) - (3*d^2*e*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(2*c) - (3*e^3*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(16*c^3) - (2*d*e^2*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(3*c) - (e^3*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(8*c) - (d^4*acosh(c*x)^2)/(4*e) - (3*d^2*e*acosh(c*x)^2)/(4*c^2) - (3*e^3*acosh(c*x)^2)/(32*c^4) + ((d + e*x)^4*acosh(c*x)^2)/(4*e)]
    @test_int [(d + e*x)^2*acosh(c*x)^2, x, 13, 2*d^2*x + (4*e^2*x)/(9*c^2) + (1/2)*d*e*x^2 + (2*e^2*x^3)/27 - (2*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/c - (4*e^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(9*c^3) - (d*e*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/c - (2*e^2*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(9*c) - (d^3*acosh(c*x)^2)/(3*e) - (d*e*acosh(c*x)^2)/(2*c^2) + ((d + e*x)^3*acosh(c*x)^2)/(3*e)]
    @test_int [(d + e*x)^1*acosh(c*x)^2, x, 9, 2*d*x + (e*x^2)/4 - (2*d*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/c - (e*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(2*c) - (d^2*acosh(c*x)^2)/(2*e) - (e*acosh(c*x)^2)/(4*c^2) + ((d + e*x)^2*acosh(c*x)^2)/(2*e)]
    @test_int [acosh(c*x)^2/(d + e*x)^1, x, 10, -(acosh(c*x)^3/(3*e)) + (acosh(c*x)^2*log(1 + (e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2))))/e + (acosh(c*x)^2*log(1 + (e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2))))/e + (2*acosh(c*x)*PolyLog(2, -((e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2)))))/e + (2*acosh(c*x)*PolyLog(2, -((e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2)))))/e - (2*PolyLog(3, -((e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2)))))/e - (2*PolyLog(3, -((e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2)))))/e]
    @test_int [acosh(c*x)^2/(d + e*x)^2, x, 10, -(acosh(c*x)^2/(e*(d + e*x))) + (2*c*acosh(c*x)*log(1 + (e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2))))/(e*sqrt(c^2*d^2 - e^2)) - (2*c*acosh(c*x)*log(1 + (e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2))))/(e*sqrt(c^2*d^2 - e^2)) + (2*c*PolyLog(2, -((e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2)))))/(e*sqrt(c^2*d^2 - e^2)) - (2*c*PolyLog(2, -((e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2)))))/(e*sqrt(c^2*d^2 - e^2))]
    @test_int [acosh(c*x)^2/(d + e*x)^3, x, 13, -((c*sqrt(-((1 - c*x)/(1 + c*x)))*(1 + c*x)*acosh(c*x))/((c^2*d^2 - e^2)*(d + e*x))) - acosh(c*x)^2/(2*e*(d + e*x)^2) + (c^3*d*acosh(c*x)*log(1 + (e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2))))/(e*(c^2*d^2 - e^2)^(3/2)) - (c^3*d*acosh(c*x)*log(1 + (e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2))))/(e*(c^2*d^2 - e^2)^(3/2)) + (c^2*log(d + e*x))/(e*(c^2*d^2 - e^2)) + (c^3*d*PolyLog(2, -((e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2)))))/(e*(c^2*d^2 - e^2)^(3/2)) - (c^3*d*PolyLog(2, -((e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2)))))/(e*(c^2*d^2 - e^2)^(3/2))]

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

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

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

    @test_int [(d + e*x)^3*(a + b*acosh(c*x)), x, 5, -((7*b*d*sqrt(-1 + c*x)*sqrt(1 + c*x)*(d + e*x)^2)/(48*c)) - (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(d + e*x)^3)/(16*c) - (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(4*d*(19*c^2*d^2 + 16*e^2) + e*(26*c^2*d^2 + 9*e^2)*x))/(96*c^3) - (b*(8*c^4*d^4 + 24*c^2*d^2*e^2 + 3*e^4)*acosh(c*x))/(32*c^4*e) + ((d + e*x)^4*(a + b*acosh(c*x)))/(4*e)]
    @test_int [(d + e*x)^2*(a + b*acosh(c*x)), x, 4, -((b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(d + e*x)^2)/(9*c)) - (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(4*(4*c^2*d^2 + e^2) + 5*c^2*d*e*x))/(18*c^3) - (b*d*(2*d^2 + (3*e^2)/c^2)*acosh(c*x))/(6*e) + ((d + e*x)^3*(a + b*acosh(c*x)))/(3*e)]
    @test_int [(d + e*x)^1*(a + b*acosh(c*x)), x, 4, -((3*b*d*sqrt(-1 + c*x)*sqrt(1 + c*x))/(4*c)) - (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(d + e*x))/(4*c) - (b*(2*d^2 + e^2/c^2)*acosh(c*x))/(4*e) + ((d + e*x)^2*(a + b*acosh(c*x)))/(2*e)]
    @test_int [(a + b*acosh(c*x))/(d + e*x)^1, x, 8, -((a + b*acosh(c*x))^2/(2*b*e)) + ((a + b*acosh(c*x))*log(1 + (e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2))))/e + ((a + b*acosh(c*x))*log(1 + (e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2))))/e + (b*PolyLog(2, -((e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2)))))/e + (b*PolyLog(2, -((e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2)))))/e]
    @test_int [(a + b*acosh(c*x))/(d + e*x)^2, x, 3, -((a + b*acosh(c*x))/(e*(d + e*x))) + (2*b*c*atanh((sqrt(c*d + e)*sqrt(1 + c*x))/(sqrt(c*d - e)*sqrt(-1 + c*x))))/(sqrt(c*d - e)*e*sqrt(c*d + e))]
    @test_int [(a + b*acosh(c*x))/(d + e*x)^3, x, 4, -((b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(2*(c^2*d^2 - e^2)*(d + e*x))) - (a + b*acosh(c*x))/(2*e*(d + e*x)^2) + (b*c^3*d*atanh((sqrt(c*d + e)*sqrt(1 + c*x))/(sqrt(c*d - e)*sqrt(-1 + c*x))))/((c*d - e)^(3/2)*e*(c*d + e)^(3/2))]
    @test_int [(a + b*acosh(c*x))/(d + e*x)^4, x, 6, If(13>=8, -((b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*(c^2*d^2 - e^2)*(d + e*x)^2)) - (b*c^3*d*sqrt(-1 + c*x)*sqrt(1 + c*x))/(2*(c*d - e)^2*(c*d + e)^2*(d + e*x)) - (a + b*acosh(c*x))/(3*e*(d + e*x)^3) + (b*c^3*(2*c^2*d^2 + e^2)*atanh((sqrt(c*d + e)*sqrt(1 + c*x))/(sqrt(c*d - e)*sqrt(-1 + c*x))))/(3*(c*d - e)^(5/2)*e*(c*d + e)^(5/2)), -((b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*(c^2*d^2 - e^2)*(d + e*x)^2)) - (b*c^3*d*sqrt(-1 + c*x)*sqrt(1 + c*x))/(2*(c^2*d^2 - e^2)^2*(d + e*x)) - (a + b*acosh(c*x))/(3*e*(d + e*x)^3) + (b*c^3*(2*c^2*d^2 + e^2)*atanh((sqrt(c*d + e)*sqrt(1 + c*x))/(sqrt(c*d - e)*sqrt(-1 + c*x))))/(3*(c*d - e)^(5/2)*e*(c*d + e)^(5/2)))]

    @test_int [(d + e*x)^3*(a + b*acosh(c*x))^2, x, 18, 2*b^2*d^3*x + (4*b^2*d*e^2*x)/(3*c^2) + (3/4)*b^2*d^2*e*x^2 + (3*b^2*e^3*x^2)/(32*c^2) + (2/9)*b^2*d*e^2*x^3 + (1/32)*b^2*e^3*x^4 - (2*b*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/c - (4*b*d*e^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(3*c^3) - (3*b*d^2*e*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(2*c) - (3*b*e^3*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(16*c^3) - (2*b*d*e^2*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(3*c) - (b*e^3*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(8*c) - (d^4*(a + b*acosh(c*x))^2)/(4*e) - (3*d^2*e*(a + b*acosh(c*x))^2)/(4*c^2) - (3*e^3*(a + b*acosh(c*x))^2)/(32*c^4) + ((d + e*x)^4*(a + b*acosh(c*x))^2)/(4*e)]
    @test_int [(d + e*x)^2*(a + b*acosh(c*x))^2, x, 13, 2*b^2*d^2*x + (4*b^2*e^2*x)/(9*c^2) + (1/2)*b^2*d*e*x^2 + (2/27)*b^2*e^2*x^3 - (2*b*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/c - (4*b*e^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(9*c^3) - (b*d*e*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/c - (2*b*e^2*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(9*c) - (d^3*(a + b*acosh(c*x))^2)/(3*e) - (d*e*(a + b*acosh(c*x))^2)/(2*c^2) + ((d + e*x)^3*(a + b*acosh(c*x))^2)/(3*e)]
    @test_int [(d + e*x)^1*(a + b*acosh(c*x))^2, x, 9, 2*b^2*d*x + (1/4)*b^2*e*x^2 - (2*b*d*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/c - (b*e*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(2*c) - (d^2*(a + b*acosh(c*x))^2)/(2*e) - (e*(a + b*acosh(c*x))^2)/(4*c^2) + ((d + e*x)^2*(a + b*acosh(c*x))^2)/(2*e)]
    @test_int [(a + b*acosh(c*x))^2/(d + e*x)^1, x, 10, -((a + b*acosh(c*x))^3/(3*b*e)) + ((a + b*acosh(c*x))^2*log(1 + (e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2))))/e + ((a + b*acosh(c*x))^2*log(1 + (e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2))))/e + (2*b*(a + b*acosh(c*x))*PolyLog(2, -((e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2)))))/e + (2*b*(a + b*acosh(c*x))*PolyLog(2, -((e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2)))))/e - (2*b^2*PolyLog(3, -((e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2)))))/e - (2*b^2*PolyLog(3, -((e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2)))))/e]
    @test_int [(a + b*acosh(c*x))^2/(d + e*x)^2, x, 10, -((a + b*acosh(c*x))^2/(e*(d + e*x))) + (2*b*c*(a + b*acosh(c*x))*log(1 + (e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2))))/(e*sqrt(c^2*d^2 - e^2)) - (2*b*c*(a + b*acosh(c*x))*log(1 + (e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2))))/(e*sqrt(c^2*d^2 - e^2)) + (2*b^2*c*PolyLog(2, -((e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2)))))/(e*sqrt(c^2*d^2 - e^2)) - (2*b^2*c*PolyLog(2, -((e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2)))))/(e*sqrt(c^2*d^2 - e^2))]
    @test_int [(a + b*acosh(c*x))^2/(d + e*x)^3, x, 13, -((b*c*sqrt(-((1 - c*x)/(1 + c*x)))*(1 + c*x)*(a + b*acosh(c*x)))/((c^2*d^2 - e^2)*(d + e*x))) - (a + b*acosh(c*x))^2/(2*e*(d + e*x)^2) + (b*c^3*d*(a + b*acosh(c*x))*log(1 + (e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2))))/(e*(c^2*d^2 - e^2)^(3/2)) - (b*c^3*d*(a + b*acosh(c*x))*log(1 + (e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2))))/(e*(c^2*d^2 - e^2)^(3/2)) + (b^2*c^2*log(d + e*x))/(e*(c^2*d^2 - e^2)) + (b^2*c^3*d*PolyLog(2, -((e*ℯ^acosh(c*x))/(c*d - sqrt(c^2*d^2 - e^2)))))/(e*(c^2*d^2 - e^2)^(3/2)) - (b^2*c^3*d*PolyLog(2, -((e*ℯ^acosh(c*x))/(c*d + sqrt(c^2*d^2 - e^2)))))/(e*(c^2*d^2 - e^2)^(3/2))]

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

    @test_int [(d + e*x)^3/(a + b*acosh(c*x)), x, 27, -((d^3*CoshIntegral(a/b + acosh(c*x))*sinh(a/b))/(b*c)) - (3*d*e^2*CoshIntegral(a/b + acosh(c*x))*sinh(a/b))/(4*b*c^3) - (3*d^2*e*CoshIntegral((2*a)/b + 2*acosh(c*x))*sinh((2*a)/b))/(2*b*c^2) - (e^3*CoshIntegral((2*a)/b + 2*acosh(c*x))*sinh((2*a)/b))/(4*b*c^4) - (3*d*e^2*CoshIntegral((3*a)/b + 3*acosh(c*x))*sinh((3*a)/b))/(4*b*c^3) - (e^3*CoshIntegral((4*a)/b + 4*acosh(c*x))*sinh((4*a)/b))/(8*b*c^4) + (d^3*cosh(a/b)*SinhIntegral(a/b + acosh(c*x)))/(b*c) + (3*d*e^2*cosh(a/b)*SinhIntegral(a/b + acosh(c*x)))/(4*b*c^3) + (3*d^2*e*cosh((2*a)/b)*SinhIntegral((2*a)/b + 2*acosh(c*x)))/(2*b*c^2) + (e^3*cosh((2*a)/b)*SinhIntegral((2*a)/b + 2*acosh(c*x)))/(4*b*c^4) + (3*d*e^2*cosh((3*a)/b)*SinhIntegral((3*a)/b + 3*acosh(c*x)))/(4*b*c^3) + (e^3*cosh((4*a)/b)*SinhIntegral((4*a)/b + 4*acosh(c*x)))/(8*b*c^4)]
    @test_int [(d + e*x)^2/(a + b*acosh(c*x)), x, 17, -((d^2*CoshIntegral(a/b + acosh(c*x))*sinh(a/b))/(b*c)) - (e^2*CoshIntegral(a/b + acosh(c*x))*sinh(a/b))/(4*b*c^3) - (d*e*CoshIntegral((2*a)/b + 2*acosh(c*x))*sinh((2*a)/b))/(b*c^2) - (e^2*CoshIntegral((3*a)/b + 3*acosh(c*x))*sinh((3*a)/b))/(4*b*c^3) + (d^2*cosh(a/b)*SinhIntegral(a/b + acosh(c*x)))/(b*c) + (e^2*cosh(a/b)*SinhIntegral(a/b + acosh(c*x)))/(4*b*c^3) + (d*e*cosh((2*a)/b)*SinhIntegral((2*a)/b + 2*acosh(c*x)))/(b*c^2) + (e^2*cosh((3*a)/b)*SinhIntegral((3*a)/b + 3*acosh(c*x)))/(4*b*c^3)]
    @test_int [(d + e*x)^1/(a + b*acosh(c*x)), x, 11, -((d*CoshIntegral(a/b + acosh(c*x))*sinh(a/b))/(b*c)) - (e*CoshIntegral((2*a)/b + 2*acosh(c*x))*sinh((2*a)/b))/(2*b*c^2) + (d*cosh(a/b)*SinhIntegral(a/b + acosh(c*x)))/(b*c) + (e*cosh((2*a)/b)*SinhIntegral((2*a)/b + 2*acosh(c*x)))/(2*b*c^2)]
    @test_int [1/((d + e*x)^1*(a + b*acosh(c*x))), x, 0, Unintegrable(1/((d + e*x)*(a + b*acosh(c*x))), x)]
    @test_int [1/((d + e*x)^2*(a + b*acosh(c*x))), x, 0, Unintegrable(1/((d + e*x)^2*(a + b*acosh(c*x))), x)]

    @test_int [(d + e*x)^2/(a + b*acosh(c*x))^2, x, 19, -((d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(b*c*(a + b*acosh(c*x)))) - (2*d*e*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(b*c*(a + b*acosh(c*x))) - (e^2*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(b*c*(a + b*acosh(c*x))) + (d^2*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(b^2*c) + (e^2*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(4*b^2*c^3) + (2*d*e*cosh((2*a)/b)*CoshIntegral((2*(a + b*acosh(c*x)))/b))/(b^2*c^2) + (3*e^2*cosh((3*a)/b)*CoshIntegral((3*(a + b*acosh(c*x)))/b))/(4*b^2*c^3) - (d^2*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(b^2*c) - (e^2*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(4*b^2*c^3) - (2*d*e*sinh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(b^2*c^2) - (3*e^2*sinh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(4*b^2*c^3)]
    @test_int [(d + e*x)^1/(a + b*acosh(c*x))^2, x, 11, -((d*sqrt(-1 + c*x)*sqrt(1 + c*x))/(b*c*(a + b*acosh(c*x)))) - (e*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(b*c*(a + b*acosh(c*x))) + (d*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(b^2*c) + (e*cosh((2*a)/b)*CoshIntegral((2*(a + b*acosh(c*x)))/b))/(b^2*c^2) - (d*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(b^2*c) - (e*sinh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(b^2*c^2)]
    @test_int [1/((d + e*x)^1*(a + b*acosh(c*x))^2), x, 0, Unintegrable(1/((d + e*x)*(a + b*acosh(c*x))^2), x)]
    @test_int [1/((d + e*x)^2*(a + b*acosh(c*x))^2), x, 0, Unintegrable(1/((d + e*x)^2*(a + b*acosh(c*x))^2), x)]

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

    @test_int [(d + e*x)^m*(a + b*acosh(c*x))^3, x, 1, ((d + e*x)^(1 + m)*(a + b*acosh(c*x))^3)/(e*(1 + m)) - (3*b*c*Unintegrable(((d + e*x)^(1 + m)*(a + b*acosh(c*x))^2)/(sqrt(-1 + c*x)*sqrt(1 + c*x)), x))/(e*(1 + m))]
    @test_int [(d + e*x)^m*(a + b*acosh(c*x))^2, x, 1, ((d + e*x)^(1 + m)*(a + b*acosh(c*x))^2)/(e*(1 + m)) - (2*b*c*Unintegrable(((d + e*x)^(1 + m)*(a + b*acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)), x))/(e*(1 + m))]
    @test_int [(d + e*x)^m*(a + b*acosh(c*x))^1, x, 3, -((sqrt(2)*b*(c*d + e)*sqrt(-1 + c*x)*(d + e*x)^m*AppellF1(1/2, 1/2, -1 - m, 3/2, (1/2)*(1 - c*x), (e*(1 - c*x))/(c*d + e)))/(((c*(d + e*x))/(c*d + e))^m*(c*e*(1 + m)))) + ((d + e*x)^(1 + m)*(a + b*acosh(c*x)))/(e*(1 + m))]
    @test_int [(d + e*x)^m/(a + b*acosh(c*x))^1, x, 0, Unintegrable((d + e*x)^m/(a + b*acosh(c*x)), x)]
    @test_int [(d + e*x)^m/(a + b*acosh(c*x))^2, x, 0, Unintegrable((d + e*x)^m/(a + b*acosh(c*x))^2, x)]

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

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

    @test_int [acosh(a*x)*(c + d*x^2)^4, x, 6, ((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)*(1 - a^2*x^2))/(315*a^9*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (4*d*(105*a^6*c^3 + 189*a^4*c^2*d + 135*a^2*c*d^2 + 35*d^3)*(1 - a^2*x^2)^2)/(945*a^9*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (2*d^2*(63*a^4*c^2 + 90*a^2*c*d + 35*d^2)*(1 - a^2*x^2)^3)/(525*a^9*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (4*d^3*(9*a^2*c + 7*d)*(1 - a^2*x^2)^4)/(441*a^9*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (d^4*(1 - a^2*x^2)^5)/(81*a^9*sqrt(-1 + a*x)*sqrt(1 + a*x)) + c^4*x*acosh(a*x) + (4/3)*c^3*d*x^3*acosh(a*x) + (6/5)*c^2*d^2*x^5*acosh(a*x) + (4/7)*c*d^3*x^7*acosh(a*x) + (1/9)*d^4*x^9*acosh(a*x)]
    @test_int [acosh(a*x)*(c + d*x^2)^3, x, 6, ((35*a^6*c^3 + 35*a^4*c^2*d + 21*a^2*c*d^2 + 5*d^3)*(1 - a^2*x^2))/(35*a^7*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (d*(35*a^4*c^2 + 42*a^2*c*d + 15*d^2)*(1 - a^2*x^2)^2)/(105*a^7*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (3*d^2*(7*a^2*c + 5*d)*(1 - a^2*x^2)^3)/(175*a^7*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (d^3*(1 - a^2*x^2)^4)/(49*a^7*sqrt(-1 + a*x)*sqrt(1 + a*x)) + c^3*x*acosh(a*x) + c^2*d*x^3*acosh(a*x) + (3/5)*c*d^2*x^5*acosh(a*x) + (1/7)*d^3*x^7*acosh(a*x)]
    @test_int [acosh(a*x)*(c + d*x^2)^2, x, 6, ((15*a^4*c^2 + 10*a^2*c*d + 3*d^2)*(1 - a^2*x^2))/(15*a^5*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (2*d*(5*a^2*c + 3*d)*(1 - a^2*x^2)^2)/(45*a^5*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (d^2*(1 - a^2*x^2)^3)/(25*a^5*sqrt(-1 + a*x)*sqrt(1 + a*x)) + c^2*x*acosh(a*x) + (2/3)*c*d*x^3*acosh(a*x) + (1/5)*d^2*x^5*acosh(a*x)]
    @test_int [acosh(a*x)*(c + d*x^2)^1, x, 3, -(((9*a^2*c + 2*d)*sqrt(-1 + a*x)*sqrt(1 + a*x))/(9*a^3)) - (d*x^2*sqrt(-1 + a*x)*sqrt(1 + a*x))/(9*a) + c*x*acosh(a*x) + (1/3)*d*x^3*acosh(a*x)]
    @test_int [acosh(a*x)/(c + d*x^2)^1, x, 18, (acosh(a*x)*log(1 - (sqrt(d)*ℯ^acosh(a*x))/(a*sqrt(-c) - sqrt((-a^2)*c - d))))/(2*sqrt(-c)*sqrt(d)) - (acosh(a*x)*log(1 + (sqrt(d)*ℯ^acosh(a*x))/(a*sqrt(-c) - sqrt((-a^2)*c - d))))/(2*sqrt(-c)*sqrt(d)) + (acosh(a*x)*log(1 - (sqrt(d)*ℯ^acosh(a*x))/(a*sqrt(-c) + sqrt((-a^2)*c - d))))/(2*sqrt(-c)*sqrt(d)) - (acosh(a*x)*log(1 + (sqrt(d)*ℯ^acosh(a*x))/(a*sqrt(-c) + sqrt((-a^2)*c - d))))/(2*sqrt(-c)*sqrt(d)) - PolyLog(2, -((sqrt(d)*ℯ^acosh(a*x))/(a*sqrt(-c) - sqrt((-a^2)*c - d))))/(2*sqrt(-c)*sqrt(d)) + PolyLog(2, (sqrt(d)*ℯ^acosh(a*x))/(a*sqrt(-c) - sqrt((-a^2)*c - d)))/(2*sqrt(-c)*sqrt(d)) - PolyLog(2, -((sqrt(d)*ℯ^acosh(a*x))/(a*sqrt(-c) + sqrt((-a^2)*c - d))))/(2*sqrt(-c)*sqrt(d)) + PolyLog(2, (sqrt(d)*ℯ^acosh(a*x))/(a*sqrt(-c) + sqrt((-a^2)*c - d)))/(2*sqrt(-c)*sqrt(d))]
    @test_int [acosh(a*x)/(c + d*x^2)^2, x, 26, -(acosh(a*x)/(4*c*sqrt(d)*(sqrt(-c) - sqrt(d)*x))) + acosh(a*x)/(4*c*sqrt(d)*(sqrt(-c) + sqrt(d)*x)) + (a*atanh((sqrt(a*sqrt(-c) - sqrt(d))*sqrt(1 + a*x))/(sqrt(a*sqrt(-c) + sqrt(d))*sqrt(-1 + a*x))))/(2*c*sqrt(a*sqrt(-c) - sqrt(d))*sqrt(a*sqrt(-c) + sqrt(d))*sqrt(d)) - (a*atanh((sqrt(a*sqrt(-c) + sqrt(d))*sqrt(1 + a*x))/(sqrt(a*sqrt(-c) - sqrt(d))*sqrt(-1 + a*x))))/(2*c*sqrt(a*sqrt(-c) - sqrt(d))*sqrt(a*sqrt(-c) + sqrt(d))*sqrt(d)) - (acosh(a*x)*log(1 - (sqrt(d)*ℯ^acosh(a*x))/(a*sqrt(-c) - sqrt((-a^2)*c - d))))/(4*(-c)^(3/2)*sqrt(d)) + (acosh(a*x)*log(1 + (sqrt(d)*ℯ^acosh(a*x))/(a*sqrt(-c) - sqrt((-a^2)*c - d))))/(4*(-c)^(3/2)*sqrt(d)) - (acosh(a*x)*log(1 - (sqrt(d)*ℯ^acosh(a*x))/(a*sqrt(-c) + sqrt((-a^2)*c - d))))/(4*(-c)^(3/2)*sqrt(d)) + (acosh(a*x)*log(1 + (sqrt(d)*ℯ^acosh(a*x))/(a*sqrt(-c) + sqrt((-a^2)*c - d))))/(4*(-c)^(3/2)*sqrt(d)) + PolyLog(2, -((sqrt(d)*ℯ^acosh(a*x))/(a*sqrt(-c) - sqrt((-a^2)*c - d))))/(4*(-c)^(3/2)*sqrt(d)) - PolyLog(2, (sqrt(d)*ℯ^acosh(a*x))/(a*sqrt(-c) - sqrt((-a^2)*c - d)))/(4*(-c)^(3/2)*sqrt(d)) + PolyLog(2, -((sqrt(d)*ℯ^acosh(a*x))/(a*sqrt(-c) + sqrt((-a^2)*c - d))))/(4*(-c)^(3/2)*sqrt(d)) - PolyLog(2, (sqrt(d)*ℯ^acosh(a*x))/(a*sqrt(-c) + sqrt((-a^2)*c - d)))/(4*(-c)^(3/2)*sqrt(d))]

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

    @test_int [acosh(a*x)*(c + d*x^2)^(1/2), x, 0, Unintegrable(sqrt(c + d*x^2)*acosh(a*x), x)]
    @test_int [acosh(a*x)/(c + d*x^2)^(1/2), x, 0, Unintegrable(acosh(a*x)/sqrt(c + d*x^2), x)]
    @test_int [acosh(a*x)/(c + d*x^2)^(3/2), x, 7, (x*acosh(a*x))/(c*sqrt(c + d*x^2)) - (sqrt(-1 + a^2*x^2)*atanh((sqrt(d)*sqrt(-1 + a^2*x^2))/(a*sqrt(c + d*x^2))))/(c*sqrt(d)*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [acosh(a*x)/(c + d*x^2)^(5/2), x, 8, (a*(1 - a^2*x^2))/(3*c*(a^2*c + d)*sqrt(-1 + a*x)*sqrt(1 + a*x)*sqrt(c + d*x^2)) + (x*acosh(a*x))/(3*c*(c + d*x^2)^(3/2)) + (2*x*acosh(a*x))/(3*c^2*sqrt(c + d*x^2)) - (2*sqrt(-1 + a^2*x^2)*atanh((sqrt(d)*sqrt(-1 + a^2*x^2))/(a*sqrt(c + d*x^2))))/(3*c^2*sqrt(d)*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [acosh(a*x)/(c + d*x^2)^(7/2), x, 9, (a*(1 - a^2*x^2))/(15*c*(a^2*c + d)*sqrt(-1 + a*x)*sqrt(1 + a*x)*(c + d*x^2)^(3/2)) + (2*a*(3*a^2*c + 2*d)*(1 - a^2*x^2))/(15*c^2*(a^2*c + d)^2*sqrt(-1 + a*x)*sqrt(1 + a*x)*sqrt(c + d*x^2)) + (x*acosh(a*x))/(5*c*(c + d*x^2)^(5/2)) + (4*x*acosh(a*x))/(15*c^2*(c + d*x^2)^(3/2)) + (8*x*acosh(a*x))/(15*c^3*sqrt(c + d*x^2)) - (8*sqrt(-1 + a^2*x^2)*atanh((sqrt(d)*sqrt(-1 + a^2*x^2))/(a*sqrt(c + d*x^2))))/(15*c^3*sqrt(d)*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [acosh(a*x)/(c + d*x^2)^(9/2), x, 10, (a*(1 - a^2*x^2))/(35*c*(a^2*c + d)*sqrt(-1 + a*x)*sqrt(1 + a*x)*(c + d*x^2)^(5/2)) + (2*a*(5*a^2*c + 3*d)*(1 - a^2*x^2))/(105*c^2*(a^2*c + d)^2*sqrt(-1 + a*x)*sqrt(1 + a*x)*(c + d*x^2)^(3/2)) + (4*a*(11*a^4*c^2 + 15*a^2*c*d + 6*d^2)*(1 - a^2*x^2))/(105*c^3*(a^2*c + d)^3*sqrt(-1 + a*x)*sqrt(1 + a*x)*sqrt(c + d*x^2)) + (x*acosh(a*x))/(7*c*(c + d*x^2)^(7/2)) + (6*x*acosh(a*x))/(35*c^2*(c + d*x^2)^(5/2)) + (8*x*acosh(a*x))/(35*c^3*(c + d*x^2)^(3/2)) + (16*x*acosh(a*x))/(35*c^4*sqrt(c + d*x^2)) - (16*sqrt(-1 + a^2*x^2)*atanh((sqrt(d)*sqrt(-1 + a^2*x^2))/(a*sqrt(c + d*x^2))))/(35*c^4*sqrt(d)*sqrt(-1 + a*x)*sqrt(1 + a*x))]

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

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

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

    @test_int [sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*(f + g*x)^3, x, 17, (b*f^2*g*x*sqrt(d - c^2*d*x^2))/(c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*g^3*x*sqrt(d - c^2*d*x^2))/(15*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*f^3*x^2*sqrt(d - c^2*d*x^2))/(4*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*b*f*g^2*x^2*sqrt(d - c^2*d*x^2))/(16*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*f^2*g*x^3*sqrt(d - c^2*d*x^2))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*g^3*x^3*sqrt(d - c^2*d*x^2))/(45*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3*b*c*f*g^2*x^4*sqrt(d - c^2*d*x^2))/(16*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*g^3*x^5*sqrt(d - c^2*d*x^2))/(25*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (1/2)*f^3*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (3*f*g^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(8*c^2) + (3/4)*f*g^2*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (f^2*g*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/c^2 - (2*g^3*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(15*c^4) - (g^3*x^2*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(5*c^2) - (f^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(4*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3*f*g^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(16*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*(f + g*x)^2, x, 14, (2*b*f*g*x*sqrt(d - c^2*d*x^2))/(3*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*f^2*x^2*sqrt(d - c^2*d*x^2))/(4*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*g^2*x^2*sqrt(d - c^2*d*x^2))/(16*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c*f*g*x^3*sqrt(d - c^2*d*x^2))/(9*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*g^2*x^4*sqrt(d - c^2*d*x^2))/(16*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (1/2)*f^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (g^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(8*c^2) + (1/4)*g^2*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (2*f*g*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(3*c^2) - (f^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(4*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (g^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(16*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*(f + g*x)^1, x, 9, (b*g*x*sqrt(d - c^2*d*x^2))/(3*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*f*x^2*sqrt(d - c^2*d*x^2))/(4*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*g*x^3*sqrt(d - c^2*d*x^2))/(9*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (1/2)*f*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (g*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(3*c^2) - (f*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(4*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))/(f + g*x)^1, x, 23, -((b*c*x*sqrt(d - c^2*d*x^2))/(g*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (a*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2))/(g*(1 - c*x)*(1 + c*x)) + (b*sqrt(d - c^2*d*x^2)*acosh(c*x))/g - (c*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*b*g*sqrt(-1 + c*x)*sqrt(1 + c*x)) + ((1 - (c^2*f^2)/g^2)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(f + g*x)) - ((1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(f + g*x)) - (a*sqrt(c^2*f^2 - g^2)*sqrt(-1 + c^2*x^2)*sqrt(d - c^2*d*x^2)*atanh((g + c^2*f*x)/(sqrt(c^2*f^2 - g^2)*sqrt(-1 + c^2*x^2))))/(g^2*(1 - c*x)*(1 + c*x)) + (b*sqrt(c^2*f^2 - g^2)*sqrt(d - c^2*d*x^2)*acosh(c*x)*log(1 + (ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2))))/(g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*sqrt(c^2*f^2 - g^2)*sqrt(d - c^2*d*x^2)*acosh(c*x)*log(1 + (ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2))))/(g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*sqrt(c^2*f^2 - g^2)*sqrt(d - c^2*d*x^2)*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2)))))/(g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*sqrt(c^2*f^2 - g^2)*sqrt(d - c^2*d*x^2)*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2)))))/(g^2*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))/(f + g*x)^2, x, 38, -((a*sqrt(d - c^2*d*x^2))/(g*(f + g*x))) + (a*c^3*f^2*sqrt(d - c^2*d*x^2)*acosh(c*x))/(g^2*(c^2*f^2 - g^2)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*sqrt(-((1 - c*x)/(1 + c*x)))*sqrt(1 + c*x)*sqrt(d - c^2*d*x^2)*acosh(c*x))/(g*sqrt(-1 + c*x)*(f + g*x)) + (b*c^3*f^2*sqrt(d - c^2*d*x^2)*acosh(c*x)^2)/(2*g^2*(c^2*f^2 - g^2)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((g + c^2*f*x)^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*b*c*(c^2*f^2 - g^2)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(f + g*x)^2) - ((1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(f + g*x)^2) - (2*a*c^2*f*sqrt(d - c^2*d*x^2)*atanh((sqrt(c*f + g)*sqrt(1 + c*x))/(sqrt(c*f - g)*sqrt(-1 + c*x))))/(sqrt(c*f - g)*g^2*sqrt(c*f + g)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^2*f*sqrt(d - c^2*d*x^2)*acosh(c*x)*log(1 + (ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2))))/(g^2*sqrt(c^2*f^2 - g^2)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^2*f*sqrt(d - c^2*d*x^2)*acosh(c*x)*log(1 + (ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2))))/(g^2*sqrt(c^2*f^2 - g^2)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c*sqrt(d - c^2*d*x^2)*log(f + g*x))/(g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^2*f*sqrt(d - c^2*d*x^2)*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2)))))/(g^2*sqrt(c^2*f^2 - g^2)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^2*f*sqrt(d - c^2*d*x^2)*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2)))))/(g^2*sqrt(c^2*f^2 - g^2)*sqrt(-1 + c*x)*sqrt(1 + c*x))]

    @test_int [(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))*(f + g*x)^3, x, 27, (3*b*d*f^2*g*x*sqrt(d - c^2*d*x^2))/(5*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*d*g^3*x*sqrt(d - c^2*d*x^2))/(35*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (5*b*c*d*f^3*x^2*sqrt(d - c^2*d*x^2))/(16*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*b*d*f*g^2*x^2*sqrt(d - c^2*d*x^2))/(32*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c*d*f^2*g*x^3*sqrt(d - c^2*d*x^2))/(5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d*g^3*x^3*sqrt(d - c^2*d*x^2))/(105*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d*f^3*x^4*sqrt(d - c^2*d*x^2))/(16*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (7*b*c*d*f*g^2*x^4*sqrt(d - c^2*d*x^2))/(32*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*b*c^3*d*f^2*g*x^5*sqrt(d - c^2*d*x^2))/(25*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (8*b*c*d*g^3*x^5*sqrt(d - c^2*d*x^2))/(175*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d*f*g^2*x^6*sqrt(d - c^2*d*x^2))/(12*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d*g^3*x^7*sqrt(d - c^2*d*x^2))/(49*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3/8)*d*f^3*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (3*d*f*g^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(16*c^2) + (3/8)*d*f*g^2*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (1/4)*d*f^3*x*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (1/2)*d*f*g^2*x^3*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (3*d*f^2*g*(1 - c*x)^2*(1 + c*x)^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(5*c^2) - (2*d*g^3*(1 - c*x)^2*(1 + c*x)^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(35*c^4) - (d*g^3*x^2*(1 - c*x)^2*(1 + c*x)^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(7*c^2) - (3*d*f^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(16*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3*d*f*g^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(32*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))*(f + g*x)^2, x, 23, (2*b*d*f*g*x*sqrt(d - c^2*d*x^2))/(5*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (5*b*c*d*f^2*x^2*sqrt(d - c^2*d*x^2))/(16*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d*g^2*x^2*sqrt(d - c^2*d*x^2))/(32*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (4*b*c*d*f*g*x^3*sqrt(d - c^2*d*x^2))/(15*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d*f^2*x^4*sqrt(d - c^2*d*x^2))/(16*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (7*b*c*d*g^2*x^4*sqrt(d - c^2*d*x^2))/(96*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*c^3*d*f*g*x^5*sqrt(d - c^2*d*x^2))/(25*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d*g^2*x^6*sqrt(d - c^2*d*x^2))/(36*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3/8)*d*f^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (d*g^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(16*c^2) + (1/8)*d*g^2*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (1/4)*d*f^2*x*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (1/6)*d*g^2*x^3*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (2*d*f*g*(1 - c*x)^2*(1 + c*x)^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(5*c^2) - (3*d*f^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(16*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (d*g^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(32*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))*(f + g*x)^1, x, 14, (b*d*g*x*sqrt(d - c^2*d*x^2))/(5*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (5*b*c*d*f*x^2*sqrt(d - c^2*d*x^2))/(16*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c*d*g*x^3*sqrt(d - c^2*d*x^2))/(15*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d*f*x^4*sqrt(d - c^2*d*x^2))/(16*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d*g*x^5*sqrt(d - c^2*d*x^2))/(25*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3/8)*d*f*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (1/4)*d*f*x*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (d*g*(1 - c*x)^2*(1 + c*x)^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(5*c^2) - (3*d*f*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(16*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))/(f + g*x)^1, x, -28, -((a*d*(c*f - g)*(c*f + g)*sqrt(d - c^2*d*x^2))/g^3) + (b*c*d*(c*f - g)*(c*f + g)*x*sqrt(d - c^2*d*x^2))/(g^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^2*d*(c*f - g)*x^2*sqrt(d - c^2*d*x^2))/(4*g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (a*d*(2 + 3*c*x - 2*c^2*x^2)*sqrt(d - c^2*d*x^2))/(6*g) + (b*c*d*x*(-12 - 9*c*x + 4*c^2*x^2)*sqrt(d - c^2*d*x^2))/(36*g*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*d*(c*f - g)*(c*f + g)*sqrt(d - c^2*d*x^2)*acosh(c*x))/g^3 - (a*d*sqrt(d - c^2*d*x^2)*acosh(c*x))/(2*g*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d*(2 + 3*c*x - 2*c^2*x^2)*sqrt(d - c^2*d*x^2)*acosh(c*x))/(6*g) - (b*d*sqrt(d - c^2*d*x^2)*acosh(c*x)^2)/(4*g*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (c*d*(c*f - g)*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(2*g^2) - (d*(c*f - g)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(4*b*g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (c*d*(c*f - g)*(c*f + g)*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*b*g^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (d*(c*f - g)^2*(c*f + g)^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*b*c*g^4*sqrt(-1 + c*x)*sqrt(1 + c*x)*(f + g*x)) + (d*(c*f - g)*(c*f + g)*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*b*c*g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(f + g*x)) - (2*a*d*(c*f - g)^(3/2)*(c*f + g)^(3/2)*sqrt(d - c^2*d*x^2)*atanh((sqrt(c*f + g)*sqrt(1 + c*x))/(sqrt(c*f - g)*sqrt(-1 + c*x))))/(g^4*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*d*(c*f - g)*(c*f + g)*sqrt(c^2*f^2 - g^2)*sqrt(d - c^2*d*x^2)*acosh(c*x)*log(1 + (ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2))))/(g^4*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d*(c*f - g)*(c*f + g)*sqrt(c^2*f^2 - g^2)*sqrt(d - c^2*d*x^2)*acosh(c*x)*log(1 + (ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2))))/(g^4*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*d*(c*f - g)*(c*f + g)*sqrt(c^2*f^2 - g^2)*sqrt(d - c^2*d*x^2)*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2)))))/(g^4*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d*(c*f - g)*(c*f + g)*sqrt(c^2*f^2 - g^2)*sqrt(d - c^2*d*x^2)*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2)))))/(g^4*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    #= [(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))/(f + g*x)^2, x, 0, 0] =#

    @test_int [(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))*(f + g*x)^3, x, 35, (3*b*d^2*f^2*g*x*sqrt(d - c^2*d*x^2))/(7*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*d^2*g^3*x*sqrt(d - c^2*d*x^2))/(63*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (25*b*c*d^2*f^3*x^2*sqrt(d - c^2*d*x^2))/(96*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (15*b*d^2*f*g^2*x^2*sqrt(d - c^2*d*x^2))/(256*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3*b*c*d^2*f^2*g*x^3*sqrt(d - c^2*d*x^2))/(7*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^2*g^3*x^3*sqrt(d - c^2*d*x^2))/(189*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*b*c^3*d^2*f^3*x^4*sqrt(d - c^2*d*x^2))/(96*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (59*b*c*d^2*f*g^2*x^4*sqrt(d - c^2*d*x^2))/(256*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (9*b*c^3*d^2*f^2*g*x^5*sqrt(d - c^2*d*x^2))/(35*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*d^2*g^3*x^5*sqrt(d - c^2*d*x^2))/(21*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (17*b*c^3*d^2*f*g^2*x^6*sqrt(d - c^2*d*x^2))/(96*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3*b*c^5*d^2*f^2*g*x^7*sqrt(d - c^2*d*x^2))/(49*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (19*b*c^3*d^2*g^3*x^7*sqrt(d - c^2*d*x^2))/(441*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3*b*c^5*d^2*f*g^2*x^8*sqrt(d - c^2*d*x^2))/(64*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^2*g^3*x^9*sqrt(d - c^2*d*x^2))/(81*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^2*f^3*(1 - c^2*x^2)^3*sqrt(d - c^2*d*x^2))/(36*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5/16)*d^2*f^3*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (15*d^2*f*g^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(128*c^2) + (15/64)*d^2*f*g^2*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (5/24)*d^2*f^3*x*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (5/16)*d^2*f*g^2*x^3*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (1/6)*d^2*f^3*x*(1 - c*x)^2*(1 + c*x)^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (3/8)*d^2*f*g^2*x^3*(1 - c*x)^2*(1 + c*x)^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (3*d^2*f^2*g*(1 - c*x)^3*(1 + c*x)^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(7*c^2) - (2*d^2*g^3*(1 - c*x)^3*(1 + c*x)^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(63*c^4) - (d^2*g^3*x^2*(1 - c*x)^3*(1 + c*x)^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(9*c^2) - (5*d^2*f^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(32*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (15*d^2*f*g^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(256*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))*(f + g*x)^2, x, 31, (2*b*d^2*f*g*x*sqrt(d - c^2*d*x^2))/(7*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (25*b*c*d^2*f^2*x^2*sqrt(d - c^2*d*x^2))/(96*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*b*d^2*g^2*x^2*sqrt(d - c^2*d*x^2))/(256*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c*d^2*f*g*x^3*sqrt(d - c^2*d*x^2))/(7*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*b*c^3*d^2*f^2*x^4*sqrt(d - c^2*d*x^2))/(96*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (59*b*c*d^2*g^2*x^4*sqrt(d - c^2*d*x^2))/(768*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (6*b*c^3*d^2*f*g*x^5*sqrt(d - c^2*d*x^2))/(35*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (17*b*c^3*d^2*g^2*x^6*sqrt(d - c^2*d*x^2))/(288*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c^5*d^2*f*g*x^7*sqrt(d - c^2*d*x^2))/(49*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^2*g^2*x^8*sqrt(d - c^2*d*x^2))/(64*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^2*f^2*(1 - c^2*x^2)^3*sqrt(d - c^2*d*x^2))/(36*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5/16)*d^2*f^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (5*d^2*g^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(128*c^2) + (5/64)*d^2*g^2*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (5/24)*d^2*f^2*x*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (5/48)*d^2*g^2*x^3*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (1/6)*d^2*f^2*x*(1 - c*x)^2*(1 + c*x)^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (1/8)*d^2*g^2*x^3*(1 - c*x)^2*(1 + c*x)^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (2*d^2*f*g*(1 - c*x)^3*(1 + c*x)^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(7*c^2) - (5*d^2*f^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(32*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (5*d^2*g^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(256*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))*(f + g*x)^1, x, 17, (b*d^2*g*x*sqrt(d - c^2*d*x^2))/(7*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (25*b*c*d^2*f*x^2*sqrt(d - c^2*d*x^2))/(96*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*d^2*g*x^3*sqrt(d - c^2*d*x^2))/(7*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*b*c^3*d^2*f*x^4*sqrt(d - c^2*d*x^2))/(96*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*b*c^3*d^2*g*x^5*sqrt(d - c^2*d*x^2))/(35*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^2*g*x^7*sqrt(d - c^2*d*x^2))/(49*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^2*f*(1 - c^2*x^2)^3*sqrt(d - c^2*d*x^2))/(36*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5/16)*d^2*f*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (5/24)*d^2*f*x*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (1/6)*d^2*f*x*(1 - c*x)^2*(1 + c*x)^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (d^2*g*(1 - c*x)^3*(1 + c*x)^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(7*c^2) - (5*d^2*f*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(32*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))/(f + g*x)^1, x, 39, (2*b*c*d^2*x*sqrt(d - c^2*d*x^2))/(15*g*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c*d^2*(c^2*f^2 - 2*g^2)*x*sqrt(d - c^2*d*x^2))/(3*g^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*d^2*(c^2*f^2 - g^2)^2*x*sqrt(d - c^2*d*x^2))/(g^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^3*d^2*f*x^2*sqrt(d - c^2*d*x^2))/(16*g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d^2*f*(c^2*f^2 - 2*g^2)*x^2*sqrt(d - c^2*d*x^2))/(4*g^4*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d^2*x^3*sqrt(d - c^2*d*x^2))/(45*g*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^3*d^2*(c^2*f^2 - 2*g^2)*x^3*sqrt(d - c^2*d*x^2))/(9*g^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^5*d^2*f*x^4*sqrt(d - c^2*d*x^2))/(16*g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^2*x^5*sqrt(d - c^2*d*x^2))/(25*g*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (a*d^2*(c^2*f^2 - g^2)^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2))/(g^5*(1 - c*x)*(1 + c*x)) + (b*d^2*(c^2*f^2 - g^2)^2*sqrt(d - c^2*d*x^2)*acosh(c*x))/g^5 + (c^2*d^2*f*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(8*g^2) - (c^2*d^2*f*(c^2*f^2 - 2*g^2)*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(2*g^4) - (c^4*d^2*f*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(4*g^2) - (2*d^2*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(15*g) - (d^2*(c^2*f^2 - 2*g^2)*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(3*g^3) - (c^2*d^2*x^2*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(5*g) + (c*d^2*f*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(16*b*g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (c*d^2*f*(c^2*f^2 - 2*g^2)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(4*b*g^4*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (c*d^2*(c^2*f^2 - g^2)^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*b*g^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (d^2*(c^2*f^2 - g^2)^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*b*c*g^6*sqrt(-1 + c*x)*sqrt(1 + c*x)*(f + g*x)) - (d^2*(c^2*f^2 - g^2)^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*b*c*g^4*sqrt(-1 + c*x)*sqrt(1 + c*x)*(f + g*x)) - (a*d^2*(c^2*f^2 - g^2)^(5/2)*sqrt(-1 + c^2*x^2)*sqrt(d - c^2*d*x^2)*atanh((g + c^2*f*x)/(sqrt(c^2*f^2 - g^2)*sqrt(-1 + c^2*x^2))))/(g^6*(1 - c*x)*(1 + c*x)) + (b*d^2*(c^2*f^2 - g^2)^(5/2)*sqrt(d - c^2*d*x^2)*acosh(c*x)*log(1 + (ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2))))/(g^6*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*d^2*(c^2*f^2 - g^2)^(5/2)*sqrt(d - c^2*d*x^2)*acosh(c*x)*log(1 + (ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2))))/(g^6*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^2*(c^2*f^2 - g^2)^(5/2)*sqrt(d - c^2*d*x^2)*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2)))))/(g^6*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*d^2*(c^2*f^2 - g^2)^(5/2)*sqrt(d - c^2*d*x^2)*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2)))))/(g^6*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    #= [(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))/(f + g*x)^2, x, 0, 0] =#

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

    @test_int [1/sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*(f + g*x)^3, x, 13, -((3*b*f^2*g*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(c*sqrt(d - c^2*d*x^2))) - (2*b*g^3*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(3*c^3*sqrt(d - c^2*d*x^2)) - (3*b*f*g^2*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(4*c*sqrt(d - c^2*d*x^2)) - (b*g^3*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x))/(9*c*sqrt(d - c^2*d*x^2)) - (3*f^2*g*(1 - c*x)*(1 + c*x)*(a + b*acosh(c*x)))/(c^2*sqrt(d - c^2*d*x^2)) - (2*g^3*(1 - c*x)*(1 + c*x)*(a + b*acosh(c*x)))/(3*c^4*sqrt(d - c^2*d*x^2)) - (3*f*g^2*x*(1 - c*x)*(1 + c*x)*(a + b*acosh(c*x)))/(2*c^2*sqrt(d - c^2*d*x^2)) - (g^3*x^2*(1 - c*x)*(1 + c*x)*(a + b*acosh(c*x)))/(3*c^2*sqrt(d - c^2*d*x^2)) + (f^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(2*b*c*sqrt(d - c^2*d*x^2)) + (3*f*g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(4*b*c^3*sqrt(d - c^2*d*x^2))]
    @test_int [1/sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*(f + g*x)^2, x, 9, -((2*b*f*g*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(c*sqrt(d - c^2*d*x^2))) - (b*g^2*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(4*c*sqrt(d - c^2*d*x^2)) - (2*f*g*(1 - c*x)*(1 + c*x)*(a + b*acosh(c*x)))/(c^2*sqrt(d - c^2*d*x^2)) - (g^2*x*(1 - c*x)*(1 + c*x)*(a + b*acosh(c*x)))/(2*c^2*sqrt(d - c^2*d*x^2)) + (f^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(2*b*c*sqrt(d - c^2*d*x^2)) + (g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(4*b*c^3*sqrt(d - c^2*d*x^2))]
    @test_int [1/sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*(f + g*x)^1, x, 6, -((b*g*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(c*sqrt(d - c^2*d*x^2))) - (g*(1 - c*x)*(1 + c*x)*(a + b*acosh(c*x)))/(c^2*sqrt(d - c^2*d*x^2)) + (f*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(2*b*c*sqrt(d - c^2*d*x^2))]
    @test_int [1/sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))/(f + g*x)^1, x, 10, (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 + (ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2))))/(sqrt(c^2*f^2 - g^2)*sqrt(d - c^2*d*x^2)) - (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 + (ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2))))/(sqrt(c^2*f^2 - g^2)*sqrt(d - c^2*d*x^2)) + (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2)))))/(sqrt(c^2*f^2 - g^2)*sqrt(d - c^2*d*x^2)) - (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2)))))/(sqrt(c^2*f^2 - g^2)*sqrt(d - c^2*d*x^2))]
    @test_int [1/sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))/(f + g*x)^2, x, 13, -((g*sqrt(-1 + c*x)*sqrt(-((1 - c*x)/(1 + c*x)))*(1 + c*x)^(3/2)*(a + b*acosh(c*x)))/((c^2*f^2 - g^2)*(f + g*x)*sqrt(d - c^2*d*x^2))) + (c^2*f*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 + (ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2))))/((c^2*f^2 - g^2)^(3/2)*sqrt(d - c^2*d*x^2)) - (c^2*f*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 + (ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2))))/((c^2*f^2 - g^2)^(3/2)*sqrt(d - c^2*d*x^2)) + (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*log(f + g*x))/((c^2*f^2 - g^2)*sqrt(d - c^2*d*x^2)) + (b*c^2*f*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2)))))/((c^2*f^2 - g^2)^(3/2)*sqrt(d - c^2*d*x^2)) - (b*c^2*f*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2)))))/((c^2*f^2 - g^2)^(3/2)*sqrt(d - c^2*d*x^2))]

    @test_int [1/(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))*(f + g*x)^3, x, 21, (b*g^3*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(c^3*d*sqrt(d - c^2*d*x^2)) - ((c*f - g)^3*(1 - c*x)*(a + b*acosh(c*x)))/(2*c^4*d*sqrt(d - c^2*d*x^2)) + ((c*f + g)^3*(1 + c*x)*(a + b*acosh(c*x)))/(2*c^4*d*sqrt(d - c^2*d*x^2)) + (g^3*(1 - c*x)*(1 + c*x)*(a + b*acosh(c*x)))/(c^4*d*sqrt(d - c^2*d*x^2)) - (3*f*g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(2*b*c^3*d*sqrt(d - c^2*d*x^2)) + (b*(c*f + g)^3*sqrt((1 - c*x)*(1 + c*x))*sqrt(1 - c^2*x^2)*log(sqrt(-((1 - c*x)/(1 + c*x)))))/(c^4*d*sqrt(-((1 - c*x)/(1 + c*x)))*(1 + c*x)*sqrt(d - c^2*d*x^2)) - (b*(c*f - g)^3*sqrt((1 - c*x)*(1 + c*x))*sqrt(1 - c^2*x^2)*log(2/(1 + c*x)))/(2*c^4*d*sqrt(-((1 - c*x)/(1 + c*x)))*(1 + c*x)*sqrt(d - c^2*d*x^2)) - (b*(c*f + g)^3*sqrt((1 - c*x)*(1 + c*x))*sqrt(1 - c^2*x^2)*log(2/(1 + c*x)))/(2*c^4*d*sqrt(-((1 - c*x)/(1 + c*x)))*(1 + c*x)*sqrt(d - c^2*d*x^2))]
    @test_int [1/(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))*(f + g*x)^2, x, 19, -(((c*f - g)^2*(1 - c*x)*(a + b*acosh(c*x)))/(2*c^3*d*sqrt(d - c^2*d*x^2))) + ((c*f + g)^2*(1 + c*x)*(a + b*acosh(c*x)))/(2*c^3*d*sqrt(d - c^2*d*x^2)) - (g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(2*b*c^3*d*sqrt(d - c^2*d*x^2)) + (b*(c*f + g)^2*sqrt((1 - c*x)*(1 + c*x))*sqrt(1 - c^2*x^2)*log(sqrt(-((1 - c*x)/(1 + c*x)))))/(c^3*d*sqrt(-((1 - c*x)/(1 + c*x)))*(1 + c*x)*sqrt(d - c^2*d*x^2)) - (b*(c*f - g)^2*sqrt((1 - c*x)*(1 + c*x))*sqrt(1 - c^2*x^2)*log(2/(1 + c*x)))/(2*c^3*d*sqrt(-((1 - c*x)/(1 + c*x)))*(1 + c*x)*sqrt(d - c^2*d*x^2)) - (b*(c*f + g)^2*sqrt((1 - c*x)*(1 + c*x))*sqrt(1 - c^2*x^2)*log(2/(1 + c*x)))/(2*c^3*d*sqrt(-((1 - c*x)/(1 + c*x)))*(1 + c*x)*sqrt(d - c^2*d*x^2))]
    @test_int [1/(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))*(f + g*x)^1, x, 5, ((g + c^2*f*x)*(a + b*acosh(c*x)))/(c^2*d*sqrt(d - c^2*d*x^2)) - (b*(c*f - g)*sqrt(-1 + c*x)*sqrt(1 + c*x)*atanh(c*x))/(c^2*d*sqrt(d - c^2*d*x^2)) - (b*f*sqrt(-1 + c*x)*sqrt(1 + c*x)*log(1 - c*x))/(c*d*sqrt(d - c^2*d*x^2)), -(((c*f - g)*(a + b*acosh(c*x)))/(c^2*d*sqrt(d - c^2*d*x^2))) + (f*(1 + c*x)*(a + b*acosh(c*x)))/(c*d*sqrt(d - c^2*d*x^2)) - (b*(c*f - g)*sqrt(-1 + c*x)*sqrt(1 + c*x)*atanh(c*x))/(c^2*d*sqrt(d - c^2*d*x^2)) - (b*f*sqrt(-1 + c*x)*sqrt(1 + c*x)*log(1 - c*x))/(c*d*sqrt(d - c^2*d*x^2))]
    @test_int [1/(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))/(f + g*x)^1, x, 27, -(((1 - c*x)*(a + b*acosh(c*x)))/(2*d*(c*f - g)*sqrt(d - c^2*d*x^2))) + ((1 + c*x)*(a + b*acosh(c*x)))/(2*d*(c*f + g)*sqrt(d - c^2*d*x^2)) - (g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 + (ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2))))/(d*(c^2*f^2 - g^2)^(3/2)*sqrt(d - c^2*d*x^2)) + (g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 + (ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2))))/(d*(c^2*f^2 - g^2)^(3/2)*sqrt(d - c^2*d*x^2)) + (b*sqrt((1 - c*x)*(1 + c*x))*sqrt(1 - c^2*x^2)*log(sqrt(-((1 - c*x)/(1 + c*x)))))/(d*(c*f + g)*sqrt(-((1 - c*x)/(1 + c*x)))*(1 + c*x)*sqrt(d - c^2*d*x^2)) - (b*sqrt((1 - c*x)*(1 + c*x))*sqrt(1 - c^2*x^2)*log(2/(1 + c*x)))/(2*d*(c*f - g)*sqrt(-((1 - c*x)/(1 + c*x)))*(1 + c*x)*sqrt(d - c^2*d*x^2)) - (b*sqrt((1 - c*x)*(1 + c*x))*sqrt(1 - c^2*x^2)*log(2/(1 + c*x)))/(2*d*(c*f + g)*sqrt(-((1 - c*x)/(1 + c*x)))*(1 + c*x)*sqrt(d - c^2*d*x^2)) - (b*g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2)))))/(d*(c^2*f^2 - g^2)^(3/2)*sqrt(d - c^2*d*x^2)) + (b*g^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2)))))/(d*(c^2*f^2 - g^2)^(3/2)*sqrt(d - c^2*d*x^2))]
    #= [1/(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))/(f + g*x)^2, x, 0, 0] =#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f+g*x)^m*(d1+c*d1*x)^(p/2)*(d2-c*d2*x)^(p/2)*(a+b*acosh(c*x))^n=#

    @test_int [((f + g*x)*(a + b*acosh(c*x))^n)/sqrt(1 - c^2*x^2), x, 7, (f*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^(1 + n))/(b*c*(1 + n)*sqrt(1 - c^2*x^2)) + (g*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((a + b*acosh(c*x))/b)))/(ℯ^(a/b)*(-((a + b*acosh(c*x))/b))^n*(2*c^2*sqrt(1 - c^2*x^2))) - (ℯ^(a/b)*g*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (a + b*acosh(c*x))/b))/(((a + b*acosh(c*x))/b)^n*(2*c^2*sqrt(1 - c^2*x^2)))]
    @test_int [((f + g*x)*(a + b*acosh(c*x))^n)/(sqrt(1 - c*x)*sqrt(1 + c*x)), x, 7, (f*sqrt(-1 + c*x)*(a + b*acosh(c*x))^(1 + n))/(b*c*(1 + n)*sqrt(1 - c*x)) + (g*sqrt(-1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((a + b*acosh(c*x))/b)))/(ℯ^(a/b)*(-((a + b*acosh(c*x))/b))^n*(2*c^2*sqrt(1 - c*x))) - (ℯ^(a/b)*g*sqrt(-1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (a + b*acosh(c*x))/b))/(((a + b*acosh(c*x))/b)^n*(2*c^2*sqrt(1 - c*x)))]
    @test_int [((f + g*x)*(a + b*acosh(c*x))^n)/(sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)), x, 7, (f*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^(1 + n))/(b*c*(1 + n)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)) + (g*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((a + b*acosh(c*x))/b)))/(ℯ^(a/b)*(-((a + b*acosh(c*x))/b))^n*(2*c^2*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))) - (ℯ^(a/b)*g*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (a + b*acosh(c*x))/b))/(((a + b*acosh(c*x))/b)^n*(2*c^2*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)))]

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

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

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

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

    @test_int [log(h*(f + g*x)^m)*(a + b*acosh(c*x))^n/sqrt(1 - c^2*x^2), x, 1, (sqrt(-1 + c*x)*sqrt(1 + c*x)*Unintegrable(((a + b*acosh(c*x))^n*log(h*(f + g*x)^m))/(sqrt(-1 + c*x)*sqrt(1 + c*x)), x))/sqrt(1 - c^2*x^2)]

    #= [log(h*(f + g*x)^m)*(a + b*acosh(c*x))^3/sqrt(1 - c^2*x^2), x, 0, 0] =#
    @test_int [log(h*(f + g*x)^m)*(a + b*acosh(c*x))^2/sqrt(1 - c^2*x^2), x, 14, (m*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^4)/(12*b^2*c*sqrt(1 - c^2*x^2)) - (m*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^3*log(1 + (ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2))))/(3*b*c*sqrt(1 - c^2*x^2)) - (m*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^3*log(1 + (ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2))))/(3*b*c*sqrt(1 - c^2*x^2)) + (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^3*log(h*(f + g*x)^m))/(3*b*c*sqrt(1 - c^2*x^2)) - (m*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2)))))/(c*sqrt(1 - c^2*x^2)) - (m*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2)))))/(c*sqrt(1 - c^2*x^2)) + (2*b*m*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*PolyLog(3, -((ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2)))))/(c*sqrt(1 - c^2*x^2)) + (2*b*m*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*PolyLog(3, -((ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2)))))/(c*sqrt(1 - c^2*x^2)) - (2*b^2*m*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(4, -((ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2)))))/(c*sqrt(1 - c^2*x^2)) - (2*b^2*m*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(4, -((ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2)))))/(c*sqrt(1 - c^2*x^2))]
    @test_int [log(h*(f + g*x)^m)*(a + b*acosh(c*x))^1/sqrt(1 - c^2*x^2), x, 12, (m*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^3)/(6*b^2*c*sqrt(1 - c^2*x^2)) - (m*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2*log(1 + (ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2))))/(2*b*c*sqrt(1 - c^2*x^2)) - (m*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2*log(1 + (ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2))))/(2*b*c*sqrt(1 - c^2*x^2)) + (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2*log(h*(f + g*x)^m))/(2*b*c*sqrt(1 - c^2*x^2)) - (m*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2)))))/(c*sqrt(1 - c^2*x^2)) - (m*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*PolyLog(2, -((ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2)))))/(c*sqrt(1 - c^2*x^2)) + (b*m*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(3, -((ℯ^acosh(c*x)*g)/(c*f - sqrt(c^2*f^2 - g^2)))))/(c*sqrt(1 - c^2*x^2)) + (b*m*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(3, -((ℯ^acosh(c*x)*g)/(c*f + sqrt(c^2*f^2 - g^2)))))/(c*sqrt(1 - c^2*x^2))]
    @test_int [log(h*(f + g*x)^m)*(a + b*acosh(c*x))^0/sqrt(1 - c^2*x^2), x, 9, (im*m*asin(c*x)^2)/(2*c) - (m*asin(c*x)*log(1 - (im*ℯ^(im*asin(c*x))*g)/(c*f - sqrt(c^2*f^2 - g^2))))/c - (m*asin(c*x)*log(1 - (im*ℯ^(im*asin(c*x))*g)/(c*f + sqrt(c^2*f^2 - g^2))))/c + (asin(c*x)*log(h*(f + g*x)^m))/c + (im*m*PolyLog(2, (im*ℯ^(im*asin(c*x))*g)/(c*f - sqrt(c^2*f^2 - g^2))))/c + (im*m*PolyLog(2, (im*ℯ^(im*asin(c*x))*g)/(c*f + sqrt(c^2*f^2 - g^2))))/c]
    @test_int [log(h*(f + g*x)^m)/(a + b*acosh(c*x))^1/sqrt(1 - c^2*x^2), x, 1, (sqrt(-1 + c*x)*sqrt(1 + c*x)*Unintegrable(log(h*(f + g*x)^m)/(sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))), x))/sqrt(1 - c^2*x^2)]

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

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

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

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

    @test_int [x^3*acosh(a + b*x), x, 6, (7*a*x^2*sqrt(-1 + a + b*x)*sqrt(1 + a + b*x))/(48*b^2) - (x^3*sqrt(-1 + a + b*x)*sqrt(1 + a + b*x))/(16*b) + (sqrt(-1 + a + b*x)*sqrt(1 + a + b*x)*(4*a*(16 + 19*a^2) - (9 + 26*a^2)*(a + b*x)))/(96*b^4) - ((3 + 24*a^2 + 8*a^4)*acosh(a + b*x))/(32*b^4) + (1/4)*x^4*acosh(a + b*x)]
    @test_int [x^2*acosh(a + b*x), x, 5, -((x^2*sqrt(-1 + a + b*x)*sqrt(1 + a + b*x))/(9*b)) - (sqrt(-1 + a + b*x)*sqrt(1 + a + b*x)*(4 + 11*a^2 - 5*a*b*x))/(18*b^3) + (a*(3 + 2*a^2)*acosh(a + b*x))/(6*b^3) + (1/3)*x^3*acosh(a + b*x)]
    @test_int [x^1*acosh(a + b*x), x, 5, (3*a*sqrt(-1 + a + b*x)*sqrt(1 + a + b*x))/(4*b^2) - (x*sqrt(-1 + a + b*x)*sqrt(1 + a + b*x))/(4*b) - ((1 + 2*a^2)*acosh(a + b*x))/(4*b^2) + (1/2)*x^2*acosh(a + b*x)]
    @test_int [x^0*acosh(a + b*x), x, 3, -((sqrt(-1 + a + b*x)*sqrt(1 + a + b*x))/b) + ((a + b*x)*acosh(a + b*x))/b]
    @test_int [acosh(a + b*x)/x^1, x, 9, (-(1/2))*acosh(a + b*x)^2 + acosh(a + b*x)*log(1 - ℯ^acosh(a + b*x)/(a - sqrt(-1 + a^2))) + acosh(a + b*x)*log(1 - ℯ^acosh(a + b*x)/(a + sqrt(-1 + a^2))) + PolyLog(2, ℯ^acosh(a + b*x)/(a - sqrt(-1 + a^2))) + PolyLog(2, ℯ^acosh(a + b*x)/(a + sqrt(-1 + a^2)))]
    @test_int [acosh(a + b*x)/x^2, x, 4, -(acosh(a + b*x)/x) - (2*b*atan((sqrt(1 - a)*sqrt(1 + a + b*x))/(sqrt(1 + a)*sqrt(-1 + a + b*x))))/sqrt(1 - a^2)]
    @test_int [acosh(a + b*x)/x^3, x, 5, (b*sqrt(-1 + a + b*x)*sqrt(1 + a + b*x))/(2*(1 - a^2)*x) - acosh(a + b*x)/(2*x^2) - (a*b^2*atan((sqrt(1 - a)*sqrt(1 + a + b*x))/(sqrt(1 + a)*sqrt(-1 + a + b*x))))/(1 - a^2)^(3/2)]
    @test_int [acosh(a + b*x)/x^4, x, 7, (b*sqrt(-1 + a + b*x)*sqrt(1 + a + b*x))/(6*(1 - a^2)*x^2) + (a*b^2*sqrt(-1 + a + b*x)*sqrt(1 + a + b*x))/(2*(1 - a^2)^2*x) - acosh(a + b*x)/(3*x^3) - ((1 + 2*a^2)*b^3*atan((sqrt(1 - a)*sqrt(1 + a + b*x))/(sqrt(1 + a)*sqrt(-1 + a + b*x))))/(3*(1 - a^2)^(5/2))]

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

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

    @test_int [1/sqrt(a + b*acosh(c + d*x)), x, 7, -((ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(2*sqrt(b)*d)) + (sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(2*sqrt(b)*d))]
    @test_int [1/sqrt(a - b*acosh(c + d*x)), x, 7, -((ℯ^(a/b)*sqrt(pi)*erf(sqrt(a - b*acosh(c + d*x))/sqrt(b)))/(2*sqrt(b)*d)) + (sqrt(pi)*erfi(sqrt(a - b*acosh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(2*sqrt(b)*d))]

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

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

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

    @test_int [(c*e + d*e*x)^4*(a + b*acosh(c + d*x)), x, 8, (-8*b*e^4*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(75*d) - (4*b*e^4*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x))/(75*d) - (b*e^4*sqrt(-1 + c + d*x)*(c + d*x)^4*sqrt(1 + c + d*x))/(25*d) + (e^4*(c + d*x)^5*(a + b*acosh(c + d*x)))/(5*d)]
    @test_int [(c*e + d*e*x)^3*(a + b*acosh(c + d*x)), x, 7, -((3*b*e^3*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x))/(32*d)) - (b*e^3*sqrt(-1 + c + d*x)*(c + d*x)^3*sqrt(1 + c + d*x))/(16*d) - (3*b*e^3*acosh(c + d*x))/(32*d) + (e^3*(c + d*x)^4*(a + b*acosh(c + d*x)))/(4*d)]
    @test_int [(c*e + d*e*x)^2*(a + b*acosh(c + d*x)), x, 6, (-2*b*e^2*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(9*d) - (b*e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x))/(9*d) + (e^2*(c + d*x)^3*(a + b*acosh(c + d*x)))/(3*d)]
    @test_int [(c*e + d*e*x)*(a + b*acosh(c + d*x)), x, 5, -((b*e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x))/(4*d)) - (b*e*acosh(c + d*x))/(4*d) + (e*(c + d*x)^2*(a + b*acosh(c + d*x)))/(2*d)]
    @test_int [a + b*acosh(c + d*x), x, 4, a*x - (b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/d + (b*(c + d*x)*acosh(c + d*x))/d]
    @test_int [(a + b*acosh(c + d*x))/(c*e + d*e*x), x, 7, (a + b*acosh(c + d*x))^2/(2*b*d*e) + ((a + b*acosh(c + d*x))*log(1 + ℯ^(-2*acosh(c + d*x))))/(d*e) - (b*PolyLog(2, -ℯ^(-2*acosh(c + d*x))))/(2*d*e)]
    @test_int [(a + b*acosh(c + d*x))/(c*e + d*e*x)^2, x, 5, -((a + b*acosh(c + d*x))/(d*e^2*(c + d*x))) + (b*atan(sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)))/(d*e^2)]
    @test_int [(a + b*acosh(c + d*x))/(c*e + d*e*x)^3, x, 4, (b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(2*d*e^3*(c + d*x)) - (a + b*acosh(c + d*x))/(2*d*e^3*(c + d*x)^2)]
    @test_int [(a + b*acosh(c + d*x))/(c*e + d*e*x)^4, x, 6, (b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(6*d*e^4*(c + d*x)^2) - (a + b*acosh(c + d*x))/(3*d*e^4*(c + d*x)^3) + (b*atan(sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)))/(6*d*e^4)]
    @test_int [(a + b*acosh(c + d*x))/(c*e + d*e*x)^5, x, 6, (b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(12*d*e^5*(c + d*x)^3) + (b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(6*d*e^5*(c + d*x)) - (a + b*acosh(c + d*x))/(4*d*e^5*(c + d*x)^4)]
    @test_int [(a + b*acosh(c + d*x))/(c*e + d*e*x)^6, x, 8, (b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(20*d*e^6*(c + d*x)^4) + (3*b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(40*d*e^6*(c + d*x)^2) - (a + b*acosh(c + d*x))/(5*d*e^6*(c + d*x)^5) + (3*b*atan(sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)))/(40*d*e^6)]

    @test_int [(c*e + d*e*x)^4*(a + b*acosh(c + d*x))^2, x, 9, (16*b^2*e^4*x)/75 + (8*b^2*e^4*(c + d*x)^3)/(225*d) + (2*b^2*e^4*(c + d*x)^5)/(125*d) - (16*b*e^4*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x)))/(75*d) - (8*b*e^4*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x)))/(75*d) - (2*b*e^4*sqrt(-1 + c + d*x)*(c + d*x)^4*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x)))/(25*d) + (e^4*(c + d*x)^5*(a + b*acosh(c + d*x))^2)/(5*d)]
    @test_int [(c*e + d*e*x)^3*(a + b*acosh(c + d*x))^2, x, 8, (3*b^2*e^3*(c + d*x)^2)/(32*d) + (b^2*e^3*(c + d*x)^4)/(32*d) - (3*b*e^3*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x)))/(16*d) - (b*e^3*sqrt(-1 + c + d*x)*(c + d*x)^3*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x)))/(8*d) - (3*e^3*(a + b*acosh(c + d*x))^2)/(32*d) + (e^3*(c + d*x)^4*(a + b*acosh(c + d*x))^2)/(4*d)]
    @test_int [(c*e + d*e*x)^2*(a + b*acosh(c + d*x))^2, x, 7, (4*b^2*e^2*x)/9 + (2*b^2*e^2*(c + d*x)^3)/(27*d) - (4*b*e^2*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x)))/(9*d) - (2*b*e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x)))/(9*d) + (e^2*(c + d*x)^3*(a + b*acosh(c + d*x))^2)/(3*d)]
    @test_int [(c*e + d*e*x)*(a + b*acosh(c + d*x))^2, x, 6, (b^2*e*(c + d*x)^2)/(4*d) - (b*e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x)))/(2*d) - (e*(a + b*acosh(c + d*x))^2)/(4*d) + (e*(c + d*x)^2*(a + b*acosh(c + d*x))^2)/(2*d)]
    @test_int [(a + b*acosh(c + d*x))^2, x, 4, 2*b^2*x - (2*b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x)))/d + ((c + d*x)*(a + b*acosh(c + d*x))^2)/d]
    @test_int [(a + b*acosh(c + d*x))^2/(c*e + d*e*x), x, 8, (a + b*acosh(c + d*x))^3/(3*b*d*e) + ((a + b*acosh(c + d*x))^2*log(1 + ℯ^(-2*acosh(c + d*x))))/(d*e) - (b*(a + b*acosh(c + d*x))*PolyLog(2, -ℯ^(-2*acosh(c + d*x))))/(d*e) - (b^2*PolyLog(3, -ℯ^(-2*acosh(c + d*x))))/(2*d*e)]
    @test_int [(a + b*acosh(c + d*x))^2/(c*e + d*e*x)^2, x, 9, -((a + b*acosh(c + d*x))^2/(d*e^2*(c + d*x))) + (4*b*(a + b*acosh(c + d*x))*atan(ℯ^acosh(c + d*x)))/(d*e^2) - (2*im*b^2*PolyLog(2, (-im)*ℯ^acosh(c + d*x)))/(d*e^2) + (2*im*b^2*PolyLog(2, im*ℯ^acosh(c + d*x)))/(d*e^2)]
    @test_int [(a + b*acosh(c + d*x))^2/(c*e + d*e*x)^3, x, 5, (b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x)))/(d*e^3*(c + d*x)) - (a + b*acosh(c + d*x))^2/(2*d*e^3*(c + d*x)^2) - (b^2*log(c + d*x))/(d*e^3)]
    @test_int [(a + b*acosh(c + d*x))^2/(c*e + d*e*x)^4, x, 11, b^2/(3*d*e^4*(c + d*x)) + (b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x)))/(3*d*e^4*(c + d*x)^2) - (a + b*acosh(c + d*x))^2/(3*d*e^4*(c + d*x)^3) + (2*b*(a + b*acosh(c + d*x))*atan(ℯ^acosh(c + d*x)))/(3*d*e^4) - (im*b^2*PolyLog(2, (-im)*ℯ^acosh(c + d*x)))/(3*d*e^4) + (im*b^2*PolyLog(2, im*ℯ^acosh(c + d*x)))/(3*d*e^4)]

    @test_int [(c*e + d*e*x)^4*(a + b*acosh(c + d*x))^3, x, 19, (16*a*b^2*e^4*x)/25 - (4144*b^3*e^4*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(5625*d) - (272*b^3*e^4*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x))/(5625*d) - (6*b^3*e^4*sqrt(-1 + c + d*x)*(c + d*x)^4*sqrt(1 + c + d*x))/(625*d) + (16*b^3*e^4*(c + d*x)*acosh(c + d*x))/(25*d) + (8*b^2*e^4*(c + d*x)^3*(a + b*acosh(c + d*x)))/(75*d) + (6*b^2*e^4*(c + d*x)^5*(a + b*acosh(c + d*x)))/(125*d) - (8*b*e^4*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^2)/(25*d) - (4*b*e^4*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^2)/(25*d) - (3*b*e^4*sqrt(-1 + c + d*x)*(c + d*x)^4*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^2)/(25*d) + (e^4*(c + d*x)^5*(a + b*acosh(c + d*x))^3)/(5*d)]
    @test_int [(c*e + d*e*x)^3*(a + b*acosh(c + d*x))^3, x, 14, -((45*b^3*e^3*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x))/(256*d)) - (3*b^3*e^3*sqrt(-1 + c + d*x)*(c + d*x)^3*sqrt(1 + c + d*x))/(128*d) - (45*b^3*e^3*acosh(c + d*x))/(256*d) + (9*b^2*e^3*(c + d*x)^2*(a + b*acosh(c + d*x)))/(32*d) + (3*b^2*e^3*(c + d*x)^4*(a + b*acosh(c + d*x)))/(32*d) - (9*b*e^3*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^2)/(32*d) - (3*b*e^3*sqrt(-1 + c + d*x)*(c + d*x)^3*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^2)/(16*d) - (3*e^3*(a + b*acosh(c + d*x))^3)/(32*d) + (e^3*(c + d*x)^4*(a + b*acosh(c + d*x))^3)/(4*d)]
    @test_int [(c*e + d*e*x)^2*(a + b*acosh(c + d*x))^3, x, 12, (4*a*b^2*e^2*x)/3 - (40*b^3*e^2*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(27*d) - (2*b^3*e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x))/(27*d) + (4*b^3*e^2*(c + d*x)*acosh(c + d*x))/(3*d) + (2*b^2*e^2*(c + d*x)^3*(a + b*acosh(c + d*x)))/(9*d) - (2*b*e^2*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^2)/(3*d) - (b*e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^2)/(3*d) + (e^2*(c + d*x)^3*(a + b*acosh(c + d*x))^3)/(3*d)]
    @test_int [(c*e + d*e*x)*(a + b*acosh(c + d*x))^3, x, 8, -((3*b^3*e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x))/(8*d)) - (3*b^3*e*acosh(c + d*x))/(8*d) + (3*b^2*e*(c + d*x)^2*(a + b*acosh(c + d*x)))/(4*d) - (3*b*e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^2)/(4*d) - (e*(a + b*acosh(c + d*x))^3)/(4*d) + (e*(c + d*x)^2*(a + b*acosh(c + d*x))^3)/(2*d)]
    @test_int [(a + b*acosh(c + d*x))^3, x, 6, 6*a*b^2*x - (6*b^3*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/d + (6*b^3*(c + d*x)*acosh(c + d*x))/d - (3*b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^2)/d + ((c + d*x)*(a + b*acosh(c + d*x))^3)/d]
    @test_int [(a + b*acosh(c + d*x))^3/(c*e + d*e*x), x, 9, (a + b*acosh(c + d*x))^4/(4*b*d*e) + ((a + b*acosh(c + d*x))^3*log(1 + ℯ^(-2*acosh(c + d*x))))/(d*e) - (3*b*(a + b*acosh(c + d*x))^2*PolyLog(2, -ℯ^(-2*acosh(c + d*x))))/(2*d*e) - (3*b^2*(a + b*acosh(c + d*x))*PolyLog(3, -ℯ^(-2*acosh(c + d*x))))/(2*d*e) - (3*b^3*PolyLog(4, -ℯ^(-2*acosh(c + d*x))))/(4*d*e)]
    @test_int [(a + b*acosh(c + d*x))^3/(c*e + d*e*x)^2, x, 11, -((a + b*acosh(c + d*x))^3/(d*e^2*(c + d*x))) + (6*b*(a + b*acosh(c + d*x))^2*atan(ℯ^acosh(c + d*x)))/(d*e^2) - (6*im*b^2*(a + b*acosh(c + d*x))*PolyLog(2, (-im)*ℯ^acosh(c + d*x)))/(d*e^2) + (6*im*b^2*(a + b*acosh(c + d*x))*PolyLog(2, im*ℯ^acosh(c + d*x)))/(d*e^2) + (6*im*b^3*PolyLog(3, (-im)*ℯ^acosh(c + d*x)))/(d*e^2) - (6*im*b^3*PolyLog(3, im*ℯ^acosh(c + d*x)))/(d*e^2)]
    @test_int [(a + b*acosh(c + d*x))^3/(c*e + d*e*x)^3, x, 9, -((3*b*(a + b*acosh(c + d*x))^2)/(2*d*e^3)) + (3*b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^2)/(2*d*e^3*(c + d*x)) - (a + b*acosh(c + d*x))^3/(2*d*e^3*(c + d*x)^2) - (3*b^2*(a + b*acosh(c + d*x))*log(1 + ℯ^(-2*acosh(c + d*x))))/(d*e^3) + (3*b^3*PolyLog(2, -ℯ^(-2*acosh(c + d*x))))/(2*d*e^3)]
    @test_int [(a + b*acosh(c + d*x))^3/(c*e + d*e*x)^4, x, 15, (b^2*(a + b*acosh(c + d*x)))/(d*e^4*(c + d*x)) + (b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^2)/(2*d*e^4*(c + d*x)^2) - (a + b*acosh(c + d*x))^3/(3*d*e^4*(c + d*x)^3) + (b*(a + b*acosh(c + d*x))^2*atan(ℯ^acosh(c + d*x)))/(d*e^4) - (b^3*atan(sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)))/(d*e^4) - (im*b^2*(a + b*acosh(c + d*x))*PolyLog(2, (-im)*ℯ^acosh(c + d*x)))/(d*e^4) + (im*b^2*(a + b*acosh(c + d*x))*PolyLog(2, im*ℯ^acosh(c + d*x)))/(d*e^4) + (im*b^3*PolyLog(3, (-im)*ℯ^acosh(c + d*x)))/(d*e^4) - (im*b^3*PolyLog(3, im*ℯ^acosh(c + d*x)))/(d*e^4)]

    @test_int [(c*e + d*e*x)^3*(a + b*acosh(c + d*x))^4, x, 16, (45*b^4*e^3*(c + d*x)^2)/(128*d) + (3*b^4*e^3*(c + d*x)^4)/(128*d) - (45*b^3*e^3*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x)))/(64*d) - (3*b^3*e^3*sqrt(-1 + c + d*x)*(c + d*x)^3*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x)))/(32*d) - (45*b^2*e^3*(a + b*acosh(c + d*x))^2)/(128*d) + (9*b^2*e^3*(c + d*x)^2*(a + b*acosh(c + d*x))^2)/(16*d) + (3*b^2*e^3*(c + d*x)^4*(a + b*acosh(c + d*x))^2)/(16*d) - (3*b*e^3*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^3)/(8*d) - (b*e^3*sqrt(-1 + c + d*x)*(c + d*x)^3*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^3)/(4*d) - (3*e^3*(a + b*acosh(c + d*x))^4)/(32*d) + (e^3*(c + d*x)^4*(a + b*acosh(c + d*x))^4)/(4*d)]
    @test_int [(c*e + d*e*x)^2*(a + b*acosh(c + d*x))^4, x, 13, (160*b^4*e^2*x)/27 + (8*b^4*e^2*(c + d*x)^3)/(81*d) - (160*b^3*e^2*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x)))/(27*d) - (8*b^3*e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x)))/(27*d) + (8*b^2*e^2*(c + d*x)*(a + b*acosh(c + d*x))^2)/(3*d) + (4*b^2*e^2*(c + d*x)^3*(a + b*acosh(c + d*x))^2)/(9*d) - (8*b*e^2*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^3)/(9*d) - (4*b*e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^3)/(9*d) + (e^2*(c + d*x)^3*(a + b*acosh(c + d*x))^4)/(3*d)]
    @test_int [(c*e + d*e*x)*(a + b*acosh(c + d*x))^4, x, 9, (3*b^4*e*(c + d*x)^2)/(4*d) - (3*b^3*e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x)))/(2*d) - (3*b^2*e*(a + b*acosh(c + d*x))^2)/(4*d) + (3*b^2*e*(c + d*x)^2*(a + b*acosh(c + d*x))^2)/(2*d) - (b*e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^3)/d - (e*(a + b*acosh(c + d*x))^4)/(4*d) + (e*(c + d*x)^2*(a + b*acosh(c + d*x))^4)/(2*d)]
    @test_int [(a + b*acosh(c + d*x))^4, x, 6, 24*b^4*x - (24*b^3*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x)))/d + (12*b^2*(c + d*x)*(a + b*acosh(c + d*x))^2)/d - (4*b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^3)/d + ((c + d*x)*(a + b*acosh(c + d*x))^4)/d]
    @test_int [(a + b*acosh(c + d*x))^4/(c*e + d*e*x), x, 10, (a + b*acosh(c + d*x))^5/(5*b*d*e) + ((a + b*acosh(c + d*x))^4*log(1 + ℯ^(-2*acosh(c + d*x))))/(d*e) - (2*b*(a + b*acosh(c + d*x))^3*PolyLog(2, -ℯ^(-2*acosh(c + d*x))))/(d*e) - (3*b^2*(a + b*acosh(c + d*x))^2*PolyLog(3, -ℯ^(-2*acosh(c + d*x))))/(d*e) - (3*b^3*(a + b*acosh(c + d*x))*PolyLog(4, -ℯ^(-2*acosh(c + d*x))))/(d*e) - (3*b^4*PolyLog(5, -ℯ^(-2*acosh(c + d*x))))/(2*d*e)]
    @test_int [(a + b*acosh(c + d*x))^4/(c*e + d*e*x)^2, x, 13, -((a + b*acosh(c + d*x))^4/(d*e^2*(c + d*x))) + (8*b*(a + b*acosh(c + d*x))^3*atan(ℯ^acosh(c + d*x)))/(d*e^2) - (12*im*b^2*(a + b*acosh(c + d*x))^2*PolyLog(2, (-im)*ℯ^acosh(c + d*x)))/(d*e^2) + (12*im*b^2*(a + b*acosh(c + d*x))^2*PolyLog(2, im*ℯ^acosh(c + d*x)))/(d*e^2) + (24*im*b^3*(a + b*acosh(c + d*x))*PolyLog(3, (-im)*ℯ^acosh(c + d*x)))/(d*e^2) - (24*im*b^3*(a + b*acosh(c + d*x))*PolyLog(3, im*ℯ^acosh(c + d*x)))/(d*e^2) - (24*im*b^4*PolyLog(4, (-im)*ℯ^acosh(c + d*x)))/(d*e^2) + (24*im*b^4*PolyLog(4, im*ℯ^acosh(c + d*x)))/(d*e^2)]
    @test_int [(a + b*acosh(c + d*x))^4/(c*e + d*e*x)^3, x, 10, -((2*b*(a + b*acosh(c + d*x))^3)/(d*e^3)) + (2*b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^3)/(d*e^3*(c + d*x)) - (a + b*acosh(c + d*x))^4/(2*d*e^3*(c + d*x)^2) - (6*b^2*(a + b*acosh(c + d*x))^2*log(1 + ℯ^(-2*acosh(c + d*x))))/(d*e^3) + (6*b^3*(a + b*acosh(c + d*x))*PolyLog(2, -ℯ^(-2*acosh(c + d*x))))/(d*e^3) + (3*b^4*PolyLog(3, -ℯ^(-2*acosh(c + d*x))))/(d*e^3)]
    @test_int [(a + b*acosh(c + d*x))^4/(c*e + d*e*x)^4, x, 21, (2*b^2*(a + b*acosh(c + d*x))^2)/(d*e^4*(c + d*x)) + (2*b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^3)/(3*d*e^4*(c + d*x)^2) - (a + b*acosh(c + d*x))^4/(3*d*e^4*(c + d*x)^3) - (8*b^3*(a + b*acosh(c + d*x))*atan(ℯ^acosh(c + d*x)))/(d*e^4) + (4*b*(a + b*acosh(c + d*x))^3*atan(ℯ^acosh(c + d*x)))/(3*d*e^4) + (4*im*b^4*PolyLog(2, (-im)*ℯ^acosh(c + d*x)))/(d*e^4) - (2*im*b^2*(a + b*acosh(c + d*x))^2*PolyLog(2, (-im)*ℯ^acosh(c + d*x)))/(d*e^4) - (4*im*b^4*PolyLog(2, im*ℯ^acosh(c + d*x)))/(d*e^4) + (2*im*b^2*(a + b*acosh(c + d*x))^2*PolyLog(2, im*ℯ^acosh(c + d*x)))/(d*e^4) + (4*im*b^3*(a + b*acosh(c + d*x))*PolyLog(3, (-im)*ℯ^acosh(c + d*x)))/(d*e^4) - (4*im*b^3*(a + b*acosh(c + d*x))*PolyLog(3, im*ℯ^acosh(c + d*x)))/(d*e^4) - (4*im*b^4*PolyLog(4, (-im)*ℯ^acosh(c + d*x)))/(d*e^4) + (4*im*b^4*PolyLog(4, im*ℯ^acosh(c + d*x)))/(d*e^4)]

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

    @test_int [(c*e + d*e*x)^4/(a + b*acosh(c + d*x)), x, 14, -((e^4*CoshIntegral((a + b*acosh(c + d*x))/b)*sinh(a/b))/(8*b*d)) - (3*e^4*CoshIntegral((3*(a + b*acosh(c + d*x)))/b)*sinh((3*a)/b))/(16*b*d) - (e^4*CoshIntegral((5*(a + b*acosh(c + d*x)))/b)*sinh((5*a)/b))/(16*b*d) + (e^4*cosh(a/b)*SinhIntegral((a + b*acosh(c + d*x))/b))/(8*b*d) + (3*e^4*cosh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c + d*x)))/b))/(16*b*d) + (e^4*cosh((5*a)/b)*SinhIntegral((5*(a + b*acosh(c + d*x)))/b))/(16*b*d)]
    @test_int [(c*e + d*e*x)^3/(a + b*acosh(c + d*x)), x, 11, -((e^3*CoshIntegral((2*(a + b*acosh(c + d*x)))/b)*sinh((2*a)/b))/(4*b*d)) - (e^3*CoshIntegral((4*(a + b*acosh(c + d*x)))/b)*sinh((4*a)/b))/(8*b*d) + (e^3*cosh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c + d*x)))/b))/(4*b*d) + (e^3*cosh((4*a)/b)*SinhIntegral((4*(a + b*acosh(c + d*x)))/b))/(8*b*d)]
    @test_int [(c*e + d*e*x)^2/(a + b*acosh(c + d*x)), x, 11, -((e^2*CoshIntegral((a + b*acosh(c + d*x))/b)*sinh(a/b))/(4*b*d)) - (e^2*CoshIntegral((3*(a + b*acosh(c + d*x)))/b)*sinh((3*a)/b))/(4*b*d) + (e^2*cosh(a/b)*SinhIntegral((a + b*acosh(c + d*x))/b))/(4*b*d) + (e^2*cosh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c + d*x)))/b))/(4*b*d)]
    @test_int [(c*e + d*e*x)/(a + b*acosh(c + d*x)), x, 8, -((e*CoshIntegral((2*(a + b*acosh(c + d*x)))/b)*sinh((2*a)/b))/(2*b*d)) + (e*cosh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c + d*x)))/b))/(2*b*d)]
    @test_int [(a + b*acosh(c + d*x))^(-1), x, 5, -((CoshIntegral((a + b*acosh(c + d*x))/b)*sinh(a/b))/(b*d)) + (cosh(a/b)*SinhIntegral((a + b*acosh(c + d*x))/b))/(b*d)]
    @test_int [1/((c*e + d*e*x)*(a + b*acosh(c + d*x))), x, 2, Unintegrable(1/((c + d*x)*(a + b*acosh(c + d*x))), x)/e]

    @test_int [(c*e + d*e*x)^4/(a + b*acosh(c + d*x))^2, x, 13, -((e^4*sqrt(-1 + c + d*x)*(c + d*x)^4*sqrt(1 + c + d*x))/(b*d*(a + b*acosh(c + d*x)))) + (e^4*cosh(a/b)*CoshIntegral((a + b*acosh(c + d*x))/b))/(8*b^2*d) + (9*e^4*cosh((3*a)/b)*CoshIntegral((3*(a + b*acosh(c + d*x)))/b))/(16*b^2*d) + (5*e^4*cosh((5*a)/b)*CoshIntegral((5*(a + b*acosh(c + d*x)))/b))/(16*b^2*d) - (e^4*sinh(a/b)*SinhIntegral((a + b*acosh(c + d*x))/b))/(8*b^2*d) - (9*e^4*sinh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c + d*x)))/b))/(16*b^2*d) - (5*e^4*sinh((5*a)/b)*SinhIntegral((5*(a + b*acosh(c + d*x)))/b))/(16*b^2*d)]
    @test_int [(c*e + d*e*x)^3/(a + b*acosh(c + d*x))^2, x, 10, -((e^3*sqrt(-1 + c + d*x)*(c + d*x)^3*sqrt(1 + c + d*x))/(b*d*(a + b*acosh(c + d*x)))) + (e^3*cosh((2*a)/b)*CoshIntegral((2*(a + b*acosh(c + d*x)))/b))/(2*b^2*d) + (e^3*cosh((4*a)/b)*CoshIntegral((4*(a + b*acosh(c + d*x)))/b))/(2*b^2*d) - (e^3*sinh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c + d*x)))/b))/(2*b^2*d) - (e^3*sinh((4*a)/b)*SinhIntegral((4*(a + b*acosh(c + d*x)))/b))/(2*b^2*d)]
    @test_int [(c*e + d*e*x)^2/(a + b*acosh(c + d*x))^2, x, 10, -((e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x))/(b*d*(a + b*acosh(c + d*x)))) + (e^2*cosh(a/b)*CoshIntegral((a + b*acosh(c + d*x))/b))/(4*b^2*d) + (3*e^2*cosh((3*a)/b)*CoshIntegral((3*(a + b*acosh(c + d*x)))/b))/(4*b^2*d) - (e^2*sinh(a/b)*SinhIntegral((a + b*acosh(c + d*x))/b))/(4*b^2*d) - (3*e^2*sinh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c + d*x)))/b))/(4*b^2*d)]
    @test_int [(c*e + d*e*x)/(a + b*acosh(c + d*x))^2, x, 6, -((e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x))/(b*d*(a + b*acosh(c + d*x)))) + (e*cosh((2*a)/b)*CoshIntegral((2*(a + b*acosh(c + d*x)))/b))/(b^2*d) - (e*sinh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c + d*x)))/b))/(b^2*d)]
    @test_int [(a + b*acosh(c + d*x))^(-2), x, 6, -((sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(b*d*(a + b*acosh(c + d*x)))) + (cosh(a/b)*CoshIntegral((a + b*acosh(c + d*x))/b))/(b^2*d) - (sinh(a/b)*SinhIntegral((a + b*acosh(c + d*x))/b))/(b^2*d)]
    @test_int [1/((c*e + d*e*x)*(a + b*acosh(c + d*x))^2), x, 2, Unintegrable(1/((c + d*x)*(a + b*acosh(c + d*x))^2), x)/e]

    @test_int [(c*e + d*e*x)^4/(a + b*acosh(c + d*x))^3, x, 26, -((e^4*sqrt(-1 + c + d*x)*(c + d*x)^4*sqrt(1 + c + d*x))/(2*b*d*(a + b*acosh(c + d*x))^2)) + (2*e^4*(c + d*x)^3)/(b^2*d*(a + b*acosh(c + d*x))) - (5*e^4*(c + d*x)^5)/(2*b^2*d*(a + b*acosh(c + d*x))) - (e^4*CoshIntegral((a + b*acosh(c + d*x))/b)*sinh(a/b))/(16*b^3*d) - (27*e^4*CoshIntegral((3*(a + b*acosh(c + d*x)))/b)*sinh((3*a)/b))/(32*b^3*d) - (25*e^4*CoshIntegral((5*(a + b*acosh(c + d*x)))/b)*sinh((5*a)/b))/(32*b^3*d) + (e^4*cosh(a/b)*SinhIntegral((a + b*acosh(c + d*x))/b))/(16*b^3*d) + (27*e^4*cosh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c + d*x)))/b))/(32*b^3*d) + (25*e^4*cosh((5*a)/b)*SinhIntegral((5*(a + b*acosh(c + d*x)))/b))/(32*b^3*d)]
    @test_int [(c*e + d*e*x)^3/(a + b*acosh(c + d*x))^3, x, 20, -((e^3*sqrt(-1 + c + d*x)*(c + d*x)^3*sqrt(1 + c + d*x))/(2*b*d*(a + b*acosh(c + d*x))^2)) + (3*e^3*(c + d*x)^2)/(2*b^2*d*(a + b*acosh(c + d*x))) - (2*e^3*(c + d*x)^4)/(b^2*d*(a + b*acosh(c + d*x))) - (e^3*CoshIntegral((2*(a + b*acosh(c + d*x)))/b)*sinh((2*a)/b))/(2*b^3*d) - (e^3*CoshIntegral((4*(a + b*acosh(c + d*x)))/b)*sinh((4*a)/b))/(b^3*d) + (e^3*cosh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c + d*x)))/b))/(2*b^3*d) + (e^3*cosh((4*a)/b)*SinhIntegral((4*(a + b*acosh(c + d*x)))/b))/(b^3*d)]
    @test_int [(c*e + d*e*x)^2/(a + b*acosh(c + d*x))^3, x, 18, -((e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x))/(2*b*d*(a + b*acosh(c + d*x))^2)) + (e^2*(c + d*x))/(b^2*d*(a + b*acosh(c + d*x))) - (3*e^2*(c + d*x)^3)/(2*b^2*d*(a + b*acosh(c + d*x))) - (e^2*CoshIntegral((a + b*acosh(c + d*x))/b)*sinh(a/b))/(8*b^3*d) - (9*e^2*CoshIntegral((3*(a + b*acosh(c + d*x)))/b)*sinh((3*a)/b))/(8*b^3*d) + (e^2*cosh(a/b)*SinhIntegral((a + b*acosh(c + d*x))/b))/(8*b^3*d) + (9*e^2*cosh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c + d*x)))/b))/(8*b^3*d)]
    @test_int [(c*e + d*e*x)/(a + b*acosh(c + d*x))^3, x, 11, -((e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x))/(2*b*d*(a + b*acosh(c + d*x))^2)) + e/(2*b^2*d*(a + b*acosh(c + d*x))) - (e*(c + d*x)^2)/(b^2*d*(a + b*acosh(c + d*x))) - (e*CoshIntegral((2*(a + b*acosh(c + d*x)))/b)*sinh((2*a)/b))/(b^3*d) + (e*cosh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c + d*x)))/b))/(b^3*d)]
    @test_int [(a + b*acosh(c + d*x))^(-3), x, 7, -(sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(2*b*d*(a + b*acosh(c + d*x))^2) - (c + d*x)/(2*b^2*d*(a + b*acosh(c + d*x))) - (CoshIntegral((a + b*acosh(c + d*x))/b)*sinh(a/b))/(2*b^3*d) + (cosh(a/b)*SinhIntegral((a + b*acosh(c + d*x))/b))/(2*b^3*d)]
    @test_int [1/((c*e + d*e*x)*(a + b*acosh(c + d*x))^3), x, 2, Unintegrable(1/((c + d*x)*(a + b*acosh(c + d*x))^3), x)/e]

    @test_int [(c*e + d*e*x)^4/(a + b*acosh(c + d*x))^4, x, 24, -((e^4*sqrt(-1 + c + d*x)*(c + d*x)^4*sqrt(1 + c + d*x))/(3*b*d*(a + b*acosh(c + d*x))^3)) + (2*e^4*(c + d*x)^3)/(3*b^2*d*(a + b*acosh(c + d*x))^2) - (5*e^4*(c + d*x)^5)/(6*b^2*d*(a + b*acosh(c + d*x))^2) + (2*e^4*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x))/(b^3*d*(a + b*acosh(c + d*x))) - (25*e^4*sqrt(-1 + c + d*x)*(c + d*x)^4*sqrt(1 + c + d*x))/(6*b^3*d*(a + b*acosh(c + d*x))) + (e^4*cosh(a/b)*CoshIntegral((a + b*acosh(c + d*x))/b))/(48*b^4*d) + (27*e^4*cosh((3*a)/b)*CoshIntegral((3*(a + b*acosh(c + d*x)))/b))/(32*b^4*d) + (125*e^4*cosh((5*a)/b)*CoshIntegral((5*(a + b*acosh(c + d*x)))/b))/(96*b^4*d) - (e^4*sinh(a/b)*SinhIntegral((a + b*acosh(c + d*x))/b))/(48*b^4*d) - (27*e^4*sinh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c + d*x)))/b))/(32*b^4*d) - (125*e^4*sinh((5*a)/b)*SinhIntegral((5*(a + b*acosh(c + d*x)))/b))/(96*b^4*d)]
    @test_int [(c*e + d*e*x)^3/(a + b*acosh(c + d*x))^4, x, 17, -((e^3*sqrt(-1 + c + d*x)*(c + d*x)^3*sqrt(1 + c + d*x))/(3*b*d*(a + b*acosh(c + d*x))^3)) + (e^3*(c + d*x)^2)/(2*b^2*d*(a + b*acosh(c + d*x))^2) - (2*e^3*(c + d*x)^4)/(3*b^2*d*(a + b*acosh(c + d*x))^2) + (e^3*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x))/(b^3*d*(a + b*acosh(c + d*x))) - (8*e^3*sqrt(-1 + c + d*x)*(c + d*x)^3*sqrt(1 + c + d*x))/(3*b^3*d*(a + b*acosh(c + d*x))) + (e^3*cosh((2*a)/b)*CoshIntegral((2*(a + b*acosh(c + d*x)))/b))/(3*b^4*d) + (4*e^3*cosh((4*a)/b)*CoshIntegral((4*(a + b*acosh(c + d*x)))/b))/(3*b^4*d) - (e^3*sinh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c + d*x)))/b))/(3*b^4*d) - (4*e^3*sinh((4*a)/b)*SinhIntegral((4*(a + b*acosh(c + d*x)))/b))/(3*b^4*d)]
    @test_int [(c*e + d*e*x)^2/(a + b*acosh(c + d*x))^4, x, 18, -((e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x))/(3*b*d*(a + b*acosh(c + d*x))^3)) + (e^2*(c + d*x))/(3*b^2*d*(a + b*acosh(c + d*x))^2) - (e^2*(c + d*x)^3)/(2*b^2*d*(a + b*acosh(c + d*x))^2) + (e^2*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(3*b^3*d*(a + b*acosh(c + d*x))) - (3*e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x))/(2*b^3*d*(a + b*acosh(c + d*x))) + (e^2*cosh(a/b)*CoshIntegral((a + b*acosh(c + d*x))/b))/(24*b^4*d) + (9*e^2*cosh((3*a)/b)*CoshIntegral((3*(a + b*acosh(c + d*x)))/b))/(8*b^4*d) - (e^2*sinh(a/b)*SinhIntegral((a + b*acosh(c + d*x))/b))/(24*b^4*d) - (9*e^2*sinh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c + d*x)))/b))/(8*b^4*d)]
    @test_int [(c*e + d*e*x)/(a + b*acosh(c + d*x))^4, x, 9, -((e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x))/(3*b*d*(a + b*acosh(c + d*x))^3)) + e/(6*b^2*d*(a + b*acosh(c + d*x))^2) - (e*(c + d*x)^2)/(3*b^2*d*(a + b*acosh(c + d*x))^2) - (2*e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x))/(3*b^3*d*(a + b*acosh(c + d*x))) + (2*e*cosh((2*a)/b)*CoshIntegral((2*(a + b*acosh(c + d*x)))/b))/(3*b^4*d) - (2*e*sinh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c + d*x)))/b))/(3*b^4*d)]
    @test_int [(a + b*acosh(c + d*x))^(-4), x, 8, -((sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(3*b*d*(a + b*acosh(c + d*x))^3)) - (c + d*x)/(6*b^2*d*(a + b*acosh(c + d*x))^2) - (sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(6*b^3*d*(a + b*acosh(c + d*x))) + (cosh(a/b)*CoshIntegral((a + b*acosh(c + d*x))/b))/(6*b^4*d) - (sinh(a/b)*SinhIntegral((a + b*acosh(c + d*x))/b))/(6*b^4*d)]
    @test_int [1/((c*e + d*e*x)*(a + b*acosh(c + d*x))^4), x, 2, Unintegrable(1/((c + d*x)*(a + b*acosh(c + d*x))^4), x)/e]

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

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

    @test_int [(c*e + d*e*x)^4*sqrt(a + b*acosh(c + d*x)), x, 21, (e^4*(c + d*x)^5*sqrt(a + b*acosh(c + d*x)))/(5*d) - (sqrt(b)*e^4*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(32*d) - (sqrt(b)*e^4*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(64*d) - (sqrt(b)*e^4*ℯ^((5*a)/b)*sqrt(pi/5)*erf((sqrt(5)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(320*d) - (sqrt(b)*e^4*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(32*d*ℯ^(a/b)) - (sqrt(b)*e^4*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(64*d*ℯ^((3*a)/b)) - (sqrt(b)*e^4*sqrt(pi/5)*erfi((sqrt(5)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(320*d*ℯ^((5*a)/b))]
    @test_int [(c*e + d*e*x)^3*sqrt(a + b*acosh(c + d*x)), x, 16, (-3*e^3*sqrt(a + b*acosh(c + d*x)))/(32*d) + (e^3*(c + d*x)^4*sqrt(a + b*acosh(c + d*x)))/(4*d) - (sqrt(b)*e^3*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(256*d) - (sqrt(b)*e^3*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(32*d) - (sqrt(b)*e^3*sqrt(pi)*erfi((2*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(256*d*ℯ^((4*a)/b)) - (sqrt(b)*e^3*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(32*d*ℯ^((2*a)/b))]
    @test_int [(c*e + d*e*x)^2*sqrt(a + b*acosh(c + d*x)), x, 16, (e^2*(c + d*x)^3*sqrt(a + b*acosh(c + d*x)))/(3*d) - (sqrt(b)*e^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(16*d) - (sqrt(b)*e^2*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(48*d) - (sqrt(b)*e^2*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(16*d*ℯ^(a/b)) - (sqrt(b)*e^2*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(48*d*ℯ^((3*a)/b))]
    @test_int [(c*e + d*e*x)*sqrt(a + b*acosh(c + d*x)), x, 11, -(e*sqrt(a + b*acosh(c + d*x)))/(4*d) + (e*(c + d*x)^2*sqrt(a + b*acosh(c + d*x)))/(2*d) - (sqrt(b)*e*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(16*d) - (sqrt(b)*e*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(16*d*ℯ^((2*a)/b))]
    @test_int [sqrt(a + b*acosh(c + d*x)), x, 8, ((c + d*x)*sqrt(a + b*acosh(c + d*x)))/d - (sqrt(b)*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(4*d) - (sqrt(b)*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(4*d*ℯ^(a/b))]
    @test_int [1/(c*e + d*e*x)*sqrt(a + b*acosh(c + d*x)), x, 2, Unintegrable(sqrt(a + b*acosh(c + d*x))/(c + d*x), x)/e]

    @test_int [(c*e + d*e*x)^3*(a + b*acosh(c + d*x))^(3/2), x, 27, (-9*b*e^3*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x)*sqrt(a + b*acosh(c + d*x)))/(64*d) - (3*b*e^3*sqrt(-1 + c + d*x)*(c + d*x)^3*sqrt(1 + c + d*x)*sqrt(a + b*acosh(c + d*x)))/(32*d) - (3*e^3*(a + b*acosh(c + d*x))^(3/2))/(32*d) + (e^3*(c + d*x)^4*(a + b*acosh(c + d*x))^(3/2))/(4*d) - (3*b^(3/2)*e^3*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(2048*d) - (3*b^(3/2)*e^3*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(128*d) + (3*b^(3/2)*e^3*sqrt(pi)*erfi((2*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(2048*d*ℯ^((4*a)/b)) + (3*b^(3/2)*e^3*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(128*d*ℯ^((2*a)/b))]
    @test_int [(c*e + d*e*x)^2*(a + b*acosh(c + d*x))^(3/2), x, 24, -(b*e^2*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*sqrt(a + b*acosh(c + d*x)))/(3*d) - (b*e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x)*sqrt(a + b*acosh(c + d*x)))/(6*d) + (e^2*(c + d*x)^3*(a + b*acosh(c + d*x))^(3/2))/(3*d) - (3*b^(3/2)*e^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(32*d) - (b^(3/2)*e^2*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(96*d) + (3*b^(3/2)*e^2*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(32*d*ℯ^(a/b)) + (b^(3/2)*e^2*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(96*d*ℯ^((3*a)/b))]
    @test_int [(c*e + d*e*x)^1*(a + b*acosh(c + d*x))^(3/2), x, 13, (-3*b*e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x)*sqrt(a + b*acosh(c + d*x)))/(8*d) - (e*(a + b*acosh(c + d*x))^(3/2))/(4*d) + (e*(c + d*x)^2*(a + b*acosh(c + d*x))^(3/2))/(2*d) - (3*b^(3/2)*e*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(64*d) + (3*b^(3/2)*e*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(64*d*ℯ^((2*a)/b))]
    @test_int [(a + b*acosh(c + d*x))^(3/2), x, 9, (-3*b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*sqrt(a + b*acosh(c + d*x)))/(2*d) + ((c + d*x)*(a + b*acosh(c + d*x))^(3/2))/d - (3*b^(3/2)*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(8*d) + (3*b^(3/2)*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(8*d*ℯ^(a/b))]
    @test_int [1/(c*e + d*e*x)*(a + b*acosh(c + d*x))^(3/2), x, 2, Unintegrable((a + b*acosh(c + d*x))^(3/2)/(c + d*x), x)/e]

    @test_int [(c*e + d*e*x)^3*(a + b*acosh(c + d*x))^(5/2), x, 29, (-225*b^2*e^3*sqrt(a + b*acosh(c + d*x)))/(2048*d) + (45*b^2*e^3*(c + d*x)^2*sqrt(a + b*acosh(c + d*x)))/(256*d) + (15*b^2*e^3*(c + d*x)^4*sqrt(a + b*acosh(c + d*x)))/(256*d) - (15*b*e^3*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^(3/2))/(64*d) - (5*b*e^3*sqrt(-1 + c + d*x)*(c + d*x)^3*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^(3/2))/(32*d) - (3*e^3*(a + b*acosh(c + d*x))^(5/2))/(32*d) + (e^3*(c + d*x)^4*(a + b*acosh(c + d*x))^(5/2))/(4*d) - (15*b^(5/2)*e^3*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(16384*d) - (15*b^(5/2)*e^3*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(512*d) - (15*b^(5/2)*e^3*sqrt(pi)*erfi((2*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(16384*d*ℯ^((4*a)/b)) - (15*b^(5/2)*e^3*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(512*d*ℯ^((2*a)/b))]
    @test_int [(c*e + d*e*x)^2*(a + b*acosh(c + d*x))^(5/2), x, 26, (5*b^2*e^2*(c + d*x)*sqrt(a + b*acosh(c + d*x)))/(6*d) + (5*b^2*e^2*(c + d*x)^3*sqrt(a + b*acosh(c + d*x)))/(36*d) - (5*b*e^2*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^(3/2))/(9*d) - (5*b*e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^(3/2))/(18*d) + (e^2*(c + d*x)^3*(a + b*acosh(c + d*x))^(5/2))/(3*d) - (15*b^(5/2)*e^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(64*d) - (5*b^(5/2)*e^2*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(576*d) - (15*b^(5/2)*e^2*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(64*d*ℯ^(a/b)) - (5*b^(5/2)*e^2*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(576*d*ℯ^((3*a)/b))]
    @test_int [(c*e + d*e*x)*(a + b*acosh(c + d*x))^(5/2), x, 14, (-15*b^2*e*sqrt(a + b*acosh(c + d*x)))/(64*d) + (15*b^2*e*(c + d*x)^2*sqrt(a + b*acosh(c + d*x)))/(32*d) - (5*b*e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^(3/2))/(8*d) - (e*(a + b*acosh(c + d*x))^(5/2))/(4*d) + (e*(c + d*x)^2*(a + b*acosh(c + d*x))^(5/2))/(2*d) - (15*b^(5/2)*e*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(256*d) - (15*b^(5/2)*e*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(256*d*ℯ^((2*a)/b))]
    @test_int [(a + b*acosh(c + d*x))^(5/2), x, 10, (15*b^2*(c + d*x)*sqrt(a + b*acosh(c + d*x)))/(4*d) - (5*b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^(3/2))/(2*d) + ((c + d*x)*(a + b*acosh(c + d*x))^(5/2))/d - (15*b^(5/2)*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(16*d) - (15*b^(5/2)*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(16*d*ℯ^(a/b))]
    @test_int [1/(c*e + d*e*x)*(a + b*acosh(c + d*x))^(5/2), x, 2, Unintegrable((a + b*acosh(c + d*x))^(5/2)/(c + d*x), x)/e]

    @test_int [(c*e + d*e*x)^2*(a + b*acosh(c + d*x))^(7/2), x, 35, (-175*b^3*e^2*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*sqrt(a + b*acosh(c + d*x)))/(54*d) - (35*b^3*e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x)*sqrt(a + b*acosh(c + d*x)))/(216*d) + (35*b^2*e^2*(c + d*x)*(a + b*acosh(c + d*x))^(3/2))/(18*d) + (35*b^2*e^2*(c + d*x)^3*(a + b*acosh(c + d*x))^(3/2))/(108*d) - (7*b*e^2*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^(5/2))/(9*d) - (7*b*e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^(5/2))/(18*d) + (e^2*(c + d*x)^3*(a + b*acosh(c + d*x))^(7/2))/(3*d) - (105*b^(7/2)*e^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(128*d) - (35*b^(7/2)*e^2*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(3456*d) + (105*b^(7/2)*e^2*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(128*d*ℯ^(a/b)) + (35*b^(7/2)*e^2*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(3456*d*ℯ^((3*a)/b))]
    @test_int [(c*e + d*e*x)^1*(a + b*acosh(c + d*x))^(7/2), x, 16, (-105*b^3*e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x)*sqrt(a + b*acosh(c + d*x)))/(128*d) - (35*b^2*e*(a + b*acosh(c + d*x))^(3/2))/(64*d) + (35*b^2*e*(c + d*x)^2*(a + b*acosh(c + d*x))^(3/2))/(32*d) - (7*b*e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^(5/2))/(8*d) - (e*(a + b*acosh(c + d*x))^(7/2))/(4*d) + (e*(c + d*x)^2*(a + b*acosh(c + d*x))^(7/2))/(2*d) - (105*b^(7/2)*e*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(1024*d) + (105*b^(7/2)*e*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(1024*d*ℯ^((2*a)/b))]
    @test_int [(a + b*acosh(c + d*x))^(7/2), x, 11, (-105*b^3*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*sqrt(a + b*acosh(c + d*x)))/(8*d) + (35*b^2*(c + d*x)*(a + b*acosh(c + d*x))^(3/2))/(4*d) - (7*b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)*(a + b*acosh(c + d*x))^(5/2))/(2*d) + ((c + d*x)*(a + b*acosh(c + d*x))^(7/2))/d - (105*b^(7/2)*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(32*d) + (105*b^(7/2)*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(32*d*ℯ^(a/b))]
    @test_int [1/(c*e + d*e*x)*(a + b*acosh(c + d*x))^(7/2), x, 2, Unintegrable((a + b*acosh(c + d*x))^(7/2)/(c + d*x), x)/e]

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

    @test_int [(c*e + d*e*x)^4/sqrt(a + b*acosh(c + d*x)), x, 20, -(e^4*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(16*sqrt(b)*d) - (e^4*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(32*sqrt(b)*d) - (e^4*ℯ^((5*a)/b)*sqrt(pi/5)*erf((sqrt(5)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(32*sqrt(b)*d) + (e^4*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(16*sqrt(b)*d*ℯ^(a/b)) + (e^4*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(32*sqrt(b)*d*ℯ^((3*a)/b)) + (e^4*sqrt(pi/5)*erfi((sqrt(5)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(32*sqrt(b)*d*ℯ^((5*a)/b))]
    @test_int [(c*e + d*e*x)^3/sqrt(a + b*acosh(c + d*x)), x, 15, -(e^3*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(32*sqrt(b)*d) - (e^3*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(8*sqrt(b)*d) + (e^3*sqrt(pi)*erfi((2*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(32*sqrt(b)*d*ℯ^((4*a)/b)) + (e^3*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(8*sqrt(b)*d*ℯ^((2*a)/b))]
    @test_int [(c*e + d*e*x)^2/sqrt(a + b*acosh(c + d*x)), x, 15, -(e^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(8*sqrt(b)*d) - (e^2*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(8*sqrt(b)*d) + (e^2*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(8*sqrt(b)*d*ℯ^(a/b)) + (e^2*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(8*sqrt(b)*d*ℯ^((3*a)/b))]
    @test_int [(c*e + d*e*x)^1/sqrt(a + b*acosh(c + d*x)), x, 10, -(e*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(4*sqrt(b)*d) + (e*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(4*sqrt(b)*d*ℯ^((2*a)/b))]
    @test_int [1/sqrt(a + b*acosh(c + d*x)), x, 7, -(ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(2*sqrt(b)*d) + (sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(2*sqrt(b)*d*ℯ^(a/b))]
    @test_int [1/(c*e + d*e*x)/sqrt(a + b*acosh(c + d*x)), x, 2, Unintegrable(1/((c + d*x)*sqrt(a + b*acosh(c + d*x))), x)/e]

    @test_int [(c*e + d*e*x)^4/(a + b*acosh(c + d*x))^(3/2), x, 19, -((2*e^4*sqrt(-1 + c + d*x)*(c + d*x)^4*sqrt(1 + c + d*x))/(b*d*sqrt(a + b*acosh(c + d*x)))) + (e^4*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(8*b^(3/2)*d) + (3*e^4*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(16*b^(3/2)*d) + (e^4*ℯ^((5*a)/b)*sqrt(5*pi)*erf((sqrt(5)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(16*b^(3/2)*d) + (e^4*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(8*b^(3/2)*d)) + (3*e^4*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(ℯ^((3*a)/b)*(16*b^(3/2)*d)) + (e^4*sqrt(5*pi)*erfi((sqrt(5)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(ℯ^((5*a)/b)*(16*b^(3/2)*d))]
    @test_int [(c*e + d*e*x)^3/(a + b*acosh(c + d*x))^(3/2), x, 14, -((2*e^3*sqrt(-1 + c + d*x)*(c + d*x)^3*sqrt(1 + c + d*x))/(b*d*sqrt(a + b*acosh(c + d*x)))) + (e^3*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(4*b^(3/2)*d) + (e^3*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(2*b^(3/2)*d) + (e^3*sqrt(pi)*erfi((2*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(ℯ^((4*a)/b)*(4*b^(3/2)*d)) + (e^3*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(ℯ^((2*a)/b)*(2*b^(3/2)*d))]
    @test_int [(c*e + d*e*x)^2/(a + b*acosh(c + d*x))^(3/2), x, 14, -((2*e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x))/(b*d*sqrt(a + b*acosh(c + d*x)))) + (e^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(4*b^(3/2)*d) + (e^2*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(4*b^(3/2)*d) + (e^2*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(4*b^(3/2)*d)) + (e^2*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(ℯ^((3*a)/b)*(4*b^(3/2)*d))]
    @test_int [(c*e + d*e*x)^1/(a + b*acosh(c + d*x))^(3/2), x, 8, -((2*e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x))/(b*d*sqrt(a + b*acosh(c + d*x)))) + (e*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(b^(3/2)*d) + (e*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(ℯ^((2*a)/b)*(b^(3/2)*d))]
    @test_int [(a + b*acosh(c + d*x))^(-3/2), x, 8, -((2*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(b*d*sqrt(a + b*acosh(c + d*x)))) + (ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(b^(3/2)*d) + (sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(b^(3/2)*d))]
    @test_int [1/(c*e + d*e*x)/(a + b*acosh(c + d*x))^(3/2), x, 2, Unintegrable(1/((c + d*x)*(a + b*acosh(c + d*x))^(3/2)), x)/e]

    @test_int [(c*e + d*e*x)^4/(a + b*acosh(c + d*x))^(5/2), x, 36, (-2*e^4*sqrt(-1 + c + d*x)*(c + d*x)^4*sqrt(1 + c + d*x))/(3*b*d*(a + b*acosh(c + d*x))^(3/2)) + (16*e^4*(c + d*x)^3)/(3*b^2*d*sqrt(a + b*acosh(c + d*x))) - (20*e^4*(c + d*x)^5)/(3*b^2*d*sqrt(a + b*acosh(c + d*x))) - (e^4*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(12*b^(5/2)*d) - (3*e^4*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(8*b^(5/2)*d) - (5*e^4*ℯ^((5*a)/b)*sqrt(5*pi)*erf((sqrt(5)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(24*b^(5/2)*d) + (e^4*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(12*b^(5/2)*d*ℯ^(a/b)) + (3*e^4*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(8*b^(5/2)*d*ℯ^((3*a)/b)) + (5*e^4*sqrt(5*pi)*erfi((sqrt(5)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(24*b^(5/2)*d*ℯ^((5*a)/b))]
    @test_int [(c*e + d*e*x)^3/(a + b*acosh(c + d*x))^(5/2), x, 26, (-2*e^3*sqrt(-1 + c + d*x)*(c + d*x)^3*sqrt(1 + c + d*x))/(3*b*d*(a + b*acosh(c + d*x))^(3/2)) + (4*e^3*(c + d*x)^2)/(b^2*d*sqrt(a + b*acosh(c + d*x))) - (16*e^3*(c + d*x)^4)/(3*b^2*d*sqrt(a + b*acosh(c + d*x))) - (2*e^3*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(3*b^(5/2)*d) - (e^3*ℯ^((2*a)/b)*sqrt(2*pi)*erf((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(3*b^(5/2)*d) + (2*e^3*sqrt(pi)*erfi((2*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(3*b^(5/2)*d*ℯ^((4*a)/b)) + (e^3*sqrt(2*pi)*erfi((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(3*b^(5/2)*d*ℯ^((2*a)/b))]
    @test_int [(c*e + d*e*x)^2/(a + b*acosh(c + d*x))^(5/2), x, 24, (-2*e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x))/(3*b*d*(a + b*acosh(c + d*x))^(3/2)) + (8*e^2*(c + d*x))/(3*b^2*d*sqrt(a + b*acosh(c + d*x))) - (4*e^2*(c + d*x)^3)/(b^2*d*sqrt(a + b*acosh(c + d*x))) - (e^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(6*b^(5/2)*d) - (e^2*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(2*b^(5/2)*d) + (e^2*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(6*b^(5/2)*d*ℯ^(a/b)) + (e^2*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(2*b^(5/2)*d*ℯ^((3*a)/b))]
    @test_int [(c*e + d*e*x)^1/(a + b*acosh(c + d*x))^(5/2), x, 13, (-2*e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x))/(3*b*d*(a + b*acosh(c + d*x))^(3/2)) + (4*e)/(3*b^2*d*sqrt(a + b*acosh(c + d*x))) - (8*e*(c + d*x)^2)/(3*b^2*d*sqrt(a + b*acosh(c + d*x))) - (2*e*ℯ^((2*a)/b)*sqrt(2*pi)*erf((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(3*b^(5/2)*d) + (2*e*sqrt(2*pi)*erfi((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(3*b^(5/2)*d*ℯ^((2*a)/b))]
    @test_int [(a + b*acosh(c + d*x))^(-5/2), x, 9, (-2*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(3*b*d*(a + b*acosh(c + d*x))^(3/2)) - (4*(c + d*x))/(3*b^2*d*sqrt(a + b*acosh(c + d*x))) - (2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(3*b^(5/2)*d) + (2*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(3*b^(5/2)*d*ℯ^(a/b))]
    @test_int [1/(c*e + d*e*x)/(a + b*acosh(c + d*x))^(5/2), x, 2, Unintegrable(1/((c + d*x)*(a + b*acosh(c + d*x))^(5/2)), x)/e]

    @test_int [(c*e + d*e*x)^4/(a + b*acosh(c + d*x))^(7/2), x, 34, (-2*e^4*sqrt(-1 + c + d*x)*(c + d*x)^4*sqrt(1 + c + d*x))/(5*b*d*(a + b*acosh(c + d*x))^(5/2)) + (16*e^4*(c + d*x)^3)/(15*b^2*d*(a + b*acosh(c + d*x))^(3/2)) - (4*e^4*(c + d*x)^5)/(3*b^2*d*(a + b*acosh(c + d*x))^(3/2)) + (32*e^4*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x))/(5*b^3*d*sqrt(a + b*acosh(c + d*x))) - (40*e^4*sqrt(-1 + c + d*x)*(c + d*x)^4*sqrt(1 + c + d*x))/(3*b^3*d*sqrt(a + b*acosh(c + d*x))) + (e^4*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(30*b^(7/2)*d) + (9*e^4*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(20*b^(7/2)*d) + (5*e^4*ℯ^((5*a)/b)*sqrt(5*pi)*erf((sqrt(5)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(12*b^(7/2)*d) + (e^4*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(30*b^(7/2)*d*ℯ^(a/b)) + (9*e^4*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(20*b^(7/2)*d*ℯ^((3*a)/b)) + (5*e^4*sqrt(5*pi)*erfi((sqrt(5)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(12*b^(7/2)*d*ℯ^((5*a)/b))]
    @test_int [(c*e + d*e*x)^3/(a + b*acosh(c + d*x))^(7/2), x, 23, (-2*e^3*sqrt(-1 + c + d*x)*(c + d*x)^3*sqrt(1 + c + d*x))/(5*b*d*(a + b*acosh(c + d*x))^(5/2)) + (4*e^3*(c + d*x)^2)/(5*b^2*d*(a + b*acosh(c + d*x))^(3/2)) - (16*e^3*(c + d*x)^4)/(15*b^2*d*(a + b*acosh(c + d*x))^(3/2)) + (16*e^3*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x))/(5*b^3*d*sqrt(a + b*acosh(c + d*x))) - (128*e^3*sqrt(-1 + c + d*x)*(c + d*x)^3*sqrt(1 + c + d*x))/(15*b^3*d*sqrt(a + b*acosh(c + d*x))) + (16*e^3*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(15*b^(7/2)*d) + (4*e^3*ℯ^((2*a)/b)*sqrt(2*pi)*erf((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(15*b^(7/2)*d) + (16*e^3*sqrt(pi)*erfi((2*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(15*b^(7/2)*d*ℯ^((4*a)/b)) + (4*e^3*sqrt(2*pi)*erfi((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(15*b^(7/2)*d*ℯ^((2*a)/b))]
    @test_int [(c*e + d*e*x)^2/(a + b*acosh(c + d*x))^(7/2), x, 24, (-2*e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x))/(5*b*d*(a + b*acosh(c + d*x))^(5/2)) + (8*e^2*(c + d*x))/(15*b^2*d*(a + b*acosh(c + d*x))^(3/2)) - (4*e^2*(c + d*x)^3)/(5*b^2*d*(a + b*acosh(c + d*x))^(3/2)) + (16*e^2*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(15*b^3*d*sqrt(a + b*acosh(c + d*x))) - (24*e^2*sqrt(-1 + c + d*x)*(c + d*x)^2*sqrt(1 + c + d*x))/(5*b^3*d*sqrt(a + b*acosh(c + d*x))) + (e^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(15*b^(7/2)*d) + (3*e^2*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(5*b^(7/2)*d) + (e^2*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(15*b^(7/2)*d*ℯ^(a/b)) + (3*e^2*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(5*b^(7/2)*d*ℯ^((3*a)/b))]
    @test_int [(c*e + d*e*x)/(a + b*acosh(c + d*x))^(7/2), x, 11, (-2*e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x))/(5*b*d*(a + b*acosh(c + d*x))^(5/2)) + (4*e)/(15*b^2*d*(a + b*acosh(c + d*x))^(3/2)) - (8*e*(c + d*x)^2)/(15*b^2*d*(a + b*acosh(c + d*x))^(3/2)) - (32*e*sqrt(-1 + c + d*x)*(c + d*x)*sqrt(1 + c + d*x))/(15*b^3*d*sqrt(a + b*acosh(c + d*x))) + (8*e*ℯ^((2*a)/b)*sqrt(2*pi)*erf((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(15*b^(7/2)*d) + (8*e*sqrt(2*pi)*erfi((sqrt(2)*sqrt(a + b*acosh(c + d*x)))/sqrt(b)))/(15*b^(7/2)*d*ℯ^((2*a)/b))]
    @test_int [(a + b*acosh(c + d*x))^(-7/2), x, 10, (-2*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(5*b*d*(a + b*acosh(c + d*x))^(5/2)) - (4*(c + d*x))/(15*b^2*d*(a + b*acosh(c + d*x))^(3/2)) - (8*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(15*b^3*d*sqrt(a + b*acosh(c + d*x))) + (4*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(15*b^(7/2)*d) + (4*sqrt(pi)*erfi(sqrt(a + b*acosh(c + d*x))/sqrt(b)))/(15*b^(7/2)*d*ℯ^(a/b))]
    @test_int [1/(c*e + d*e*x)/(a + b*acosh(c + d*x))^(7/2), x, 2, Unintegrable(1/((c + d*x)*(a + b*acosh(c + d*x))^(7/2)), x)/e]

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

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

    @test_int [(c*e + d*e*x)^(7/2)*(a + b*acosh(c + d*x)), x, 8, -((28*b*e^2*sqrt(-1 + c + d*x)*(e*(c + d*x))^(3/2)*sqrt(1 + c + d*x))/(405*d)) - (4*b*sqrt(-1 + c + d*x)*(e*(c + d*x))^(7/2)*sqrt(1 + c + d*x))/(81*d) + (2*(e*(c + d*x))^(9/2)*(a + b*acosh(c + d*x)))/(9*d*e) - (28*b*e^3*sqrt(1 - c - d*x)*sqrt(e*(c + d*x))*Elliptic.E(asin(sqrt(1 + c + d*x)/sqrt(2)), 2))/(135*d*sqrt(-c - d*x)*sqrt(-1 + c + d*x))]
    @test_int [(c*e + d*e*x)^(5/2)*(a + b*acosh(c + d*x)), x, 8, -((20*b*e^2*sqrt(-1 + c + d*x)*sqrt(e*(c + d*x))*sqrt(1 + c + d*x))/(147*d)) - (4*b*sqrt(-1 + c + d*x)*(e*(c + d*x))^(5/2)*sqrt(1 + c + d*x))/(49*d) + (2*(e*(c + d*x))^(7/2)*(a + b*acosh(c + d*x)))/(7*d*e) - (20*b*e^(5/2)*sqrt(1 - c - d*x)*Elliptic.F(asin(sqrt(e*(c + d*x))/sqrt(e)), -1))/(147*d*sqrt(-1 + c + d*x))]
    @test_int [(c*e + d*e*x)^(3/2)*(a + b*acosh(c + d*x)), x, 6, -((4*b*sqrt(-1 + c + d*x)*(e*(c + d*x))^(3/2)*sqrt(1 + c + d*x))/(25*d)) + (2*(e*(c + d*x))^(5/2)*(a + b*acosh(c + d*x)))/(5*d*e) - (12*b*e*sqrt(1 - c - d*x)*sqrt(e*(c + d*x))*Elliptic.E(asin(sqrt(1 + c + d*x)/sqrt(2)), 2))/(25*d*sqrt(-c - d*x)*sqrt(-1 + c + d*x))]
    @test_int [sqrt(c*e + d*e*x)*(a + b*acosh(c + d*x)), x, 6, -((4*b*sqrt(-1 + c + d*x)*sqrt(e*(c + d*x))*sqrt(1 + c + d*x))/(9*d)) + (2*(e*(c + d*x))^(3/2)*(a + b*acosh(c + d*x)))/(3*d*e) - (4*b*sqrt(e)*sqrt(1 - c - d*x)*Elliptic.F(asin(sqrt(e*(c + d*x))/sqrt(e)), -1))/(9*d*sqrt(-1 + c + d*x))]
    @test_int [(a + b*acosh(c + d*x))/sqrt(c*e + d*e*x), x, 4, (2*sqrt(e*(c + d*x))*(a + b*acosh(c + d*x)))/(d*e) - (4*b*sqrt(1 - c - d*x)*sqrt(e*(c + d*x))*Elliptic.E(asin(sqrt(1 + c + d*x)/sqrt(2)), 2))/(d*e*sqrt(-c - d*x)*sqrt(-1 + c + d*x))]
    @test_int [(a + b*acosh(c + d*x))/(c*e + d*e*x)^(3/2), x, 4, -((2*(a + b*acosh(c + d*x)))/(d*e*sqrt(e*(c + d*x)))) + (4*b*sqrt(1 - c - d*x)*Elliptic.F(asin(sqrt(e*(c + d*x))/sqrt(e)), -1))/(d*e^(3/2)*sqrt(-1 + c + d*x))]
    @test_int [(a + b*acosh(c + d*x))/(c*e + d*e*x)^(5/2), x, 7, (4*b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(3*d*e^2*sqrt(e*(c + d*x))) - (2*(a + b*acosh(c + d*x)))/(3*d*e*(e*(c + d*x))^(3/2)) - (4*b*sqrt(1 - c - d*x)*sqrt(e*(c + d*x))*Elliptic.E(asin(sqrt(1 + c + d*x)/sqrt(2)), 2))/(3*d*e^3*sqrt(-c - d*x)*sqrt(-1 + c + d*x))]
    @test_int [(a + b*acosh(c + d*x))/(c*e + d*e*x)^(7/2), x, 7, (4*b*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))/(15*d*e^2*(e*(c + d*x))^(3/2)) - (2*(a + b*acosh(c + d*x)))/(5*d*e*(e*(c + d*x))^(5/2)) + (4*b*sqrt(1 - c - d*x)*Elliptic.F(asin(sqrt(e*(c + d*x))/sqrt(e)), -1))/(15*d*e^(7/2)*sqrt(-1 + c + d*x))]

    @test_int [(c*e + d*e*x)^(7/2)*(a + b*acosh(c + d*x))^2, x, 3, (2*(e*(c + d*x))^(9/2)*(a + b*acosh(c + d*x))^2)/(9*d*e) - (1/(99*d*e^2*sqrt(-1 + c + d*x)))*(8*b*sqrt(1 - c - d*x)*(e*(c + d*x))^(11/2)*(a + b*acosh(c + d*x))*HypergeometricFunctions._₂F₁(1/2, 11/4, 15/4, (c + d*x)^2)) - (16*b^2*(e*(c + d*x))^(13/2)*HypergeometricPFQ([1, 13/4, 13/4], [15/4, 17/4], (c + d*x)^2))/(1287*d*e^3)]
    @test_int [(c*e + d*e*x)^(5/2)*(a + b*acosh(c + d*x))^2, x, 3, (2*(e*(c + d*x))^(7/2)*(a + b*acosh(c + d*x))^2)/(7*d*e) - (1/(63*d*e^2*sqrt(-1 + c + d*x)))*(8*b*sqrt(1 - c - d*x)*(e*(c + d*x))^(9/2)*(a + b*acosh(c + d*x))*HypergeometricFunctions._₂F₁(1/2, 9/4, 13/4, (c + d*x)^2)) - (16*b^2*(e*(c + d*x))^(11/2)*HypergeometricPFQ([1, 11/4, 11/4], [13/4, 15/4], (c + d*x)^2))/(693*d*e^3)]
    @test_int [(c*e + d*e*x)^(3/2)*(a + b*acosh(c + d*x))^2, x, 3, (2*(e*(c + d*x))^(5/2)*(a + b*acosh(c + d*x))^2)/(5*d*e) - (1/(35*d*e^2*sqrt(-1 + c + d*x)))*(8*b*sqrt(1 - c - d*x)*(e*(c + d*x))^(7/2)*(a + b*acosh(c + d*x))*HypergeometricFunctions._₂F₁(1/2, 7/4, 11/4, (c + d*x)^2)) - (16*b^2*(e*(c + d*x))^(9/2)*HypergeometricPFQ([1, 9/4, 9/4], [11/4, 13/4], (c + d*x)^2))/(315*d*e^3)]
    @test_int [sqrt(c*e + d*e*x)*(a + b*acosh(c + d*x))^2, x, 3, (2*(e*(c + d*x))^(3/2)*(a + b*acosh(c + d*x))^2)/(3*d*e) - (8*b*sqrt(1 - c - d*x)*(e*(c + d*x))^(5/2)*(a + b*acosh(c + d*x))*HypergeometricFunctions._₂F₁(1/2, 5/4, 9/4, (c + d*x)^2))/(15*d*e^2*sqrt(-1 + c + d*x)) - (16*b^2*(e*(c + d*x))^(7/2)*HypergeometricPFQ([1, 7/4, 7/4], [9/4, 11/4], (c + d*x)^2))/(105*d*e^3)]
    @test_int [(a + b*acosh(c + d*x))^2/sqrt(c*e + d*e*x), x, 3, (2*sqrt(e*(c + d*x))*(a + b*acosh(c + d*x))^2)/(d*e) - (8*b*sqrt(1 - c - d*x)*(e*(c + d*x))^(3/2)*(a + b*acosh(c + d*x))*HypergeometricFunctions._₂F₁(1/2, 3/4, 7/4, (c + d*x)^2))/(3*d*e^2*sqrt(-1 + c + d*x)) - (16*b^2*(e*(c + d*x))^(5/2)*HypergeometricPFQ([1, 5/4, 5/4], [7/4, 9/4], (c + d*x)^2))/(15*d*e^3)]
    @test_int [(a + b*acosh(c + d*x))^2/(c*e + d*e*x)^(3/2), x, 3, -((2*(a + b*acosh(c + d*x))^2)/(d*e*sqrt(e*(c + d*x)))) + (8*b*sqrt(1 - c - d*x)*sqrt(e*(c + d*x))*(a + b*acosh(c + d*x))*HypergeometricFunctions._₂F₁(1/4, 1/2, 5/4, (c + d*x)^2))/(d*e^2*sqrt(-1 + c + d*x)) + (16*b^2*(e*(c + d*x))^(3/2)*HypergeometricPFQ([3/4, 3/4, 1], [5/4, 7/4], (c + d*x)^2))/(3*d*e^3)]
    @test_int [(a + b*acosh(c + d*x))^2/(c*e + d*e*x)^(5/2), x, 3, -((2*(a + b*acosh(c + d*x))^2)/(3*d*e*(e*(c + d*x))^(3/2))) - (8*b*sqrt(1 - c - d*x)*(a + b*acosh(c + d*x))*HypergeometricFunctions._₂F₁(-(1/4), 1/2, 3/4, (c + d*x)^2))/(3*d*e^2*sqrt(-1 + c + d*x)*sqrt(e*(c + d*x))) - (16*b^2*sqrt(e*(c + d*x))*HypergeometricPFQ([1/4, 1/4, 1], [3/4, 5/4], (c + d*x)^2))/(3*d*e^3)]
    @test_int [(a + b*acosh(c + d*x))^2/(c*e + d*e*x)^(7/2), x, 3, -((2*(a + b*acosh(c + d*x))^2)/(5*d*e*(e*(c + d*x))^(5/2))) - (8*b*sqrt(1 - c - d*x)*(a + b*acosh(c + d*x))*HypergeometricFunctions._₂F₁(-(3/4), 1/2, 1/4, (c + d*x)^2))/(15*d*e^2*sqrt(-1 + c + d*x)*(e*(c + d*x))^(3/2)) + (16*b^2*HypergeometricPFQ([-(1/4), -(1/4), 1], [1/4, 3/4], (c + d*x)^2))/(15*d*e^3*sqrt(e*(c + d*x)))]

    @test_int [(c*e + d*e*x)^(3/2)*(a + b*acosh(c + d*x))^3, x, 2, (2*(e*(c + d*x))^(5/2)*(a + b*acosh(c + d*x))^3)/(5*d*e) - (6*b*Unintegrable(((e*(c + d*x))^(5/2)*(a + b*acosh(c + d*x))^2)/(sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)), x))/(5*e)]
    @test_int [sqrt(c*e + d*e*x)*(a + b*acosh(c + d*x))^3, x, 2, (2*(e*(c + d*x))^(3/2)*(a + b*acosh(c + d*x))^3)/(3*d*e) - (2*b*Unintegrable(((e*(c + d*x))^(3/2)*(a + b*acosh(c + d*x))^2)/(sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)), x))/e]
    @test_int [(a + b*acosh(c + d*x))^3/sqrt(c*e + d*e*x), x, 2, (2*sqrt(e*(c + d*x))*(a + b*acosh(c + d*x))^3)/(d*e) - (6*b*Unintegrable((sqrt(e*(c + d*x))*(a + b*acosh(c + d*x))^2)/(sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)), x))/e]
    @test_int [(a + b*acosh(c + d*x))^3/(c*e + d*e*x)^(3/2), x, 2, -((2*(a + b*acosh(c + d*x))^3)/(d*e*sqrt(e*(c + d*x)))) + (6*b*Unintegrable((a + b*acosh(c + d*x))^2/(sqrt(-1 + c + d*x)*sqrt(e*(c + d*x))*sqrt(1 + c + d*x)), x))/e]
    @test_int [(a + b*acosh(c + d*x))^3/(c*e + d*e*x)^(5/2), x, 2, -((2*(a + b*acosh(c + d*x))^3)/(3*d*e*(e*(c + d*x))^(3/2))) + (2*b*Unintegrable((a + b*acosh(c + d*x))^2/(sqrt(-1 + c + d*x)*(e*(c + d*x))^(3/2)*sqrt(1 + c + d*x)), x))/e]
    @test_int [(a + b*acosh(c + d*x))^3/(c*e + d*e*x)^(7/2), x, 2, -((2*(a + b*acosh(c + d*x))^3)/(5*d*e*(e*(c + d*x))^(5/2))) + (6*b*Unintegrable((a + b*acosh(c + d*x))^2/(sqrt(-1 + c + d*x)*(e*(c + d*x))^(5/2)*sqrt(1 + c + d*x)), x))/(5*e)]

    @test_int [(c*e + d*e*x)^(3/2)*(a + b*acosh(c + d*x))^4, x, 2, (2*(e*(c + d*x))^(5/2)*(a + b*acosh(c + d*x))^4)/(5*d*e) - (8*b*Unintegrable(((e*(c + d*x))^(5/2)*(a + b*acosh(c + d*x))^3)/(sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)), x))/(5*e)]
    @test_int [sqrt(c*e + d*e*x)*(a + b*acosh(c + d*x))^4, x, 2, (2*(e*(c + d*x))^(3/2)*(a + b*acosh(c + d*x))^4)/(3*d*e) - (8*b*Unintegrable(((e*(c + d*x))^(3/2)*(a + b*acosh(c + d*x))^3)/(sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)), x))/(3*e)]
    @test_int [(a + b*acosh(c + d*x))^4/sqrt(c*e + d*e*x), x, 2, (2*sqrt(e*(c + d*x))*(a + b*acosh(c + d*x))^4)/(d*e) - (8*b*Unintegrable((sqrt(e*(c + d*x))*(a + b*acosh(c + d*x))^3)/(sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)), x))/e]
    @test_int [(a + b*acosh(c + d*x))^4/(c*e + d*e*x)^(3/2), x, 2, -((2*(a + b*acosh(c + d*x))^4)/(d*e*sqrt(e*(c + d*x)))) + (8*b*Unintegrable((a + b*acosh(c + d*x))^3/(sqrt(-1 + c + d*x)*sqrt(e*(c + d*x))*sqrt(1 + c + d*x)), x))/e]
    @test_int [(a + b*acosh(c + d*x))^4/(c*e + d*e*x)^(5/2), x, 2, -((2*(a + b*acosh(c + d*x))^4)/(3*d*e*(e*(c + d*x))^(3/2))) + (8*b*Unintegrable((a + b*acosh(c + d*x))^3/(sqrt(-1 + c + d*x)*(e*(c + d*x))^(3/2)*sqrt(1 + c + d*x)), x))/(3*e)]
    @test_int [(a + b*acosh(c + d*x))^4/(c*e + d*e*x)^(7/2), x, 2, -((2*(a + b*acosh(c + d*x))^4)/(5*d*e*(e*(c + d*x))^(5/2))) + (8*b*Unintegrable((a + b*acosh(c + d*x))^3/(sqrt(-1 + c + d*x)*(e*(c + d*x))^(5/2)*sqrt(1 + c + d*x)), x))/(5*e)]

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

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

    @test_int [(c*e + d*e*x)^m*(a + b*acosh(c + d*x))^4, x, 2, ((e*(c + d*x))^(1 + m)*(a + b*acosh(c + d*x))^4)/(d*e*(1 + m)) - (4*b*Unintegrable(((e*(c + d*x))^(1 + m)*(a + b*acosh(c + d*x))^3)/(sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)), x))/(e*(1 + m))]
    @test_int [(c*e + d*e*x)^m*(a + b*acosh(c + d*x))^3, x, 2, ((e*(c + d*x))^(1 + m)*(a + b*acosh(c + d*x))^3)/(d*e*(1 + m)) - (3*b*Unintegrable(((e*(c + d*x))^(1 + m)*(a + b*acosh(c + d*x))^2)/(sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)), x))/(e*(1 + m))]
    @test_int [(c*e + d*e*x)^m*(a + b*acosh(c + d*x))^2, x, 3, If(13>=8, ((e*(c + d*x))^(1 + m)*(a + b*acosh(c + d*x))^2)/(d*e*(1 + m)) - (2*b*sqrt(1 - c - d*x)*(e*(c + d*x))^(2 + m)*(a + b*acosh(c + d*x))*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, (c + d*x)^2))/(d*e^2*(1 + m)*(2 + m)*sqrt(-1 + c + d*x)) - (2*b^2*(e*(c + d*x))^(3 + m)*HypergeometricPFQ([1, 3/2 + m/2, 3/2 + m/2], [2 + m/2, 5/2 + m/2], (c + d*x)^2))/(d*e^3*(1 + m)*(2 + m)*(3 + m)), ((e*(c + d*x))^(1 + m)*(a + b*acosh(c + d*x))^2)/(d*e*(1 + m)) - (2*b*sqrt(1 - c - d*x)*(e*(c + d*x))^(2 + m)*(a + b*acosh(c + d*x))*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, (c + d*x)^2))/(d*e^2*(1 + m)*(2 + m)*sqrt(-1 + c + d*x)) - (2*b^2*(e*(c + d*x))^(3 + m)*HypergeometricPFQ([1, 3/2 + m/2, 3/2 + m/2], [2 + m/2, 5/2 + m/2], (c + d*x)^2))/(d*e^3*(3 + m)*(2 + 3*m + m^2)))]
    @test_int [(c*e + d*e*x)^m*(a + b*acosh(c + d*x)), x, 5, ((e*(c + d*x))^(1 + m)*(a + b*acosh(c + d*x)))/(d*e*(1 + m)) - (b*(e*(c + d*x))^(2 + m)*(1 - (c + d*x)^2)*HypergeometricFunctions._₂F₁(1, (3 + m)/2, (4 + m)/2, (c + d*x)^2))/(d*e^2*(1 + m)*(2 + m)*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x)), ((e*(c + d*x))^(1 + m)*(a + b*acosh(c + d*x)))/(d*e*(1 + m)) - (b*(e*(c + d*x))^(2 + m)*sqrt(1 - (c + d*x)^2)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, (c + d*x)^2))/(d*e^2*(1 + m)*(2 + m)*sqrt(-1 + c + d*x)*sqrt(1 + c + d*x))]
    @test_int [(c*e + d*e*x)^m/(a + b*acosh(c + d*x)), x, 1, Unintegrable((e*(c + d*x))^m/(a + b*acosh(c + d*x)), x)]

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

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

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

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

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

    @test_int [x^2*acosh(sqrt(x)), x, 7, (-(5/48))*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*sqrt(x) - (5/72)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*x^(3/2) - (1/18)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*x^(5/2) - (5*acosh(sqrt(x)))/48 + (1/3)*x^3*acosh(sqrt(x))]
    @test_int [x^1*acosh(sqrt(x)), x, 6, (-(3/16))*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*sqrt(x) - (1/8)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*x^(3/2) - (3*acosh(sqrt(x)))/16 + (1/2)*x^2*acosh(sqrt(x))]
    @test_int [x^0*acosh(sqrt(x)), x, 5, (-(1/2))*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*sqrt(x) - acosh(sqrt(x))/2 + x*acosh(sqrt(x))]
    @test_int [acosh(sqrt(x))/x^1, x, 5, -acosh(sqrt(x))^2 + 2*acosh(sqrt(x))*log(1 + ℯ^(2*acosh(sqrt(x)))) + PolyLog(2, -ℯ^(2*acosh(sqrt(x))))]
    @test_int [acosh(sqrt(x))/x^2, x, 3, (sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x)))/sqrt(x) - acosh(sqrt(x))/x]
    @test_int [acosh(sqrt(x))/x^3, x, 4, (sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x)))/(6*x^(3/2)) + (sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x)))/(3*sqrt(x)) - acosh(sqrt(x))/(2*x^2)]

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

    @test_int [acosh(1/x), x, 3, x*asech(x) + sqrt(1/(1 + x))*sqrt(1 + x)*asin(x)]

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

    @test_int [acosh(a*x^n)/x, x, 5, -(acosh(a*x^n)^2/(2*n)) + (acosh(a*x^n)*log(1 + ℯ^(2*acosh(a*x^n))))/n + PolyLog(2, -ℯ^(2*acosh(a*x^n)))/(2*n)]

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*acosh(c+d*x^2))^n*when*c^2=1=#

    @test_int [(a + b*acosh(1 + d*x^2))^4, x, 3, 384*b^4*x - (192*b^3*(2*x^2 + d*x^4)*(a + b*acosh(1 + d*x^2)))/(x*sqrt(d*x^2)*sqrt(2 + d*x^2)) + 48*b^2*x*(a + b*acosh(1 + d*x^2))^2 - (8*b*(2*x^2 + d*x^4)*(a + b*acosh(1 + d*x^2))^3)/(x*sqrt(d*x^2)*sqrt(2 + d*x^2)) + x*(a + b*acosh(1 + d*x^2))^4]
    @test_int [(a + b*acosh(1 + d*x^2))^3, x, 7, 24*a*b^2*x - (48*b^3*sqrt((d*x^2)/(2 + d*x^2))*(2 + d*x^2))/(d*x) + 24*b^3*x*acosh(1 + d*x^2) - (6*b*(2*x^2 + d*x^4)*(a + b*acosh(1 + d*x^2))^2)/(x*sqrt(d*x^2)*sqrt(2 + d*x^2)) + x*(a + b*acosh(1 + d*x^2))^3]
    @test_int [(a + b*acosh(1 + d*x^2))^2, x, 2, 8*b^2*x - (4*b*(2*x^2 + d*x^4)*(a + b*acosh(1 + d*x^2)))/(x*sqrt(d*x^2)*sqrt(2 + d*x^2)) + x*(a + b*acosh(1 + d*x^2))^2]
    @test_int [(a + b*acosh(1 + d*x^2))^1, x, 6, a*x - (2*b*sqrt((d*x^2)/(2 + d*x^2))*(2 + d*x^2))/(d*x) + b*x*acosh(1 + d*x^2)]
    @test_int [1/(a + b*acosh(1 + d*x^2))^1, x, 1, (x*cosh(a/(2*b))*CoshIntegral((a + b*acosh(1 + d*x^2))/(2*b)))/(sqrt(2)*b*sqrt(d*x^2)) - (x*sinh(a/(2*b))*SinhIntegral((a + b*acosh(1 + d*x^2))/(2*b)))/(sqrt(2)*b*sqrt(d*x^2))]
    @test_int [1/(a + b*acosh(1 + d*x^2))^2, x, 1, -((sqrt(d*x^2)*sqrt(2 + d*x^2))/(2*b*d*x*(a + b*acosh(1 + d*x^2)))) - (x*CoshIntegral((a + b*acosh(1 + d*x^2))/(2*b))*sinh(a/(2*b)))/(2*sqrt(2)*b^2*sqrt(d*x^2)) + (x*cosh(a/(2*b))*SinhIntegral((a + b*acosh(1 + d*x^2))/(2*b)))/(2*sqrt(2)*b^2*sqrt(d*x^2))]
    @test_int [1/(a + b*acosh(1 + d*x^2))^3, x, 2, -((2*x^2 + d*x^4)/(4*b*x*sqrt(d*x^2)*sqrt(2 + d*x^2)*(a + b*acosh(1 + d*x^2))^2)) - x/(8*b^2*(a + b*acosh(1 + d*x^2))) + (x*cosh(a/(2*b))*CoshIntegral((a + b*acosh(1 + d*x^2))/(2*b)))/(8*sqrt(2)*b^3*sqrt(d*x^2)) - (x*sinh(a/(2*b))*SinhIntegral((a + b*acosh(1 + d*x^2))/(2*b)))/(8*sqrt(2)*b^3*sqrt(d*x^2))]

    @test_int [(a + b*acosh(-1 + d*x^2))^4, x, 3, 384*b^4*x + (192*b^3*(2*x^2 - d*x^4)*(a + b*acosh(-1 + d*x^2)))/(x*sqrt(d*x^2)*sqrt(-2 + d*x^2)) + 48*b^2*x*(a + b*acosh(-1 + d*x^2))^2 + (8*b*(2*x^2 - d*x^4)*(a + b*acosh(-1 + d*x^2))^3)/(x*sqrt(d*x^2)*sqrt(-2 + d*x^2)) + x*(a + b*acosh(-1 + d*x^2))^4]
    @test_int [(a + b*acosh(-1 + d*x^2))^3, x, 5, 24*a*b^2*x - 48*b^3*sqrt(1 - 2/(d*x^2))*x + 24*b^3*x*acosh(-1 + d*x^2) + (6*b*(2*x^2 - d*x^4)*(a + b*acosh(-1 + d*x^2))^2)/(x*sqrt(d*x^2)*sqrt(-2 + d*x^2)) + x*(a + b*acosh(-1 + d*x^2))^3]
    @test_int [(a + b*acosh(-1 + d*x^2))^2, x, 2, 8*b^2*x + (4*b*(2*x^2 - d*x^4)*(a + b*acosh(-1 + d*x^2)))/(x*sqrt(d*x^2)*sqrt(-2 + d*x^2)) + x*(a + b*acosh(-1 + d*x^2))^2]
    @test_int [(a + b*acosh(-1 + d*x^2))^1, x, 4, a*x - 2*b*sqrt(1 - 2/(d*x^2))*x + b*x*acosh(-1 + d*x^2)]
    @test_int [1/(a + b*acosh(-1 + d*x^2))^1, x, 1, -((x*CoshIntegral((a + b*acosh(-1 + d*x^2))/(2*b))*sinh(a/(2*b)))/(sqrt(2)*b*sqrt(d*x^2))) + (x*cosh(a/(2*b))*SinhIntegral((a + b*acosh(-1 + d*x^2))/(2*b)))/(sqrt(2)*b*sqrt(d*x^2))]
    @test_int [1/(a + b*acosh(-1 + d*x^2))^2, x, 1, -((sqrt(d*x^2)*sqrt(-2 + d*x^2))/(2*b*d*x*(a + b*acosh(-1 + d*x^2)))) + (x*cosh(a/(2*b))*CoshIntegral((a + b*acosh(-1 + d*x^2))/(2*b)))/(2*sqrt(2)*b^2*sqrt(d*x^2)) - (x*sinh(a/(2*b))*SinhIntegral((a + b*acosh(-1 + d*x^2))/(2*b)))/(2*sqrt(2)*b^2*sqrt(d*x^2))]
    @test_int [1/(a + b*acosh(-1 + d*x^2))^3, x, 2, (2*x^2 - d*x^4)/(4*b*x*sqrt(d*x^2)*sqrt(-2 + d*x^2)*(a + b*acosh(-1 + d*x^2))^2) - x/(8*b^2*(a + b*acosh(-1 + d*x^2))) - (x*CoshIntegral((a + b*acosh(-1 + d*x^2))/(2*b))*sinh(a/(2*b)))/(8*sqrt(2)*b^3*sqrt(d*x^2)) + (x*cosh(a/(2*b))*SinhIntegral((a + b*acosh(-1 + d*x^2))/(2*b)))/(8*sqrt(2)*b^3*sqrt(d*x^2))]

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

    @test_int [(a + b*acosh(1 + d*x^2))^(5/2), x, 2, -((5*b*(2*x^2 + d*x^4)*(a + b*acosh(1 + d*x^2))^(3/2))/(x*sqrt(d*x^2)*sqrt(2 + d*x^2))) + x*(a + b*acosh(1 + d*x^2))^(5/2) - (15*b^(5/2)*sqrt(pi/2)*erfi(sqrt(a + b*acosh(1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) - sinh(a/(2*b)))*sinh((1/2)*acosh(1 + d*x^2)))/(d*x) + (15*b^(5/2)*sqrt(pi/2)*erf(sqrt(a + b*acosh(1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) + sinh(a/(2*b)))*sinh((1/2)*acosh(1 + d*x^2)))/(d*x) + (30*b^2*sqrt(a + b*acosh(1 + d*x^2))*sinh((1/2)*acosh(1 + d*x^2))^2)/(d*x)]
    @test_int [(a + b*acosh(1 + d*x^2))^(3/2), x, 2, -((3*b*(2*x^2 + d*x^4)*sqrt(a + b*acosh(1 + d*x^2)))/(x*sqrt(d*x^2)*sqrt(2 + d*x^2))) + x*(a + b*acosh(1 + d*x^2))^(3/2) + (3*b^(3/2)*sqrt(pi/2)*erfi(sqrt(a + b*acosh(1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) - sinh(a/(2*b)))*sinh((1/2)*acosh(1 + d*x^2)))/(d*x) + (3*b^(3/2)*sqrt(pi/2)*erf(sqrt(a + b*acosh(1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) + sinh(a/(2*b)))*sinh((1/2)*acosh(1 + d*x^2)))/(d*x)]
    @test_int [(a + b*acosh(1 + d*x^2))^(1/2), x, 1, -((sqrt(b)*sqrt(pi/2)*erfi(sqrt(a + b*acosh(1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) - sinh(a/(2*b)))*sinh((1/2)*acosh(1 + d*x^2)))/(d*x)) + (sqrt(b)*sqrt(pi/2)*erf(sqrt(a + b*acosh(1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) + sinh(a/(2*b)))*sinh((1/2)*acosh(1 + d*x^2)))/(d*x) + (2*sqrt(a + b*acosh(1 + d*x^2))*sinh((1/2)*acosh(1 + d*x^2))^2)/(d*x)]
    @test_int [1/(a + b*acosh(1 + d*x^2))^(1/2), x, 1, (sqrt(pi/2)*erfi(sqrt(a + b*acosh(1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) - sinh(a/(2*b)))*sinh((1/2)*acosh(1 + d*x^2)))/(sqrt(b)*d*x) + (sqrt(pi/2)*erf(sqrt(a + b*acosh(1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) + sinh(a/(2*b)))*sinh((1/2)*acosh(1 + d*x^2)))/(sqrt(b)*d*x)]
    @test_int [1/(a + b*acosh(1 + d*x^2))^(3/2), x, 1, -((sqrt(d*x^2)*sqrt(2 + d*x^2))/(b*d*x*sqrt(a + b*acosh(1 + d*x^2)))) + (sqrt(pi/2)*erfi(sqrt(a + b*acosh(1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) - sinh(a/(2*b)))*sinh((1/2)*acosh(1 + d*x^2)))/(b^(3/2)*d*x) - (sqrt(pi/2)*erf(sqrt(a + b*acosh(1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) + sinh(a/(2*b)))*sinh((1/2)*acosh(1 + d*x^2)))/(b^(3/2)*d*x)]
    @test_int [1/(a + b*acosh(1 + d*x^2))^(5/2), x, 2, -((2*x^2 + d*x^4)/(3*b*x*sqrt(d*x^2)*sqrt(2 + d*x^2)*(a + b*acosh(1 + d*x^2))^(3/2))) - x/(3*b^2*sqrt(a + b*acosh(1 + d*x^2))) + (sqrt(pi/2)*erfi(sqrt(a + b*acosh(1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) - sinh(a/(2*b)))*sinh((1/2)*acosh(1 + d*x^2)))/(3*b^(5/2)*d*x) + (sqrt(pi/2)*erf(sqrt(a + b*acosh(1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) + sinh(a/(2*b)))*sinh((1/2)*acosh(1 + d*x^2)))/(3*b^(5/2)*d*x)]
    @test_int [1/(a + b*acosh(1 + d*x^2))^(7/2), x, 2, -((2*x^2 + d*x^4)/(5*b*x*sqrt(d*x^2)*sqrt(2 + d*x^2)*(a + b*acosh(1 + d*x^2))^(5/2))) - x/(15*b^2*(a + b*acosh(1 + d*x^2))^(3/2)) - (sqrt(d*x^2)*sqrt(2 + d*x^2))/(15*b^3*d*x*sqrt(a + b*acosh(1 + d*x^2))) + (sqrt(pi/2)*erfi(sqrt(a + b*acosh(1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) - sinh(a/(2*b)))*sinh((1/2)*acosh(1 + d*x^2)))/(15*b^(7/2)*d*x) - (sqrt(pi/2)*erf(sqrt(a + b*acosh(1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) + sinh(a/(2*b)))*sinh((1/2)*acosh(1 + d*x^2)))/(15*b^(7/2)*d*x)]

    @test_int [(a + b*acosh(-1 + d*x^2))^(5/2), x, 2, (5*b*(2*x^2 - d*x^4)*(a + b*acosh(-1 + d*x^2))^(3/2))/(x*sqrt(d*x^2)*sqrt(-2 + d*x^2)) + x*(a + b*acosh(-1 + d*x^2))^(5/2) + (30*b^2*sqrt(a + b*acosh(-1 + d*x^2))*cosh((1/2)*acosh(-1 + d*x^2))^2)/(d*x) - (15*b^(5/2)*sqrt(pi/2)*cosh((1/2)*acosh(-1 + d*x^2))*erfi(sqrt(a + b*acosh(-1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) - sinh(a/(2*b))))/(d*x) - (15*b^(5/2)*sqrt(pi/2)*cosh((1/2)*acosh(-1 + d*x^2))*erf(sqrt(a + b*acosh(-1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) + sinh(a/(2*b))))/(d*x)]
    @test_int [(a + b*acosh(-1 + d*x^2))^(3/2), x, 2, (3*b*(2*x^2 - d*x^4)*sqrt(a + b*acosh(-1 + d*x^2)))/(x*sqrt(d*x^2)*sqrt(-2 + d*x^2)) + x*(a + b*acosh(-1 + d*x^2))^(3/2) + (3*b^(3/2)*sqrt(pi/2)*cosh((1/2)*acosh(-1 + d*x^2))*erfi(sqrt(a + b*acosh(-1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) - sinh(a/(2*b))))/(d*x) - (3*b^(3/2)*sqrt(pi/2)*cosh((1/2)*acosh(-1 + d*x^2))*erf(sqrt(a + b*acosh(-1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) + sinh(a/(2*b))))/(d*x)]
    @test_int [(a + b*acosh(-1 + d*x^2))^(1/2), x, 1, (2*sqrt(a + b*acosh(-1 + d*x^2))*cosh((1/2)*acosh(-1 + d*x^2))^2)/(d*x) - (sqrt(b)*sqrt(pi/2)*cosh((1/2)*acosh(-1 + d*x^2))*erfi(sqrt(a + b*acosh(-1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) - sinh(a/(2*b))))/(d*x) - (sqrt(b)*sqrt(pi/2)*cosh((1/2)*acosh(-1 + d*x^2))*erf(sqrt(a + b*acosh(-1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) + sinh(a/(2*b))))/(d*x)]
    @test_int [1/(a + b*acosh(-1 + d*x^2))^(1/2), x, 1, (sqrt(pi/2)*cosh((1/2)*acosh(-1 + d*x^2))*erfi(sqrt(a + b*acosh(-1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) - sinh(a/(2*b))))/(sqrt(b)*d*x) - (sqrt(pi/2)*cosh((1/2)*acosh(-1 + d*x^2))*erf(sqrt(a + b*acosh(-1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) + sinh(a/(2*b))))/(sqrt(b)*d*x)]
    @test_int [1/(a + b*acosh(-1 + d*x^2))^(3/2), x, 1, -((sqrt(d*x^2)*sqrt(-2 + d*x^2))/(b*d*x*sqrt(a + b*acosh(-1 + d*x^2)))) + (sqrt(pi/2)*cosh((1/2)*acosh(-1 + d*x^2))*erfi(sqrt(a + b*acosh(-1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) - sinh(a/(2*b))))/(b^(3/2)*d*x) + (sqrt(pi/2)*cosh((1/2)*acosh(-1 + d*x^2))*erf(sqrt(a + b*acosh(-1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) + sinh(a/(2*b))))/(b^(3/2)*d*x)]
    @test_int [1/(a + b*acosh(-1 + d*x^2))^(5/2), x, 2, (2*x^2 - d*x^4)/(3*b*x*sqrt(d*x^2)*sqrt(-2 + d*x^2)*(a + b*acosh(-1 + d*x^2))^(3/2)) - x/(3*b^2*sqrt(a + b*acosh(-1 + d*x^2))) + (sqrt(pi/2)*cosh((1/2)*acosh(-1 + d*x^2))*erfi(sqrt(a + b*acosh(-1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) - sinh(a/(2*b))))/(3*b^(5/2)*d*x) - (sqrt(pi/2)*cosh((1/2)*acosh(-1 + d*x^2))*erf(sqrt(a + b*acosh(-1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) + sinh(a/(2*b))))/(3*b^(5/2)*d*x)]
    @test_int [1/(a + b*acosh(-1 + d*x^2))^(7/2), x, 2, (2*x^2 - d*x^4)/(5*b*x*sqrt(d*x^2)*sqrt(-2 + d*x^2)*(a + b*acosh(-1 + d*x^2))^(5/2)) - x/(15*b^2*(a + b*acosh(-1 + d*x^2))^(3/2)) - (sqrt(d*x^2)*sqrt(-2 + d*x^2))/(15*b^3*d*x*sqrt(a + b*acosh(-1 + d*x^2))) + (sqrt(pi/2)*cosh((1/2)*acosh(-1 + d*x^2))*erfi(sqrt(a + b*acosh(-1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) - sinh(a/(2*b))))/(15*b^(7/2)*d*x) + (sqrt(pi/2)*cosh((1/2)*acosh(-1 + d*x^2))*erf(sqrt(a + b*acosh(-1 + d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(a/(2*b)) + sinh(a/(2*b))))/(15*b^(7/2)*d*x)]

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

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

    @test_int [(a + b*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))^3/(1 - c^2*x^2), x, 8, -((a + b*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))^4/(4*b*c)) - ((a + b*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))^3*log(1 + ℯ^(-2*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))))/c + (3*b*(a + b*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))^2*PolyLog(2, -ℯ^(-2*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))))/(2*c) + (3*b^2*(a + b*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))*PolyLog(3, -ℯ^(-2*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))))/(2*c) + (3*b^3*PolyLog(4, -ℯ^(-2*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))))/(4*c)]
    @test_int [(a + b*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))^2/(1 - c^2*x^2), x, 7, -((a + b*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))^3/(3*b*c)) - ((a + b*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))^2*log(1 + ℯ^(-2*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))))/c + (b*(a + b*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))*PolyLog(2, -ℯ^(-2*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))))/c + (b^2*PolyLog(3, -ℯ^(-2*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))))/(2*c)]
    @test_int [(a + b*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))^1/(1 - c^2*x^2), x, 6, -((a + b*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))^2/(2*b*c)) - ((a + b*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))*log(1 + ℯ^(-2*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))))/c + (b*PolyLog(2, -ℯ^(-2*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))))/(2*c)]
    @test_int [1/((a + b*acosh(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*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))), x)]
    @test_int [1/((a + b*acosh(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*acosh(sqrt(1 - c*x)/sqrt(1 + c*x)))^2), x)]

    #= ::Title::Closed:: =#
    #=Integrands*involving*inverse*hyperbolic*cosines*of*exponentials=#

    #= ::Subsection::Closed:: =#
    #=x^m*acosh(c*ℯ^(a+b*x))=#

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

    #= ::Title::Closed:: =#
    #=Integrands*involving*exponentials*of*inverse*hyperbolic*cosines=#

    #= ::Subsection::Closed:: =#
    #=x^m*ℯ^(acosh(a+b*x)^n)=#

    @test_int [x^3*ℯ^acosh(a + b*x), x, 5, 1/(ℯ^(3*acosh(a + b*x))*(48*b^4)) - (3*a)/(ℯ^(2*acosh(a + b*x))*(16*b^4)) + (1 + 6*a^2)/(ℯ^acosh(a + b*x)*(8*b^4)) - (a*(3 + 4*a^2)*ℯ^(2*acosh(a + b*x)))/(16*b^4) + ((1 + 6*a^2)*ℯ^(3*acosh(a + b*x)))/(24*b^4) - (3*a*ℯ^(4*acosh(a + b*x)))/(32*b^4) + ℯ^(5*acosh(a + b*x))/(80*b^4) + (a*(3 + 4*a^2)*acosh(a + b*x))/(8*b^4)]
    @test_int [x^2*ℯ^acosh(a + b*x), x, 5, 1/(ℯ^(2*acosh(a + b*x))*(16*b^3)) - a/(ℯ^acosh(a + b*x)*(2*b^3)) + ((1 + 4*a^2)*ℯ^(2*acosh(a + b*x)))/(16*b^3) - (a*ℯ^(3*acosh(a + b*x)))/(6*b^3) + ℯ^(4*acosh(a + b*x))/(32*b^3) - ((1 + 4*a^2)*acosh(a + b*x))/(8*b^3)]
    @test_int [x^1*ℯ^acosh(a + b*x), x, 5, 1/(ℯ^acosh(a + b*x)*(4*b^2)) - (a*ℯ^(2*acosh(a + b*x)))/(4*b^2) + ℯ^(3*acosh(a + b*x))/(12*b^2) + (a*acosh(a + b*x))/(2*b^2)]
    @test_int [x^0*ℯ^acosh(a + b*x), x, 5, ℯ^(2*acosh(a + b*x))/(4*b) - acosh(a + b*x)/(2*b)]
    @test_int [ℯ^acosh(a + b*x)/x^1, x, 9, b*x + sqrt(-1 + a + b*x)*sqrt(1 + a + b*x) + 2*a*asinh(sqrt(-1 + a + b*x)/sqrt(2)) + 2*sqrt(1 - a^2)*atan((sqrt(1 - a)*sqrt(1 + a + b*x))/(sqrt(1 + a)*sqrt(-1 + a + b*x))) + a*log(x)]
    @test_int [ℯ^acosh(a + b*x)/x^2, x, 9, -(a/x) - (sqrt(-1 + a + b*x)*sqrt(1 + a + b*x))/x + 2*b*asinh(sqrt(-1 + a + b*x)/sqrt(2)) - (2*a*b*atan((sqrt(1 - a)*sqrt(1 + a + b*x))/(sqrt(1 + a)*sqrt(-1 + a + b*x))))/sqrt(1 - a^2) + b*log(x)]
    @test_int [ℯ^acosh(a + b*x)/x^3, x, 7, -(a/(2*x^2)) - b/x + (b*sqrt(-1 + a + b*x)*sqrt(1 + a + b*x))/(2*(1 - a^2)*x) - (sqrt(-1 + a + b*x)*(1 + a + b*x)^(3/2))/(2*(1 + a)*x^2) - (b^2*atan((sqrt(1 - a)*sqrt(1 + a + b*x))/(sqrt(1 + a)*sqrt(-1 + a + b*x))))/(1 - a^2)^(3/2)]
    @test_int [ℯ^acosh(a + b*x)/x^4, x, 8, -(a/(3*x^3)) - b/(2*x^2) + (a*b^2*sqrt(-1 + a + b*x)*sqrt(1 + a + b*x))/(2*(1 - a^2)^2*x) - (a*b*sqrt(-1 + a + b*x)*(1 + a + b*x)^(3/2))/(2*(1 - a)*(1 + a)^2*x^2) + ((-1 + a + b*x)^(3/2)*(1 + a + b*x)^(3/2))/(3*(1 - a^2)*x^3) - (a*b^3*atan((sqrt(1 - a)*sqrt(1 + a + b*x))/(sqrt(1 + a)*sqrt(-1 + a + b*x))))/(1 - a^2)^(5/2)]
    @test_int [ℯ^acosh(a + b*x)/x^5, x, 10, -(a/(4*x^4)) - b/(3*x^3) - (sqrt(-1 + a + b*x)*sqrt(1 + a + b*x))/(4*x^4) + (a*b*sqrt(-1 + a + b*x)*sqrt(1 + a + b*x))/(12*(1 - a^2)*x^3) + ((3 + 2*a^2)*b^2*sqrt(-1 + a + b*x)*sqrt(1 + a + b*x))/(24*(1 - a^2)^2*x^2) + (a*(13 + 2*a^2)*b^3*sqrt(-1 + a + b*x)*sqrt(1 + a + b*x))/(24*(1 - a^2)^3*x) - ((1 + 4*a^2)*b^4*atan((sqrt(1 - a)*sqrt(1 + a + b*x))/(sqrt(1 + a)*sqrt(-1 + a + b*x))))/(4*(1 - a^2)^(7/2))]

    @test_int [x^3*ℯ^(acosh(a + b*x)^2), x, 37, -((sqrt(pi)*erfi(-2 + acosh(a + b*x)))/(32*b^4*ℯ^4)) - (sqrt(pi)*erfi(-1 + acosh(a + b*x)))/(16*b^4*ℯ) - (3*a^2*sqrt(pi)*erfi(-1 + acosh(a + b*x)))/(8*b^4*ℯ) + (sqrt(pi)*erfi(1 + acosh(a + b*x)))/(16*b^4*ℯ) + (3*a^2*sqrt(pi)*erfi(1 + acosh(a + b*x)))/(8*b^4*ℯ) + (sqrt(pi)*erfi(2 + acosh(a + b*x)))/(32*b^4*ℯ^4) + (3*a*sqrt(pi)*erfi((1/2)*(-3 + 2*acosh(a + b*x))))/(16*b^4*ℯ^(9/4)) + (3*a*sqrt(pi)*erfi((1/2)*(-1 + 2*acosh(a + b*x))))/(16*b^4*ℯ^(1/4)) + (a^3*sqrt(pi)*erfi((1/2)*(-1 + 2*acosh(a + b*x))))/(4*b^4*ℯ^(1/4)) - (3*a*sqrt(pi)*erfi((1/2)*(1 + 2*acosh(a + b*x))))/(16*b^4*ℯ^(1/4)) - (a^3*sqrt(pi)*erfi((1/2)*(1 + 2*acosh(a + b*x))))/(4*b^4*ℯ^(1/4)) - (3*a*sqrt(pi)*erfi((1/2)*(3 + 2*acosh(a + b*x))))/(16*b^4*ℯ^(9/4))]
    @test_int [x^2*ℯ^(acosh(a + b*x)^2), x, 27, (a*sqrt(pi)*erfi(-1 + acosh(a + b*x)))/(4*b^3*ℯ) - (a*sqrt(pi)*erfi(1 + acosh(a + b*x)))/(4*b^3*ℯ) - (sqrt(pi)*erfi((1/2)*(-3 + 2*acosh(a + b*x))))/(16*b^3*ℯ^(9/4)) - (sqrt(pi)*erfi((1/2)*(-1 + 2*acosh(a + b*x))))/(16*b^3*ℯ^(1/4)) - (a^2*sqrt(pi)*erfi((1/2)*(-1 + 2*acosh(a + b*x))))/(4*b^3*ℯ^(1/4)) + (sqrt(pi)*erfi((1/2)*(1 + 2*acosh(a + b*x))))/(16*b^3*ℯ^(1/4)) + (a^2*sqrt(pi)*erfi((1/2)*(1 + 2*acosh(a + b*x))))/(4*b^3*ℯ^(1/4)) + (sqrt(pi)*erfi((1/2)*(3 + 2*acosh(a + b*x))))/(16*b^3*ℯ^(9/4))]
    @test_int [x^1*ℯ^(acosh(a + b*x)^2), x, 17, -((sqrt(pi)*erfi(-1 + acosh(a + b*x)))/(8*b^2*ℯ)) + (sqrt(pi)*erfi(1 + acosh(a + b*x)))/(8*b^2*ℯ) + (a*sqrt(pi)*erfi((1/2)*(-1 + 2*acosh(a + b*x))))/(4*b^2*ℯ^(1/4)) - (a*sqrt(pi)*erfi((1/2)*(1 + 2*acosh(a + b*x))))/(4*b^2*ℯ^(1/4))]
    @test_int [x^0*ℯ^(acosh(a + b*x)^2), x, 7, -((sqrt(pi)*erfi((1/2)*(-1 + 2*acosh(a + b*x))))/(4*b*ℯ^(1/4))) + (sqrt(pi)*erfi((1/2)*(1 + 2*acosh(a + b*x))))/(4*b*ℯ^(1/4))]
    @test_int [ℯ^(acosh(a + b*x)^2)/x^1, x, 0, CannotIntegrate(ℯ^acosh(a + b*x)^2/x, x)]
    @test_int [ℯ^(acosh(a + b*x)^2)/x^2, x, 0, CannotIntegrate(ℯ^acosh(a + b*x)^2/x^2, x)]

    #= ::Title::Closed:: =#
    #=Miscellaneous*integrands*involving*inverse*hyperbolic*cosines=#

    @test_int [acosh(a + b*x)/((a*d)/b + d*x), x, 7, -(acosh(a + b*x)^2/(2*d)) + (acosh(a + b*x)*log(1 + ℯ^(2*acosh(a + b*x))))/d + PolyLog(2, -ℯ^(2*acosh(a + b*x)))/(2*d)]

    @test_int [x/(sqrt(-1 + x)*sqrt(1 + x)*acosh(x)), x, 2, CoshIntegral(acosh(x))]

    @test_int [x^3*acosh(a + b*x^4), x, 4, -((sqrt(-1 + a + b*x^4)*sqrt(1 + a + b*x^4))/(4*b)) + ((a + b*x^4)*acosh(a + b*x^4))/(4*b)]

    @test_int [x^(n-1)*acosh(a + b*x^n), x, 4, -((sqrt(-1 + a + b*x^n)*sqrt(1 + a + b*x^n))/(b*n)) + ((a + b*x^n)*acosh(a + b*x^n))/(b*n)]

    @test_int [acosh(c/(a + b*x)), x, 5, ((a + b*x)*asech(a/c + (b*x)/c))/b - (2*c*atan(sqrt(((1 - a/c)*c - b*x)/(a + c + b*x))))/b]

    @test_int [acosh(sqrt(1 + b*x^2))^n/sqrt(1 + b*x^2), x, 2, (sqrt(-1 + sqrt(1 + b*x^2))*sqrt(1 + sqrt(1 + b*x^2))*acosh(sqrt(1 + b*x^2))^(1 + n))/(b*(1 + n)*x)]
    @test_int [1/(acosh(sqrt(1 + b*x^2))*sqrt(1 + b*x^2)), x, 2, (sqrt(-1 + sqrt(1 + b*x^2))*sqrt(1 + sqrt(1 + b*x^2))*log(acosh(sqrt(1 + b*x^2))))/(b*x)]
    end

max_stars_repo_path: test/7 Inverse hyperbolic functions/7.2 Inverse hyperbolic cosine/7.2.5 Inverse hyperbolic cosine functions.jl