text:
@testset "7.1.5 Inverse hyperbolic sine functions" begin
    (a, b, c, d, e, f, g, h, m, n, x, ) = @variables a b c d e f g h m n x

    #= ::Package:: =#

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

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

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

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

    @test_int [asinh(c*x)^1/(d + e*x), x, 8, -(asinh(c*x)^2/(2*e)) + (asinh(c*x)*log(1 + (e*ℯ^asinh(c*x))/(c*d - sqrt(c^2*d^2 + e^2))))/e + (asinh(c*x)*log(1 + (e*ℯ^asinh(c*x))/(c*d + sqrt(c^2*d^2 + e^2))))/e + PolyLog(2, -((e*ℯ^asinh(c*x))/(c*d - sqrt(c^2*d^2 + e^2))))/e + PolyLog(2, -((e*ℯ^asinh(c*x))/(c*d + sqrt(c^2*d^2 + e^2))))/e]

    @test_int [asinh(c*x)^2/(d + e*x), x, 10, -(asinh(c*x)^3/(3*e)) + (asinh(c*x)^2*log(1 + (e*ℯ^asinh(c*x))/(c*d - sqrt(c^2*d^2 + e^2))))/e + (asinh(c*x)^2*log(1 + (e*ℯ^asinh(c*x))/(c*d + sqrt(c^2*d^2 + e^2))))/e + (2*asinh(c*x)*PolyLog(2, -((e*ℯ^asinh(c*x))/(c*d - sqrt(c^2*d^2 + e^2)))))/e + (2*asinh(c*x)*PolyLog(2, -((e*ℯ^asinh(c*x))/(c*d + sqrt(c^2*d^2 + e^2)))))/e - (2*PolyLog(3, -((e*ℯ^asinh(c*x))/(c*d - sqrt(c^2*d^2 + e^2)))))/e - (2*PolyLog(3, -((e*ℯ^asinh(c*x))/(c*d + sqrt(c^2*d^2 + e^2)))))/e]

    @test_int [asinh(c*x)^3/(d + e*x), x, 12, -(asinh(c*x)^4/(4*e)) + (asinh(c*x)^3*log(1 + (e*ℯ^asinh(c*x))/(c*d - sqrt(c^2*d^2 + e^2))))/e + (asinh(c*x)^3*log(1 + (e*ℯ^asinh(c*x))/(c*d + sqrt(c^2*d^2 + e^2))))/e + (3*asinh(c*x)^2*PolyLog(2, -((e*ℯ^asinh(c*x))/(c*d - sqrt(c^2*d^2 + e^2)))))/e + (3*asinh(c*x)^2*PolyLog(2, -((e*ℯ^asinh(c*x))/(c*d + sqrt(c^2*d^2 + e^2)))))/e - (6*asinh(c*x)*PolyLog(3, -((e*ℯ^asinh(c*x))/(c*d - sqrt(c^2*d^2 + e^2)))))/e - (6*asinh(c*x)*PolyLog(3, -((e*ℯ^asinh(c*x))/(c*d + sqrt(c^2*d^2 + e^2)))))/e + (6*PolyLog(4, -((e*ℯ^asinh(c*x))/(c*d - sqrt(c^2*d^2 + e^2)))))/e + (6*PolyLog(4, -((e*ℯ^asinh(c*x))/(c*d + sqrt(c^2*d^2 + e^2)))))/e]

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

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

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

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

    @test_int [(d + e*x)^3*(a + b*asinh(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^2*x^2)*(a + b*asinh(c*x)))/c + (4*b*d*e^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(3*c^3) - (3*b*d^2*e*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2*c) + (3*b*e^3*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(16*c^3) - (2*b*d*e^2*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(3*c) - (b*e^3*x^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(8*c) - (d^4*(a + b*asinh(c*x))^2)/(4*e) + (3*d^2*e*(a + b*asinh(c*x))^2)/(4*c^2) - (3*e^3*(a + b*asinh(c*x))^2)/(32*c^4) + ((d + e*x)^4*(a + b*asinh(c*x))^2)/(4*e)]
    @test_int [(d + e*x)^2*(a + b*asinh(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^2*x^2)*(a + b*asinh(c*x)))/c + (4*b*e^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(9*c^3) - (b*d*e*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/c - (2*b*e^2*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(9*c) - (d^3*(a + b*asinh(c*x))^2)/(3*e) + (d*e*(a + b*asinh(c*x))^2)/(2*c^2) + ((d + e*x)^3*(a + b*asinh(c*x))^2)/(3*e)]
    @test_int [(d + e*x)^1*(a + b*asinh(c*x))^2, x, 9, 2*b^2*d*x + (1/4)*b^2*e*x^2 - (2*b*d*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/c - (b*e*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2*c) - (d^2*(a + b*asinh(c*x))^2)/(2*e) + (e*(a + b*asinh(c*x))^2)/(4*c^2) + ((d + e*x)^2*(a + b*asinh(c*x))^2)/(2*e)]
    @test_int [(d + e*x)^0*(a + b*asinh(c*x))^2, x, 3, 2*b^2*x - (2*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/c + x*(a + b*asinh(c*x))^2]
    @test_int [(a + b*asinh(c*x))^2/(d + e*x)^1, x, 10, -((a + b*asinh(c*x))^3/(3*b*e)) + ((a + b*asinh(c*x))^2*log(1 + (e*ℯ^asinh(c*x))/(c*d - sqrt(c^2*d^2 + e^2))))/e + ((a + b*asinh(c*x))^2*log(1 + (e*ℯ^asinh(c*x))/(c*d + sqrt(c^2*d^2 + e^2))))/e + (2*b*(a + b*asinh(c*x))*PolyLog(2, -((e*ℯ^asinh(c*x))/(c*d - sqrt(c^2*d^2 + e^2)))))/e + (2*b*(a + b*asinh(c*x))*PolyLog(2, -((e*ℯ^asinh(c*x))/(c*d + sqrt(c^2*d^2 + e^2)))))/e - (2*b^2*PolyLog(3, -((e*ℯ^asinh(c*x))/(c*d - sqrt(c^2*d^2 + e^2)))))/e - (2*b^2*PolyLog(3, -((e*ℯ^asinh(c*x))/(c*d + sqrt(c^2*d^2 + e^2)))))/e]
    @test_int [(a + b*asinh(c*x))^2/(d + e*x)^2, x, 10, -((a + b*asinh(c*x))^2/(e*(d + e*x))) + (2*b*c*(a + b*asinh(c*x))*log(1 + (e*ℯ^asinh(c*x))/(c*d - sqrt(c^2*d^2 + e^2))))/(e*sqrt(c^2*d^2 + e^2)) - (2*b*c*(a + b*asinh(c*x))*log(1 + (e*ℯ^asinh(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^asinh(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^asinh(c*x))/(c*d + sqrt(c^2*d^2 + e^2)))))/(e*sqrt(c^2*d^2 + e^2))]
    @test_int [(a + b*asinh(c*x))^2/(d + e*x)^3, x, 13, -((b*c*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/((c^2*d^2 + e^2)*(d + e*x))) - (a + b*asinh(c*x))^2/(2*e*(d + e*x)^2) + (b*c^3*d*(a + b*asinh(c*x))*log(1 + (e*ℯ^asinh(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*asinh(c*x))*log(1 + (e*ℯ^asinh(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^asinh(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^asinh(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*asinh(c*x)), x, 27, (d^3*cosh(a/b)*CoshIntegral(a/b + asinh(c*x)))/(b*c) - (3*d*e^2*cosh(a/b)*CoshIntegral(a/b + asinh(c*x)))/(4*b*c^3) + (3*d*e^2*cosh((3*a)/b)*CoshIntegral((3*a)/b + 3*asinh(c*x)))/(4*b*c^3) - (3*d^2*e*CoshIntegral((2*a)/b + 2*asinh(c*x))*sinh((2*a)/b))/(2*b*c^2) + (e^3*CoshIntegral((2*a)/b + 2*asinh(c*x))*sinh((2*a)/b))/(4*b*c^4) - (e^3*CoshIntegral((4*a)/b + 4*asinh(c*x))*sinh((4*a)/b))/(8*b*c^4) - (d^3*sinh(a/b)*SinhIntegral(a/b + asinh(c*x)))/(b*c) + (3*d*e^2*sinh(a/b)*SinhIntegral(a/b + asinh(c*x)))/(4*b*c^3) + (3*d^2*e*cosh((2*a)/b)*SinhIntegral((2*a)/b + 2*asinh(c*x)))/(2*b*c^2) - (e^3*cosh((2*a)/b)*SinhIntegral((2*a)/b + 2*asinh(c*x)))/(4*b*c^4) - (3*d*e^2*sinh((3*a)/b)*SinhIntegral((3*a)/b + 3*asinh(c*x)))/(4*b*c^3) + (e^3*cosh((4*a)/b)*SinhIntegral((4*a)/b + 4*asinh(c*x)))/(8*b*c^4)]
    @test_int [(d + e*x)^2/(a + b*asinh(c*x)), x, 17, (d^2*cosh(a/b)*CoshIntegral(a/b + asinh(c*x)))/(b*c) - (e^2*cosh(a/b)*CoshIntegral(a/b + asinh(c*x)))/(4*b*c^3) + (e^2*cosh((3*a)/b)*CoshIntegral((3*a)/b + 3*asinh(c*x)))/(4*b*c^3) - (d*e*CoshIntegral((2*a)/b + 2*asinh(c*x))*sinh((2*a)/b))/(b*c^2) - (d^2*sinh(a/b)*SinhIntegral(a/b + asinh(c*x)))/(b*c) + (e^2*sinh(a/b)*SinhIntegral(a/b + asinh(c*x)))/(4*b*c^3) + (d*e*cosh((2*a)/b)*SinhIntegral((2*a)/b + 2*asinh(c*x)))/(b*c^2) - (e^2*sinh((3*a)/b)*SinhIntegral((3*a)/b + 3*asinh(c*x)))/(4*b*c^3)]
    @test_int [(d + e*x)^1/(a + b*asinh(c*x)), x, 11, (d*cosh(a/b)*CoshIntegral(a/b + asinh(c*x)))/(b*c) - (e*CoshIntegral((2*a)/b + 2*asinh(c*x))*sinh((2*a)/b))/(2*b*c^2) - (d*sinh(a/b)*SinhIntegral(a/b + asinh(c*x)))/(b*c) + (e*cosh((2*a)/b)*SinhIntegral((2*a)/b + 2*asinh(c*x)))/(2*b*c^2)]
    @test_int [(d + e*x)^0/(a + b*asinh(c*x)), x, 4, (cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(b*c) - (sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(b*c)]
    @test_int [1/((d + e*x)^1*(a + b*asinh(c*x))), x, 0, Unintegrable(1/((d + e*x)*(a + b*asinh(c*x))), x)]
    @test_int [1/((d + e*x)^2*(a + b*asinh(c*x))), x, 0, Unintegrable(1/((d + e*x)^2*(a + b*asinh(c*x))), x)]

    @test_int [(d + e*x)^2/(a + b*asinh(c*x))^2, x, 19, -((d^2*sqrt(1 + c^2*x^2))/(b*c*(a + b*asinh(c*x)))) - (2*d*e*x*sqrt(1 + c^2*x^2))/(b*c*(a + b*asinh(c*x))) - (e^2*x^2*sqrt(1 + c^2*x^2))/(b*c*(a + b*asinh(c*x))) + (2*d*e*cosh((2*a)/b)*CoshIntegral((2*(a + b*asinh(c*x)))/b))/(b^2*c^2) - (d^2*CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(b^2*c) + (e^2*CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(4*b^2*c^3) - (3*e^2*CoshIntegral((3*(a + b*asinh(c*x)))/b)*sinh((3*a)/b))/(4*b^2*c^3) + (d^2*cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(b^2*c) - (e^2*cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(4*b^2*c^3) - (2*d*e*sinh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(b^2*c^2) + (3*e^2*cosh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(4*b^2*c^3)]
    @test_int [(d + e*x)^1/(a + b*asinh(c*x))^2, x, 11, -((d*sqrt(1 + c^2*x^2))/(b*c*(a + b*asinh(c*x)))) - (e*x*sqrt(1 + c^2*x^2))/(b*c*(a + b*asinh(c*x))) + (e*cosh((2*a)/b)*CoshIntegral((2*(a + b*asinh(c*x)))/b))/(b^2*c^2) - (d*CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(b^2*c) + (d*cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(b^2*c) - (e*sinh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(b^2*c^2)]
    @test_int [(d + e*x)^0/(a + b*asinh(c*x))^2, x, 5, -(sqrt(1 + c^2*x^2)/(b*c*(a + b*asinh(c*x)))) - (CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(b^2*c) + (cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(b^2*c)]
    @test_int [1/((d + e*x)^1*(a + b*asinh(c*x))^2), x, 0, Unintegrable(1/((d + e*x)*(a + b*asinh(c*x))^2), x)]
    @test_int [1/((d + e*x)^2*(a + b*asinh(c*x))^2), x, 0, Unintegrable(1/((d + e*x)^2*(a + b*asinh(c*x))^2), x)]

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

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

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

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

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

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

    @test_int [sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*(f + g*x)^3, x, 16, -((b*f^2*g*x*sqrt(d + c^2*d*x^2))/(c*sqrt(1 + c^2*x^2))) + (2*b*g^3*x*sqrt(d + c^2*d*x^2))/(15*c^3*sqrt(1 + c^2*x^2)) - (b*c*f^3*x^2*sqrt(d + c^2*d*x^2))/(4*sqrt(1 + c^2*x^2)) - (3*b*f*g^2*x^2*sqrt(d + c^2*d*x^2))/(16*c*sqrt(1 + c^2*x^2)) - (b*c*f^2*g*x^3*sqrt(d + c^2*d*x^2))/(3*sqrt(1 + c^2*x^2)) - (b*g^3*x^3*sqrt(d + c^2*d*x^2))/(45*c*sqrt(1 + c^2*x^2)) - (3*b*c*f*g^2*x^4*sqrt(d + c^2*d*x^2))/(16*sqrt(1 + c^2*x^2)) - (b*c*g^3*x^5*sqrt(d + c^2*d*x^2))/(25*sqrt(1 + c^2*x^2)) + (1/2)*f^3*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (3*f*g^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(8*c^2) + (3/4)*f*g^2*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (f^2*g*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/c^2 - (g^3*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(3*c^4) + (g^3*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(5*c^4) + (f^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(4*b*c*sqrt(1 + c^2*x^2)) - (3*f*g^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(16*b*c^3*sqrt(1 + c^2*x^2))]
    @test_int [sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*(f + g*x)^2, x, 13, -((2*b*f*g*x*sqrt(d + c^2*d*x^2))/(3*c*sqrt(1 + c^2*x^2))) - (b*c*f^2*x^2*sqrt(d + c^2*d*x^2))/(4*sqrt(1 + c^2*x^2)) - (b*g^2*x^2*sqrt(d + c^2*d*x^2))/(16*c*sqrt(1 + c^2*x^2)) - (2*b*c*f*g*x^3*sqrt(d + c^2*d*x^2))/(9*sqrt(1 + c^2*x^2)) - (b*c*g^2*x^4*sqrt(d + c^2*d*x^2))/(16*sqrt(1 + c^2*x^2)) + (1/2)*f^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (g^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(8*c^2) + (1/4)*g^2*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (2*f*g*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(3*c^2) + (f^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(4*b*c*sqrt(1 + c^2*x^2)) - (g^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(16*b*c^3*sqrt(1 + c^2*x^2))]
    @test_int [sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*(f + g*x)^1, x, 8, -((b*g*x*sqrt(d + c^2*d*x^2))/(3*c*sqrt(1 + c^2*x^2))) - (b*c*f*x^2*sqrt(d + c^2*d*x^2))/(4*sqrt(1 + c^2*x^2)) - (b*c*g*x^3*sqrt(d + c^2*d*x^2))/(9*sqrt(1 + c^2*x^2)) + (1/2)*f*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (g*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(3*c^2) + (f*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(4*b*c*sqrt(1 + c^2*x^2))]
    @test_int [sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))/(f + g*x)^1, x, 22, (a*sqrt(d + c^2*d*x^2))/g - (b*c*x*sqrt(d + c^2*d*x^2))/(g*sqrt(1 + c^2*x^2)) + (b*sqrt(d + c^2*d*x^2)*asinh(c*x))/g - (c*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*b*g*sqrt(1 + c^2*x^2)) - ((1 + (c^2*f^2)/g^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*b*c*(f + g*x)*sqrt(1 + c^2*x^2)) + (sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*b*c*(f + g*x)) - (a*sqrt(c^2*f^2 + g^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*sqrt(1 + c^2*x^2)) + (b*sqrt(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2)*asinh(c*x)*log(1 + (ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2))))/(g^2*sqrt(1 + c^2*x^2)) - (b*sqrt(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2)*asinh(c*x)*log(1 + (ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2))))/(g^2*sqrt(1 + c^2*x^2)) + (b*sqrt(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2)*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2)))))/(g^2*sqrt(1 + c^2*x^2)) - (b*sqrt(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2)*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2)))))/(g^2*sqrt(1 + c^2*x^2))]
    @test_int [sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))/(f + g*x)^2, x, 35, -((a*sqrt(d + c^2*d*x^2))/(g*(f + g*x))) - (b*sqrt(d + c^2*d*x^2)*asinh(c*x))/(g*(f + g*x)) + (a*c^3*f^2*sqrt(d + c^2*d*x^2)*asinh(c*x))/(g^2*(c^2*f^2 + g^2)*sqrt(1 + c^2*x^2)) + (b*c^3*f^2*sqrt(d + c^2*d*x^2)*asinh(c*x)^2)/(2*g^2*(c^2*f^2 + g^2)*sqrt(1 + c^2*x^2)) - ((g - c^2*f*x)^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*b*c*(c^2*f^2 + g^2)*(f + g*x)^2*sqrt(1 + c^2*x^2)) + (sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*b*c*(f + g*x)^2) + (a*c^2*f*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*sqrt(c^2*f^2 + g^2)*sqrt(1 + c^2*x^2)) - (b*c^2*f*sqrt(d + c^2*d*x^2)*asinh(c*x)*log(1 + (ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2))))/(g^2*sqrt(c^2*f^2 + g^2)*sqrt(1 + c^2*x^2)) + (b*c^2*f*sqrt(d + c^2*d*x^2)*asinh(c*x)*log(1 + (ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2))))/(g^2*sqrt(c^2*f^2 + g^2)*sqrt(1 + c^2*x^2)) + (b*c*sqrt(d + c^2*d*x^2)*log(f + g*x))/(g^2*sqrt(1 + c^2*x^2)) - (b*c^2*f*sqrt(d + c^2*d*x^2)*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2)))))/(g^2*sqrt(c^2*f^2 + g^2)*sqrt(1 + c^2*x^2)) + (b*c^2*f*sqrt(d + c^2*d*x^2)*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2)))))/(g^2*sqrt(c^2*f^2 + g^2)*sqrt(1 + c^2*x^2))]

    @test_int [(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))*(f + g*x)^3, x, 24, -((3*b*d*f^2*g*x*sqrt(d + c^2*d*x^2))/(5*c*sqrt(1 + c^2*x^2))) + (2*b*d*g^3*x*sqrt(d + c^2*d*x^2))/(35*c^3*sqrt(1 + c^2*x^2)) - (5*b*c*d*f^3*x^2*sqrt(d + c^2*d*x^2))/(16*sqrt(1 + c^2*x^2)) - (3*b*d*f*g^2*x^2*sqrt(d + c^2*d*x^2))/(32*c*sqrt(1 + c^2*x^2)) - (2*b*c*d*f^2*g*x^3*sqrt(d + c^2*d*x^2))/(5*sqrt(1 + c^2*x^2)) - (b*d*g^3*x^3*sqrt(d + c^2*d*x^2))/(105*c*sqrt(1 + c^2*x^2)) - (b*c^3*d*f^3*x^4*sqrt(d + c^2*d*x^2))/(16*sqrt(1 + c^2*x^2)) - (7*b*c*d*f*g^2*x^4*sqrt(d + c^2*d*x^2))/(32*sqrt(1 + c^2*x^2)) - (3*b*c^3*d*f^2*g*x^5*sqrt(d + c^2*d*x^2))/(25*sqrt(1 + c^2*x^2)) - (8*b*c*d*g^3*x^5*sqrt(d + c^2*d*x^2))/(175*sqrt(1 + c^2*x^2)) - (b*c^3*d*f*g^2*x^6*sqrt(d + c^2*d*x^2))/(12*sqrt(1 + c^2*x^2)) - (b*c^3*d*g^3*x^7*sqrt(d + c^2*d*x^2))/(49*sqrt(1 + c^2*x^2)) + (3/8)*d*f^3*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (3*d*f*g^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(16*c^2) + (3/8)*d*f*g^2*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (1/4)*d*f^3*x*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (1/2)*d*f*g^2*x^3*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (3*d*f^2*g*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(5*c^2) - (d*g^3*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(5*c^4) + (d*g^3*(1 + c^2*x^2)^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(7*c^4) + (3*d*f^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(16*b*c*sqrt(1 + c^2*x^2)) - (3*d*f*g^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(32*b*c^3*sqrt(1 + c^2*x^2))]
    @test_int [(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))*(f + g*x)^2, x, 20, -((2*b*d*f*g*x*sqrt(d + c^2*d*x^2))/(5*c*sqrt(1 + c^2*x^2))) - (5*b*c*d*f^2*x^2*sqrt(d + c^2*d*x^2))/(16*sqrt(1 + c^2*x^2)) - (b*d*g^2*x^2*sqrt(d + c^2*d*x^2))/(32*c*sqrt(1 + c^2*x^2)) - (4*b*c*d*f*g*x^3*sqrt(d + c^2*d*x^2))/(15*sqrt(1 + c^2*x^2)) - (b*c^3*d*f^2*x^4*sqrt(d + c^2*d*x^2))/(16*sqrt(1 + c^2*x^2)) - (7*b*c*d*g^2*x^4*sqrt(d + c^2*d*x^2))/(96*sqrt(1 + c^2*x^2)) - (2*b*c^3*d*f*g*x^5*sqrt(d + c^2*d*x^2))/(25*sqrt(1 + c^2*x^2)) - (b*c^3*d*g^2*x^6*sqrt(d + c^2*d*x^2))/(36*sqrt(1 + c^2*x^2)) + (3/8)*d*f^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (d*g^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(16*c^2) + (1/8)*d*g^2*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (1/4)*d*f^2*x*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (1/6)*d*g^2*x^3*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (2*d*f*g*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(5*c^2) + (3*d*f^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(16*b*c*sqrt(1 + c^2*x^2)) - (d*g^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(32*b*c^3*sqrt(1 + c^2*x^2))]
    @test_int [(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))*(f + g*x)^1, x, 12, -((b*d*g*x*sqrt(d + c^2*d*x^2))/(5*c*sqrt(1 + c^2*x^2))) - (5*b*c*d*f*x^2*sqrt(d + c^2*d*x^2))/(16*sqrt(1 + c^2*x^2)) - (2*b*c*d*g*x^3*sqrt(d + c^2*d*x^2))/(15*sqrt(1 + c^2*x^2)) - (b*c^3*d*f*x^4*sqrt(d + c^2*d*x^2))/(16*sqrt(1 + c^2*x^2)) - (b*c^3*d*g*x^5*sqrt(d + c^2*d*x^2))/(25*sqrt(1 + c^2*x^2)) + (3/8)*d*f*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (1/4)*d*f*x*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (d*g*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(5*c^2) + (3*d*f*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(16*b*c*sqrt(1 + c^2*x^2))]
    @test_int [(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))/(f + g*x)^1, x, 29, (a*d*(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2))/g^3 - (b*c*d*x*sqrt(d + c^2*d*x^2))/(3*g*sqrt(1 + c^2*x^2)) - (b*c*d*(c^2*f^2 + g^2)*x*sqrt(d + c^2*d*x^2))/(g^3*sqrt(1 + c^2*x^2)) + (b*c^3*d*f*x^2*sqrt(d + c^2*d*x^2))/(4*g^2*sqrt(1 + c^2*x^2)) - (b*c^3*d*x^3*sqrt(d + c^2*d*x^2))/(9*g*sqrt(1 + c^2*x^2)) + (b*d*(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2)*asinh(c*x))/g^3 - (c^2*d*f*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(2*g^2) + (d*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(3*g) - (c*d*f*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(4*b*g^2*sqrt(1 + c^2*x^2)) - (c*d*(c^2*f^2 + g^2)*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*b*g^3*sqrt(1 + c^2*x^2)) - (d*(c^2*f^2 + g^2)^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*b*c*g^4*(f + g*x)*sqrt(1 + c^2*x^2)) + (d*(c^2*f^2 + g^2)*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*b*c*g^2*(f + g*x)) - (a*d*(c^2*f^2 + g^2)^(3/2)*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^4*sqrt(1 + c^2*x^2)) + (b*d*(c^2*f^2 + g^2)^(3/2)*sqrt(d + c^2*d*x^2)*asinh(c*x)*log(1 + (ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2))))/(g^4*sqrt(1 + c^2*x^2)) - (b*d*(c^2*f^2 + g^2)^(3/2)*sqrt(d + c^2*d*x^2)*asinh(c*x)*log(1 + (ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2))))/(g^4*sqrt(1 + c^2*x^2)) + (b*d*(c^2*f^2 + g^2)^(3/2)*sqrt(d + c^2*d*x^2)*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2)))))/(g^4*sqrt(1 + c^2*x^2)) - (b*d*(c^2*f^2 + g^2)^(3/2)*sqrt(d + c^2*d*x^2)*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2)))))/(g^4*sqrt(1 + c^2*x^2))]
    #= [(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))/(f + g*x)^2, x, 71, -((2*a*c^2*d*f*sqrt(d + c^2*d*x^2))/g^3) - (a*d*(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2))/(g^3*(f + g*x)) + (2*b*c^3*d*f*x*sqrt(d + c^2*d*x^2))/(g^3*sqrt(1 + c^2*x^2)) - (b*c^3*d*x^2*sqrt(d + c^2*d*x^2))/(4*g^2*sqrt(1 + c^2*x^2)) - (2*b*c^2*d*f*sqrt(d + c^2*d*x^2)*asinh(c*x))/g^3 - (b*d*(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2)*asinh(c*x))/(g^3*(f + g*x)) + (a*c^3*d*f^2*sqrt(d + c^2*d*x^2)*asinh(c*x))/(g^4*sqrt(1 + c^2*x^2)) + (b*c^3*d*f^2*sqrt(d + c^2*d*x^2)*asinh(c*x)^2)/(2*g^4*sqrt(1 + c^2*x^2)) + (c^2*d*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(2*g^2) + (c*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(4*b*g^2*sqrt(1 + c^2*x^2)) + (c^3*d*f*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(b*g^3*sqrt(1 + c^2*x^2)) - (d*(g - c^2*f*x)^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*b*c*g^2*(f + g*x)^2*sqrt(1 + c^2*x^2)) + (c*d*f*(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(b*g^4*(f + g*x)*sqrt(1 + c^2*x^2)) + (d*(c^2*f^2 + g^2)*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*b*c*g^2*(f + g*x)^2) - (c*d*f*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(b*g^2*(f + g*x)) + (3*a*c^2*d*f*sqrt(c^2*f^2 + g^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^4*sqrt(1 + c^2*x^2)) - (3*b*c^2*d*f*sqrt(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2)*asinh(c*x)*log(1 + (ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2))))/(g^4*sqrt(1 + c^2*x^2)) + (3*b*c^2*d*f*sqrt(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2)*asinh(c*x)*log(1 + (ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2))))/(g^4*sqrt(1 + c^2*x^2)) + (b*c*d*(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2)*log(f + g*x))/(g^4*sqrt(1 + c^2*x^2)) - (3*b*c^2*d*f*sqrt(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2)*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2)))))/(g^4*sqrt(1 + c^2*x^2)) + (3*b*c^2*d*f*sqrt(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2)*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2)))))/(g^4*sqrt(1 + c^2*x^2))] =#

    @test_int [(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))*(f + g*x)^3, x, 30, -((3*b*d^2*f^2*g*x*sqrt(d + c^2*d*x^2))/(7*c*sqrt(1 + c^2*x^2))) + (2*b*d^2*g^3*x*sqrt(d + c^2*d*x^2))/(63*c^3*sqrt(1 + c^2*x^2)) - (25*b*c*d^2*f^3*x^2*sqrt(d + c^2*d*x^2))/(96*sqrt(1 + c^2*x^2)) - (15*b*d^2*f*g^2*x^2*sqrt(d + c^2*d*x^2))/(256*c*sqrt(1 + c^2*x^2)) - (3*b*c*d^2*f^2*g*x^3*sqrt(d + c^2*d*x^2))/(7*sqrt(1 + c^2*x^2)) - (b*d^2*g^3*x^3*sqrt(d + c^2*d*x^2))/(189*c*sqrt(1 + c^2*x^2)) - (5*b*c^3*d^2*f^3*x^4*sqrt(d + c^2*d*x^2))/(96*sqrt(1 + c^2*x^2)) - (59*b*c*d^2*f*g^2*x^4*sqrt(d + c^2*d*x^2))/(256*sqrt(1 + c^2*x^2)) - (9*b*c^3*d^2*f^2*g*x^5*sqrt(d + c^2*d*x^2))/(35*sqrt(1 + c^2*x^2)) - (b*c*d^2*g^3*x^5*sqrt(d + c^2*d*x^2))/(21*sqrt(1 + c^2*x^2)) - (17*b*c^3*d^2*f*g^2*x^6*sqrt(d + c^2*d*x^2))/(96*sqrt(1 + c^2*x^2)) - (3*b*c^5*d^2*f^2*g*x^7*sqrt(d + c^2*d*x^2))/(49*sqrt(1 + c^2*x^2)) - (19*b*c^3*d^2*g^3*x^7*sqrt(d + c^2*d*x^2))/(441*sqrt(1 + c^2*x^2)) - (3*b*c^5*d^2*f*g^2*x^8*sqrt(d + c^2*d*x^2))/(64*sqrt(1 + c^2*x^2)) - (b*c^5*d^2*g^3*x^9*sqrt(d + c^2*d*x^2))/(81*sqrt(1 + c^2*x^2)) - (b*d^2*f^3*(1 + c^2*x^2)^(5/2)*sqrt(d + c^2*d*x^2))/(36*c) + (5/16)*d^2*f^3*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (15*d^2*f*g^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(128*c^2) + (15/64)*d^2*f*g^2*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (5/24)*d^2*f^3*x*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (5/16)*d^2*f*g^2*x^3*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (1/6)*d^2*f^3*x*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (3/8)*d^2*f*g^2*x^3*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (3*d^2*f^2*g*(1 + c^2*x^2)^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(7*c^2) - (d^2*g^3*(1 + c^2*x^2)^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(7*c^4) + (d^2*g^3*(1 + c^2*x^2)^4*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(9*c^4) + (5*d^2*f^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(32*b*c*sqrt(1 + c^2*x^2)) - (15*d^2*f*g^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(256*b*c^3*sqrt(1 + c^2*x^2))]
    @test_int [(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))*(f + g*x)^2, x, 26, -((2*b*d^2*f*g*x*sqrt(d + c^2*d*x^2))/(7*c*sqrt(1 + c^2*x^2))) - (25*b*c*d^2*f^2*x^2*sqrt(d + c^2*d*x^2))/(96*sqrt(1 + c^2*x^2)) - (5*b*d^2*g^2*x^2*sqrt(d + c^2*d*x^2))/(256*c*sqrt(1 + c^2*x^2)) - (2*b*c*d^2*f*g*x^3*sqrt(d + c^2*d*x^2))/(7*sqrt(1 + c^2*x^2)) - (5*b*c^3*d^2*f^2*x^4*sqrt(d + c^2*d*x^2))/(96*sqrt(1 + c^2*x^2)) - (59*b*c*d^2*g^2*x^4*sqrt(d + c^2*d*x^2))/(768*sqrt(1 + c^2*x^2)) - (6*b*c^3*d^2*f*g*x^5*sqrt(d + c^2*d*x^2))/(35*sqrt(1 + c^2*x^2)) - (17*b*c^3*d^2*g^2*x^6*sqrt(d + c^2*d*x^2))/(288*sqrt(1 + c^2*x^2)) - (2*b*c^5*d^2*f*g*x^7*sqrt(d + c^2*d*x^2))/(49*sqrt(1 + c^2*x^2)) - (b*c^5*d^2*g^2*x^8*sqrt(d + c^2*d*x^2))/(64*sqrt(1 + c^2*x^2)) - (b*d^2*f^2*(1 + c^2*x^2)^(5/2)*sqrt(d + c^2*d*x^2))/(36*c) + (5/16)*d^2*f^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (5*d^2*g^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(128*c^2) + (5/64)*d^2*g^2*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (5/24)*d^2*f^2*x*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (5/48)*d^2*g^2*x^3*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (1/6)*d^2*f^2*x*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (1/8)*d^2*g^2*x^3*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (2*d^2*f*g*(1 + c^2*x^2)^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(7*c^2) + (5*d^2*f^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(32*b*c*sqrt(1 + c^2*x^2)) - (5*d^2*g^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(256*b*c^3*sqrt(1 + c^2*x^2))]
    @test_int [(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))*(f + g*x)^1, x, 14, -((b*d^2*g*x*sqrt(d + c^2*d*x^2))/(7*c*sqrt(1 + c^2*x^2))) - (25*b*c*d^2*f*x^2*sqrt(d + c^2*d*x^2))/(96*sqrt(1 + c^2*x^2)) - (b*c*d^2*g*x^3*sqrt(d + c^2*d*x^2))/(7*sqrt(1 + c^2*x^2)) - (5*b*c^3*d^2*f*x^4*sqrt(d + c^2*d*x^2))/(96*sqrt(1 + c^2*x^2)) - (3*b*c^3*d^2*g*x^5*sqrt(d + c^2*d*x^2))/(35*sqrt(1 + c^2*x^2)) - (b*c^5*d^2*g*x^7*sqrt(d + c^2*d*x^2))/(49*sqrt(1 + c^2*x^2)) - (b*d^2*f*(1 + c^2*x^2)^(5/2)*sqrt(d + c^2*d*x^2))/(36*c) + (5/16)*d^2*f*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (5/24)*d^2*f*x*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (1/6)*d^2*f*x*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (d^2*g*(1 + c^2*x^2)^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(7*c^2) + (5*d^2*f*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(32*b*c*sqrt(1 + c^2*x^2))]
    @test_int [(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))/(f + g*x)^1, x, 37, (a*d^2*(c^2*f^2 + g^2)^2*sqrt(d + c^2*d*x^2))/g^5 + (2*b*c*d^2*x*sqrt(d + c^2*d*x^2))/(15*g*sqrt(1 + c^2*x^2)) - (b*c*d^2*(c^2*f^2 + g^2)^2*x*sqrt(d + c^2*d*x^2))/(g^5*sqrt(1 + c^2*x^2)) - (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^2*x^2)) + (b*c^3*d^2*f*x^2*sqrt(d + c^2*d*x^2))/(16*g^2*sqrt(1 + c^2*x^2)) + (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^2*x^2)) - (b*c^3*d^2*x^3*sqrt(d + c^2*d*x^2))/(45*g*sqrt(1 + c^2*x^2)) - (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^2*x^2)) + (b*c^5*d^2*f*x^4*sqrt(d + c^2*d*x^2))/(16*g^2*sqrt(1 + c^2*x^2)) - (b*c^5*d^2*x^5*sqrt(d + c^2*d*x^2))/(25*g*sqrt(1 + c^2*x^2)) + (b*d^2*(c^2*f^2 + g^2)^2*sqrt(d + c^2*d*x^2)*asinh(c*x))/g^5 - (c^2*d^2*f*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(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*asinh(c*x)))/(2*g^4) - (c^4*d^2*f*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(4*g^2) - (d^2*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(3*g) + (d^2*(c^2*f^2 + 2*g^2)*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(3*g^3) + (d^2*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(5*g) + (c*d^2*f*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(16*b*g^2*sqrt(1 + c^2*x^2)) - (c*d^2*f*(c^2*f^2 + 2*g^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(4*b*g^4*sqrt(1 + c^2*x^2)) - (c*d^2*(c^2*f^2 + g^2)^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*b*g^5*sqrt(1 + c^2*x^2)) - (d^2*(c^2*f^2 + g^2)^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*b*c*g^6*(f + g*x)*sqrt(1 + c^2*x^2)) + (d^2*(c^2*f^2 + g^2)^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*b*c*g^4*(f + g*x)) - (a*d^2*(c^2*f^2 + g^2)^(5/2)*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*sqrt(1 + c^2*x^2)) + (b*d^2*(c^2*f^2 + g^2)^(5/2)*sqrt(d + c^2*d*x^2)*asinh(c*x)*log(1 + (ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2))))/(g^6*sqrt(1 + c^2*x^2)) - (b*d^2*(c^2*f^2 + g^2)^(5/2)*sqrt(d + c^2*d*x^2)*asinh(c*x)*log(1 + (ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2))))/(g^6*sqrt(1 + c^2*x^2)) + (b*d^2*(c^2*f^2 + g^2)^(5/2)*sqrt(d + c^2*d*x^2)*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2)))))/(g^6*sqrt(1 + c^2*x^2)) - (b*d^2*(c^2*f^2 + g^2)^(5/2)*sqrt(d + c^2*d*x^2)*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2)))))/(g^6*sqrt(1 + c^2*x^2))]
    #= [(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))/(f + g*x)^2, x, 78, -((4*a*c^2*d^2*f*(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2))/g^5) - (a*d^2*(c^2*f^2 + g^2)^2*sqrt(d + c^2*d*x^2))/(g^5*(f + g*x)) + (2*b*c^3*d^2*f*x*sqrt(d + c^2*d*x^2))/(3*g^3*sqrt(1 + c^2*x^2)) + (4*b*c^3*d^2*f*(c^2*f^2 + g^2)*x*sqrt(d + c^2*d*x^2))/(g^5*sqrt(1 + c^2*x^2)) - (b*c^3*d^2*x^2*sqrt(d + c^2*d*x^2))/(16*g^2*sqrt(1 + c^2*x^2)) - (b*c^3*d^2*(3*c^2*f^2 + 2*g^2)*x^2*sqrt(d + c^2*d*x^2))/(4*g^4*sqrt(1 + c^2*x^2)) + (2*b*c^5*d^2*f*x^3*sqrt(d + c^2*d*x^2))/(9*g^3*sqrt(1 + c^2*x^2)) - (b*c^5*d^2*x^4*sqrt(d + c^2*d*x^2))/(16*g^2*sqrt(1 + c^2*x^2)) - (4*b*c^2*d^2*f*(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2)*asinh(c*x))/g^5 - (b*d^2*(c^2*f^2 + g^2)^2*sqrt(d + c^2*d*x^2)*asinh(c*x))/(g^5*(f + g*x)) + (a*c^3*d^2*f^2*(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2)*asinh(c*x))/(g^6*sqrt(1 + c^2*x^2)) + (b*c^3*d^2*f^2*(c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2)*asinh(c*x)^2)/(2*g^6*sqrt(1 + c^2*x^2)) + (c^2*d^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(8*g^2) + (c^2*d^2*(3*c^2*f^2 + 2*g^2)*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(2*g^4) + (c^4*d^2*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(4*g^2) - (2*c^2*d^2*f*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(3*g^3) - (c*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(16*b*g^2*sqrt(1 + c^2*x^2)) + (c*d^2*(3*c^2*f^2 + 2*g^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(4*b*g^4*sqrt(1 + c^2*x^2)) + (2*c^3*d^2*f*(c^2*f^2 + g^2)*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(b*g^5*sqrt(1 + c^2*x^2)) - (d^2*(c^2*f^2 + g^2)*(g - c^2*f*x)^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*b*c*g^4*(f + g*x)^2*sqrt(1 + c^2*x^2)) + (2*c*d^2*f*(c^2*f^2 + g^2)^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(b*g^6*(f + g*x)*sqrt(1 + c^2*x^2)) + (d^2*(c^2*f^2 + g^2)^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*b*c*g^4*(f + g*x)^2) - (2*c*d^2*f*(c^2*f^2 + g^2)*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(b*g^4*(f + g*x)) + (5*a*c^2*d^2*f*(c^2*f^2 + g^2)^(3/2)*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*sqrt(1 + c^2*x^2)) - (5*b*c^2*d^2*f*(c^2*f^2 + g^2)^(3/2)*sqrt(d + c^2*d*x^2)*asinh(c*x)*log(1 + (ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2))))/(g^6*sqrt(1 + c^2*x^2)) + (5*b*c^2*d^2*f*(c^2*f^2 + g^2)^(3/2)*sqrt(d + c^2*d*x^2)*asinh(c*x)*log(1 + (ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2))))/(g^6*sqrt(1 + c^2*x^2)) + (b*c*d^2*(c^2*f^2 + g^2)^2*sqrt(d + c^2*d*x^2)*log(f + g*x))/(g^6*sqrt(1 + c^2*x^2)) - (5*b*c^2*d^2*f*(c^2*f^2 + g^2)^(3/2)*sqrt(d + c^2*d*x^2)*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2)))))/(g^6*sqrt(1 + c^2*x^2)) + (5*b*c^2*d^2*f*(c^2*f^2 + g^2)^(3/2)*sqrt(d + c^2*d*x^2)*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2)))))/(g^6*sqrt(1 + c^2*x^2))] =#

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

    @test_int [1/sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*(f + g*x)^3, x, 13, -((3*b*f^2*g*x*sqrt(1 + c^2*x^2))/(c*sqrt(d + c^2*d*x^2))) + (2*b*g^3*x*sqrt(1 + c^2*x^2))/(3*c^3*sqrt(d + c^2*d*x^2)) - (3*b*f*g^2*x^2*sqrt(1 + c^2*x^2))/(4*c*sqrt(d + c^2*d*x^2)) - (b*g^3*x^3*sqrt(1 + c^2*x^2))/(9*c*sqrt(d + c^2*d*x^2)) + (3*f^2*g*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c^2*sqrt(d + c^2*d*x^2)) - (2*g^3*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(3*c^4*sqrt(d + c^2*d*x^2)) + (3*f*g^2*x*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2*c^2*sqrt(d + c^2*d*x^2)) + (g^3*x^2*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(3*c^2*sqrt(d + c^2*d*x^2)) + (f^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(2*b*c*sqrt(d + c^2*d*x^2)) - (3*f*g^2*sqrt(1 + c^2*x^2)*(a + b*asinh(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*asinh(c*x))*(f + g*x)^2, x, 9, -((2*b*f*g*x*sqrt(1 + c^2*x^2))/(c*sqrt(d + c^2*d*x^2))) - (b*g^2*x^2*sqrt(1 + c^2*x^2))/(4*c*sqrt(d + c^2*d*x^2)) + (2*f*g*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c^2*sqrt(d + c^2*d*x^2)) + (g^2*x*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2*c^2*sqrt(d + c^2*d*x^2)) + (f^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(2*b*c*sqrt(d + c^2*d*x^2)) - (g^2*sqrt(1 + c^2*x^2)*(a + b*asinh(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*asinh(c*x))*(f + g*x)^1, x, 6, -((b*g*x*sqrt(1 + c^2*x^2))/(c*sqrt(d + c^2*d*x^2))) + (g*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c^2*sqrt(d + c^2*d*x^2)) + (f*sqrt(1 + c^2*x^2)*(a + b*asinh(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*asinh(c*x))*(f + g*x)^0, x, 1, (sqrt(1 + c^2*x^2)*(a + b*asinh(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*asinh(c*x))/(f + g*x)^1, x, 10, (sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*log(1 + (ℯ^asinh(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^2*x^2)*(a + b*asinh(c*x))*log(1 + (ℯ^asinh(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^2*x^2)*PolyLog(2, -((ℯ^asinh(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^2*x^2)*PolyLog(2, -((ℯ^asinh(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*asinh(c*x))/(f + g*x)^2, x, 13, -((g*(1 + c^2*x^2)*(a + b*asinh(c*x)))/((c^2*f^2 + g^2)*(f + g*x)*sqrt(d + c^2*d*x^2))) + (c^2*f*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*log(1 + (ℯ^asinh(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^2*x^2)*(a + b*asinh(c*x))*log(1 + (ℯ^asinh(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^2*x^2)*log(f + g*x))/((c^2*f^2 + g^2)*sqrt(d + c^2*d*x^2)) + (b*c^2*f*sqrt(1 + c^2*x^2)*PolyLog(2, -((ℯ^asinh(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^2*x^2)*PolyLog(2, -((ℯ^asinh(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))]

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

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

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

    @test_int [log(h*(f + g*x)^m)*(a + b*asinh(c*x))^n/sqrt(1 + c^2*x^2), x, 0, Unintegrable(((a + b*asinh(c*x))^n*log(h*(f + g*x)^m))/sqrt(1 + c^2*x^2), x)]

    #= [log(h*(f + g*x)^m)*(a + b*asinh(c*x))^3/sqrt(1 + c^2*x^2), x, 18, (m*(a + b*asinh(c*x))^5)/(20*b^2*c) - (m*(a + b*asinh(c*x))^4*log(1 + (ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2))))/(4*b*c) - (m*(a + b*asinh(c*x))^4*log(1 + (ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2))))/(4*b*c) + ((a + b*asinh(c*x))^4*log(h*(f + g*x)^m))/(4*b*c) - (m*(a + b*asinh(c*x))^3*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2)))))/c - (m*(a + b*asinh(c*x))^3*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2)))))/c + (3*b*m*(a + b*asinh(c*x))^2*PolyLog(3, -((ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2)))))/c + (3*b*m*(a + b*asinh(c*x))^2*PolyLog(3, -((ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2)))))/c - (6*b^2*m*(a + b*asinh(c*x))*PolyLog(4, -((ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2)))))/c - (6*b^2*m*(a + b*asinh(c*x))*PolyLog(4, -((ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2)))))/c + (6*b^3*m*PolyLog(5, -((ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2)))))/c + (6*b^3*m*PolyLog(5, -((ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2)))))/c] =#
    @test_int [log(h*(f + g*x)^m)*(a + b*asinh(c*x))^2/sqrt(1 + c^2*x^2), x, 13, (m*(a + b*asinh(c*x))^4)/(12*b^2*c) - (m*(a + b*asinh(c*x))^3*log(1 + (ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2))))/(3*b*c) - (m*(a + b*asinh(c*x))^3*log(1 + (ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2))))/(3*b*c) + ((a + b*asinh(c*x))^3*log(h*(f + g*x)^m))/(3*b*c) - (m*(a + b*asinh(c*x))^2*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2)))))/c - (m*(a + b*asinh(c*x))^2*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2)))))/c + (2*b*m*(a + b*asinh(c*x))*PolyLog(3, -((ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2)))))/c + (2*b*m*(a + b*asinh(c*x))*PolyLog(3, -((ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2)))))/c - (2*b^2*m*PolyLog(4, -((ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2)))))/c - (2*b^2*m*PolyLog(4, -((ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2)))))/c]
    @test_int [log(h*(f + g*x)^m)*(a + b*asinh(c*x))^1/sqrt(1 + c^2*x^2), x, 11, (m*(a + b*asinh(c*x))^3)/(6*b^2*c) - (m*(a + b*asinh(c*x))^2*log(1 + (ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2))))/(2*b*c) - (m*(a + b*asinh(c*x))^2*log(1 + (ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2))))/(2*b*c) + ((a + b*asinh(c*x))^2*log(h*(f + g*x)^m))/(2*b*c) - (m*(a + b*asinh(c*x))*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2)))))/c - (m*(a + b*asinh(c*x))*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2)))))/c + (b*m*PolyLog(3, -((ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2)))))/c + (b*m*PolyLog(3, -((ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2)))))/c]
    @test_int [log(h*(f + g*x)^m)*(a + b*asinh(c*x))^0/sqrt(1 + c^2*x^2), x, 9, (m*asinh(c*x)^2)/(2*c) - (m*asinh(c*x)*log(1 + (ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2))))/c - (m*asinh(c*x)*log(1 + (ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2))))/c + (asinh(c*x)*log(h*(f + g*x)^m))/c - (m*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f - sqrt(c^2*f^2 + g^2)))))/c - (m*PolyLog(2, -((ℯ^asinh(c*x)*g)/(c*f + sqrt(c^2*f^2 + g^2)))))/c]
    @test_int [log(h*(f + g*x)^m)/(a + b*asinh(c*x))^1/sqrt(1 + c^2*x^2), x, 0, Unintegrable(log(h*(f + g*x)^m)/(sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x)]

    #= ::Title:: =#
    #=Integrands*Involving*Inverse*Hyperbolic*Sines=#

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

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

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

    @test_int [x^3*asinh(a + b*x), x, 6, (7*a*x^2*sqrt(1 + (a + b*x)^2))/(48*b^2) - (x^3*sqrt(1 + (a + b*x)^2))/(16*b) - ((4*a*(16 - 19*a^2) - (9 - 26*a^2)*(a + b*x))*sqrt(1 + (a + b*x)^2))/(96*b^4) - ((3 - 24*a^2 + 8*a^4)*asinh(a + b*x))/(32*b^4) + (1/4)*x^4*asinh(a + b*x)]
    @test_int [x^2*asinh(a + b*x), x, 5, -((x^2*sqrt(1 + (a + b*x)^2))/(9*b)) + ((4 - 11*a^2 + 5*a*b*x)*sqrt(1 + (a + b*x)^2))/(18*b^3) - (a*(3 - 2*a^2)*asinh(a + b*x))/(6*b^3) + (1/3)*x^3*asinh(a + b*x)]
    @test_int [x^1*asinh(a + b*x), x, 5, (3*a*sqrt(1 + (a + b*x)^2))/(4*b^2) - (x*sqrt(1 + (a + b*x)^2))/(4*b) + ((1 - 2*a^2)*asinh(a + b*x))/(4*b^2) + (1/2)*x^2*asinh(a + b*x)]
    @test_int [x^0*asinh(a + b*x), x, 3, -(sqrt(1 + (a + b*x)^2)/b) + ((a + b*x)*asinh(a + b*x))/b]
    @test_int [asinh(a + b*x)/x^1, x, 9, (-(1/2))*asinh(a + b*x)^2 + asinh(a + b*x)*log(1 - ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))) + asinh(a + b*x)*log(1 - ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))) + PolyLog(2, ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))) + PolyLog(2, ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2)))]
    @test_int [asinh(a + b*x)/x^2, x, 4, -(asinh(a + b*x)/x) - (b*atanh((1 + a*(a + b*x))/(sqrt(1 + a^2)*sqrt(1 + (a + b*x)^2))))/sqrt(1 + a^2)]
    @test_int [asinh(a + b*x)/x^3, x, 5, -((b*sqrt(1 + (a + b*x)^2))/(2*(1 + a^2)*x)) - asinh(a + b*x)/(2*x^2) + (a*b^2*atanh((1 + a*(a + b*x))/(sqrt(1 + a^2)*sqrt(1 + (a + b*x)^2))))/(2*(1 + a^2)^(3/2))]
    @test_int [asinh(a + b*x)/x^4, x, 6, -((b*sqrt(1 + (a + b*x)^2))/(6*(1 + a^2)*x^2)) + (a*b^2*sqrt(1 + (a + b*x)^2))/(2*(1 + a^2)^2*x) - asinh(a + b*x)/(3*x^3) + ((1 - 2*a^2)*b^3*atanh((1 + a*(a + b*x))/(sqrt(1 + a^2)*sqrt(1 + (a + b*x)^2))))/(6*(1 + a^2)^(5/2))]
    @test_int [asinh(a + b*x)/x^5, x, 7, -((b*sqrt(1 + (a + b*x)^2))/(12*(1 + a^2)*x^3)) + (5*a*b^2*sqrt(1 + (a + b*x)^2))/(24*(1 + a^2)^2*x^2) + ((4 - 11*a^2)*b^3*sqrt(1 + (a + b*x)^2))/(24*(1 + a^2)^3*x) - asinh(a + b*x)/(4*x^4) - (a*(3 - 2*a^2)*b^4*atanh((1 + a*(a + b*x))/(sqrt(1 + a^2)*sqrt(1 + (a + b*x)^2))))/(8*(1 + a^2)^(7/2))]

    @test_int [x^3*asinh(a + b*x)^2, x, 19, (4*a*x)/(3*b^3) - (2*a^3*x)/b^3 - (3*(a + b*x)^2)/(32*b^4) + (3*a^2*(a + b*x)^2)/(4*b^4) - (2*a*(a + b*x)^3)/(9*b^4) + (a + b*x)^4/(32*b^4) - (4*a*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/(3*b^4) + (2*a^3*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/b^4 + (3*(a + b*x)*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/(16*b^4) - (3*a^2*(a + b*x)*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/(2*b^4) + (2*a*(a + b*x)^2*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/(3*b^4) - ((a + b*x)^3*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/(8*b^4) - (3*asinh(a + b*x)^2)/(32*b^4) + (3*a^2*asinh(a + b*x)^2)/(4*b^4) - (a^4*asinh(a + b*x)^2)/(4*b^4) + (1/4)*x^4*asinh(a + b*x)^2]
    @test_int [x^2*asinh(a + b*x)^2, x, 14, -((4*x)/(9*b^2)) + (2*a^2*x)/b^2 - (a*(a + b*x)^2)/(2*b^3) + (2*(a + b*x)^3)/(27*b^3) + (4*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/(9*b^3) - (2*a^2*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/b^3 + (a*(a + b*x)*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/b^3 - (2*(a + b*x)^2*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/(9*b^3) - (a*asinh(a + b*x)^2)/(2*b^3) + (a^3*asinh(a + b*x)^2)/(3*b^3) + (1/3)*x^3*asinh(a + b*x)^2]
    @test_int [x^1*asinh(a + b*x)^2, x, 10, -((2*a*x)/b) + (a + b*x)^2/(4*b^2) + (2*a*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/b^2 - ((a + b*x)*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/(2*b^2) + asinh(a + b*x)^2/(4*b^2) - (a^2*asinh(a + b*x)^2)/(2*b^2) + (1/2)*x^2*asinh(a + b*x)^2]
    @test_int [x^0*asinh(a + b*x)^2, x, 4, 2*x - (2*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/b + ((a + b*x)*asinh(a + b*x)^2)/b]
    @test_int [asinh(a + b*x)^2/x^1, x, 11, (-(1/3))*asinh(a + b*x)^3 + asinh(a + b*x)^2*log(1 - ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))) + asinh(a + b*x)^2*log(1 - ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))) + 2*asinh(a + b*x)*PolyLog(2, ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))) + 2*asinh(a + b*x)*PolyLog(2, ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))) - 2*PolyLog(3, ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))) - 2*PolyLog(3, ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2)))]
    @test_int [asinh(a + b*x)^2/x^2, x, 11, -(asinh(a + b*x)^2/x) - (2*b*asinh(a + b*x)*log(1 - ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))))/sqrt(1 + a^2) + (2*b*asinh(a + b*x)*log(1 - ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))))/sqrt(1 + a^2) - (2*b*PolyLog(2, ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))))/sqrt(1 + a^2) + (2*b*PolyLog(2, ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))))/sqrt(1 + a^2)]
    @test_int [asinh(a + b*x)^2/x^3, x, 14, -((b*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/((1 + a^2)*x)) - asinh(a + b*x)^2/(2*x^2) + (a*b^2*asinh(a + b*x)*log(1 - ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))))/(1 + a^2)^(3/2) - (a*b^2*asinh(a + b*x)*log(1 - ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))))/(1 + a^2)^(3/2) + (b^2*log(x))/(1 + a^2) + (a*b^2*PolyLog(2, ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))))/(1 + a^2)^(3/2) - (a*b^2*PolyLog(2, ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))))/(1 + a^2)^(3/2)]
    @test_int [asinh(a + b*x)^2/x^4, x, 40, -(b^2/(3*(1 + a^2)*x)) - (b*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/(3*(1 + a^2)*x^2) + (a*b^2*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/((1 + a^2)^2*x) - asinh(a + b*x)^2/(3*x^3) - (a^2*b^3*asinh(a + b*x)*log(1 - ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))))/(1 + a^2)^(5/2) + (b^3*asinh(a + b*x)*log(1 - ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))))/(3*(1 + a^2)^(3/2)) + (a^2*b^3*asinh(a + b*x)*log(1 - ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))))/(1 + a^2)^(5/2) - (b^3*asinh(a + b*x)*log(1 - ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))))/(3*(1 + a^2)^(3/2)) - (a*b^3*log(x))/(1 + a^2)^2 - (a^2*b^3*PolyLog(2, ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))))/(1 + a^2)^(5/2) + (b^3*PolyLog(2, ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))))/(3*(1 + a^2)^(3/2)) + (a^2*b^3*PolyLog(2, ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))))/(1 + a^2)^(5/2) - (b^3*PolyLog(2, ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))))/(3*(1 + a^2)^(3/2))]

    @test_int [x^2*asinh(a + b*x)^3, x, 18, (14*sqrt(1 + (a + b*x)^2))/(9*b^3) - (6*a^2*sqrt(1 + (a + b*x)^2))/b^3 + (3*a*(a + b*x)*sqrt(1 + (a + b*x)^2))/(4*b^3) - (2*(1 + (a + b*x)^2)^(3/2))/(27*b^3) - (3*a*asinh(a + b*x))/(4*b^3) - (4*(a + b*x)*asinh(a + b*x))/(3*b^3) + (6*a^2*(a + b*x)*asinh(a + b*x))/b^3 - (3*a*(a + b*x)^2*asinh(a + b*x))/(2*b^3) + (2*(a + b*x)^3*asinh(a + b*x))/(9*b^3) + (2*sqrt(1 + (a + b*x)^2)*asinh(a + b*x)^2)/(3*b^3) - (3*a^2*sqrt(1 + (a + b*x)^2)*asinh(a + b*x)^2)/b^3 + (3*a*(a + b*x)*sqrt(1 + (a + b*x)^2)*asinh(a + b*x)^2)/(2*b^3) - ((a + b*x)^2*sqrt(1 + (a + b*x)^2)*asinh(a + b*x)^2)/(3*b^3) - (a*asinh(a + b*x)^3)/(2*b^3) + (a^3*asinh(a + b*x)^3)/(3*b^3) + (1/3)*x^3*asinh(a + b*x)^3]
    @test_int [x^1*asinh(a + b*x)^3, x, 12, (6*a*sqrt(1 + (a + b*x)^2))/b^2 - (3*(a + b*x)*sqrt(1 + (a + b*x)^2))/(8*b^2) + (3*asinh(a + b*x))/(8*b^2) - (6*a*(a + b*x)*asinh(a + b*x))/b^2 + (3*(a + b*x)^2*asinh(a + b*x))/(4*b^2) + (3*a*sqrt(1 + (a + b*x)^2)*asinh(a + b*x)^2)/b^2 - (3*(a + b*x)*sqrt(1 + (a + b*x)^2)*asinh(a + b*x)^2)/(4*b^2) + asinh(a + b*x)^3/(4*b^2) - (a^2*asinh(a + b*x)^3)/(2*b^2) + (1/2)*x^2*asinh(a + b*x)^3]
    @test_int [x^0*asinh(a + b*x)^3, x, 5, (-6*sqrt(1 + (a + b*x)^2))/b + (6*(a + b*x)*asinh(a + b*x))/b - (3*sqrt(1 + (a + b*x)^2)*asinh(a + b*x)^2)/b + ((a + b*x)*asinh(a + b*x)^3)/b]
    @test_int [asinh(a + b*x)^3/x^1, x, 13, (-(1/4))*asinh(a + b*x)^4 + asinh(a + b*x)^3*log(1 - ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))) + asinh(a + b*x)^3*log(1 - ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))) + 3*asinh(a + b*x)^2*PolyLog(2, ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))) + 3*asinh(a + b*x)^2*PolyLog(2, ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))) - 6*asinh(a + b*x)*PolyLog(3, ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))) - 6*asinh(a + b*x)*PolyLog(3, ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))) + 6*PolyLog(4, ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))) + 6*PolyLog(4, ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2)))]
    @test_int [asinh(a + b*x)^3/x^2, x, 13, -(asinh(a + b*x)^3/x) - (3*b*asinh(a + b*x)^2*log(1 - ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))))/sqrt(1 + a^2) + (3*b*asinh(a + b*x)^2*log(1 - ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))))/sqrt(1 + a^2) - (6*b*asinh(a + b*x)*PolyLog(2, ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))))/sqrt(1 + a^2) + (6*b*asinh(a + b*x)*PolyLog(2, ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))))/sqrt(1 + a^2) + (6*b*PolyLog(3, ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))))/sqrt(1 + a^2) - (6*b*PolyLog(3, ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))))/sqrt(1 + a^2)]
    @test_int [asinh(a + b*x)^3/x^3, x, 21, -((3*b^2*asinh(a + b*x)^2)/(2*(1 + a^2))) - (3*b*sqrt(1 + (a + b*x)^2)*asinh(a + b*x)^2)/(2*(1 + a^2)*x) - asinh(a + b*x)^3/(2*x^2) + (3*b^2*asinh(a + b*x)*log(1 - ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))))/(1 + a^2) + (3*a*b^2*asinh(a + b*x)^2*log(1 - ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))))/(2*(1 + a^2)^(3/2)) + (3*b^2*asinh(a + b*x)*log(1 - ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))))/(1 + a^2) - (3*a*b^2*asinh(a + b*x)^2*log(1 - ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))))/(2*(1 + a^2)^(3/2)) + (3*b^2*PolyLog(2, ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))))/(1 + a^2) + (3*a*b^2*asinh(a + b*x)*PolyLog(2, ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))))/(1 + a^2)^(3/2) + (3*b^2*PolyLog(2, ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))))/(1 + a^2) - (3*a*b^2*asinh(a + b*x)*PolyLog(2, ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))))/(1 + a^2)^(3/2) - (3*a*b^2*PolyLog(3, ℯ^asinh(a + b*x)/(a - sqrt(1 + a^2))))/(1 + a^2)^(3/2) + (3*a*b^2*PolyLog(3, ℯ^asinh(a + b*x)/(a + sqrt(1 + a^2))))/(1 + a^2)^(3/2)]

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

    @test_int [x^2/asinh(a + b*x), x, 14, -CoshIntegral(asinh(a + b*x))/(4*b^3) + (a^2*CoshIntegral(asinh(a + b*x)))/b^3 + CoshIntegral(3*asinh(a + b*x))/(4*b^3) - (a*SinhIntegral(2*asinh(a + b*x)))/b^3]
    @test_int [x^1/asinh(a + b*x), x, 10, -((a*CoshIntegral(asinh(a + b*x)))/b^2) + SinhIntegral(2*asinh(a + b*x))/(2*b^2)]
    @test_int [x^0*asinh(a + b*x)^(-1), x, 3, CoshIntegral(asinh(a + b*x))/b]
    @test_int [1/(x^1*asinh(a + b*x)), x, 1, Unintegrable(1/(x*asinh(a + b*x)), x)]

    @test_int [x^2/asinh(a + b*x)^2, x, 12, -((a^2*sqrt(1 + (a + b*x)^2))/(b^3*asinh(a + b*x))) + (2*a*(a + b*x)*sqrt(1 + (a + b*x)^2))/(b^3*asinh(a + b*x)) - ((a + b*x)^2*sqrt(1 + (a + b*x)^2))/(b^3*asinh(a + b*x)) - (2*a*CoshIntegral(2*asinh(a + b*x)))/b^3 - SinhIntegral(asinh(a + b*x))/(4*b^3) + (a^2*SinhIntegral(asinh(a + b*x)))/b^3 + (3*SinhIntegral(3*asinh(a + b*x)))/(4*b^3)]
    @test_int [x^1/asinh(a + b*x)^2, x, 8, (a*sqrt(1 + (a + b*x)^2))/(b^2*asinh(a + b*x)) - ((a + b*x)*sqrt(1 + (a + b*x)^2))/(b^2*asinh(a + b*x)) + CoshIntegral(2*asinh(a + b*x))/b^2 - (a*SinhIntegral(asinh(a + b*x)))/b^2]
    @test_int [x^0/asinh(a + b*x)^2, x, 4, -(sqrt(1 + (a + b*x)^2)/(b*asinh(a + b*x))) + SinhIntegral(asinh(a + b*x))/b]
    @test_int [1/(x^1*asinh(a + b*x)^2), x, 1, Unintegrable(1/(x*asinh(a + b*x)^2), x)]

    @test_int [x^2/asinh(a + b*x)^3, x, 24, -((a^2*sqrt(1 + (a + b*x)^2))/(2*b^3*asinh(a + b*x)^2)) + (a*(a + b*x)*sqrt(1 + (a + b*x)^2))/(b^3*asinh(a + b*x)^2) - ((a + b*x)^2*sqrt(1 + (a + b*x)^2))/(2*b^3*asinh(a + b*x)^2) + a/(b^3*asinh(a + b*x)) - (a + b*x)/(b^3*asinh(a + b*x)) - (a^2*(a + b*x))/(2*b^3*asinh(a + b*x)) + (2*a*(a + b*x)^2)/(b^3*asinh(a + b*x)) - (3*(a + b*x)^3)/(2*b^3*asinh(a + b*x)) - CoshIntegral(asinh(a + b*x))/(8*b^3) + (a^2*CoshIntegral(asinh(a + b*x)))/(2*b^3) + (9*CoshIntegral(3*asinh(a + b*x)))/(8*b^3) - (2*a*SinhIntegral(2*asinh(a + b*x)))/b^3]
    @test_int [x^1/asinh(a + b*x)^3, x, 14, (a*sqrt(1 + (a + b*x)^2))/(2*b^2*asinh(a + b*x)^2) - ((a + b*x)*sqrt(1 + (a + b*x)^2))/(2*b^2*asinh(a + b*x)^2) - 1/(2*b^2*asinh(a + b*x)) + (a*(a + b*x))/(2*b^2*asinh(a + b*x)) - (a + b*x)^2/(b^2*asinh(a + b*x)) - (a*CoshIntegral(asinh(a + b*x)))/(2*b^2) + SinhIntegral(2*asinh(a + b*x))/b^2]
    @test_int [x^0/asinh(a + b*x)^3, x, 5, -sqrt(1 + (a + b*x)^2)/(2*b*asinh(a + b*x)^2) - (a + b*x)/(2*b*asinh(a + b*x)) + CoshIntegral(asinh(a + b*x))/(2*b)]
    @test_int [1/(x*asinh(a + b*x)^3), x, 1, Unintegrable(1/(x*asinh(a + b*x)^3), x)]

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

    @test_int [x^m*(a + b*asinh(c + d*x))^n, x, 1, Unintegrable(x^m*(a + b*asinh(c + d*x))^n, x)]

    @test_int [x^2*(a + b*asinh(c + d*x))^n, x, 22, (3^(-1 - n)*(a + b*asinh(c + d*x))^n*Gamma(1 + n, -((3*(a + b*asinh(c + d*x)))/b)))/(ℯ^((3*a)/b)*(-((a + b*asinh(c + d*x))/b))^n*(8*d^3)) - (2^(-2 - n)*c*(a + b*asinh(c + d*x))^n*Gamma(1 + n, -((2*(a + b*asinh(c + d*x)))/b)))/(ℯ^((2*a)/b)*(-((a + b*asinh(c + d*x))/b))^n*d^3) - ((a + b*asinh(c + d*x))^n*Gamma(1 + n, -((a + b*asinh(c + d*x))/b)))/(ℯ^(a/b)*(-((a + b*asinh(c + d*x))/b))^n*(8*d^3)) + (c^2*(a + b*asinh(c + d*x))^n*Gamma(1 + n, -((a + b*asinh(c + d*x))/b)))/(ℯ^(a/b)*(-((a + b*asinh(c + d*x))/b))^n*(2*d^3)) + (ℯ^(a/b)*(a + b*asinh(c + d*x))^n*Gamma(1 + n, (a + b*asinh(c + d*x))/b))/(((a + b*asinh(c + d*x))/b)^n*(8*d^3)) - (c^2*ℯ^(a/b)*(a + b*asinh(c + d*x))^n*Gamma(1 + n, (a + b*asinh(c + d*x))/b))/(((a + b*asinh(c + d*x))/b)^n*(2*d^3)) - (2^(-2 - n)*c*ℯ^((2*a)/b)*(a + b*asinh(c + d*x))^n*Gamma(1 + n, (2*(a + b*asinh(c + d*x)))/b))/(((a + b*asinh(c + d*x))/b)^n*d^3) - (3^(-1 - n)*ℯ^((3*a)/b)*(a + b*asinh(c + d*x))^n*Gamma(1 + n, (3*(a + b*asinh(c + d*x)))/b))/(((a + b*asinh(c + d*x))/b)^n*(8*d^3))]
    @test_int [x^1*(a + b*asinh(c + d*x))^n, x, 14, (2^(-3 - n)*(a + b*asinh(c + d*x))^n*Gamma(1 + n, -((2*(a + b*asinh(c + d*x)))/b)))/(ℯ^((2*a)/b)*(-((a + b*asinh(c + d*x))/b))^n*d^2) - (c*(a + b*asinh(c + d*x))^n*Gamma(1 + n, -((a + b*asinh(c + d*x))/b)))/(ℯ^(a/b)*(-((a + b*asinh(c + d*x))/b))^n*(2*d^2)) + (c*ℯ^(a/b)*(a + b*asinh(c + d*x))^n*Gamma(1 + n, (a + b*asinh(c + d*x))/b))/(((a + b*asinh(c + d*x))/b)^n*(2*d^2)) + (2^(-3 - n)*ℯ^((2*a)/b)*(a + b*asinh(c + d*x))^n*Gamma(1 + n, (2*(a + b*asinh(c + d*x)))/b))/(((a + b*asinh(c + d*x))/b)^n*d^2)]
    @test_int [x^0*(a + b*asinh(c + d*x))^n, x, 5, ((a + b*asinh(c + d*x))^n*Gamma(1 + n, -((a + b*asinh(c + d*x))/b)))/(ℯ^(a/b)*(-((a + b*asinh(c + d*x))/b))^n*(2*d)) - (ℯ^(a/b)*(a + b*asinh(c + d*x))^n*Gamma(1 + n, (a + b*asinh(c + d*x))/b))/(((a + b*asinh(c + d*x))/b)^n*(2*d))]
    @test_int [(a + b*asinh(c + d*x))^n/x^1, x, 1, Unintegrable((a + b*asinh(c + d*x))^n/x, x)]

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

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

    @test_int [x^2*(a + b*asinh(c + d*x))^(1/2), x, 23, (c^2*(c + d*x)*sqrt(a + b*asinh(c + d*x)))/d^3 + ((c + d*x)^3*sqrt(a + b*asinh(c + d*x)))/(3*d^3) - (c*sqrt(a + b*asinh(c + d*x))*cosh(2*asinh(c + d*x)))/(2*d^3) - (sqrt(b)*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(16*d^3) + (sqrt(b)*c^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(4*d^3) + (sqrt(b)*c*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(8*d^3) + (sqrt(b)*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(48*d^3) + (sqrt(b)*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(16*d^3)) - (sqrt(b)*c^2*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(4*d^3)) + (sqrt(b)*c*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(ℯ^((2*a)/b)*(8*d^3)) - (sqrt(b)*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(ℯ^((3*a)/b)*(48*d^3))]
    @test_int [x^1*(a + b*asinh(c + d*x))^(1/2), x, 14, -((c*(c + d*x)*sqrt(a + b*asinh(c + d*x)))/d^2) + (sqrt(a + b*asinh(c + d*x))*cosh(2*asinh(c + d*x)))/(4*d^2) - (sqrt(b)*c*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(4*d^2) - (sqrt(b)*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(16*d^2) + (sqrt(b)*c*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(4*d^2)) - (sqrt(b)*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(ℯ^((2*a)/b)*(16*d^2))]
    @test_int [x^0*(a + b*asinh(c + d*x))^(1/2), x, 8, ((c + d*x)*sqrt(a + b*asinh(c + d*x)))/d + (sqrt(b)*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(4*d) - (sqrt(b)*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(4*d))]

    @test_int [x^1*(a + b*asinh(c + d*x))^(3/2), x, 16, (3*b*c*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(2*d^2) - (c*(c + d*x)*(a + b*asinh(c + d*x))^(3/2))/d^2 + ((a + b*asinh(c + d*x))^(3/2)*cosh(2*asinh(c + d*x)))/(4*d^2) - (3*b^(3/2)*c*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(8*d^2) - (3*b^(3/2)*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(64*d^2) - (3*b^(3/2)*c*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(8*d^2)) + (3*b^(3/2)*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(ℯ^((2*a)/b)*(64*d^2)) - (3*b*sqrt(a + b*asinh(c + d*x))*sinh(2*asinh(c + d*x)))/(16*d^2)]
    @test_int [x^0*(a + b*asinh(c + d*x))^(3/2), x, 9, -((3*b*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(2*d)) + ((c + d*x)*(a + b*asinh(c + d*x))^(3/2))/d + (3*b^(3/2)*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(8*d) + (3*b^(3/2)*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(8*d))]

    @test_int [x^1*(a + b*asinh(c + d*x))^(5/2), x, 18, -((15*b^2*c*(c + d*x)*sqrt(a + b*asinh(c + d*x)))/(4*d^2)) + (5*b*c*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(3/2))/(2*d^2) - (c*(c + d*x)*(a + b*asinh(c + d*x))^(5/2))/d^2 + (15*b^2*sqrt(a + b*asinh(c + d*x))*cosh(2*asinh(c + d*x)))/(64*d^2) + ((a + b*asinh(c + d*x))^(5/2)*cosh(2*asinh(c + d*x)))/(4*d^2) - (15*b^(5/2)*c*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(16*d^2) - (15*b^(5/2)*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(256*d^2) + (15*b^(5/2)*c*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(16*d^2)) - (15*b^(5/2)*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(ℯ^((2*a)/b)*(256*d^2)) - (5*b*(a + b*asinh(c + d*x))^(3/2)*sinh(2*asinh(c + d*x)))/(16*d^2)]
    @test_int [x^0*(a + b*asinh(c + d*x))^(5/2), x, 10, (15*b^2*(c + d*x)*sqrt(a + b*asinh(c + d*x)))/(4*d) - (5*b*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(3/2))/(2*d) + ((c + d*x)*(a + b*asinh(c + d*x))^(5/2))/d + (15*b^(5/2)*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(16*d) - (15*b^(5/2)*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(16*d))]

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

    @test_int [x^2/(a + b*asinh(c + d*x))^(1/2), x, 20, -((ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(8*sqrt(b)*d^3)) + (c^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(2*sqrt(b)*d^3) + (c*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(2*sqrt(b)*d^3) + (ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(8*sqrt(b)*d^3) - (sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(8*sqrt(b)*d^3)) + (c^2*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(2*sqrt(b)*d^3)) - (c*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(ℯ^((2*a)/b)*(2*sqrt(b)*d^3)) + (sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(ℯ^((3*a)/b)*(8*sqrt(b)*d^3))]
    @test_int [x^1/(a + b*asinh(c + d*x))^(1/2), x, 12, -((c*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(2*sqrt(b)*d^2)) - (ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(4*sqrt(b)*d^2) - (c*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(2*sqrt(b)*d^2)) + (sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(ℯ^((2*a)/b)*(4*sqrt(b)*d^2))]
    @test_int [x^0/(a + b*asinh(c + d*x))^(1/2), x, 7, (ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(2*sqrt(b)*d) + (sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(2*sqrt(b)*d))]

    @test_int [x^1/(a + b*asinh(c + d*x))^(3/2), x, 16, (2*c*sqrt(1 + (c + d*x)^2))/(b*d^2*sqrt(a + b*asinh(c + d*x))) - (2*(c + d*x)*sqrt(1 + (c + d*x)^2))/(b*d^2*sqrt(a + b*asinh(c + d*x))) + (c*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(b^(3/2)*d^2) + (ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(b^(3/2)*d^2) - (c*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(b^(3/2)*d^2)) + (sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(ℯ^((2*a)/b)*(b^(3/2)*d^2))]
    @test_int [x^0/(a + b*asinh(c + d*x))^(3/2), x, 8, -((2*sqrt(1 + (c + d*x)^2))/(b*d*sqrt(a + b*asinh(c + d*x)))) - (ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(b^(3/2)*d) + (sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(b^(3/2)*d))]

    @test_int [x^1/(a + b*asinh(c + d*x))^(5/2), x, 22, (2*c*sqrt(1 + (c + d*x)^2))/(3*b*d^2*(a + b*asinh(c + d*x))^(3/2)) - (2*(c + d*x)*sqrt(1 + (c + d*x)^2))/(3*b*d^2*(a + b*asinh(c + d*x))^(3/2)) - 4/(3*b^2*d^2*sqrt(a + b*asinh(c + d*x))) + (4*c*(c + d*x))/(3*b^2*d^2*sqrt(a + b*asinh(c + d*x))) - (8*(c + d*x)^2)/(3*b^2*d^2*sqrt(a + b*asinh(c + d*x))) - (2*c*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(3*b^(5/2)*d^2) - (2*ℯ^((2*a)/b)*sqrt(2*pi)*erf((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(3*b^(5/2)*d^2) - (2*c*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(3*b^(5/2)*d^2)) + (2*sqrt(2*pi)*erfi((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(ℯ^((2*a)/b)*(3*b^(5/2)*d^2))]
    @test_int [x^0/(a + b*asinh(c + d*x))^(5/2), x, 9, -((2*sqrt(1 + (c + d*x)^2))/(3*b*d*(a + b*asinh(c + d*x))^(3/2))) - (4*(c + d*x))/(3*b^2*d*sqrt(a + b*asinh(c + d*x))) + (2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(3*b^(5/2)*d) + (2*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(3*b^(5/2)*d))]

    @test_int [x^1/(a + b*asinh(c + d*x))^(7/2), x, 21, (2*c*sqrt(1 + (c + d*x)^2))/(5*b*d^2*(a + b*asinh(c + d*x))^(5/2)) - (2*(c + d*x)*sqrt(1 + (c + d*x)^2))/(5*b*d^2*(a + b*asinh(c + d*x))^(5/2)) - 4/(15*b^2*d^2*(a + b*asinh(c + d*x))^(3/2)) + (4*c*(c + d*x))/(15*b^2*d^2*(a + b*asinh(c + d*x))^(3/2)) - (8*(c + d*x)^2)/(15*b^2*d^2*(a + b*asinh(c + d*x))^(3/2)) + (8*c*sqrt(1 + (c + d*x)^2))/(15*b^3*d^2*sqrt(a + b*asinh(c + d*x))) - (32*(c + d*x)*sqrt(1 + (c + d*x)^2))/(15*b^3*d^2*sqrt(a + b*asinh(c + d*x))) + (4*c*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(15*b^(7/2)*d^2) + (8*ℯ^((2*a)/b)*sqrt(2*pi)*erf((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(15*b^(7/2)*d^2) - (4*c*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(15*b^(7/2)*d^2)) + (8*sqrt(2*pi)*erfi((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(ℯ^((2*a)/b)*(15*b^(7/2)*d^2))]
    @test_int [x^0/(a + b*asinh(c + d*x))^(7/2), x, 10, -((2*sqrt(1 + (c + d*x)^2))/(5*b*d*(a + b*asinh(c + d*x))^(5/2))) - (4*(c + d*x))/(15*b^2*d*(a + b*asinh(c + d*x))^(3/2)) - (8*sqrt(1 + (c + d*x)^2))/(15*b^3*d*sqrt(a + b*asinh(c + d*x))) - (4*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(15*b^(7/2)*d) + (4*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(ℯ^(a/b)*(15*b^(7/2)*d))]

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

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

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

    @test_int [(c*e + d*e*x)^4*(a + b*asinh(c + d*x)), x, 6, -((b*e^4*sqrt(1 + (c + d*x)^2))/(5*d)) + (2*b*e^4*(1 + (c + d*x)^2)^(3/2))/(15*d) - (b*e^4*(1 + (c + d*x)^2)^(5/2))/(25*d) + (e^4*(c + d*x)^5*(a + b*asinh(c + d*x)))/(5*d)]
    @test_int [(c*e + d*e*x)^3*(a + b*asinh(c + d*x)), x, 6, (3*b*e^3*(c + d*x)*sqrt(1 + (c + d*x)^2))/(32*d) - (b*e^3*(c + d*x)^3*sqrt(1 + (c + d*x)^2))/(16*d) - (3*b*e^3*asinh(c + d*x))/(32*d) + (e^3*(c + d*x)^4*(a + b*asinh(c + d*x)))/(4*d)]
    @test_int [(c*e + d*e*x)^2*(a + b*asinh(c + d*x)), x, 6, (b*e^2*sqrt(1 + (c + d*x)^2))/(3*d) - (b*e^2*(1 + (c + d*x)^2)^(3/2))/(9*d) + (e^2*(c + d*x)^3*(a + b*asinh(c + d*x)))/(3*d)]
    @test_int [(c*e + d*e*x)*(a + b*asinh(c + d*x)), x, 5, -(b*e*(c + d*x)*sqrt(1 + (c + d*x)^2))/(4*d) + (b*e*asinh(c + d*x))/(4*d) + (e*(c + d*x)^2*(a + b*asinh(c + d*x)))/(2*d)]
    @test_int [a + b*asinh(c + d*x), x, 4, a*x - (b*sqrt(1 + (c + d*x)^2))/d + (b*(c + d*x)*asinh(c + d*x))/d]
    @test_int [(a + b*asinh(c + d*x))/(c*e + d*e*x), x, 7, (a + b*asinh(c + d*x))^2/(2*b*d*e) + ((a + b*asinh(c + d*x))*log(1 - ℯ^(-2*asinh(c + d*x))))/(d*e) - (b*PolyLog(2, ℯ^(-2*asinh(c + d*x))))/(2*d*e)]
    @test_int [(a + b*asinh(c + d*x))/(c*e + d*e*x)^2, x, 6, -((a + b*asinh(c + d*x))/(d*e^2*(c + d*x))) - (b*atanh(sqrt(1 + (c + d*x)^2)))/(d*e^2)]
    @test_int [(a + b*asinh(c + d*x))/(c*e + d*e*x)^3, x, 4, -(b*sqrt(1 + (c + d*x)^2))/(2*d*e^3*(c + d*x)) - (a + b*asinh(c + d*x))/(2*d*e^3*(c + d*x)^2)]
    @test_int [(a + b*asinh(c + d*x))/(c*e + d*e*x)^4, x, 7, -(b*sqrt(1 + (c + d*x)^2))/(6*d*e^4*(c + d*x)^2) - (a + b*asinh(c + d*x))/(3*d*e^4*(c + d*x)^3) + (b*atanh(sqrt(1 + (c + d*x)^2)))/(6*d*e^4)]
    @test_int [(a + b*asinh(c + d*x))/(c*e + d*e*x)^5, x, 5, -(b*sqrt(1 + (c + d*x)^2))/(12*d*e^5*(c + d*x)^3) + (b*sqrt(1 + (c + d*x)^2))/(6*d*e^5*(c + d*x)) - (a + b*asinh(c + d*x))/(4*d*e^5*(c + d*x)^4)]
    @test_int [(a + b*asinh(c + d*x))/(c*e + d*e*x)^6, x, 8, -(b*sqrt(1 + (c + d*x)^2))/(20*d*e^6*(c + d*x)^4) + (3*b*sqrt(1 + (c + d*x)^2))/(40*d*e^6*(c + d*x)^2) - (a + b*asinh(c + d*x))/(5*d*e^6*(c + d*x)^5) - (3*b*atanh(sqrt(1 + (c + d*x)^2)))/(40*d*e^6)]

    @test_int [(c*e + d*e*x)^m*(a + b*asinh(c + d*x))^2, x, 3, If(13>=8, ((e*(c + d*x))^(1 + m)*(a + b*asinh(c + d*x))^2)/(d*e*(1 + m)) - (2*b*(e*(c + d*x))^(2 + m)*(a + b*asinh(c + d*x))*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, -(c + d*x)^2))/(d*e^2*(1 + m)*(2 + m)) + (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*asinh(c + d*x))^2)/(d*e*(1 + m)) - (2*b*(e*(c + d*x))^(2 + m)*(a + b*asinh(c + d*x))*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, -(c + d*x)^2))/(d*e^2*(1 + m)*(2 + m)) + (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)^4*(a + b*asinh(c + d*x))^2, x, 9, (16/75)*b^2*e^4*x - (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)^2)*(a + b*asinh(c + d*x)))/(75*d) + (8*b*e^4*(c + d*x)^2*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x)))/(75*d) - (2*b*e^4*(c + d*x)^4*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x)))/(25*d) + (e^4*(c + d*x)^5*(a + b*asinh(c + d*x))^2)/(5*d)]
    @test_int [(c*e + d*e*x)^3*(a + b*asinh(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*(c + d*x)*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x)))/(16*d) - (b*e^3*(c + d*x)^3*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x)))/(8*d) - (3*e^3*(a + b*asinh(c + d*x))^2)/(32*d) + (e^3*(c + d*x)^4*(a + b*asinh(c + d*x))^2)/(4*d)]
    @test_int [(c*e + d*e*x)^2*(a + b*asinh(c + d*x))^2, x, 7, (-(4/9))*b^2*e^2*x + (2*b^2*e^2*(c + d*x)^3)/(27*d) + (4*b*e^2*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x)))/(9*d) - (2*b*e^2*(c + d*x)^2*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x)))/(9*d) + (e^2*(c + d*x)^3*(a + b*asinh(c + d*x))^2)/(3*d)]
    @test_int [(c*e + d*e*x)*(a + b*asinh(c + d*x))^2, x, 6, (b^2*e*(c + d*x)^2)/(4*d) - (b*e*(c + d*x)*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x)))/(2*d) + (e*(a + b*asinh(c + d*x))^2)/(4*d) + (e*(c + d*x)^2*(a + b*asinh(c + d*x))^2)/(2*d)]
    @test_int [(a + b*asinh(c + d*x))^2, x, 4, 2*b^2*x - (2*b*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x)))/d + ((c + d*x)*(a + b*asinh(c + d*x))^2)/d]
    @test_int [(a + b*asinh(c + d*x))^2/(c*e + d*e*x), x, 8, (a + b*asinh(c + d*x))^3/(3*b*d*e) + ((a + b*asinh(c + d*x))^2*log(1 - ℯ^(-2*asinh(c + d*x))))/(d*e) - (b*(a + b*asinh(c + d*x))*PolyLog(2, ℯ^(-2*asinh(c + d*x))))/(d*e) - (b^2*PolyLog(3, ℯ^(-2*asinh(c + d*x))))/(2*d*e)]
    @test_int [(a + b*asinh(c + d*x))^2/(c*e + d*e*x)^2, x, 9, -((a + b*asinh(c + d*x))^2/(d*e^2*(c + d*x))) - (4*b*(a + b*asinh(c + d*x))*atanh(ℯ^asinh(c + d*x)))/(d*e^2) - (2*b^2*PolyLog(2, -ℯ^asinh(c + d*x)))/(d*e^2) + (2*b^2*PolyLog(2, ℯ^asinh(c + d*x)))/(d*e^2)]
    @test_int [(a + b*asinh(c + d*x))^2/(c*e + d*e*x)^3, x, 5, -((b*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x)))/(d*e^3*(c + d*x))) - (a + b*asinh(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*asinh(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)^2)*(a + b*asinh(c + d*x)))/(3*d*e^4*(c + d*x)^2) - (a + b*asinh(c + d*x))^2/(3*d*e^4*(c + d*x)^3) + (2*b*(a + b*asinh(c + d*x))*atanh(ℯ^asinh(c + d*x)))/(3*d*e^4) + (b^2*PolyLog(2, -ℯ^asinh(c + d*x)))/(3*d*e^4) - (b^2*PolyLog(2, ℯ^asinh(c + d*x)))/(3*d*e^4)]

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

    @test_int [(c*e + d*e*x)^4*(a + b*asinh(c + d*x))^3, x, 17, (16/25)*a*b^2*e^4*x - (298*b^3*e^4*sqrt(1 + (c + d*x)^2))/(375*d) + (76*b^3*e^4*(1 + (c + d*x)^2)^(3/2))/(1125*d) - (6*b^3*e^4*(1 + (c + d*x)^2)^(5/2))/(625*d) + (16*b^3*e^4*(c + d*x)*asinh(c + d*x))/(25*d) - (8*b^2*e^4*(c + d*x)^3*(a + b*asinh(c + d*x)))/(75*d) + (6*b^2*e^4*(c + d*x)^5*(a + b*asinh(c + d*x)))/(125*d) - (8*b*e^4*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^2)/(25*d) + (4*b*e^4*(c + d*x)^2*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^2)/(25*d) - (3*b*e^4*(c + d*x)^4*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^2)/(25*d) + (e^4*(c + d*x)^5*(a + b*asinh(c + d*x))^3)/(5*d)]
    @test_int [(c*e + d*e*x)^3*(a + b*asinh(c + d*x))^3, x, 13, (45*b^3*e^3*(c + d*x)*sqrt(1 + (c + d*x)^2))/(256*d) - (3*b^3*e^3*(c + d*x)^3*sqrt(1 + (c + d*x)^2))/(128*d) - (45*b^3*e^3*asinh(c + d*x))/(256*d) - (9*b^2*e^3*(c + d*x)^2*(a + b*asinh(c + d*x)))/(32*d) + (3*b^2*e^3*(c + d*x)^4*(a + b*asinh(c + d*x)))/(32*d) + (9*b*e^3*(c + d*x)*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^2)/(32*d) - (3*b*e^3*(c + d*x)^3*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^2)/(16*d) - (3*e^3*(a + b*asinh(c + d*x))^3)/(32*d) + (e^3*(c + d*x)^4*(a + b*asinh(c + d*x))^3)/(4*d)]
    @test_int [(c*e + d*e*x)^2*(a + b*asinh(c + d*x))^3, x, 12, (-(4/3))*a*b^2*e^2*x + (14*b^3*e^2*sqrt(1 + (c + d*x)^2))/(9*d) - (2*b^3*e^2*(1 + (c + d*x)^2)^(3/2))/(27*d) - (4*b^3*e^2*(c + d*x)*asinh(c + d*x))/(3*d) + (2*b^2*e^2*(c + d*x)^3*(a + b*asinh(c + d*x)))/(9*d) + (2*b*e^2*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^2)/(3*d) - (b*e^2*(c + d*x)^2*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^2)/(3*d) + (e^2*(c + d*x)^3*(a + b*asinh(c + d*x))^3)/(3*d)]
    @test_int [(c*e + d*e*x)*(a + b*asinh(c + d*x))^3, x, 8, (-3*b^3*e*(c + d*x)*sqrt(1 + (c + d*x)^2))/(8*d) + (3*b^3*e*asinh(c + d*x))/(8*d) + (3*b^2*e*(c + d*x)^2*(a + b*asinh(c + d*x)))/(4*d) - (3*b*e*(c + d*x)*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^2)/(4*d) + (e*(a + b*asinh(c + d*x))^3)/(4*d) + (e*(c + d*x)^2*(a + b*asinh(c + d*x))^3)/(2*d)]
    @test_int [(a + b*asinh(c + d*x))^3, x, 6, 6*a*b^2*x - (6*b^3*sqrt(1 + (c + d*x)^2))/d + (6*b^3*(c + d*x)*asinh(c + d*x))/d - (3*b*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^2)/d + ((c + d*x)*(a + b*asinh(c + d*x))^3)/d]
    @test_int [(a + b*asinh(c + d*x))^3/(c*e + d*e*x), x, 9, (a + b*asinh(c + d*x))^4/(4*b*d*e) + ((a + b*asinh(c + d*x))^3*log(1 - ℯ^(-2*asinh(c + d*x))))/(d*e) - (3*b*(a + b*asinh(c + d*x))^2*PolyLog(2, ℯ^(-2*asinh(c + d*x))))/(2*d*e) - (3*b^2*(a + b*asinh(c + d*x))*PolyLog(3, ℯ^(-2*asinh(c + d*x))))/(2*d*e) - (3*b^3*PolyLog(4, ℯ^(-2*asinh(c + d*x))))/(4*d*e)]
    @test_int [(a + b*asinh(c + d*x))^3/(c*e + d*e*x)^2, x, 11, -((a + b*asinh(c + d*x))^3/(d*e^2*(c + d*x))) - (6*b*(a + b*asinh(c + d*x))^2*atanh(ℯ^asinh(c + d*x)))/(d*e^2) - (6*b^2*(a + b*asinh(c + d*x))*PolyLog(2, -ℯ^asinh(c + d*x)))/(d*e^2) + (6*b^2*(a + b*asinh(c + d*x))*PolyLog(2, ℯ^asinh(c + d*x)))/(d*e^2) + (6*b^3*PolyLog(3, -ℯ^asinh(c + d*x)))/(d*e^2) - (6*b^3*PolyLog(3, ℯ^asinh(c + d*x)))/(d*e^2)]
    @test_int [(a + b*asinh(c + d*x))^3/(c*e + d*e*x)^3, x, 9, (3*b*(a + b*asinh(c + d*x))^2)/(2*d*e^3) - (3*b*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^2)/(2*d*e^3*(c + d*x)) - (a + b*asinh(c + d*x))^3/(2*d*e^3*(c + d*x)^2) + (3*b^2*(a + b*asinh(c + d*x))*log(1 - ℯ^(-2*asinh(c + d*x))))/(d*e^3) - (3*b^3*PolyLog(2, ℯ^(-2*asinh(c + d*x))))/(2*d*e^3)]
    @test_int [(a + b*asinh(c + d*x))^3/(c*e + d*e*x)^4, x, 16, -((b^2*(a + b*asinh(c + d*x)))/(d*e^4*(c + d*x))) - (b*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^2)/(2*d*e^4*(c + d*x)^2) - (a + b*asinh(c + d*x))^3/(3*d*e^4*(c + d*x)^3) + (b*(a + b*asinh(c + d*x))^2*atanh(ℯ^asinh(c + d*x)))/(d*e^4) - (b^3*atanh(sqrt(1 + (c + d*x)^2)))/(d*e^4) + (b^2*(a + b*asinh(c + d*x))*PolyLog(2, -ℯ^asinh(c + d*x)))/(d*e^4) - (b^2*(a + b*asinh(c + d*x))*PolyLog(2, ℯ^asinh(c + d*x)))/(d*e^4) - (b^3*PolyLog(3, -ℯ^asinh(c + d*x)))/(d*e^4) + (b^3*PolyLog(3, ℯ^asinh(c + d*x)))/(d*e^4)]

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

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

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

    @test_int [(c*e + d*e*x)^m/(a + b*asinh(c + d*x)), x, 1, Unintegrable((e*(c + d*x))^m/(a + b*asinh(c + d*x)), x)]

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

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

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

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

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

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

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

    @test_int [(c*e + d*e*x)^4*(a + b*asinh(c + d*x))^(3/2), x, 43, (-4*b*e^4*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(25*d) + (2*b*e^4*(c + d*x)^2*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(25*d) - (3*b*e^4*(c + d*x)^4*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(50*d) + (e^4*(c + d*x)^5*(a + b*asinh(c + d*x))^(3/2))/(5*d) + (3*b^(3/2)*e^4*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(64*d) - (b^(3/2)*e^4*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(200*d) - (3*b^(3/2)*e^4*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(3200*d) + (3*b^(3/2)*e^4*ℯ^((5*a)/b)*sqrt(pi/5)*erf((sqrt(5)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(3200*d) + (3*b^(3/2)*e^4*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(64*d*ℯ^(a/b)) - (b^(3/2)*e^4*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(200*d*ℯ^((3*a)/b)) - (3*b^(3/2)*e^4*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(3200*d*ℯ^((3*a)/b)) + (3*b^(3/2)*e^4*sqrt(pi/5)*erfi((sqrt(5)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(3200*d*ℯ^((5*a)/b))]
    @test_int [(c*e + d*e*x)^3*(a + b*asinh(c + d*x))^(3/2), x, 27, (9*b*e^3*(c + d*x)*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(64*d) - (3*b*e^3*(c + d*x)^3*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(32*d) - (3*e^3*(a + b*asinh(c + d*x))^(3/2))/(32*d) + (e^3*(c + d*x)^4*(a + b*asinh(c + d*x))^(3/2))/(4*d) - (3*b^(3/2)*e^3*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*asinh(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*asinh(c + d*x)))/sqrt(b)))/(128*d) + (3*b^(3/2)*e^3*sqrt(pi)*erfi((2*sqrt(a + b*asinh(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*asinh(c + d*x)))/sqrt(b)))/(128*d*ℯ^((2*a)/b))]
    @test_int [(c*e + d*e*x)^2*(a + b*asinh(c + d*x))^(3/2), x, 24, (b*e^2*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(3*d) - (b*e^2*(c + d*x)^2*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(6*d) + (e^2*(c + d*x)^3*(a + b*asinh(c + d*x))^(3/2))/(3*d) - (3*b^(3/2)*e^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(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*asinh(c + d*x)))/sqrt(b)))/(96*d) - (3*b^(3/2)*e^2*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(32*d*ℯ^(a/b)) + (b^(3/2)*e^2*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(96*d*ℯ^((3*a)/b))]
    @test_int [(c*e + d*e*x)^1*(a + b*asinh(c + d*x))^(3/2), x, 13, (-3*b*e*(c + d*x)*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(8*d) + (e*(a + b*asinh(c + d*x))^(3/2))/(4*d) + (e*(c + d*x)^2*(a + b*asinh(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*asinh(c + d*x)))/sqrt(b)))/(64*d) + (3*b^(3/2)*e*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(64*d*ℯ^((2*a)/b))]
    @test_int [(a + b*asinh(c + d*x))^(3/2), x, 9, (-3*b*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(2*d) + ((c + d*x)*(a + b*asinh(c + d*x))^(3/2))/d + (3*b^(3/2)*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(8*d) + (3*b^(3/2)*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(8*d*ℯ^(a/b))]
    @test_int [1/(c*e + d*e*x)*(a + b*asinh(c + d*x))^(3/2), x, 2, Unintegrable((a + b*asinh(c + d*x))^(3/2)/(c + d*x), x)/e]

    @test_int [(c*e + d*e*x)^4*(a + b*asinh(c + d*x))^(5/2), x, 46, (2*b^2*e^4*(c + d*x)*sqrt(a + b*asinh(c + d*x)))/(5*d) - (b^2*e^4*(c + d*x)^3*sqrt(a + b*asinh(c + d*x)))/(15*d) + (3*b^2*e^4*(c + d*x)^5*sqrt(a + b*asinh(c + d*x)))/(100*d) - (4*b*e^4*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(3/2))/(15*d) + (2*b*e^4*(c + d*x)^2*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(3/2))/(15*d) - (b*e^4*(c + d*x)^4*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(3/2))/(10*d) + (e^4*(c + d*x)^5*(a + b*asinh(c + d*x))^(5/2))/(5*d) + (15*b^(5/2)*e^4*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(128*d) - (b^(5/2)*e^4*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(240*d) - (b^(5/2)*e^4*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(1280*d) + (3*b^(5/2)*e^4*ℯ^((5*a)/b)*sqrt(pi/5)*erf((sqrt(5)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(6400*d) - (15*b^(5/2)*e^4*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(128*d*ℯ^(a/b)) + (b^(5/2)*e^4*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(240*d*ℯ^((3*a)/b)) + (b^(5/2)*e^4*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(1280*d*ℯ^((3*a)/b)) - (3*b^(5/2)*e^4*sqrt(pi/5)*erfi((sqrt(5)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(6400*d*ℯ^((5*a)/b))]
    @test_int [(c*e + d*e*x)^3*(a + b*asinh(c + d*x))^(5/2), x, 29, (-225*b^2*e^3*sqrt(a + b*asinh(c + d*x)))/(2048*d) - (45*b^2*e^3*(c + d*x)^2*sqrt(a + b*asinh(c + d*x)))/(256*d) + (15*b^2*e^3*(c + d*x)^4*sqrt(a + b*asinh(c + d*x)))/(256*d) + (15*b*e^3*(c + d*x)*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(3/2))/(64*d) - (5*b*e^3*(c + d*x)^3*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(3/2))/(32*d) - (3*e^3*(a + b*asinh(c + d*x))^(5/2))/(32*d) + (e^3*(c + d*x)^4*(a + b*asinh(c + d*x))^(5/2))/(4*d) - (15*b^(5/2)*e^3*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*asinh(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*asinh(c + d*x)))/sqrt(b)))/(512*d) - (15*b^(5/2)*e^3*sqrt(pi)*erfi((2*sqrt(a + b*asinh(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*asinh(c + d*x)))/sqrt(b)))/(512*d*ℯ^((2*a)/b))]
    @test_int [(c*e + d*e*x)^2*(a + b*asinh(c + d*x))^(5/2), x, 26, (-5*b^2*e^2*(c + d*x)*sqrt(a + b*asinh(c + d*x)))/(6*d) + (5*b^2*e^2*(c + d*x)^3*sqrt(a + b*asinh(c + d*x)))/(36*d) + (5*b*e^2*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(3/2))/(9*d) - (5*b*e^2*(c + d*x)^2*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(3/2))/(18*d) + (e^2*(c + d*x)^3*(a + b*asinh(c + d*x))^(5/2))/(3*d) - (15*b^(5/2)*e^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(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*asinh(c + d*x)))/sqrt(b)))/(576*d) + (15*b^(5/2)*e^2*sqrt(pi)*erfi(sqrt(a + b*asinh(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*asinh(c + d*x)))/sqrt(b)))/(576*d*ℯ^((3*a)/b))]
    @test_int [(c*e + d*e*x)*(a + b*asinh(c + d*x))^(5/2), x, 14, (15*b^2*e*sqrt(a + b*asinh(c + d*x)))/(64*d) + (15*b^2*e*(c + d*x)^2*sqrt(a + b*asinh(c + d*x)))/(32*d) - (5*b*e*(c + d*x)*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(3/2))/(8*d) + (e*(a + b*asinh(c + d*x))^(5/2))/(4*d) + (e*(c + d*x)^2*(a + b*asinh(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*asinh(c + d*x)))/sqrt(b)))/(256*d) - (15*b^(5/2)*e*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(256*d*ℯ^((2*a)/b))]
    @test_int [(a + b*asinh(c + d*x))^(5/2), x, 10, (15*b^2*(c + d*x)*sqrt(a + b*asinh(c + d*x)))/(4*d) - (5*b*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(3/2))/(2*d) + ((c + d*x)*(a + b*asinh(c + d*x))^(5/2))/d + (15*b^(5/2)*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(16*d) - (15*b^(5/2)*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(16*d*ℯ^(a/b))]
    @test_int [1/(c*e + d*e*x)*(a + b*asinh(c + d*x))^(5/2), x, 2, Unintegrable((a + b*asinh(c + d*x))^(5/2)/(c + d*x), x)/e]

    @test_int [(c*e + d*e*x)^4*(a + b*asinh(c + d*x))^(7/2), x, 77, (-1813*b^3*e^4*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(1125*d) + (119*b^3*e^4*(c + d*x)^2*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(1125*d) - (21*b^3*e^4*(c + d*x)^4*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(1000*d) + (14*b^2*e^4*(c + d*x)*(a + b*asinh(c + d*x))^(3/2))/(15*d) - (7*b^2*e^4*(c + d*x)^3*(a + b*asinh(c + d*x))^(3/2))/(45*d) + (7*b^2*e^4*(c + d*x)^5*(a + b*asinh(c + d*x))^(3/2))/(100*d) - (28*b*e^4*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(5/2))/(75*d) + (14*b*e^4*(c + d*x)^2*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(5/2))/(75*d) - (7*b*e^4*(c + d*x)^4*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(5/2))/(50*d) + (e^4*(c + d*x)^5*(a + b*asinh(c + d*x))^(7/2))/(5*d) + (105*b^(7/2)*e^4*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(256*d) - (119*b^(7/2)*e^4*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(18000*d) - (21*b^(7/2)*e^4*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(64000*d) + (21*b^(7/2)*e^4*ℯ^((5*a)/b)*sqrt(pi/5)*erf((sqrt(5)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(64000*d) + (105*b^(7/2)*e^4*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(256*d*ℯ^(a/b)) - (119*b^(7/2)*e^4*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(18000*d*ℯ^((3*a)/b)) - (21*b^(7/2)*e^4*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(64000*d*ℯ^((3*a)/b)) + (21*b^(7/2)*e^4*sqrt(pi/5)*erfi((sqrt(5)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(64000*d*ℯ^((5*a)/b))]
    @test_int [(c*e + d*e*x)^3*(a + b*asinh(c + d*x))^(7/2), x, 42, (1575*b^3*e^3*(c + d*x)*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(4096*d) - (105*b^3*e^3*(c + d*x)^3*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(2048*d) - (525*b^2*e^3*(a + b*asinh(c + d*x))^(3/2))/(2048*d) - (105*b^2*e^3*(c + d*x)^2*(a + b*asinh(c + d*x))^(3/2))/(256*d) + (35*b^2*e^3*(c + d*x)^4*(a + b*asinh(c + d*x))^(3/2))/(256*d) + (21*b*e^3*(c + d*x)*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(5/2))/(64*d) - (7*b*e^3*(c + d*x)^3*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(5/2))/(32*d) - (3*e^3*(a + b*asinh(c + d*x))^(7/2))/(32*d) + (e^3*(c + d*x)^4*(a + b*asinh(c + d*x))^(7/2))/(4*d) - (105*b^(7/2)*e^3*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(131072*d) + (105*b^(7/2)*e^3*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(2048*d) + (105*b^(7/2)*e^3*sqrt(pi)*erfi((2*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(131072*d*ℯ^((4*a)/b)) - (105*b^(7/2)*e^3*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(2048*d*ℯ^((2*a)/b))]
    @test_int [(c*e + d*e*x)^2*(a + b*asinh(c + d*x))^(7/2), x, 35, (175*b^3*e^2*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(54*d) - (35*b^3*e^2*(c + d*x)^2*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(216*d) - (35*b^2*e^2*(c + d*x)*(a + b*asinh(c + d*x))^(3/2))/(18*d) + (35*b^2*e^2*(c + d*x)^3*(a + b*asinh(c + d*x))^(3/2))/(108*d) + (7*b*e^2*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(5/2))/(9*d) - (7*b*e^2*(c + d*x)^2*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(5/2))/(18*d) + (e^2*(c + d*x)^3*(a + b*asinh(c + d*x))^(7/2))/(3*d) - (105*b^(7/2)*e^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(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*asinh(c + d*x)))/sqrt(b)))/(3456*d) - (105*b^(7/2)*e^2*sqrt(pi)*erfi(sqrt(a + b*asinh(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*asinh(c + d*x)))/sqrt(b)))/(3456*d*ℯ^((3*a)/b))]
    @test_int [(c*e + d*e*x)^1*(a + b*asinh(c + d*x))^(7/2), x, 16, (-105*b^3*e*(c + d*x)*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(128*d) + (35*b^2*e*(a + b*asinh(c + d*x))^(3/2))/(64*d) + (35*b^2*e*(c + d*x)^2*(a + b*asinh(c + d*x))^(3/2))/(32*d) - (7*b*e*(c + d*x)*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(5/2))/(8*d) + (e*(a + b*asinh(c + d*x))^(7/2))/(4*d) + (e*(c + d*x)^2*(a + b*asinh(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*asinh(c + d*x)))/sqrt(b)))/(1024*d) + (105*b^(7/2)*e*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(1024*d*ℯ^((2*a)/b))]
    @test_int [(a + b*asinh(c + d*x))^(7/2), x, 11, (-105*b^3*sqrt(1 + (c + d*x)^2)*sqrt(a + b*asinh(c + d*x)))/(8*d) + (35*b^2*(c + d*x)*(a + b*asinh(c + d*x))^(3/2))/(4*d) - (7*b*sqrt(1 + (c + d*x)^2)*(a + b*asinh(c + d*x))^(5/2))/(2*d) + ((c + d*x)*(a + b*asinh(c + d*x))^(7/2))/d + (105*b^(7/2)*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(32*d) + (105*b^(7/2)*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(32*d*ℯ^(a/b))]
    @test_int [1/(c*e + d*e*x)*(a + b*asinh(c + d*x))^(7/2), x, 2, Unintegrable((a + b*asinh(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*asinh(c + d*x)), x, 20, (e^4*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(16*sqrt(b)*d) - (e^4*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(32*sqrt(b)*d) + (e^4*ℯ^((5*a)/b)*sqrt(pi/5)*erf((sqrt(5)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(32*sqrt(b)*d) + (e^4*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(16*sqrt(b)*d*ℯ^(a/b)) - (e^4*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(32*sqrt(b)*d*ℯ^((3*a)/b)) + (e^4*sqrt(pi/5)*erfi((sqrt(5)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(32*sqrt(b)*d*ℯ^((5*a)/b))]
    @test_int [(c*e + d*e*x)^3/sqrt(a + b*asinh(c + d*x)), x, 15, -(e^3*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(32*sqrt(b)*d) + (e^3*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(8*sqrt(b)*d) + (e^3*sqrt(pi)*erfi((2*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(32*sqrt(b)*d*ℯ^((4*a)/b)) - (e^3*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(8*sqrt(b)*d*ℯ^((2*a)/b))]
    @test_int [(c*e + d*e*x)^2/sqrt(a + b*asinh(c + d*x)), x, 15, -(e^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(8*sqrt(b)*d) + (e^2*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(8*sqrt(b)*d) - (e^2*sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(8*sqrt(b)*d*ℯ^(a/b)) + (e^2*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(8*sqrt(b)*d*ℯ^((3*a)/b))]
    @test_int [(c*e + d*e*x)^1/sqrt(a + b*asinh(c + d*x)), x, 10, -(e*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(4*sqrt(b)*d) + (e*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c + d*x)))/sqrt(b)))/(4*sqrt(b)*d*ℯ^((2*a)/b))]
    @test_int [1/sqrt(a + b*asinh(c + d*x)), x, 7, (ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(2*sqrt(b)*d) + (sqrt(pi)*erfi(sqrt(a + b*asinh(c + d*x))/sqrt(b)))/(2*sqrt(b)*d*ℯ^(a/b))]
    @test_int [1/(c*e + d*e*x)/sqrt(a + b*asinh(c + d*x)), x, 2, Unintegrable(1/((c + d*x)*sqrt(a + b*asinh(c + d*x))), x)/e]

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

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

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

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

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

    @test_int [(c*e + d*e*x)^(7/2)*(a + b*asinh(c + d*x)), x, 8, (28*b*e^2*(e*(c + d*x))^(3/2)*sqrt(1 + (c + d*x)^2))/(405*d) - (4*b*(e*(c + d*x))^(7/2)*sqrt(1 + (c + d*x)^2))/(81*d) - (28*b*e^3*sqrt(e*(c + d*x))*sqrt(1 + (c + d*x)^2))/(135*d*(1 + c + d*x)) + (2*(e*(c + d*x))^(9/2)*(a + b*asinh(c + d*x)))/(9*d*e) + (28*b*e^(7/2)*(1 + c + d*x)*sqrt((1 + (c + d*x)^2)/(1 + c + d*x)^2)*Elliptic.E(2*atan(sqrt(e*(c + d*x))/sqrt(e)), 1/2))/(135*d*sqrt(1 + (c + d*x)^2)) - (14*b*e^(7/2)*(1 + c + d*x)*sqrt((1 + (c + d*x)^2)/(1 + c + d*x)^2)*Elliptic.F(2*atan(sqrt(e*(c + d*x))/sqrt(e)), 1/2))/(135*d*sqrt(1 + (c + d*x)^2))]
    @test_int [(c*e + d*e*x)^(5/2)*(a + b*asinh(c + d*x)), x, 6, (20*b*e^2*sqrt(e*(c + d*x))*sqrt(1 + (c + d*x)^2))/(147*d) - (4*b*(e*(c + d*x))^(5/2)*sqrt(1 + (c + d*x)^2))/(49*d) + (2*(e*(c + d*x))^(7/2)*(a + b*asinh(c + d*x)))/(7*d*e) - (10*b*e^(5/2)*(1 + c + d*x)*sqrt((1 + (c + d*x)^2)/(1 + c + d*x)^2)*Elliptic.F(2*atan(sqrt(e*(c + d*x))/sqrt(e)), 1/2))/(147*d*sqrt(1 + (c + d*x)^2))]
    @test_int [(c*e + d*e*x)^(3/2)*(a + b*asinh(c + d*x)), x, 7, -((4*b*(e*(c + d*x))^(3/2)*sqrt(1 + (c + d*x)^2))/(25*d)) + (12*b*e*sqrt(e*(c + d*x))*sqrt(1 + (c + d*x)^2))/(25*d*(1 + c + d*x)) + (2*(e*(c + d*x))^(5/2)*(a + b*asinh(c + d*x)))/(5*d*e) - (12*b*e^(3/2)*(1 + c + d*x)*sqrt((1 + (c + d*x)^2)/(1 + c + d*x)^2)*Elliptic.E(2*atan(sqrt(e*(c + d*x))/sqrt(e)), 1/2))/(25*d*sqrt(1 + (c + d*x)^2)) + (6*b*e^(3/2)*(1 + c + d*x)*sqrt((1 + (c + d*x)^2)/(1 + c + d*x)^2)*Elliptic.F(2*atan(sqrt(e*(c + d*x))/sqrt(e)), 1/2))/(25*d*sqrt(1 + (c + d*x)^2))]
    @test_int [sqrt(c*e + d*e*x)*(a + b*asinh(c + d*x)), x, 5, -((4*b*sqrt(e*(c + d*x))*sqrt(1 + (c + d*x)^2))/(9*d)) + (2*(e*(c + d*x))^(3/2)*(a + b*asinh(c + d*x)))/(3*d*e) + (2*b*sqrt(e)*(1 + c + d*x)*sqrt((1 + (c + d*x)^2)/(1 + c + d*x)^2)*Elliptic.F(2*atan(sqrt(e*(c + d*x))/sqrt(e)), 1/2))/(9*d*sqrt(1 + (c + d*x)^2))]
    @test_int [(a + b*asinh(c + d*x))/sqrt(c*e + d*e*x), x, 6, -((4*b*sqrt(e*(c + d*x))*sqrt(1 + (c + d*x)^2))/(d*e*(1 + c + d*x))) + (2*sqrt(e*(c + d*x))*(a + b*asinh(c + d*x)))/(d*e) + (4*b*(1 + c + d*x)*sqrt((1 + (c + d*x)^2)/(1 + c + d*x)^2)*Elliptic.E(2*atan(sqrt(e*(c + d*x))/sqrt(e)), 1/2))/(d*sqrt(e)*sqrt(1 + (c + d*x)^2)) - (2*b*(1 + c + d*x)*sqrt((1 + (c + d*x)^2)/(1 + c + d*x)^2)*Elliptic.F(2*atan(sqrt(e*(c + d*x))/sqrt(e)), 1/2))/(d*sqrt(e)*sqrt(1 + (c + d*x)^2))]
    @test_int [(a + b*asinh(c + d*x))/(c*e + d*e*x)^(3/2), x, 4, -((2*(a + b*asinh(c + d*x)))/(d*e*sqrt(e*(c + d*x)))) + (2*b*(1 + c + d*x)*sqrt((1 + (c + d*x)^2)/(1 + c + d*x)^2)*Elliptic.F(2*atan(sqrt(e*(c + d*x))/sqrt(e)), 1/2))/(d*e^(3/2)*sqrt(1 + (c + d*x)^2))]
    @test_int [(a + b*asinh(c + d*x))/(c*e + d*e*x)^(5/2), x, 7, -((4*b*sqrt(1 + (c + d*x)^2))/(3*d*e^2*sqrt(e*(c + d*x)))) + (4*b*sqrt(e*(c + d*x))*sqrt(1 + (c + d*x)^2))/(3*d*e^3*(1 + c + d*x)) - (2*(a + b*asinh(c + d*x)))/(3*d*e*(e*(c + d*x))^(3/2)) - (4*b*(1 + c + d*x)*sqrt((1 + (c + d*x)^2)/(1 + c + d*x)^2)*Elliptic.E(2*atan(sqrt(e*(c + d*x))/sqrt(e)), 1/2))/(3*d*e^(5/2)*sqrt(1 + (c + d*x)^2)) + (2*b*(1 + c + d*x)*sqrt((1 + (c + d*x)^2)/(1 + c + d*x)^2)*Elliptic.F(2*atan(sqrt(e*(c + d*x))/sqrt(e)), 1/2))/(3*d*e^(5/2)*sqrt(1 + (c + d*x)^2))]
    @test_int [(a + b*asinh(c + d*x))/(c*e + d*e*x)^(7/2), x, 5, -((4*b*sqrt(1 + (c + d*x)^2))/(15*d*e^2*(e*(c + d*x))^(3/2))) - (2*(a + b*asinh(c + d*x)))/(5*d*e*(e*(c + d*x))^(5/2)) - (2*b*(1 + c + d*x)*sqrt((1 + (c + d*x)^2)/(1 + c + d*x)^2)*Elliptic.F(2*atan(sqrt(e*(c + d*x))/sqrt(e)), 1/2))/(15*d*e^(7/2)*sqrt(1 + (c + d*x)^2))]

    @test_int [(c*e + d*e*x)^(7/2)*(a + b*asinh(c + d*x))^2, x, 3, (2*(e*(c + d*x))^(9/2)*(a + b*asinh(c + d*x))^2)/(9*d*e) - (8*b*(e*(c + d*x))^(11/2)*(a + b*asinh(c + d*x))*HypergeometricFunctions._₂F₁(1/2, 11/4, 15/4, -(c + d*x)^2))/(99*d*e^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*asinh(c + d*x))^2, x, 3, (2*(e*(c + d*x))^(7/2)*(a + b*asinh(c + d*x))^2)/(7*d*e) - (8*b*(e*(c + d*x))^(9/2)*(a + b*asinh(c + d*x))*HypergeometricFunctions._₂F₁(1/2, 9/4, 13/4, -(c + d*x)^2))/(63*d*e^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*asinh(c + d*x))^2, x, 3, (2*(e*(c + d*x))^(5/2)*(a + b*asinh(c + d*x))^2)/(5*d*e) - (8*b*(e*(c + d*x))^(7/2)*(a + b*asinh(c + d*x))*HypergeometricFunctions._₂F₁(1/2, 7/4, 11/4, -(c + d*x)^2))/(35*d*e^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*asinh(c + d*x))^2, x, 3, (2*(e*(c + d*x))^(3/2)*(a + b*asinh(c + d*x))^2)/(3*d*e) - (8*b*(e*(c + d*x))^(5/2)*(a + b*asinh(c + d*x))*HypergeometricFunctions._₂F₁(1/2, 5/4, 9/4, -(c + d*x)^2))/(15*d*e^2) + (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*asinh(c + d*x))^2/sqrt(c*e + d*e*x), x, 3, (2*sqrt(e*(c + d*x))*(a + b*asinh(c + d*x))^2)/(d*e) - (8*b*(e*(c + d*x))^(3/2)*(a + b*asinh(c + d*x))*HypergeometricFunctions._₂F₁(1/2, 3/4, 7/4, -(c + d*x)^2))/(3*d*e^2) + (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*asinh(c + d*x))^2/(c*e + d*e*x)^(3/2), x, 3, -((2*(a + b*asinh(c + d*x))^2)/(d*e*sqrt(e*(c + d*x)))) + (8*b*sqrt(e*(c + d*x))*(a + b*asinh(c + d*x))*HypergeometricFunctions._₂F₁(1/4, 1/2, 5/4, -(c + d*x)^2))/(d*e^2) - (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*asinh(c + d*x))^2/(c*e + d*e*x)^(5/2), x, 3, -((2*(a + b*asinh(c + d*x))^2)/(3*d*e*(e*(c + d*x))^(3/2))) - (8*b*(a + b*asinh(c + d*x))*HypergeometricFunctions._₂F₁(-(1/4), 1/2, 3/4, -(c + d*x)^2))/(3*d*e^2*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*asinh(c + d*x))^2/(c*e + d*e*x)^(7/2), x, 3, -((2*(a + b*asinh(c + d*x))^2)/(5*d*e*(e*(c + d*x))^(5/2))) - (8*b*(a + b*asinh(c + d*x))*HypergeometricFunctions._₂F₁(-(3/4), 1/2, 1/4, -(c + d*x)^2))/(15*d*e^2*(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)^(7/2)*(a + b*asinh(c + d*x))^3, x, 2, (2*(e*(c + d*x))^(9/2)*(a + b*asinh(c + d*x))^3)/(9*d*e) - (2*b*Unintegrable(((e*(c + d*x))^(9/2)*(a + b*asinh(c + d*x))^2)/sqrt(1 + (c + d*x)^2), x))/(3*e)]
    @test_int [(c*e + d*e*x)^(5/2)*(a + b*asinh(c + d*x))^3, x, 2, (2*(e*(c + d*x))^(7/2)*(a + b*asinh(c + d*x))^3)/(7*d*e) - (6*b*Unintegrable(((e*(c + d*x))^(7/2)*(a + b*asinh(c + d*x))^2)/sqrt(1 + (c + d*x)^2), x))/(7*e)]
    @test_int [(c*e + d*e*x)^(3/2)*(a + b*asinh(c + d*x))^3, x, 2, (2*(e*(c + d*x))^(5/2)*(a + b*asinh(c + d*x))^3)/(5*d*e) - (6*b*Unintegrable(((e*(c + d*x))^(5/2)*(a + b*asinh(c + d*x))^2)/sqrt(1 + (c + d*x)^2), x))/(5*e)]
    @test_int [sqrt(c*e + d*e*x)*(a + b*asinh(c + d*x))^3, x, 2, (2*(e*(c + d*x))^(3/2)*(a + b*asinh(c + d*x))^3)/(3*d*e) - (2*b*Unintegrable(((e*(c + d*x))^(3/2)*(a + b*asinh(c + d*x))^2)/sqrt(1 + (c + d*x)^2), x))/e]
    @test_int [(a + b*asinh(c + d*x))^3/sqrt(c*e + d*e*x), x, 2, (2*sqrt(e*(c + d*x))*(a + b*asinh(c + d*x))^3)/(d*e) - (6*b*Unintegrable((sqrt(e*(c + d*x))*(a + b*asinh(c + d*x))^2)/sqrt(1 + (c + d*x)^2), x))/e]
    @test_int [(a + b*asinh(c + d*x))^3/(c*e + d*e*x)^(3/2), x, 2, -((2*(a + b*asinh(c + d*x))^3)/(d*e*sqrt(e*(c + d*x)))) + (6*b*Unintegrable((a + b*asinh(c + d*x))^2/(sqrt(e*(c + d*x))*sqrt(1 + (c + d*x)^2)), x))/e]
    @test_int [(a + b*asinh(c + d*x))^3/(c*e + d*e*x)^(5/2), x, 2, -((2*(a + b*asinh(c + d*x))^3)/(3*d*e*(e*(c + d*x))^(3/2))) + (2*b*Unintegrable((a + b*asinh(c + d*x))^2/((e*(c + d*x))^(3/2)*sqrt(1 + (c + d*x)^2)), x))/e]
    @test_int [(a + b*asinh(c + d*x))^3/(c*e + d*e*x)^(7/2), x, 2, -((2*(a + b*asinh(c + d*x))^3)/(5*d*e*(e*(c + d*x))^(5/2))) + (6*b*Unintegrable((a + b*asinh(c + d*x))^2/((e*(c + d*x))^(5/2)*sqrt(1 + (c + d*x)^2)), x))/(5*e)]

    @test_int [(c*e + d*e*x)^(7/2)*(a + b*asinh(c + d*x))^4, x, 2, (2*(e*(c + d*x))^(9/2)*(a + b*asinh(c + d*x))^4)/(9*d*e) - (8*b*Unintegrable(((e*(c + d*x))^(9/2)*(a + b*asinh(c + d*x))^3)/sqrt(1 + (c + d*x)^2), x))/(9*e)]
    @test_int [(c*e + d*e*x)^(5/2)*(a + b*asinh(c + d*x))^4, x, 2, (2*(e*(c + d*x))^(7/2)*(a + b*asinh(c + d*x))^4)/(7*d*e) - (8*b*Unintegrable(((e*(c + d*x))^(7/2)*(a + b*asinh(c + d*x))^3)/sqrt(1 + (c + d*x)^2), x))/(7*e)]
    @test_int [(c*e + d*e*x)^(3/2)*(a + b*asinh(c + d*x))^4, x, 2, (2*(e*(c + d*x))^(5/2)*(a + b*asinh(c + d*x))^4)/(5*d*e) - (8*b*Unintegrable(((e*(c + d*x))^(5/2)*(a + b*asinh(c + d*x))^3)/sqrt(1 + (c + d*x)^2), x))/(5*e)]
    @test_int [sqrt(c*e + d*e*x)*(a + b*asinh(c + d*x))^4, x, 2, (2*(e*(c + d*x))^(3/2)*(a + b*asinh(c + d*x))^4)/(3*d*e) - (8*b*Unintegrable(((e*(c + d*x))^(3/2)*(a + b*asinh(c + d*x))^3)/sqrt(1 + (c + d*x)^2), x))/(3*e)]
    @test_int [(a + b*asinh(c + d*x))^4/sqrt(c*e + d*e*x), x, 2, (2*sqrt(e*(c + d*x))*(a + b*asinh(c + d*x))^4)/(d*e) - (8*b*Unintegrable((sqrt(e*(c + d*x))*(a + b*asinh(c + d*x))^3)/sqrt(1 + (c + d*x)^2), x))/e]
    @test_int [(a + b*asinh(c + d*x))^4/(c*e + d*e*x)^(3/2), x, 2, -((2*(a + b*asinh(c + d*x))^4)/(d*e*sqrt(e*(c + d*x)))) + (8*b*Unintegrable((a + b*asinh(c + d*x))^3/(sqrt(e*(c + d*x))*sqrt(1 + (c + d*x)^2)), x))/e]
    @test_int [(a + b*asinh(c + d*x))^4/(c*e + d*e*x)^(5/2), x, 2, -((2*(a + b*asinh(c + d*x))^4)/(3*d*e*(e*(c + d*x))^(3/2))) + (8*b*Unintegrable((a + b*asinh(c + d*x))^3/((e*(c + d*x))^(3/2)*sqrt(1 + (c + d*x)^2)), x))/(3*e)]
    @test_int [(a + b*asinh(c + d*x))^4/(c*e + d*e*x)^(7/2), x, 2, -((2*(a + b*asinh(c + d*x))^4)/(5*d*e*(e*(c + d*x))^(5/2))) + (8*b*Unintegrable((a + b*asinh(c + d*x))^3/((e*(c + d*x))^(5/2)*sqrt(1 + (c + d*x)^2)), x))/(5*e)]

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(1+(a+b*x)^2)^(m/2)*asinh(a +b*x)^n=#

    #= ::Subsubsection::Closed:: =#
    #=m>0=#

    @test_int [sqrt(1 + a^2 + 2*a*b*x + b^2*x^2)*asinh(a + b*x)^3, x, 7, -((3*(a + b*x)^2)/(8*b)) + (3*(a + b*x)*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/(4*b) - (3*asinh(a + b*x)^2)/(8*b) - (3*(a + b*x)^2*asinh(a + b*x)^2)/(4*b) + ((a + b*x)*sqrt(1 + (a + b*x)^2)*asinh(a + b*x)^3)/(2*b) + asinh(a + b*x)^4/(8*b)]
    @test_int [sqrt(1 + a^2 + 2*a*b*x + b^2*x^2)*asinh(a + b*x)^2, x, 6, ((a + b*x)*sqrt(1 + (a + b*x)^2))/(4*b) - asinh(a + b*x)/(4*b) - ((a + b*x)^2*asinh(a + b*x))/(2*b) + ((a + b*x)*sqrt(1 + (a + b*x)^2)*asinh(a + b*x)^2)/(2*b) + asinh(a + b*x)^3/(6*b)]
    @test_int [sqrt(1 + a^2 + 2*a*b*x + b^2*x^2)*asinh(a + b*x), x, 4, -(a + b*x)^2/(4*b) + ((a + b*x)*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/(2*b) + asinh(a + b*x)^2/(4*b)]
    @test_int [sqrt(1 + a^2 + 2*a*b*x + b^2*x^2)/asinh(a + b*x), x, 5, CoshIntegral(2*asinh(a + b*x))/(2*b) + log(asinh(a + b*x))/(2*b)]
    @test_int [sqrt(1 + a^2 + 2*a*b*x + b^2*x^2)/asinh(a + b*x)^2, x, 6, -((1 + (a + b*x)^2)/(b*asinh(a + b*x))) + SinhIntegral(2*asinh(a + b*x))/b]
    @test_int [sqrt(1 + a^2 + 2*a*b*x + b^2*x^2)/asinh(a + b*x)^3, x, 4, -(1 + (a + b*x)^2)/(2*b*asinh(a + b*x)^2) - ((a + b*x)*sqrt(1 + (a + b*x)^2))/(b*asinh(a + b*x)) + CoshIntegral(2*asinh(a + b*x))/b]

    @test_int [(1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2)*asinh(a + b*x)^3, x, 15, -((51*(a + b*x)^2)/(128*b)) - (3*(a + b*x)^4)/(128*b) + (45*(a + b*x)*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/(64*b) + (3*(a + b*x)*(1 + (a + b*x)^2)^(3/2)*asinh(a + b*x))/(32*b) - (27*asinh(a + b*x)^2)/(128*b) - (9*(a + b*x)^2*asinh(a + b*x)^2)/(16*b) - (3*(1 + (a + b*x)^2)^2*asinh(a + b*x)^2)/(16*b) + (3*(a + b*x)*sqrt(1 + (a + b*x)^2)*asinh(a + b*x)^3)/(8*b) + ((a + b*x)*(1 + (a + b*x)^2)^(3/2)*asinh(a + b*x)^3)/(4*b) + (3*asinh(a + b*x)^4)/(32*b)]
    @test_int [(1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2)*asinh(a + b*x)^2, x, 11, (15*(a + b*x)*sqrt(1 + (a + b*x)^2))/(64*b) + ((a + b*x)*(1 + (a + b*x)^2)^(3/2))/(32*b) - (9*asinh(a + b*x))/(64*b) - (3*(a + b*x)^2*asinh(a + b*x))/(8*b) - ((1 + (a + b*x)^2)^2*asinh(a + b*x))/(8*b) + (3*(a + b*x)*sqrt(1 + (a + b*x)^2)*asinh(a + b*x)^2)/(8*b) + ((a + b*x)*(1 + (a + b*x)^2)^(3/2)*asinh(a + b*x)^2)/(4*b) + asinh(a + b*x)^3/(8*b)]
    @test_int [(1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2)*asinh(a + b*x), x, 7, -((5*(a + b*x)^2)/(16*b)) - (a + b*x)^4/(16*b) + (3*(a + b*x)*sqrt(1 + (a + b*x)^2)*asinh(a + b*x))/(8*b) + ((a + b*x)*(1 + (a + b*x)^2)^(3/2)*asinh(a + b*x))/(4*b) + (3*asinh(a + b*x)^2)/(16*b)]
    @test_int [(1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2)/asinh(a + b*x), x, 6, CoshIntegral(2*asinh(a + b*x))/(2*b) + CoshIntegral(4*asinh(a + b*x))/(8*b) + (3*log(asinh(a + b*x)))/(8*b)]
    @test_int [(1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2)/asinh(a + b*x)^2, x, 7, -((1 + (a + b*x)^2)^2/(b*asinh(a + b*x))) + SinhIntegral(2*asinh(a + b*x))/b + SinhIntegral(4*asinh(a + b*x))/(2*b)]
    @test_int [(1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2)/asinh(a + b*x)^3, x, 11, -(1 + (a + b*x)^2)^2/(2*b*asinh(a + b*x)^2) - (2*(a + b*x)*(1 + (a + b*x)^2)^(3/2))/(b*asinh(a + b*x)) + CoshIntegral(2*asinh(a + b*x))/b + CoshIntegral(4*asinh(a + b*x))/b]

    #= ::Subsubsection::Closed:: =#
    #=m<0=#

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

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

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

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

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

    @test_int [x^3*asinh(a*x^2), x, 5, -((x^2*sqrt(1 + a^2*x^4))/(8*a)) + asinh(a*x^2)/(8*a^2) + (1/4)*x^4*asinh(a*x^2)]
    @test_int [x^2*asinh(a*x^2), x, 4, -((2*x*sqrt(1 + a^2*x^4))/(9*a)) + (1/3)*x^3*asinh(a*x^2) + ((1 + a*x^2)*sqrt((1 + a^2*x^4)/(1 + a*x^2)^2)*Elliptic.F(2*atan(sqrt(a)*x), 1/2))/(9*a^(3/2)*sqrt(1 + a^2*x^4))]
    @test_int [x^1*asinh(a*x^2), x, 3, -(sqrt(1 + a^2*x^4)/(2*a)) + (1/2)*x^2*asinh(a*x^2)]
    @test_int [x^0*asinh(a*x^2), x, 5, -((2*x*sqrt(1 + a^2*x^4))/(1 + a*x^2)) + x*asinh(a*x^2) + (2*(1 + a*x^2)*sqrt((1 + a^2*x^4)/(1 + a*x^2)^2)*Elliptic.E(2*atan(sqrt(a)*x), 1/2))/(sqrt(a)*sqrt(1 + a^2*x^4)) - ((1 + a*x^2)*sqrt((1 + a^2*x^4)/(1 + a*x^2)^2)*Elliptic.F(2*atan(sqrt(a)*x), 1/2))/(sqrt(a)*sqrt(1 + a^2*x^4))]
    @test_int [asinh(a*x^2)/x^1, x, 5, (-(1/4))*asinh(a*x^2)^2 + (1/2)*asinh(a*x^2)*log(1 - ℯ^(2*asinh(a*x^2))) + (1/4)*PolyLog(2, ℯ^(2*asinh(a*x^2)))]
    @test_int [asinh(a*x^2)/x^2, x, 3, -(asinh(a*x^2)/x) + (sqrt(a)*(1 + a*x^2)*sqrt((1 + a^2*x^4)/(1 + a*x^2)^2)*Elliptic.F(2*atan(sqrt(a)*x), 1/2))/sqrt(1 + a^2*x^4)]
    @test_int [asinh(a*x^2)/x^3, x, 5, -(asinh(a*x^2)/(2*x^2)) - (1/2)*a*atanh(sqrt(1 + a^2*x^4))]
    @test_int [asinh(a*x^2)/x^4, x, 6, -((2*a*sqrt(1 + a^2*x^4))/(3*x)) + (2*a^2*x*sqrt(1 + a^2*x^4))/(3*(1 + a*x^2)) - asinh(a*x^2)/(3*x^3) - (2*a^(3/2)*(1 + a*x^2)*sqrt((1 + a^2*x^4)/(1 + a*x^2)^2)*Elliptic.E(2*atan(sqrt(a)*x), 1/2))/(3*sqrt(1 + a^2*x^4)) + (a^(3/2)*(1 + a*x^2)*sqrt((1 + a^2*x^4)/(1 + a*x^2)^2)*Elliptic.F(2*atan(sqrt(a)*x), 1/2))/(3*sqrt(1 + a^2*x^4))]

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

    @test_int [x^2*asinh(sqrt(x)), x, 7, (-(5/48))*sqrt(x)*sqrt(1 + x) + (5/72)*x^(3/2)*sqrt(1 + x) - (1/18)*x^(5/2)*sqrt(1 + x) + (5*asinh(sqrt(x)))/48 + (1/3)*x^3*asinh(sqrt(x))]
    @test_int [x^1*asinh(sqrt(x)), x, 6, (3/16)*sqrt(x)*sqrt(1 + x) - (1/8)*x^(3/2)*sqrt(1 + x) - (3*asinh(sqrt(x)))/16 + (1/2)*x^2*asinh(sqrt(x))]
    @test_int [x^0*asinh(sqrt(x)), x, 6, (-(1/2))*sqrt(x)*sqrt(1 + x) + asinh(sqrt(x))/2 + x*asinh(sqrt(x))]
    @test_int [asinh(sqrt(x))/x^1, x, 5, -asinh(sqrt(x))^2 + 2*asinh(sqrt(x))*log(1 - ℯ^(2*asinh(sqrt(x)))) + PolyLog(2, ℯ^(2*asinh(sqrt(x))))]
    @test_int [asinh(sqrt(x))/x^2, x, 3, -(sqrt(1 + x)/sqrt(x)) - asinh(sqrt(x))/x]
    @test_int [asinh(sqrt(x))/x^3, x, 4, -(sqrt(1 + x)/(6*x^(3/2))) + sqrt(1 + x)/(3*sqrt(x)) - asinh(sqrt(x))/(2*x^2)]
    @test_int [asinh(sqrt(x))/x^4, x, 5, -(sqrt(1 + x)/(15*x^(5/2))) + (4*sqrt(1 + x))/(45*x^(3/2)) - (8*sqrt(1 + x))/(45*sqrt(x)) - asinh(sqrt(x))/(3*x^3)]
    @test_int [asinh(sqrt(x))/x^5, x, 6, -(sqrt(1 + x)/(28*x^(7/2))) + (3*sqrt(1 + x))/(70*x^(5/2)) - (2*sqrt(1 + x))/(35*x^(3/2)) + (4*sqrt(1 + x))/(35*sqrt(x)) - asinh(sqrt(x))/(4*x^4)]

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

    @test_int [x^2*asinh(a/x), x, 6, (1/6)*a*sqrt(1 + a^2/x^2)*x^2 + (1/3)*x^3*acsch(x/a) - (1/6)*a^3*atanh(sqrt(1 + a^2/x^2))]
    @test_int [x^1*asinh(a/x), x, 3, (1/2)*a*sqrt(1 + a^2/x^2)*x + (1/2)*x^2*acsch(x/a)]
    @test_int [x^0*asinh(a/x), x, 5, x*acsch(x/a) + a*atanh(sqrt(1 + a^2/x^2))]
    @test_int [asinh(a/x)/x^1, x, 5, (1/2)*asinh(a/x)^2 - asinh(a/x)*log(1 - ℯ^(2*asinh(a/x))) - (1/2)*PolyLog(2, ℯ^(2*asinh(a/x)))]
    @test_int [asinh(a/x)/x^2, x, 3, sqrt(1 + a^2/x^2)/a - acsch(x/a)/x]
    @test_int [asinh(a/x)/x^3, x, 5, sqrt(1 + a^2/x^2)/(4*a*x) - acsch(x/a)/(4*a^2) - acsch(x/a)/(2*x^2)]
    @test_int [asinh(a/x)/x^4, x, 5, -(sqrt(1 + a^2/x^2)/(3*a^3)) + (1 + a^2/x^2)^(3/2)/(9*a^3) - acsch(x/a)/(3*x^3)]

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

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

    @test_int [x^2*asinh(a*x^n), x, 3, (1/3)*x^3*asinh(a*x^n) - (a*n*x^(3 + n)*HypergeometricFunctions._₂F₁(1/2, (3 + n)/(2*n), (3*(1 + n))/(2*n), (-a^2)*x^(2*n)))/(3*(3 + n))]
    @test_int [x^1*asinh(a*x^n), x, 3, (1/2)*x^2*asinh(a*x^n) - (a*n*x^(2 + n)*HypergeometricFunctions._₂F₁(1/2, (2 + n)/(2*n), (1/2)*(3 + 2/n), (-a^2)*x^(2*n)))/(2*(2 + n))]
    @test_int [x^0*asinh(a*x^n), x, 3, x*asinh(a*x^n) - (a*n*x^(1 + n)*HypergeometricFunctions._₂F₁(1/2, (1 + n)/(2*n), (1/2)*(3 + 1/n), (-a^2)*x^(2*n)))/(1 + n)]
    @test_int [asinh(a*x^n)/x^1, x, 5, -(asinh(a*x^n)^2/(2*n)) + (asinh(a*x^n)*log(1 - ℯ^(2*asinh(a*x^n))))/n + PolyLog(2, ℯ^(2*asinh(a*x^n)))/(2*n)]
    @test_int [asinh(a*x^n)/x^2, x, 3, -(asinh(a*x^n)/x) - (a*n*x^(-1 + n)*HypergeometricFunctions._₂F₁(1/2, -((1 - n)/(2*n)), (1/2)*(3 - 1/n), (-a^2)*x^(2*n)))/(1 - n)]
    @test_int [asinh(a*x^n)/x^3, x, 3, -(asinh(a*x^n)/(2*x^2)) - (a*n*x^(-2 + n)*HypergeometricFunctions._₂F₁(1/2, (1/2)*(1 - 2/n), (1/2)*(3 - 2/n), (-a^2)*x^(2*n)))/(2*(2 - n))]

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

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

    @test_int [(a + b*asinh(im + d*x^2))^4, x, 3, 384*b^4*x - (192*b^3*sqrt(2*im*d*x^2 + d^2*x^4)*(a + im*b*asin(1 - im*d*x^2)))/(d*x) + 48*b^2*x*(a + im*b*asin(1 - im*d*x^2))^2 - (8*b*sqrt(2*im*d*x^2 + d^2*x^4)*(a + im*b*asin(1 - im*d*x^2))^3)/(d*x) + x*(a + im*b*asin(1 - im*d*x^2))^4]
    @test_int [(a + b*asinh(im + d*x^2))^3, x, 5, 24*a*b^2*x - (48*b^3*sqrt(2*im*d*x^2 + d^2*x^4))/(d*x) + 24*im*b^3*x*asin(1 - im*d*x^2) - (6*b*sqrt(2*im*d*x^2 + d^2*x^4)*(a + im*b*asin(1 - im*d*x^2))^2)/(d*x) + x*(a + im*b*asin(1 - im*d*x^2))^3]
    @test_int [(a + b*asinh(im + d*x^2))^2, x, 2, 8*b^2*x - (4*b*sqrt(2*im*d*x^2 + d^2*x^4)*(a + im*b*asin(1 - im*d*x^2)))/(d*x) + x*(a + im*b*asin(1 - im*d*x^2))^2]
    @test_int [(a + b*asinh(im + d*x^2))^1, x, 4, a*x - (2*b*sqrt(2*im*d*x^2 + d^2*x^4))/(d*x) + im*b*x*asin(1 - im*d*x^2)]
    @test_int [1/(a + b*asinh(im + d*x^2))^1, x, 1, (x*CosIntegral(-((im*(a + im*b*asin(1 - im*d*x^2)))/(2*b)))*(im*cosh(a/(2*b)) - sinh(a/(2*b))))/(2*b*(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2)))) - (x*(im*cosh(a/(2*b)) + sinh(a/(2*b)))*SinIntegral((im*a)/(2*b) - (1/2)*asin(1 - im*d*x^2)))/(2*b*(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2))))]
    @test_int [1/(a + b*asinh(im + d*x^2))^2, x, 1, -(sqrt(2*im*d*x^2 + d^2*x^4)/(2*b*d*x*(a + im*b*asin(1 - im*d*x^2)))) + (x*CosIntegral(-((im*(a + im*b*asin(1 - im*d*x^2)))/(2*b)))*(cosh(a/(2*b)) - im*sinh(a/(2*b))))/(4*b^2*(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2)))) + (x*(cosh(a/(2*b)) + im*sinh(a/(2*b)))*SinIntegral((im*a)/(2*b) - (1/2)*asin(1 - im*d*x^2)))/(4*b^2*(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2))))]
    @test_int [1/(a + b*asinh(im + d*x^2))^3, x, 2, -(sqrt(2*im*d*x^2 + d^2*x^4)/(4*b*d*x*(a + im*b*asin(1 - im*d*x^2))^2)) - x/(8*b^2*(a + im*b*asin(1 - im*d*x^2))) + (x*CosIntegral(-((im*(a + im*b*asin(1 - im*d*x^2)))/(2*b)))*(im*cosh(a/(2*b)) - sinh(a/(2*b))))/(16*b^3*(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2)))) - (x*(im*cosh(a/(2*b)) + sinh(a/(2*b)))*SinIntegral((im*a)/(2*b) - (1/2)*asin(1 - im*d*x^2)))/(16*b^3*(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2))))]

    @test_int [(a + b*asinh(-im + d*x^2))^4, x, 3, 384*b^4*x - (192*b^3*sqrt(-2*im*d*x^2 + d^2*x^4)*(a - im*b*asin(1 + im*d*x^2)))/(d*x) + 48*b^2*x*(a - im*b*asin(1 + im*d*x^2))^2 - (8*b*sqrt(-2*im*d*x^2 + d^2*x^4)*(a - im*b*asin(1 + im*d*x^2))^3)/(d*x) + x*(a - im*b*asin(1 + im*d*x^2))^4]
    @test_int [(a + b*asinh(-im + d*x^2))^3, x, 5, 24*a*b^2*x - (48*b^3*sqrt(-2*im*d*x^2 + d^2*x^4))/(d*x) - 24*im*b^3*x*asin(1 + im*d*x^2) - (6*b*sqrt(-2*im*d*x^2 + d^2*x^4)*(a - im*b*asin(1 + im*d*x^2))^2)/(d*x) + x*(a - im*b*asin(1 + im*d*x^2))^3]
    @test_int [(a + b*asinh(-im + d*x^2))^2, x, 2, 8*b^2*x - (4*b*sqrt(-2*im*d*x^2 + d^2*x^4)*(a - im*b*asin(1 + im*d*x^2)))/(d*x) + x*(a - im*b*asin(1 + im*d*x^2))^2]
    @test_int [(a + b*asinh(-im + d*x^2))^1, x, 4, a*x - (2*b*sqrt(-2*im*d*x^2 + d^2*x^4))/(d*x) - im*b*x*asin(1 + im*d*x^2)]
    @test_int [1/(a + b*asinh(-im + d*x^2))^1, x, 1, -((x*CosIntegral((im*(a - im*b*asin(1 + im*d*x^2)))/(2*b))*(im*cosh(a/(2*b)) + sinh(a/(2*b))))/(2*b*(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2))))) + (x*(cosh(a/(2*b)) + im*sinh(a/(2*b)))*SinhIntegral((a - im*b*asin(1 + im*d*x^2))/(2*b)))/(2*b*(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2))))]
    @test_int [1/(a + b*asinh(-im + d*x^2))^2, x, 1, -(sqrt(-2*im*d*x^2 + d^2*x^4)/(2*b*d*x*(a - im*b*asin(1 + im*d*x^2)))) + (x*CosIntegral((im*(a - im*b*asin(1 + im*d*x^2)))/(2*b))*(cosh(a/(2*b)) + im*sinh(a/(2*b))))/(4*b^2*(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2)))) - (x*(im*cosh(a/(2*b)) + sinh(a/(2*b)))*SinhIntegral((a - im*b*asin(1 + im*d*x^2))/(2*b)))/(4*b^2*(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2))))]
    @test_int [1/(a + b*asinh(-im + d*x^2))^3, x, 2, -(sqrt(-2*im*d*x^2 + d^2*x^4)/(4*b*d*x*(a - im*b*asin(1 + im*d*x^2))^2)) - x/(8*b^2*(a - im*b*asin(1 + im*d*x^2))) - (x*CosIntegral((im*(a - im*b*asin(1 + im*d*x^2)))/(2*b))*(im*cosh(a/(2*b)) + sinh(a/(2*b))))/(16*b^3*(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2)))) + (x*(cosh(a/(2*b)) + im*sinh(a/(2*b)))*SinhIntegral((a - im*b*asin(1 + im*d*x^2))/(2*b)))/(16*b^3*(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2))))]

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

    @test_int [(a + b*asinh(im + d*x^2))^(5/2), x, 2, 15*b^2*x*sqrt(a + im*b*asin(1 - im*d*x^2)) - (5*b*sqrt(2*im*d*x^2 + d^2*x^4)*(a + im*b*asin(1 - im*d*x^2))^(3/2))/(d*x) + x*(a + im*b*asin(1 - im*d*x^2))^(5/2) + (15*b^2*sqrt(pi)*x*FresnelS((sqrt(-(im/b))*sqrt(a + im*b*asin(1 - im*d*x^2)))/sqrt(pi))*(cosh(a/(2*b)) + im*sinh(a/(2*b))))/(sqrt(-(im/b))*(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2)))) - (15*sqrt(-(im/b))*b^3*sqrt(pi)*x*FresnelC((sqrt(-(im/b))*sqrt(a + im*b*asin(1 - im*d*x^2)))/sqrt(pi))*(im*cosh(a/(2*b)) + sinh(a/(2*b))))/(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2)))]
    @test_int [(a + b*asinh(im + d*x^2))^(3/2), x, 2, -((3*b*sqrt(2*im*d*x^2 + d^2*x^4)*sqrt(a + im*b*asin(1 - im*d*x^2)))/(d*x)) + x*(a + im*b*asin(1 - im*d*x^2))^(3/2) + (3*sqrt(im*b)*b*sqrt(pi)*x*FresnelC(sqrt(a + im*b*asin(1 - im*d*x^2))/(sqrt(im*b)*sqrt(pi)))*(im*cosh(a/(2*b)) - sinh(a/(2*b))))/(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2))) - (3*b^2*sqrt(pi)*x*FresnelS(sqrt(a + im*b*asin(1 - im*d*x^2))/(sqrt(im*b)*sqrt(pi)))*(cosh(a/(2*b)) - im*sinh(a/(2*b))))/(sqrt(im*b)*(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2))))]
    @test_int [(a + b*asinh(im + d*x^2))^(1/2), x, 1, x*sqrt(a + im*b*asin(1 - im*d*x^2)) + (sqrt(pi)*x*FresnelS((sqrt(-(im/b))*sqrt(a + im*b*asin(1 - im*d*x^2)))/sqrt(pi))*(cosh(a/(2*b)) + im*sinh(a/(2*b))))/(sqrt(-(im/b))*(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2)))) - (sqrt(-(im/b))*b*sqrt(pi)*x*FresnelC((sqrt(-(im/b))*sqrt(a + im*b*asin(1 - im*d*x^2)))/sqrt(pi))*(im*cosh(a/(2*b)) + sinh(a/(2*b))))/(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2)))]
    @test_int [1/(a + b*asinh(im + d*x^2))^(1/2), x, 1, -((sqrt(pi)*x*FresnelS(sqrt(a + im*b*asin(1 - im*d*x^2))/(sqrt(im*b)*sqrt(pi)))*(cosh(a/(2*b)) - im*sinh(a/(2*b))))/(sqrt(im*b)*(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2))))) - (sqrt(pi)*x*FresnelC(sqrt(a + im*b*asin(1 - im*d*x^2))/(sqrt(im*b)*sqrt(pi)))*(cosh(a/(2*b)) + im*sinh(a/(2*b))))/(sqrt(im*b)*(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2))))]
    @test_int [1/(a + b*asinh(im + d*x^2))^(3/2), x, 1, -(sqrt(2*im*d*x^2 + d^2*x^4)/(b*d*x*sqrt(a + im*b*asin(1 - im*d*x^2)))) - ((-(im/b))^(3/2)*sqrt(pi)*x*FresnelC((sqrt(-(im/b))*sqrt(a + im*b*asin(1 - im*d*x^2)))/sqrt(pi))*(cosh(a/(2*b)) - im*sinh(a/(2*b))))/(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2))) + ((-(im/b))^(3/2)*sqrt(pi)*x*FresnelS((sqrt(-(im/b))*sqrt(a + im*b*asin(1 - im*d*x^2)))/sqrt(pi))*(cosh(a/(2*b)) + im*sinh(a/(2*b))))/(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2)))]
    @test_int [1/(a + b*asinh(im + d*x^2))^(5/2), x, 2, -(sqrt(2*im*d*x^2 + d^2*x^4)/(3*b*d*x*(a + im*b*asin(1 - im*d*x^2))^(3/2))) - x/(3*b^2*sqrt(a + im*b*asin(1 - im*d*x^2))) - (sqrt(pi)*x*FresnelS(sqrt(a + im*b*asin(1 - im*d*x^2))/(sqrt(im*b)*sqrt(pi)))*(cosh(a/(2*b)) - im*sinh(a/(2*b))))/(3*sqrt(im*b)*b^2*(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2)))) - (sqrt(pi)*x*FresnelC(sqrt(a + im*b*asin(1 - im*d*x^2))/(sqrt(im*b)*sqrt(pi)))*(cosh(a/(2*b)) + im*sinh(a/(2*b))))/(3*sqrt(im*b)*b^2*(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2))))]
    @test_int [1/(a + b*asinh(im + d*x^2))^(7/2), x, 2, -(sqrt(2*im*d*x^2 + d^2*x^4)/(5*b*d*x*(a + im*b*asin(1 - im*d*x^2))^(5/2))) - x/(15*b^2*(a + im*b*asin(1 - im*d*x^2))^(3/2)) - sqrt(2*im*d*x^2 + d^2*x^4)/(15*b^3*d*x*sqrt(a + im*b*asin(1 - im*d*x^2))) - ((-(im/b))^(3/2)*sqrt(pi)*x*FresnelC((sqrt(-(im/b))*sqrt(a + im*b*asin(1 - im*d*x^2)))/sqrt(pi))*(cosh(a/(2*b)) - im*sinh(a/(2*b))))/(15*b^2*(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2)))) + ((-(im/b))^(3/2)*sqrt(pi)*x*FresnelS((sqrt(-(im/b))*sqrt(a + im*b*asin(1 - im*d*x^2)))/sqrt(pi))*(cosh(a/(2*b)) + im*sinh(a/(2*b))))/(15*b^2*(cos((1/2)*asin(1 - im*d*x^2)) - sin((1/2)*asin(1 - im*d*x^2))))]

    @test_int [(a + b*asinh(-im + d*x^2))^(5/2), x, 2, 15*b^2*x*sqrt(a - im*b*asin(1 + im*d*x^2)) - (5*b*sqrt(-2*im*d*x^2 + d^2*x^4)*(a - im*b*asin(1 + im*d*x^2))^(3/2))/(d*x) + x*(a - im*b*asin(1 + im*d*x^2))^(5/2) + (15*b^2*sqrt(pi)*x*FresnelS((sqrt(im/b)*sqrt(a - im*b*asin(1 + im*d*x^2)))/sqrt(pi))*(cosh(a/(2*b)) - im*sinh(a/(2*b))))/(sqrt(im/b)*(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2)))) - (15*b^2*sqrt(pi)*x*FresnelC((sqrt(im/b)*sqrt(a - im*b*asin(1 + im*d*x^2)))/sqrt(pi))*(cosh(a/(2*b)) + im*sinh(a/(2*b))))/(sqrt(im/b)*(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2))))]
    @test_int [(a + b*asinh(-im + d*x^2))^(3/2), x, 2, -((3*b*sqrt(-2*im*d*x^2 + d^2*x^4)*sqrt(a - im*b*asin(1 + im*d*x^2)))/(d*x)) + x*(a - im*b*asin(1 + im*d*x^2))^(3/2) - (3*b^2*sqrt(pi)*x*FresnelS(sqrt(a - im*b*asin(1 + im*d*x^2))/(sqrt((-im)*b)*sqrt(pi)))*(cosh(a/(2*b)) + im*sinh(a/(2*b))))/(sqrt((-im)*b)*(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2)))) - (3*sqrt((-im)*b)*b*sqrt(pi)*x*FresnelC(sqrt(a - im*b*asin(1 + im*d*x^2))/(sqrt((-im)*b)*sqrt(pi)))*(im*cosh(a/(2*b)) + sinh(a/(2*b))))/(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2)))]
    @test_int [(a + b*asinh(-im + d*x^2))^(1/2), x, 1, x*sqrt(a - im*b*asin(1 + im*d*x^2)) + (sqrt(pi)*x*FresnelS((sqrt(im/b)*sqrt(a - im*b*asin(1 + im*d*x^2)))/sqrt(pi))*(cosh(a/(2*b)) - im*sinh(a/(2*b))))/(sqrt(im/b)*(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2)))) - (sqrt(pi)*x*FresnelC((sqrt(im/b)*sqrt(a - im*b*asin(1 + im*d*x^2)))/sqrt(pi))*(cosh(a/(2*b)) + im*sinh(a/(2*b))))/(sqrt(im/b)*(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2))))]
    @test_int [1/(a + b*asinh(-im + d*x^2))^(1/2), x, 1, -((sqrt(pi)*x*FresnelC(sqrt(a - im*b*asin(1 + im*d*x^2))/(sqrt((-im)*b)*sqrt(pi)))*(cosh(a/(2*b)) - im*sinh(a/(2*b))))/(sqrt((-im)*b)*(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2))))) - (sqrt(pi)*x*FresnelS(sqrt(a - im*b*asin(1 + im*d*x^2))/(sqrt((-im)*b)*sqrt(pi)))*(cosh(a/(2*b)) + im*sinh(a/(2*b))))/(sqrt((-im)*b)*(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2))))]
    @test_int [1/(a + b*asinh(-im + d*x^2))^(3/2), x, 1, -(sqrt(-2*im*d*x^2 + d^2*x^4)/(b*d*x*sqrt(a - im*b*asin(1 + im*d*x^2)))) + ((im/b)^(3/2)*sqrt(pi)*x*FresnelS((sqrt(im/b)*sqrt(a - im*b*asin(1 + im*d*x^2)))/sqrt(pi))*(cosh(a/(2*b)) - im*sinh(a/(2*b))))/(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2))) - ((im/b)^(3/2)*sqrt(pi)*x*FresnelC((sqrt(im/b)*sqrt(a - im*b*asin(1 + im*d*x^2)))/sqrt(pi))*(cosh(a/(2*b)) + im*sinh(a/(2*b))))/(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2)))]
    @test_int [1/(a + b*asinh(-im + d*x^2))^(5/2), x, 2, -(sqrt(-2*im*d*x^2 + d^2*x^4)/(3*b*d*x*(a - im*b*asin(1 + im*d*x^2))^(3/2))) - x/(3*b^2*sqrt(a - im*b*asin(1 + im*d*x^2))) - (sqrt(pi)*x*FresnelS(sqrt(a - im*b*asin(1 + im*d*x^2))/(sqrt((-im)*b)*sqrt(pi)))*(cosh(a/(2*b)) + im*sinh(a/(2*b))))/(3*sqrt((-im)*b)*b^2*(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2)))) - (sqrt((-im)*b)*sqrt(pi)*x*FresnelC(sqrt(a - im*b*asin(1 + im*d*x^2))/(sqrt((-im)*b)*sqrt(pi)))*(im*cosh(a/(2*b)) + sinh(a/(2*b))))/(3*b^3*(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2))))]
    @test_int [1/(a + b*asinh(-im + d*x^2))^(7/2), x, 2, -(sqrt(-2*im*d*x^2 + d^2*x^4)/(5*b*d*x*(a - im*b*asin(1 + im*d*x^2))^(5/2))) - x/(15*b^2*(a - im*b*asin(1 + im*d*x^2))^(3/2)) - sqrt(-2*im*d*x^2 + d^2*x^4)/(15*b^3*d*x*sqrt(a - im*b*asin(1 + im*d*x^2))) - ((im/b)^(3/2)*sqrt(pi)*x*FresnelC((sqrt(im/b)*sqrt(a - im*b*asin(1 + im*d*x^2)))/sqrt(pi))*(cosh(a/(2*b)) + im*sinh(a/(2*b))))/(15*b^2*(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2)))) + (sqrt(im/b)*sqrt(pi)*x*FresnelS((sqrt(im/b)*sqrt(a - im*b*asin(1 + im*d*x^2)))/sqrt(pi))*(im*cosh(a/(2*b)) + sinh(a/(2*b))))/(15*b^3*(cos((1/2)*asin(1 + im*d*x^2)) - sin((1/2)*asin(1 + im*d*x^2))))]

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

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

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

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

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

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

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

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

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

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

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

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

    @test_int [x/(sqrt(1 + x^2)*asinh(x)), x, 2, SinhIntegral(asinh(x))]

    @test_int [x^3*asinh(a + b*x^4), x, 4, -(sqrt(1 + (a + b*x^4)^2)/(4*b)) + ((a + b*x^4)*asinh(a + b*x^4))/(4*b)]

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

    @test_int [asinh(c/(a + b*x)), x, 6, ((a + b*x)*acsch(a/c + (b*x)/c))/b + (c*atanh(sqrt(1 + 1/(a/c + (b*x)/c)^2)))/b]

    @test_int [x/asinh(sinh(x)), x, -1, asinh(sinh(x)) + log(asinh(sinh(x)))*(-asinh(sinh(x)) + x*sqrt(cosh(x)^2)*sech(x))]

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

max_stars_repo_path: test/7 Inverse hyperbolic functions/7.1 Inverse hyperbolic sine/7.1.5 Inverse hyperbolic sine functions.jl