text:
@testset "7.1.4 (f x)^m (d+e x^2)^p (a+b arcsinh(c x))^n" begin
    (a, b, c, d, e, f, m, n, x, ) = @variables a b c d e f m n x

    #= ::Package:: =#

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

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

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

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

    @test_int [x^4*(d + c^2*d*x^2)*(a + b*asinh(c*x)), x, 5, (-2*b*d*sqrt(1 + c^2*x^2))/(35*c^5) - (b*d*(1 + c^2*x^2)^(3/2))/(105*c^5) + (8*b*d*(1 + c^2*x^2)^(5/2))/(175*c^5) - (b*d*(1 + c^2*x^2)^(7/2))/(49*c^5) + (d*x^5*(a + b*asinh(c*x)))/5 + (c^2*d*x^7*(a + b*asinh(c*x)))/7]
    @test_int [x^3*(d + c^2*d*x^2)*(a + b*asinh(c*x)), x, 6, (b*d*x*sqrt(1 + c^2*x^2))/(24*c^3) - (b*d*x^3*sqrt(1 + c^2*x^2))/(36*c) - (b*c*d*x^5*sqrt(1 + c^2*x^2))/36 - (b*d*asinh(c*x))/(24*c^4) + (d*x^4*(a + b*asinh(c*x)))/4 + (c^2*d*x^6*(a + b*asinh(c*x)))/6]
    @test_int [x^2*(d + c^2*d*x^2)*(a + b*asinh(c*x)), x, 5, (2*b*d*sqrt(1 + c^2*x^2))/(15*c^3) + (b*d*(1 + c^2*x^2)^(3/2))/(45*c^3) - (b*d*(1 + c^2*x^2)^(5/2))/(25*c^3) + (d*x^3*(a + b*asinh(c*x)))/3 + (c^2*d*x^5*(a + b*asinh(c*x)))/5]
    @test_int [x^1*(d + c^2*d*x^2)*(a + b*asinh(c*x)), x, 4, (-3*b*d*x*sqrt(1 + c^2*x^2))/(32*c) - (b*d*x*(1 + c^2*x^2)^(3/2))/(16*c) - (3*b*d*asinh(c*x))/(32*c^2) + (d*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(4*c^2)]
    @test_int [x^0*(d + c^2*d*x^2)*(a + b*asinh(c*x)), x, 5, (-2*b*d*sqrt(1 + c^2*x^2))/(3*c) - (b*d*(1 + c^2*x^2)^(3/2))/(9*c) + d*x*(a + b*asinh(c*x)) + (c^2*d*x^3*(a + b*asinh(c*x)))/3]
    @test_int [((d + c^2*d*x^2)*(a + b*asinh(c*x)))/x^1, x, 8, (-(1/4))*b*c*d*x*sqrt(1 + c^2*x^2) - (1/4)*b*d*asinh(c*x) + (1/2)*d*(1 + c^2*x^2)*(a + b*asinh(c*x)) + (d*(a + b*asinh(c*x))^2)/(2*b) + d*(a + b*asinh(c*x))*log(1 - ℯ^(-2*asinh(c*x))) - (1/2)*b*d*PolyLog(2, ℯ^(-2*asinh(c*x)))]
    @test_int [((d + c^2*d*x^2)*(a + b*asinh(c*x)))/x^2, x, 6, -(b*c*d*sqrt(1 + c^2*x^2)) - (d*(a + b*asinh(c*x)))/x + c^2*d*x*(a + b*asinh(c*x)) - b*c*d*atanh(sqrt(1 + c^2*x^2))]
    @test_int [((d + c^2*d*x^2)*(a + b*asinh(c*x)))/x^3, x, 8, -((b*c*d*sqrt(1 + c^2*x^2))/(2*x)) + (1/2)*b*c^2*d*asinh(c*x) - (d*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2*x^2) + (c^2*d*(a + b*asinh(c*x))^2)/(2*b) + c^2*d*(a + b*asinh(c*x))*log(1 - ℯ^(-2*asinh(c*x))) - (1/2)*b*c^2*d*PolyLog(2, ℯ^(-2*asinh(c*x)))]
    @test_int [((d + c^2*d*x^2)*(a + b*asinh(c*x)))/x^4, x, 6, -(b*c*d*sqrt(1 + c^2*x^2))/(6*x^2) - (d*(a + b*asinh(c*x)))/(3*x^3) - (c^2*d*(a + b*asinh(c*x)))/x - (5*b*c^3*d*atanh(sqrt(1 + c^2*x^2)))/6]

    @test_int [x^4*(d + c^2*d*x^2)^2*(a + b*asinh(c*x)), x, 6, (-8*b*d^2*sqrt(1 + c^2*x^2))/(315*c^5) - (4*b*d^2*(1 + c^2*x^2)^(3/2))/(945*c^5) - (b*d^2*(1 + c^2*x^2)^(5/2))/(525*c^5) + (10*b*d^2*(1 + c^2*x^2)^(7/2))/(441*c^5) - (b*d^2*(1 + c^2*x^2)^(9/2))/(81*c^5) + (d^2*x^5*(a + b*asinh(c*x)))/5 + (2*c^2*d^2*x^7*(a + b*asinh(c*x)))/7 + (c^4*d^2*x^9*(a + b*asinh(c*x)))/9]
    @test_int [x^3*(d + c^2*d*x^2)^2*(a + b*asinh(c*x)), x, 7, (73*b*d^2*x*sqrt(1 + c^2*x^2))/(3072*c^3) - (73*b*d^2*x^3*sqrt(1 + c^2*x^2))/(4608*c) - (43*b*c*d^2*x^5*sqrt(1 + c^2*x^2))/1152 - (b*c^3*d^2*x^7*sqrt(1 + c^2*x^2))/64 - (73*b*d^2*asinh(c*x))/(3072*c^4) + (d^2*x^4*(a + b*asinh(c*x)))/4 + (c^2*d^2*x^6*(a + b*asinh(c*x)))/3 + (c^4*d^2*x^8*(a + b*asinh(c*x)))/8]
    @test_int [x^2*(d + c^2*d*x^2)^2*(a + b*asinh(c*x)), x, 5, (8*b*d^2*sqrt(1 + c^2*x^2))/(105*c^3) + (4*b*d^2*(1 + c^2*x^2)^(3/2))/(315*c^3) + (b*d^2*(1 + c^2*x^2)^(5/2))/(175*c^3) - (b*d^2*(1 + c^2*x^2)^(7/2))/(49*c^3) + (d^2*x^3*(a + b*asinh(c*x)))/3 + (2*c^2*d^2*x^5*(a + b*asinh(c*x)))/5 + (c^4*d^2*x^7*(a + b*asinh(c*x)))/7]
    @test_int [x*(d + c^2*d*x^2)^2*(a + b*asinh(c*x)), x, 5, (-5*b*d^2*x*sqrt(1 + c^2*x^2))/(96*c) - (5*b*d^2*x*(1 + c^2*x^2)^(3/2))/(144*c) - (b*d^2*x*(1 + c^2*x^2)^(5/2))/(36*c) - (5*b*d^2*asinh(c*x))/(96*c^2) + (d^2*(1 + c^2*x^2)^3*(a + b*asinh(c*x)))/(6*c^2)]
    @test_int [(d + c^2*d*x^2)^2*(a + b*asinh(c*x)), x, 5, (-8*b*d^2*sqrt(1 + c^2*x^2))/(15*c) - (4*b*d^2*(1 + c^2*x^2)^(3/2))/(45*c) - (b*d^2*(1 + c^2*x^2)^(5/2))/(25*c) + d^2*x*(a + b*asinh(c*x)) + (2*c^2*d^2*x^3*(a + b*asinh(c*x)))/3 + (c^4*d^2*x^5*(a + b*asinh(c*x)))/5]
    @test_int [((d + c^2*d*x^2)^2*(a + b*asinh(c*x)))/x, x, 12, (-(11/32))*b*c*d^2*x*sqrt(1 + c^2*x^2) - (1/16)*b*c*d^2*x*(1 + c^2*x^2)^(3/2) - (11/32)*b*d^2*asinh(c*x) + (1/2)*d^2*(1 + c^2*x^2)*(a + b*asinh(c*x)) + (1/4)*d^2*(1 + c^2*x^2)^2*(a + b*asinh(c*x)) + (d^2*(a + b*asinh(c*x))^2)/(2*b) + d^2*(a + b*asinh(c*x))*log(1 - ℯ^(-2*asinh(c*x))) - (1/2)*b*d^2*PolyLog(2, ℯ^(-2*asinh(c*x)))]
    @test_int [((d + c^2*d*x^2)^2*(a + b*asinh(c*x)))/x^2, x, 7, (-5*b*c*d^2*sqrt(1 + c^2*x^2))/3 - (b*c*d^2*(1 + c^2*x^2)^(3/2))/9 - (d^2*(a + b*asinh(c*x)))/x + 2*c^2*d^2*x*(a + b*asinh(c*x)) + (c^4*d^2*x^3*(a + b*asinh(c*x)))/3 - b*c*d^2*atanh(sqrt(1 + c^2*x^2))]
    @test_int [((d + c^2*d*x^2)^2*(a + b*asinh(c*x)))/x^3, x, 12, (1/4)*b*c^3*d^2*x*sqrt(1 + c^2*x^2) - (b*c*d^2*(1 + c^2*x^2)^(3/2))/(2*x) + (1/4)*b*c^2*d^2*asinh(c*x) + c^2*d^2*(1 + c^2*x^2)*(a + b*asinh(c*x)) - (d^2*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(2*x^2) + (c^2*d^2*(a + b*asinh(c*x))^2)/b + 2*c^2*d^2*(a + b*asinh(c*x))*log(1 - ℯ^(-2*asinh(c*x))) - b*c^2*d^2*PolyLog(2, ℯ^(-2*asinh(c*x)))]
    @test_int [((d + c^2*d*x^2)^2*(a + b*asinh(c*x)))/x^4, x, 7, -(b*c^3*d^2*sqrt(1 + c^2*x^2)) - (b*c*d^2*sqrt(1 + c^2*x^2))/(6*x^2) - (d^2*(a + b*asinh(c*x)))/(3*x^3) - (2*c^2*d^2*(a + b*asinh(c*x)))/x + c^4*d^2*x*(a + b*asinh(c*x)) - (11*b*c^3*d^2*atanh(sqrt(1 + c^2*x^2)))/6]

    @test_int [x^4*(d + c^2*d*x^2)^3*(a + b*asinh(c*x)), x, 5, (-16*b*d^3*sqrt(1 + c^2*x^2))/(1155*c^5) - (8*b*d^3*(1 + c^2*x^2)^(3/2))/(3465*c^5) - (2*b*d^3*(1 + c^2*x^2)^(5/2))/(1925*c^5) - (b*d^3*(1 + c^2*x^2)^(7/2))/(1617*c^5) + (4*b*d^3*(1 + c^2*x^2)^(9/2))/(297*c^5) - (b*d^3*(1 + c^2*x^2)^(11/2))/(121*c^5) + (d^3*x^5*(a + b*asinh(c*x)))/5 + (3*c^2*d^3*x^7*(a + b*asinh(c*x)))/7 + (c^4*d^3*x^9*(a + b*asinh(c*x)))/3 + (c^6*d^3*x^11*(a + b*asinh(c*x)))/11]
    @test_int [x^3*(d + c^2*d*x^2)^3*(a + b*asinh(c*x)), x, 8, (49*b*d^3*x*sqrt(1 + c^2*x^2))/(5120*c^3) + (49*b*d^3*x*(1 + c^2*x^2)^(3/2))/(7680*c^3) + (49*b*d^3*x*(1 + c^2*x^2)^(5/2))/(9600*c^3) + (7*b*d^3*x*(1 + c^2*x^2)^(7/2))/(1600*c^3) - (b*d^3*x*(1 + c^2*x^2)^(9/2))/(100*c^3) + (49*b*d^3*asinh(c*x))/(5120*c^4) - (d^3*(1 + c^2*x^2)^4*(a + b*asinh(c*x)))/(8*c^4) + (d^3*(1 + c^2*x^2)^5*(a + b*asinh(c*x)))/(10*c^4)]
    @test_int [x^2*(d + c^2*d*x^2)^3*(a + b*asinh(c*x)), x, 5, (16*b*d^3*sqrt(1 + c^2*x^2))/(315*c^3) + (8*b*d^3*(1 + c^2*x^2)^(3/2))/(945*c^3) + (2*b*d^3*(1 + c^2*x^2)^(5/2))/(525*c^3) + (b*d^3*(1 + c^2*x^2)^(7/2))/(441*c^3) - (b*d^3*(1 + c^2*x^2)^(9/2))/(81*c^3) + (d^3*x^3*(a + b*asinh(c*x)))/3 + (3*c^2*d^3*x^5*(a + b*asinh(c*x)))/5 + (3*c^4*d^3*x^7*(a + b*asinh(c*x)))/7 + (c^6*d^3*x^9*(a + b*asinh(c*x)))/9]
    @test_int [x*(d + c^2*d*x^2)^3*(a + b*asinh(c*x)), x, 6, (-35*b*d^3*x*sqrt(1 + c^2*x^2))/(1024*c) - (35*b*d^3*x*(1 + c^2*x^2)^(3/2))/(1536*c) - (7*b*d^3*x*(1 + c^2*x^2)^(5/2))/(384*c) - (b*d^3*x*(1 + c^2*x^2)^(7/2))/(64*c) - (35*b*d^3*asinh(c*x))/(1024*c^2) + (d^3*(1 + c^2*x^2)^4*(a + b*asinh(c*x)))/(8*c^2)]
    @test_int [(d + c^2*d*x^2)^3*(a + b*asinh(c*x)), x, 5, (-16*b*d^3*sqrt(1 + c^2*x^2))/(35*c) - (8*b*d^3*(1 + c^2*x^2)^(3/2))/(105*c) - (6*b*d^3*(1 + c^2*x^2)^(5/2))/(175*c) - (b*d^3*(1 + c^2*x^2)^(7/2))/(49*c) + d^3*x*(a + b*asinh(c*x)) + c^2*d^3*x^3*(a + b*asinh(c*x)) + (3*c^4*d^3*x^5*(a + b*asinh(c*x)))/5 + (c^6*d^3*x^7*(a + b*asinh(c*x)))/7]
    @test_int [((d + c^2*d*x^2)^3*(a + b*asinh(c*x)))/x, x, 17, (-(19/48))*b*c*d^3*x*sqrt(1 + c^2*x^2) - (7/72)*b*c*d^3*x*(1 + c^2*x^2)^(3/2) - (1/36)*b*c*d^3*x*(1 + c^2*x^2)^(5/2) - (19/48)*b*d^3*asinh(c*x) + (1/2)*d^3*(1 + c^2*x^2)*(a + b*asinh(c*x)) + (1/4)*d^3*(1 + c^2*x^2)^2*(a + b*asinh(c*x)) + (1/6)*d^3*(1 + c^2*x^2)^3*(a + b*asinh(c*x)) + (d^3*(a + b*asinh(c*x))^2)/(2*b) + d^3*(a + b*asinh(c*x))*log(1 - ℯ^(-2*asinh(c*x))) - (1/2)*b*d^3*PolyLog(2, ℯ^(-2*asinh(c*x)))]
    @test_int [((d + c^2*d*x^2)^3*(a + b*asinh(c*x)))/x^2, x, 7, (-11*b*c*d^3*sqrt(1 + c^2*x^2))/5 - (b*c*d^3*(1 + c^2*x^2)^(3/2))/5 - (b*c*d^3*(1 + c^2*x^2)^(5/2))/25 - (d^3*(a + b*asinh(c*x)))/x + 3*c^2*d^3*x*(a + b*asinh(c*x)) + c^4*d^3*x^3*(a + b*asinh(c*x)) + (c^6*d^3*x^5*(a + b*asinh(c*x)))/5 - b*c*d^3*atanh(sqrt(1 + c^2*x^2))]
    @test_int [((d + c^2*d*x^2)^3*(a + b*asinh(c*x)))/x^3, x, 17, (-(3/32))*b*c^3*d^3*x*sqrt(1 + c^2*x^2) + (7/16)*b*c^3*d^3*x*(1 + c^2*x^2)^(3/2) - (b*c*d^3*(1 + c^2*x^2)^(5/2))/(2*x) - (3/32)*b*c^2*d^3*asinh(c*x) + (3/2)*c^2*d^3*(1 + c^2*x^2)*(a + b*asinh(c*x)) + (3/4)*c^2*d^3*(1 + c^2*x^2)^2*(a + b*asinh(c*x)) - (d^3*(1 + c^2*x^2)^3*(a + b*asinh(c*x)))/(2*x^2) + (3*c^2*d^3*(a + b*asinh(c*x))^2)/(2*b) + 3*c^2*d^3*(a + b*asinh(c*x))*log(1 - ℯ^(-2*asinh(c*x))) - (3/2)*b*c^2*d^3*PolyLog(2, ℯ^(-2*asinh(c*x)))]
    @test_int [((d + c^2*d*x^2)^3*(a + b*asinh(c*x)))/x^4, x, 8, (-(8/3))*b*c^3*d^3*sqrt(1 + c^2*x^2) - (b*c*d^3*sqrt(1 + c^2*x^2))/(6*x^2) - (1/9)*b*c^3*d^3*(1 + c^2*x^2)^(3/2) - (d^3*(a + b*asinh(c*x)))/(3*x^3) - (3*c^2*d^3*(a + b*asinh(c*x)))/x + 3*c^4*d^3*x*(a + b*asinh(c*x)) + (1/3)*c^6*d^3*x^3*(a + b*asinh(c*x)) - (17/6)*b*c^3*d^3*atanh(sqrt(1 + c^2*x^2))]

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

    @test_int [(x^4*(a + b*asinh(c*x)))/(d + c^2*d*x^2), x, 12, (4*b*sqrt(1 + c^2*x^2))/(3*c^5*d) - (b*(1 + c^2*x^2)^(3/2))/(9*c^5*d) - (x*(a + b*asinh(c*x)))/(c^4*d) + (x^3*(a + b*asinh(c*x)))/(3*c^2*d) + (2*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c^5*d) - (im*b*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^5*d) + (im*b*PolyLog(2, im*ℯ^asinh(c*x)))/(c^5*d)]
    @test_int [(x^3*(a + b*asinh(c*x)))/(d + c^2*d*x^2), x, 8, -(b*x*sqrt(1 + c^2*x^2))/(4*c^3*d) + (b*asinh(c*x))/(4*c^4*d) + (x^2*(a + b*asinh(c*x)))/(2*c^2*d) + (a + b*asinh(c*x))^2/(2*b*c^4*d) - ((a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(c^4*d) - (b*PolyLog(2, -ℯ^(2*asinh(c*x))))/(2*c^4*d)]
    @test_int [(x^2*(a + b*asinh(c*x)))/(d + c^2*d*x^2), x, 8, -((b*sqrt(1 + c^2*x^2))/(c^3*d)) + (x*(a + b*asinh(c*x)))/(c^2*d) - (2*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c^3*d) + (im*b*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^3*d) - (im*b*PolyLog(2, im*ℯ^asinh(c*x)))/(c^3*d)]
    @test_int [(x*(a + b*asinh(c*x)))/(d + c^2*d*x^2), x, 5, -(a + b*asinh(c*x))^2/(2*b*c^2*d) + ((a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(c^2*d) + (b*PolyLog(2, -ℯ^(2*asinh(c*x))))/(2*c^2*d)]
    @test_int [(a + b*asinh(c*x))/(d + c^2*d*x^2), x, 6, (2*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c*d) - (im*b*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c*d) + (im*b*PolyLog(2, im*ℯ^asinh(c*x)))/(c*d)]
    @test_int [(a + b*asinh(c*x))/(x*(d + c^2*d*x^2)), x, 7, (-2*(a + b*asinh(c*x))*atanh(ℯ^(2*asinh(c*x))))/d - (b*PolyLog(2, -ℯ^(2*asinh(c*x))))/(2*d) + (b*PolyLog(2, ℯ^(2*asinh(c*x))))/(2*d)]
    @test_int [(a + b*asinh(c*x))/(x^2*(d + c^2*d*x^2)), x, 10, -((a + b*asinh(c*x))/(d*x)) - (2*c*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/d - (b*c*atanh(sqrt(1 + c^2*x^2)))/d + (im*b*c*PolyLog(2, (-im)*ℯ^asinh(c*x)))/d - (im*b*c*PolyLog(2, im*ℯ^asinh(c*x)))/d]
    @test_int [(a + b*asinh(c*x))/(x^3*(d + c^2*d*x^2)), x, 9, -(b*c*sqrt(1 + c^2*x^2))/(2*d*x) - (a + b*asinh(c*x))/(2*d*x^2) + (2*c^2*(a + b*asinh(c*x))*atanh(ℯ^(2*asinh(c*x))))/d + (b*c^2*PolyLog(2, -ℯ^(2*asinh(c*x))))/(2*d) - (b*c^2*PolyLog(2, ℯ^(2*asinh(c*x))))/(2*d)]
    @test_int [(a + b*asinh(c*x))/(x^4*(d + c^2*d*x^2)), x, 15, -(b*c*sqrt(1 + c^2*x^2))/(6*d*x^2) - (a + b*asinh(c*x))/(3*d*x^3) + (c^2*(a + b*asinh(c*x)))/(d*x) + (2*c^3*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/d + (7*b*c^3*atanh(sqrt(1 + c^2*x^2)))/(6*d) - (im*b*c^3*PolyLog(2, (-im)*ℯ^asinh(c*x)))/d + (im*b*c^3*PolyLog(2, im*ℯ^asinh(c*x)))/d]

    @test_int [(x^4*(a + b*asinh(c*x)))/(d + c^2*d*x^2)^2, x, 12, b/(2*c^5*d^2*sqrt(1 + c^2*x^2)) - (b*sqrt(1 + c^2*x^2))/(c^5*d^2) + (3*x*(a + b*asinh(c*x)))/(2*c^4*d^2) - (x^3*(a + b*asinh(c*x)))/(2*c^2*d^2*(1 + c^2*x^2)) - (3*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c^5*d^2) + (((3*im)/2)*b*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^5*d^2) - (((3*im)/2)*b*PolyLog(2, im*ℯ^asinh(c*x)))/(c^5*d^2)]
    @test_int [(x^3*(a + b*asinh(c*x)))/(d + c^2*d*x^2)^2, x, 8, -(b*x)/(2*c^3*d^2*sqrt(1 + c^2*x^2)) + (b*asinh(c*x))/(2*c^4*d^2) - (x^2*(a + b*asinh(c*x)))/(2*c^2*d^2*(1 + c^2*x^2)) - (a + b*asinh(c*x))^2/(2*b*c^4*d^2) + ((a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(c^4*d^2) + (b*PolyLog(2, -ℯ^(2*asinh(c*x))))/(2*c^4*d^2)]
    @test_int [(x^2*(a + b*asinh(c*x)))/(d + c^2*d*x^2)^2, x, 8, -b/(2*c^3*d^2*sqrt(1 + c^2*x^2)) - (x*(a + b*asinh(c*x)))/(2*c^2*d^2*(1 + c^2*x^2)) + ((a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c^3*d^2) - ((im/2)*b*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^3*d^2) + ((im/2)*b*PolyLog(2, im*ℯ^asinh(c*x)))/(c^3*d^2)]
    @test_int [(x*(a + b*asinh(c*x)))/(d + c^2*d*x^2)^2, x, 2, (b*x)/(2*c*d^2*sqrt(1 + c^2*x^2)) - (a + b*asinh(c*x))/(2*c^2*d^2*(1 + c^2*x^2))]
    @test_int [(a + b*asinh(c*x))/(d + c^2*d*x^2)^2, x, 8, b/(2*c*d^2*sqrt(1 + c^2*x^2)) + (x*(a + b*asinh(c*x)))/(2*d^2*(1 + c^2*x^2)) + ((a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c*d^2) - ((im/2)*b*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c*d^2) + ((im/2)*b*PolyLog(2, im*ℯ^asinh(c*x)))/(c*d^2)]
    @test_int [(a + b*asinh(c*x))/(x*(d + c^2*d*x^2)^2), x, 9, -(b*c*x)/(2*d^2*sqrt(1 + c^2*x^2)) + (a + b*asinh(c*x))/(2*d^2*(1 + c^2*x^2)) - (2*(a + b*asinh(c*x))*atanh(ℯ^(2*asinh(c*x))))/d^2 - (b*PolyLog(2, -ℯ^(2*asinh(c*x))))/(2*d^2) + (b*PolyLog(2, ℯ^(2*asinh(c*x))))/(2*d^2)]
    @test_int [(a + b*asinh(c*x))/(x^2*(d + c^2*d*x^2)^2), x, 13, -(b*c)/(2*d^2*sqrt(1 + c^2*x^2)) - (a + b*asinh(c*x))/(d^2*x*(1 + c^2*x^2)) - (3*c^2*x*(a + b*asinh(c*x)))/(2*d^2*(1 + c^2*x^2)) - (3*c*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/d^2 - (b*c*atanh(sqrt(1 + c^2*x^2)))/d^2 + (((3*im)/2)*b*c*PolyLog(2, (-im)*ℯ^asinh(c*x)))/d^2 - (((3*im)/2)*b*c*PolyLog(2, im*ℯ^asinh(c*x)))/d^2]
    @test_int [(a + b*asinh(c*x))/(x^3*(d + c^2*d*x^2)^2), x, 12, -(b*c)/(2*d^2*x*sqrt(1 + c^2*x^2)) - (c^2*(a + b*asinh(c*x)))/(d^2*(1 + c^2*x^2)) - (a + b*asinh(c*x))/(2*d^2*x^2*(1 + c^2*x^2)) + (4*c^2*(a + b*asinh(c*x))*atanh(ℯ^(2*asinh(c*x))))/d^2 + (b*c^2*PolyLog(2, -ℯ^(2*asinh(c*x))))/d^2 - (b*c^2*PolyLog(2, ℯ^(2*asinh(c*x))))/d^2]
    @test_int [(a + b*asinh(c*x))/(x^4*(d + c^2*d*x^2)^2), x, 19, (b*c^3)/(3*d^2*sqrt(1 + c^2*x^2)) - (b*c)/(6*d^2*x^2*sqrt(1 + c^2*x^2)) - (a + b*asinh(c*x))/(3*d^2*x^3*(1 + c^2*x^2)) + (5*c^2*(a + b*asinh(c*x)))/(3*d^2*x*(1 + c^2*x^2)) + (5*c^4*x*(a + b*asinh(c*x)))/(2*d^2*(1 + c^2*x^2)) + (5*c^3*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/d^2 + (13*b*c^3*atanh(sqrt(1 + c^2*x^2)))/(6*d^2) - (5*im*b*c^3*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(2*d^2) + (5*im*b*c^3*PolyLog(2, im*ℯ^asinh(c*x)))/(2*d^2)]

    @test_int [(x^4*(a + b*asinh(c*x)))/(d + c^2*d*x^2)^3, x, 12, b/(12*c^5*d^3*(1 + c^2*x^2)^(3/2)) - (5*b)/(8*c^5*d^3*sqrt(1 + c^2*x^2)) - (x^3*(a + b*asinh(c*x)))/(4*c^2*d^3*(1 + c^2*x^2)^2) - (3*x*(a + b*asinh(c*x)))/(8*c^4*d^3*(1 + c^2*x^2)) + (3*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(4*c^5*d^3) - (((3*im)/8)*b*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^5*d^3) + (((3*im)/8)*b*PolyLog(2, im*ℯ^asinh(c*x)))/(c^5*d^3)]
    @test_int [(x^3*(a + b*asinh(c*x)))/(d + c^2*d*x^2)^3, x, 4, (b*x^3)/(12*c*d^3*(1 + c^2*x^2)^(3/2)) + (b*x)/(4*c^3*d^3*sqrt(1 + c^2*x^2)) - (b*asinh(c*x))/(4*c^4*d^3) + (x^4*(a + b*asinh(c*x)))/(4*d^3*(1 + c^2*x^2)^2)]
    @test_int [(x^2*(a + b*asinh(c*x)))/(d + c^2*d*x^2)^3, x, 10, -b/(12*c^3*d^3*(1 + c^2*x^2)^(3/2)) + b/(8*c^3*d^3*sqrt(1 + c^2*x^2)) - (x*(a + b*asinh(c*x)))/(4*c^2*d^3*(1 + c^2*x^2)^2) + (x*(a + b*asinh(c*x)))/(8*c^2*d^3*(1 + c^2*x^2)) + ((a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(4*c^3*d^3) - ((im/8)*b*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^3*d^3) + ((im/8)*b*PolyLog(2, im*ℯ^asinh(c*x)))/(c^3*d^3)]
    @test_int [(x*(a + b*asinh(c*x)))/(d + c^2*d*x^2)^3, x, 3, (b*x)/(12*c*d^3*(1 + c^2*x^2)^(3/2)) + (b*x)/(6*c*d^3*sqrt(1 + c^2*x^2)) - (a + b*asinh(c*x))/(4*c^2*d^3*(1 + c^2*x^2)^2)]
    @test_int [(a + b*asinh(c*x))/(d + c^2*d*x^2)^3, x, 10, b/(12*c*d^3*(1 + c^2*x^2)^(3/2)) + (3*b)/(8*c*d^3*sqrt(1 + c^2*x^2)) + (x*(a + b*asinh(c*x)))/(4*d^3*(1 + c^2*x^2)^2) + (3*x*(a + b*asinh(c*x)))/(8*d^3*(1 + c^2*x^2)) + (3*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(4*c*d^3) - (((3*im)/8)*b*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c*d^3) + (((3*im)/8)*b*PolyLog(2, im*ℯ^asinh(c*x)))/(c*d^3)]
    @test_int [(a + b*asinh(c*x))/(x*(d + c^2*d*x^2)^3), x, 12, -(b*c*x)/(12*d^3*(1 + c^2*x^2)^(3/2)) - (2*b*c*x)/(3*d^3*sqrt(1 + c^2*x^2)) + (a + b*asinh(c*x))/(4*d^3*(1 + c^2*x^2)^2) + (a + b*asinh(c*x))/(2*d^3*(1 + c^2*x^2)) - (2*(a + b*asinh(c*x))*atanh(ℯ^(2*asinh(c*x))))/d^3 - (b*PolyLog(2, -ℯ^(2*asinh(c*x))))/(2*d^3) + (b*PolyLog(2, ℯ^(2*asinh(c*x))))/(2*d^3)]
    @test_int [(a + b*asinh(c*x))/(x^2*(d + c^2*d*x^2)^3), x, 16, -(b*c)/(12*d^3*(1 + c^2*x^2)^(3/2)) - (7*b*c)/(8*d^3*sqrt(1 + c^2*x^2)) - (a + b*asinh(c*x))/(d^3*x*(1 + c^2*x^2)^2) - (5*c^2*x*(a + b*asinh(c*x)))/(4*d^3*(1 + c^2*x^2)^2) - (15*c^2*x*(a + b*asinh(c*x)))/(8*d^3*(1 + c^2*x^2)) - (15*c*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(4*d^3) - (b*c*atanh(sqrt(1 + c^2*x^2)))/d^3 + (((15*im)/8)*b*c*PolyLog(2, (-im)*ℯ^asinh(c*x)))/d^3 - (((15*im)/8)*b*c*PolyLog(2, im*ℯ^asinh(c*x)))/d^3]
    @test_int [(a + b*asinh(c*x))/(x^3*(d + c^2*d*x^2)^3), x, 16, -(b*c)/(2*d^3*x*(1 + c^2*x^2)^(3/2)) - (5*b*c^3*x)/(12*d^3*(1 + c^2*x^2)^(3/2)) + (2*b*c^3*x)/(3*d^3*sqrt(1 + c^2*x^2)) - (3*c^2*(a + b*asinh(c*x)))/(4*d^3*(1 + c^2*x^2)^2) - (a + b*asinh(c*x))/(2*d^3*x^2*(1 + c^2*x^2)^2) - (3*c^2*(a + b*asinh(c*x)))/(2*d^3*(1 + c^2*x^2)) + (6*c^2*(a + b*asinh(c*x))*atanh(ℯ^(2*asinh(c*x))))/d^3 + (3*b*c^2*PolyLog(2, -ℯ^(2*asinh(c*x))))/(2*d^3) - (3*b*c^2*PolyLog(2, ℯ^(2*asinh(c*x))))/(2*d^3)]
    @test_int [(a + b*asinh(c*x))/(x^4*(d + c^2*d*x^2)^3), x, 23, -((b*c^3)/(12*d^3*(1 + c^2*x^2)^(3/2))) - (b*c)/(6*d^3*x^2*(1 + c^2*x^2)^(3/2)) + (29*b*c^3)/(24*d^3*sqrt(1 + c^2*x^2)) - (a + b*asinh(c*x))/(3*d^3*x^3*(1 + c^2*x^2)^2) + (7*c^2*(a + b*asinh(c*x)))/(3*d^3*x*(1 + c^2*x^2)^2) + (35*c^4*x*(a + b*asinh(c*x)))/(12*d^3*(1 + c^2*x^2)^2) + (35*c^4*x*(a + b*asinh(c*x)))/(8*d^3*(1 + c^2*x^2)) + (35*c^3*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(4*d^3) + (19*b*c^3*atanh(sqrt(1 + c^2*x^2)))/(6*d^3) - (35*im*b*c^3*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(8*d^3) + (35*im*b*c^3*PolyLog(2, im*ℯ^asinh(c*x)))/(8*d^3)]

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

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

    @test_int [x^3*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)), x, 3, (2*b*sqrt(pi)*x)/(15*c^3) - (b*sqrt(pi)*x^3)/(45*c) - (1/25)*b*c*sqrt(pi)*x^5 - ((pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*c^4*pi) + ((pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x)))/(5*c^4*pi^2)]
    @test_int [x^2*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)), x, 5, -((b*sqrt(pi)*x^2)/(16*c)) - (1/16)*b*c*sqrt(pi)*x^4 + (sqrt(pi)*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(8*c^2) + (1/4)*x^3*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)) - (sqrt(pi)*(a + b*asinh(c*x))^2)/(16*b*c^3)]
    @test_int [x^1*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)), x, 2, -((b*sqrt(pi)*x)/(3*c)) - (1/9)*b*c*sqrt(pi)*x^3 + ((pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*c^2*pi)]
    @test_int [x^0*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)), x, 3, (-(1/4))*b*c*sqrt(pi)*x^2 + (1/2)*x*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)) + (sqrt(pi)*(a + b*asinh(c*x))^2)/(4*b*c)]
    @test_int [(sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/x^1, x, 8, (-b)*c*sqrt(pi)*x + sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)) - 2*sqrt(pi)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)) - b*sqrt(pi)*PolyLog(2, -ℯ^asinh(c*x)) + b*sqrt(pi)*PolyLog(2, ℯ^asinh(c*x))]
    @test_int [(sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/x^2, x, 3, -((sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/x) + (c*sqrt(pi)*(a + b*asinh(c*x))^2)/(2*b) + b*c*sqrt(pi)*log(x)]
    @test_int [(sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/x^3, x, 8, -((b*c*sqrt(pi))/(2*x)) - (sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(2*x^2) - c^2*sqrt(pi)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)) - (1/2)*b*c^2*sqrt(pi)*PolyLog(2, -ℯ^asinh(c*x)) + (1/2)*b*c^2*sqrt(pi)*PolyLog(2, ℯ^asinh(c*x))]
    @test_int [(sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/x^4, x, 3, -((b*c*sqrt(pi))/(6*x^2)) - ((pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*pi*x^3) + (1/3)*b*c^3*sqrt(pi)*log(x)]

    @test_int [x^3*(pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)), x, 4, (2*b*pi^(3/2)*x)/(35*c^3) - (b*pi^(3/2)*x^3)/(105*c) - (8/175)*b*c*pi^(3/2)*x^5 - (1/49)*b*c^3*pi^(3/2)*x^7 - ((pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x)))/(5*c^4*pi) + ((pi + c^2*pi*x^2)^(7/2)*(a + b*asinh(c*x)))/(7*c^4*pi^2)]
    @test_int [x^2*(pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)), x, 8, -((b*pi^(3/2)*x^2)/(32*c)) - (7/96)*b*c*pi^(3/2)*x^4 - (1/36)*b*c^3*pi^(3/2)*x^6 + (pi^(3/2)*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(16*c^2) + (1/8)*pi*x^3*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)) + (1/6)*x^3*(pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)) - (pi^(3/2)*(a + b*asinh(c*x))^2)/(32*b*c^3)]
    @test_int [x^1*(pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)), x, 3, -((b*pi^(3/2)*x)/(5*c)) - (2/15)*b*c*pi^(3/2)*x^3 - (1/25)*b*c^3*pi^(3/2)*x^5 + ((pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x)))/(5*c^2*pi)]
    @test_int [x^0*(pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)), x, 6, (-(5/16))*b*c*pi^(3/2)*x^2 - (1/16)*b*c^3*pi^(3/2)*x^4 + (3/8)*pi*x*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)) + (1/4)*x*(pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)) + (3*pi^(3/2)*(a + b*asinh(c*x))^2)/(16*b*c)]
    @test_int [((pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)))/x^1, x, 10, (-(4/3))*b*c*pi^(3/2)*x - (1/9)*b*c^3*pi^(3/2)*x^3 + pi*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)) + (1/3)*(pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)) - 2*pi^(3/2)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)) - b*pi^(3/2)*PolyLog(2, -ℯ^asinh(c*x)) + b*pi^(3/2)*PolyLog(2, ℯ^asinh(c*x))]
    @test_int [((pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)))/x^2, x, 6, (-(1/4))*b*c^3*pi^(3/2)*x^2 + (3/2)*c^2*pi*x*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)) - ((pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)))/x + (3*c*pi^(3/2)*(a + b*asinh(c*x))^2)/(4*b) + b*c*pi^(3/2)*log(x)]
    @test_int [((pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)))/x^3, x, 11, -((b*c*pi^(3/2))/(2*x)) - b*c^3*pi^(3/2)*x + (3/2)*c^2*pi*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)) - ((pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)))/(2*x^2) - 3*c^2*pi^(3/2)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)) - (3/2)*b*c^2*pi^(3/2)*PolyLog(2, -ℯ^asinh(c*x)) + (3/2)*b*c^2*pi^(3/2)*PolyLog(2, ℯ^asinh(c*x))]
    @test_int [((pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)))/x^4, x, 6, -((b*c*pi^(3/2))/(6*x^2)) - (c^2*pi*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/x - ((pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*x^3) + (c^3*pi^(3/2)*(a + b*asinh(c*x))^2)/(2*b) + (4/3)*b*c^3*pi^(3/2)*log(x)]

    @test_int [x^3*(pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x)), x, 4, (2*b*pi^(5/2)*x)/(63*c^3) - (b*pi^(5/2)*x^3)/(189*c) - (1/21)*b*c*pi^(5/2)*x^5 - (19/441)*b*c^3*pi^(5/2)*x^7 - (1/81)*b*c^5*pi^(5/2)*x^9 - ((pi + c^2*pi*x^2)^(7/2)*(a + b*asinh(c*x)))/(7*c^4*pi) + ((pi + c^2*pi*x^2)^(9/2)*(a + b*asinh(c*x)))/(9*c^4*pi^2)]
    @test_int [x^2*(pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x)), x, 12, -((5*b*pi^(5/2)*x^2)/(256*c)) - (59/768)*b*c*pi^(5/2)*x^4 - (17/288)*b*c^3*pi^(5/2)*x^6 - (1/64)*b*c^5*pi^(5/2)*x^8 + (5*pi^(5/2)*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(128*c^2) + (5/64)*pi^2*x^3*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)) + (5/48)*pi*x^3*(pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)) + (1/8)*x^3*(pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x)) - (5*pi^(5/2)*(a + b*asinh(c*x))^2)/(256*b*c^3)]
    @test_int [x^1*(pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x)), x, 3, -((b*pi^(5/2)*x)/(7*c)) - (1/7)*b*c*pi^(5/2)*x^3 - (3/35)*b*c^3*pi^(5/2)*x^5 - (1/49)*b*c^5*pi^(5/2)*x^7 + ((pi + c^2*pi*x^2)^(7/2)*(a + b*asinh(c*x)))/(7*c^2*pi)]
    @test_int [x^0*(pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x)), x, 8, (-(25/96))*b*c*pi^(5/2)*x^2 - (5/96)*b*c^3*pi^(5/2)*x^4 - (b*pi^(5/2)*(1 + c^2*x^2)^3)/(36*c) + (5/16)*pi^2*x*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)) + (5/24)*pi*x*(pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)) + (1/6)*x*(pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x)) + (5*pi^(5/2)*(a + b*asinh(c*x))^2)/(32*b*c)]
    @test_int [((pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x)))/x^1, x, 13, (-(23/15))*b*c*pi^(5/2)*x - (11/45)*b*c^3*pi^(5/2)*x^3 - (1/25)*b*c^5*pi^(5/2)*x^5 + pi^2*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)) + (1/3)*pi*(pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)) + (1/5)*(pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x)) - 2*pi^(5/2)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)) - b*pi^(5/2)*PolyLog(2, -ℯ^asinh(c*x)) + b*pi^(5/2)*PolyLog(2, ℯ^asinh(c*x))]
    @test_int [((pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x)))/x^2, x, 10, (-(9/16))*b*c^3*pi^(5/2)*x^2 - (1/16)*b*c^5*pi^(5/2)*x^4 + (15/8)*c^2*pi^2*x*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)) + (5/4)*c^2*pi*x*(pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)) - ((pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x)))/x + (15*c*pi^(5/2)*(a + b*asinh(c*x))^2)/(16*b) + b*c*pi^(5/2)*log(x)]
    @test_int [((pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x)))/x^3, x, 13, -((b*c*pi^(5/2))/(2*x)) - (7/3)*b*c^3*pi^(5/2)*x - (1/9)*b*c^5*pi^(5/2)*x^3 + (5/2)*c^2*pi^2*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)) + (5/6)*c^2*pi*(pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)) - ((pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x)))/(2*x^2) - 5*c^2*pi^(5/2)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)) - (5/2)*b*c^2*pi^(5/2)*PolyLog(2, -ℯ^asinh(c*x)) + (5/2)*b*c^2*pi^(5/2)*PolyLog(2, ℯ^asinh(c*x))]
    @test_int [((pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x)))/x^4, x, 10, -((b*c*pi^(5/2))/(6*x^2)) - (1/4)*b*c^5*pi^(5/2)*x^2 + (5/2)*c^4*pi^2*x*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)) - (5*c^2*pi*(pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*x) - ((pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x)))/(3*x^3) + (5*c^3*pi^(5/2)*(a + b*asinh(c*x))^2)/(4*b) + (7/3)*b*c^3*pi^(5/2)*log(x)]

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

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

    @test_int [(x^5*(a + b*asinh(c*x)))/sqrt(pi + c^2*pi*x^2), x, 6, -((8*b*x)/(15*c^5*sqrt(pi))) + (4*b*x^3)/(45*c^3*sqrt(pi)) - (b*x^5)/(25*c*sqrt(pi)) + (8*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(15*c^6*pi) - (4*x^2*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(15*c^4*pi) + (x^4*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(5*c^2*pi)]
    @test_int [(x^4*(a + b*asinh(c*x)))/sqrt(pi + c^2*pi*x^2), x, 5, (3*b*x^2)/(16*c^3*sqrt(pi)) - (b*x^4)/(16*c*sqrt(pi)) - (3*x*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(8*c^4*pi) + (x^3*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(4*c^2*pi) + (3*(a + b*asinh(c*x))^2)/(16*b*c^5*sqrt(pi))]
    @test_int [(x^3*(a + b*asinh(c*x)))/sqrt(pi + c^2*pi*x^2), x, 4, (2*b*x)/(3*c^3*sqrt(pi)) - (b*x^3)/(9*c*sqrt(pi)) - (2*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(3*c^4*pi) + (x^2*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(3*c^2*pi)]
    @test_int [(x^2*(a + b*asinh(c*x)))/sqrt(pi + c^2*pi*x^2), x, 3, -((b*x^2)/(4*c*sqrt(pi))) + (x*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(2*c^2*pi) - (a + b*asinh(c*x))^2/(4*b*c^3*sqrt(pi))]
    @test_int [(x^1*(a + b*asinh(c*x)))/sqrt(pi + c^2*pi*x^2), x, 2, -((b*x)/(c*sqrt(pi))) + (sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(c^2*pi)]
    @test_int [x^0*(a + b*asinh(c*x))/sqrt(pi + c^2*pi*x^2), x, 1, (a + b*asinh(c*x))^2/(2*b*c*sqrt(pi))]
    @test_int [(a + b*asinh(c*x))/(x^1*sqrt(pi + c^2*pi*x^2)), x, 6, -((2*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/sqrt(pi)) - (b*PolyLog(2, -ℯ^asinh(c*x)))/sqrt(pi) + (b*PolyLog(2, ℯ^asinh(c*x)))/sqrt(pi)]
    @test_int [(a + b*asinh(c*x))/(x^2*sqrt(pi + c^2*pi*x^2)), x, 2, -((sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(pi*x)) + (b*c*log(x))/sqrt(pi)]
    @test_int [(a + b*asinh(c*x))/(x^3*sqrt(pi + c^2*pi*x^2)), x, 8, -((b*c)/(2*sqrt(pi)*x)) - (sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(2*pi*x^2) + (c^2*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/sqrt(pi) + (b*c^2*PolyLog(2, -ℯ^asinh(c*x)))/(2*sqrt(pi)) - (b*c^2*PolyLog(2, ℯ^asinh(c*x)))/(2*sqrt(pi))]
    @test_int [(a + b*asinh(c*x))/(x^4*sqrt(pi + c^2*pi*x^2)), x, 4, -((b*c)/(6*sqrt(pi)*x^2)) - (sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(3*pi*x^3) + (2*c^2*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(3*pi*x) - (2*b*c^3*log(x))/(3*sqrt(pi))]

    @test_int [(x^5*(a + b*asinh(c*x)))/(pi + c^2*pi*x^2)^(3/2), x, 5, (5*b*x)/(3*c^5*pi^(3/2)) - (b*x^3)/(9*c^3*pi^(3/2)) - (a + b*asinh(c*x))/(c^6*pi*sqrt(pi + c^2*pi*x^2)) - (2*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(c^6*pi^2) + ((pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*c^6*pi^3) + (b*atan(c*x))/(c^6*pi^(3/2))]
    @test_int [(x^4*(a + b*asinh(c*x)))/(pi + c^2*pi*x^2)^(3/2), x, 7, -((b*x^2)/(4*c^3*pi^(3/2))) - (x^3*(a + b*asinh(c*x)))/(c^2*pi*sqrt(pi + c^2*pi*x^2)) + (3*x*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(2*c^4*pi^2) - (3*(a + b*asinh(c*x))^2)/(4*b*c^5*pi^(3/2)) - (b*log(1 + c^2*x^2))/(2*c^5*pi^(3/2))]
    @test_int [(x^3*(a + b*asinh(c*x)))/(pi + c^2*pi*x^2)^(3/2), x, 4, -((b*x)/(c^3*pi^(3/2))) + (a + b*asinh(c*x))/(c^4*pi*sqrt(pi + c^2*pi*x^2)) + (sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(c^4*pi^2) - (b*atan(c*x))/(c^4*pi^(3/2))]
    @test_int [(x^2*(a + b*asinh(c*x)))/(pi + c^2*pi*x^2)^(3/2), x, 3, -((x*(a + b*asinh(c*x)))/(c^2*pi*sqrt(pi + c^2*pi*x^2))) + (a + b*asinh(c*x))^2/(2*b*c^3*pi^(3/2)) + (b*log(1 + c^2*x^2))/(2*c^3*pi^(3/2))]
    @test_int [(x^1*(a + b*asinh(c*x)))/(pi + c^2*pi*x^2)^(3/2), x, 2, -((a + b*asinh(c*x))/(c^2*pi*sqrt(pi + c^2*pi*x^2))) + (b*atan(c*x))/(c^2*pi^(3/2))]
    @test_int [x^0*(a + b*asinh(c*x))/(pi + c^2*pi*x^2)^(3/2), x, 2, (x*(a + b*asinh(c*x)))/(pi*sqrt(pi + c^2*pi*x^2)) - (b*log(1 + c^2*x^2))/(2*c*pi^(3/2))]
    @test_int [(a + b*asinh(c*x))/(x^1*(pi + c^2*pi*x^2)^(3/2)), x, 8, (a + b*asinh(c*x))/(pi*sqrt(pi + c^2*pi*x^2)) - (b*atan(c*x))/pi^(3/2) - (2*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/pi^(3/2) - (b*PolyLog(2, -ℯ^asinh(c*x)))/pi^(3/2) + (b*PolyLog(2, ℯ^asinh(c*x)))/pi^(3/2)]
    @test_int [(a + b*asinh(c*x))/(x^2*(pi + c^2*pi*x^2)^(3/2)), x, 5, -((a + b*asinh(c*x))/(pi*x*sqrt(pi + c^2*pi*x^2))) - (2*c^2*x*(a + b*asinh(c*x)))/(pi*sqrt(pi + c^2*pi*x^2)) + (b*c*log(x))/pi^(3/2) + (b*c*log(1 + c^2*x^2))/(2*pi^(3/2))]
    @test_int [(a + b*asinh(c*x))/(x^3*(pi + c^2*pi*x^2)^(3/2)), x, 11, -((b*c)/(2*pi^(3/2)*x)) - (3*c^2*(a + b*asinh(c*x)))/(2*pi*sqrt(pi + c^2*pi*x^2)) - (a + b*asinh(c*x))/(2*pi*x^2*sqrt(pi + c^2*pi*x^2)) + (b*c^2*atan(c*x))/pi^(3/2) + (3*c^2*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/pi^(3/2) + (3*b*c^2*PolyLog(2, -ℯ^asinh(c*x)))/(2*pi^(3/2)) - (3*b*c^2*PolyLog(2, ℯ^asinh(c*x)))/(2*pi^(3/2))]
    @test_int [(a + b*asinh(c*x))/(x^4*(pi + c^2*pi*x^2)^(3/2)), x, 5, -((b*c)/(6*pi^(3/2)*x^2)) - (a + b*asinh(c*x))/(3*pi*x^3*sqrt(pi + c^2*pi*x^2)) + (4*c^2*(a + b*asinh(c*x)))/(3*pi*x*sqrt(pi + c^2*pi*x^2)) + (8*c^4*x*(a + b*asinh(c*x)))/(3*pi*sqrt(pi + c^2*pi*x^2)) - (5*b*c^3*log(x))/(3*pi^(3/2)) - (b*c^3*log(1 + c^2*x^2))/(2*pi^(3/2))]

    @test_int [(x^6*(a + b*asinh(c*x)))/(pi + c^2*pi*x^2)^(5/2), x, 11, -((b*x^2)/(4*c^5*pi^(5/2))) - b/(6*c^7*pi^(5/2)*(1 + c^2*x^2)) - (x^5*(a + b*asinh(c*x)))/(3*c^2*pi*(pi + c^2*pi*x^2)^(3/2)) - (5*x^3*(a + b*asinh(c*x)))/(3*c^4*pi^2*sqrt(pi + c^2*pi*x^2)) + (5*x*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(2*c^6*pi^3) - (5*(a + b*asinh(c*x))^2)/(4*b*c^7*pi^(5/2)) - (7*b*log(1 + c^2*x^2))/(6*c^7*pi^(5/2))]
    @test_int [(x^5*(a + b*asinh(c*x)))/(pi + c^2*pi*x^2)^(5/2), x, 5, -((b*x)/(c^5*pi^(5/2))) + (b*x)/(6*c^5*pi^(5/2)*(1 + c^2*x^2)) - (a + b*asinh(c*x))/(3*c^6*pi*(pi + c^2*pi*x^2)^(3/2)) + (2*(a + b*asinh(c*x)))/(c^6*pi^2*sqrt(pi + c^2*pi*x^2)) + (sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x)))/(c^6*pi^3) - (11*b*atan(c*x))/(6*c^6*pi^(5/2))]
    @test_int [(x^4*(a + b*asinh(c*x)))/(pi + c^2*pi*x^2)^(5/2), x, 7, b/(6*c^5*pi^(5/2)*(1 + c^2*x^2)) - (x^3*(a + b*asinh(c*x)))/(3*c^2*pi*(pi + c^2*pi*x^2)^(3/2)) - (x*(a + b*asinh(c*x)))/(c^4*pi^2*sqrt(pi + c^2*pi*x^2)) + (a + b*asinh(c*x))^2/(2*b*c^5*pi^(5/2)) + (2*b*log(1 + c^2*x^2))/(3*c^5*pi^(5/2))]
    @test_int [(x^3*(a + b*asinh(c*x)))/(pi + c^2*pi*x^2)^(5/2), x, 4, -((b*x)/(6*c^3*pi^(5/2)*(1 + c^2*x^2))) + (a + b*asinh(c*x))/(3*c^4*pi*(pi + c^2*pi*x^2)^(3/2)) - (a + b*asinh(c*x))/(c^4*pi^2*sqrt(pi + c^2*pi*x^2)) + (5*b*atan(c*x))/(6*c^4*pi^(5/2))]
    @test_int [(x^2*(a + b*asinh(c*x)))/(pi + c^2*pi*x^2)^(5/2), x, 4, -(b/(6*c^3*pi^(5/2)*(1 + c^2*x^2))) + (x^3*(a + b*asinh(c*x)))/(3*pi*(pi + c^2*pi*x^2)^(3/2)) - (b*log(1 + c^2*x^2))/(6*c^3*pi^(5/2))]
    @test_int [(x^1*(a + b*asinh(c*x)))/(pi + c^2*pi*x^2)^(5/2), x, 3, (b*x)/(6*c*pi^(5/2)*(1 + c^2*x^2)) - (a + b*asinh(c*x))/(3*c^2*pi*(pi + c^2*pi*x^2)^(3/2)) + (b*atan(c*x))/(6*c^2*pi^(5/2))]
    @test_int [x^0*(a + b*asinh(c*x))/(pi + c^2*pi*x^2)^(5/2), x, 4, b/(6*c*pi^(5/2)*(1 + c^2*x^2)) + (x*(a + b*asinh(c*x)))/(3*pi*(pi + c^2*pi*x^2)^(3/2)) + (2*x*(a + b*asinh(c*x)))/(3*pi^2*sqrt(pi + c^2*pi*x^2)) - (b*log(1 + c^2*x^2))/(3*c*pi^(5/2))]
    @test_int [(a + b*asinh(c*x))/(x^1*(pi + c^2*pi*x^2)^(5/2)), x, 11, -((b*c*x)/(6*pi^(5/2)*(1 + c^2*x^2))) + (a + b*asinh(c*x))/(3*pi*(pi + c^2*pi*x^2)^(3/2)) + (a + b*asinh(c*x))/(pi^2*sqrt(pi + c^2*pi*x^2)) - (7*b*atan(c*x))/(6*pi^(5/2)) - (2*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/pi^(5/2) - (b*PolyLog(2, -ℯ^asinh(c*x)))/pi^(5/2) + (b*PolyLog(2, ℯ^asinh(c*x)))/pi^(5/2)]
    @test_int [(a + b*asinh(c*x))/(x^2*(pi + c^2*pi*x^2)^(5/2)), x, 5, -((b*c)/(6*pi^(5/2)*(1 + c^2*x^2))) - (a + b*asinh(c*x))/(pi*x*(pi + c^2*pi*x^2)^(3/2)) - (4*c^2*x*(a + b*asinh(c*x)))/(3*pi*(pi + c^2*pi*x^2)^(3/2)) - (8*c^2*x*(a + b*asinh(c*x)))/(3*pi^2*sqrt(pi + c^2*pi*x^2)) + (b*c*log(x))/pi^(5/2) + (5*b*c*log(1 + c^2*x^2))/(6*pi^(5/2))]
    @test_int [(a + b*asinh(c*x))/(x^3*(pi + c^2*pi*x^2)^(5/2)), x, 15, -((3*b*c)/(4*pi^(5/2)*x)) + (b*c)/(4*pi^(5/2)*x*(1 + c^2*x^2)) + (5*b*c^3*x)/(12*pi^(5/2)*(1 + c^2*x^2)) - (5*c^2*(a + b*asinh(c*x)))/(6*pi*(pi + c^2*pi*x^2)^(3/2)) - (a + b*asinh(c*x))/(2*pi*x^2*(pi + c^2*pi*x^2)^(3/2)) - (5*c^2*(a + b*asinh(c*x)))/(2*pi^2*sqrt(pi + c^2*pi*x^2)) + (13*b*c^2*atan(c*x))/(6*pi^(5/2)) + (5*c^2*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/pi^(5/2) + (5*b*c^2*PolyLog(2, -ℯ^asinh(c*x)))/(2*pi^(5/2)) - (5*b*c^2*PolyLog(2, ℯ^asinh(c*x)))/(2*pi^(5/2))]
    @test_int [(a + b*asinh(c*x))/(x^4*(pi + c^2*pi*x^2)^(5/2)), x, 5, -((b*c)/(6*pi^(5/2)*x^2)) + (b*c^3)/(6*pi^(5/2)*(1 + c^2*x^2)) - (a + b*asinh(c*x))/(3*pi*x^3*(pi + c^2*pi*x^2)^(3/2)) + (2*c^2*(a + b*asinh(c*x)))/(pi*x*(pi + c^2*pi*x^2)^(3/2)) + (8*c^4*x*(a + b*asinh(c*x)))/(3*pi*(pi + c^2*pi*x^2)^(3/2)) + (16*c^4*x*(a + b*asinh(c*x)))/(3*pi^2*sqrt(pi + c^2*pi*x^2)) - (8*b*c^3*log(x))/(3*pi^(5/2)) - (4*b*c^3*log(1 + c^2*x^2))/(3*pi^(5/2))]

    @test_int [asinh(a*x)/(c + a^2*c*x^2)^(7/2), x, 6, 1/(20*a*c^3*(1 + a^2*x^2)^(3/2)*sqrt(c + a^2*c*x^2)) + 2/(15*a*c^3*sqrt(1 + a^2*x^2)*sqrt(c + a^2*c*x^2)) + (x*asinh(a*x))/(5*c*(c + a^2*c*x^2)^(5/2)) + (4*x*asinh(a*x))/(15*c^2*(c + a^2*c*x^2)^(3/2)) + (8*x*asinh(a*x))/(15*c^3*sqrt(c + a^2*c*x^2)) - (4*sqrt(1 + a^2*x^2)*log(1 + a^2*x^2))/(15*a*c^3*sqrt(c + a^2*c*x^2))]

    @test_int [(x^4*asinh(a*x))/sqrt(1 + a^2*x^2), x, 5, (3*x^2)/(16*a^3) - x^4/(16*a) - (3*x*sqrt(1 + a^2*x^2)*asinh(a*x))/(8*a^4) + (x^3*sqrt(1 + a^2*x^2)*asinh(a*x))/(4*a^2) + (3*asinh(a*x)^2)/(16*a^5)]
    @test_int [(x^3*asinh(a*x))/sqrt(1 + a^2*x^2), x, 4, (2*x)/(3*a^3) - x^3/(9*a) - (2*sqrt(1 + a^2*x^2)*asinh(a*x))/(3*a^4) + (x^2*sqrt(1 + a^2*x^2)*asinh(a*x))/(3*a^2)]
    @test_int [(x^2*asinh(a*x))/sqrt(1 + a^2*x^2), x, 3, -x^2/(4*a) + (x*sqrt(1 + a^2*x^2)*asinh(a*x))/(2*a^2) - asinh(a*x)^2/(4*a^3)]
    @test_int [(x^1*asinh(a*x))/sqrt(1 + a^2*x^2), x, 2, -(x/a) + (sqrt(1 + a^2*x^2)*asinh(a*x))/a^2]
    @test_int [asinh(a*x)/sqrt(1 + a^2*x^2), x, 1, asinh(a*x)^2/(2*a)]
    @test_int [asinh(a*x)/(x^1*sqrt(1 + a^2*x^2)), x, 6, -2*asinh(a*x)*atanh(ℯ^asinh(a*x)) - PolyLog(2, -ℯ^asinh(a*x)) + PolyLog(2, ℯ^asinh(a*x))]
    @test_int [asinh(a*x)/(x^2*sqrt(1 + a^2*x^2)), x, 2, -((sqrt(1 + a^2*x^2)*asinh(a*x))/x) + a*log(x)]
    @test_int [asinh(a*x)/(x^3*sqrt(1 + a^2*x^2)), x, 8, -a/(2*x) - (sqrt(1 + a^2*x^2)*asinh(a*x))/(2*x^2) + a^2*asinh(a*x)*atanh(ℯ^asinh(a*x)) + (a^2*PolyLog(2, -ℯ^asinh(a*x)))/2 - (a^2*PolyLog(2, ℯ^asinh(a*x)))/2]

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

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

    @test_int [x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)), x, 3, (2*b*x*sqrt(d + c^2*d*x^2))/(15*c^3*sqrt(1 + c^2*x^2)) - (b*x^3*sqrt(d + c^2*d*x^2))/(45*c*sqrt(1 + c^2*x^2)) - (b*c*x^5*sqrt(d + c^2*d*x^2))/(25*sqrt(1 + c^2*x^2)) - ((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*c^4*d) + ((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)))/(5*c^4*d^2)]
    @test_int [x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)), x, 5, -(b*x^2*sqrt(d + c^2*d*x^2))/(16*c*sqrt(1 + c^2*x^2)) - (b*c*x^4*sqrt(d + c^2*d*x^2))/(16*sqrt(1 + c^2*x^2)) + (x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(8*c^2) + (x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/4 - (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 [x^1*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)), x, 2, -(b*x*sqrt(d + c^2*d*x^2))/(3*c*sqrt(1 + c^2*x^2)) - (b*c*x^3*sqrt(d + c^2*d*x^2))/(9*sqrt(1 + c^2*x^2)) + ((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*c^2*d)]
    @test_int [x^0*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)), x, 3, -(b*c*x^2*sqrt(d + c^2*d*x^2))/(4*sqrt(1 + c^2*x^2)) + (x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/2 + (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)))/x^1, x, 8, -((b*c*x*sqrt(d + c^2*d*x^2))/sqrt(1 + c^2*x^2)) + sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) - (2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (b*sqrt(d + c^2*d*x^2)*PolyLog(2, -ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) + (b*sqrt(d + c^2*d*x^2)*PolyLog(2, ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2)]
    @test_int [(sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/x^2, x, 3, -((sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/x) + (c*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*b*sqrt(1 + c^2*x^2)) + (b*c*sqrt(d + c^2*d*x^2)*log(x))/sqrt(1 + c^2*x^2)]
    @test_int [(sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/x^3, x, 8, -((b*c*sqrt(d + c^2*d*x^2))/(2*x*sqrt(1 + c^2*x^2))) - (sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(2*x^2) - (c^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (b*c^2*sqrt(d + c^2*d*x^2)*PolyLog(2, -ℯ^asinh(c*x)))/(2*sqrt(1 + c^2*x^2)) + (b*c^2*sqrt(d + c^2*d*x^2)*PolyLog(2, ℯ^asinh(c*x)))/(2*sqrt(1 + c^2*x^2))]
    @test_int [(sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/x^4, x, 3, -((b*c*sqrt(d + c^2*d*x^2))/(6*x^2*sqrt(1 + c^2*x^2))) - ((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*d*x^3) + (b*c^3*sqrt(d + c^2*d*x^2)*log(x))/(3*sqrt(1 + c^2*x^2))]

    @test_int [x^3*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)), x, 4, (2*b*d*x*sqrt(d + c^2*d*x^2))/(35*c^3*sqrt(1 + c^2*x^2)) - (b*d*x^3*sqrt(d + c^2*d*x^2))/(105*c*sqrt(1 + c^2*x^2)) - (8*b*c*d*x^5*sqrt(d + c^2*d*x^2))/(175*sqrt(1 + c^2*x^2)) - (b*c^3*d*x^7*sqrt(d + c^2*d*x^2))/(49*sqrt(1 + c^2*x^2)) - ((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)))/(5*c^4*d) + ((d + c^2*d*x^2)^(7/2)*(a + b*asinh(c*x)))/(7*c^4*d^2)]
    @test_int [x^2*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)), x, 8, -(b*d*x^2*sqrt(d + c^2*d*x^2))/(32*c*sqrt(1 + c^2*x^2)) - (7*b*c*d*x^4*sqrt(d + c^2*d*x^2))/(96*sqrt(1 + c^2*x^2)) - (b*c^3*d*x^6*sqrt(d + c^2*d*x^2))/(36*sqrt(1 + c^2*x^2)) + (d*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(16*c^2) + (d*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/8 + (x^3*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/6 - (d*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 [x^1*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)), x, 3, -(b*d*x*sqrt(d + c^2*d*x^2))/(5*c*sqrt(1 + c^2*x^2)) - (2*b*c*d*x^3*sqrt(d + c^2*d*x^2))/(15*sqrt(1 + c^2*x^2)) - (b*c^3*d*x^5*sqrt(d + c^2*d*x^2))/(25*sqrt(1 + c^2*x^2)) + ((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)))/(5*c^2*d)]
    @test_int [x^0*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)), x, 6, (-5*b*c*d*x^2*sqrt(d + c^2*d*x^2))/(16*sqrt(1 + c^2*x^2)) - (b*c^3*d*x^4*sqrt(d + c^2*d*x^2))/(16*sqrt(1 + c^2*x^2)) + (3*d*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/8 + (x*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/4 + (3*d*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)))/x^1, x, 10, -((4*b*c*d*x*sqrt(d + c^2*d*x^2))/(3*sqrt(1 + c^2*x^2))) - (b*c^3*d*x^3*sqrt(d + c^2*d*x^2))/(9*sqrt(1 + c^2*x^2)) + d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (1/3)*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)) - (2*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (b*d*sqrt(d + c^2*d*x^2)*PolyLog(2, -ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) + (b*d*sqrt(d + c^2*d*x^2)*PolyLog(2, ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2)]
    @test_int [((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/x^2, x, 6, -(b*c^3*d*x^2*sqrt(d + c^2*d*x^2))/(4*sqrt(1 + c^2*x^2)) + (3*c^2*d*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/2 - ((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/x + (3*c*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(4*b*sqrt(1 + c^2*x^2)) + (b*c*d*sqrt(d + c^2*d*x^2)*log(x))/sqrt(1 + c^2*x^2)]
    @test_int [((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/x^3, x, 11, -((b*c*d*sqrt(d + c^2*d*x^2))/(2*x*sqrt(1 + c^2*x^2))) - (b*c^3*d*x*sqrt(d + c^2*d*x^2))/sqrt(1 + c^2*x^2) + (3/2)*c^2*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) - ((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/(2*x^2) - (3*c^2*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (3*b*c^2*d*sqrt(d + c^2*d*x^2)*PolyLog(2, -ℯ^asinh(c*x)))/(2*sqrt(1 + c^2*x^2)) + (3*b*c^2*d*sqrt(d + c^2*d*x^2)*PolyLog(2, ℯ^asinh(c*x)))/(2*sqrt(1 + c^2*x^2))]
    @test_int [((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/x^4, x, 6, -(b*c*d*sqrt(d + c^2*d*x^2))/(6*x^2*sqrt(1 + c^2*x^2)) - (c^2*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/x - ((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*x^3) + (c^3*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*b*sqrt(1 + c^2*x^2)) + (4*b*c^3*d*sqrt(d + c^2*d*x^2)*log(x))/(3*sqrt(1 + c^2*x^2))]

    @test_int [x^3*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)), x, 4, (2*b*d^2*x*sqrt(d + c^2*d*x^2))/(63*c^3*sqrt(1 + c^2*x^2)) - (b*d^2*x^3*sqrt(d + c^2*d*x^2))/(189*c*sqrt(1 + c^2*x^2)) - (b*c*d^2*x^5*sqrt(d + c^2*d*x^2))/(21*sqrt(1 + c^2*x^2)) - (19*b*c^3*d^2*x^7*sqrt(d + c^2*d*x^2))/(441*sqrt(1 + c^2*x^2)) - (b*c^5*d^2*x^9*sqrt(d + c^2*d*x^2))/(81*sqrt(1 + c^2*x^2)) - ((d + c^2*d*x^2)^(7/2)*(a + b*asinh(c*x)))/(7*c^4*d) + ((d + c^2*d*x^2)^(9/2)*(a + b*asinh(c*x)))/(9*c^4*d^2)]
    @test_int [x^2*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)), x, 12, (-5*b*d^2*x^2*sqrt(d + c^2*d*x^2))/(256*c*sqrt(1 + c^2*x^2)) - (59*b*c*d^2*x^4*sqrt(d + c^2*d*x^2))/(768*sqrt(1 + c^2*x^2)) - (17*b*c^3*d^2*x^6*sqrt(d + c^2*d*x^2))/(288*sqrt(1 + c^2*x^2)) - (b*c^5*d^2*x^8*sqrt(d + c^2*d*x^2))/(64*sqrt(1 + c^2*x^2)) + (5*d^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(128*c^2) + (5*d^2*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/64 + (5*d*x^3*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/48 + (x^3*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)))/8 - (5*d^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 [x^1*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)), x, 3, -(b*d^2*x*sqrt(d + c^2*d*x^2))/(7*c*sqrt(1 + c^2*x^2)) - (b*c*d^2*x^3*sqrt(d + c^2*d*x^2))/(7*sqrt(1 + c^2*x^2)) - (3*b*c^3*d^2*x^5*sqrt(d + c^2*d*x^2))/(35*sqrt(1 + c^2*x^2)) - (b*c^5*d^2*x^7*sqrt(d + c^2*d*x^2))/(49*sqrt(1 + c^2*x^2)) + ((d + c^2*d*x^2)^(7/2)*(a + b*asinh(c*x)))/(7*c^2*d)]
    @test_int [x^0*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)), x, 8, (-25*b*c*d^2*x^2*sqrt(d + c^2*d*x^2))/(96*sqrt(1 + c^2*x^2)) - (5*b*c^3*d^2*x^4*sqrt(d + c^2*d*x^2))/(96*sqrt(1 + c^2*x^2)) - (b*d^2*(1 + c^2*x^2)^(5/2)*sqrt(d + c^2*d*x^2))/(36*c) + (5*d^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/16 + (5*d*x*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/24 + (x*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)))/6 + (5*d^2*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)))/x^1, x, 13, -((23*b*c*d^2*x*sqrt(d + c^2*d*x^2))/(15*sqrt(1 + c^2*x^2))) - (11*b*c^3*d^2*x^3*sqrt(d + c^2*d*x^2))/(45*sqrt(1 + c^2*x^2)) - (b*c^5*d^2*x^5*sqrt(d + c^2*d*x^2))/(25*sqrt(1 + c^2*x^2)) + d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (1/3)*d*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)) + (1/5)*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)) - (2*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (b*d^2*sqrt(d + c^2*d*x^2)*PolyLog(2, -ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) + (b*d^2*sqrt(d + c^2*d*x^2)*PolyLog(2, ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2)]
    @test_int [((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)))/x^2, x, 10, (-9*b*c^3*d^2*x^2*sqrt(d + c^2*d*x^2))/(16*sqrt(1 + c^2*x^2)) - (b*c^5*d^2*x^4*sqrt(d + c^2*d*x^2))/(16*sqrt(1 + c^2*x^2)) + (15*c^2*d^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/8 + (5*c^2*d*x*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/4 - ((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)))/x + (15*c*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(16*b*sqrt(1 + c^2*x^2)) + (b*c*d^2*sqrt(d + c^2*d*x^2)*log(x))/sqrt(1 + c^2*x^2)]
    @test_int [((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)))/x^3, x, 13, -((b*c*d^2*sqrt(d + c^2*d*x^2))/(2*x*sqrt(1 + c^2*x^2))) - (7*b*c^3*d^2*x*sqrt(d + c^2*d*x^2))/(3*sqrt(1 + c^2*x^2)) - (b*c^5*d^2*x^3*sqrt(d + c^2*d*x^2))/(9*sqrt(1 + c^2*x^2)) + (5/2)*c^2*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (5/6)*c^2*d*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)) - ((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)))/(2*x^2) - (5*c^2*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (5*b*c^2*d^2*sqrt(d + c^2*d*x^2)*PolyLog(2, -ℯ^asinh(c*x)))/(2*sqrt(1 + c^2*x^2)) + (5*b*c^2*d^2*sqrt(d + c^2*d*x^2)*PolyLog(2, ℯ^asinh(c*x)))/(2*sqrt(1 + c^2*x^2))]
    @test_int [((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)))/x^4, x, 10, -(b*c*d^2*sqrt(d + c^2*d*x^2))/(6*x^2*sqrt(1 + c^2*x^2)) - (b*c^5*d^2*x^2*sqrt(d + c^2*d*x^2))/(4*sqrt(1 + c^2*x^2)) + (5*c^4*d^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/2 - (5*c^2*d*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*x) - ((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)))/(3*x^3) + (5*c^3*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(4*b*sqrt(1 + c^2*x^2)) + (7*b*c^3*d^2*sqrt(d + c^2*d*x^2)*log(x))/(3*sqrt(1 + c^2*x^2))]

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

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

    @test_int [x^5*(a + b*asinh(c*x))/sqrt(d + c^2*d*x^2), x, 6, (-8*b*x*sqrt(1 + c^2*x^2))/(15*c^5*sqrt(d + c^2*d*x^2)) + (4*b*x^3*sqrt(1 + c^2*x^2))/(45*c^3*sqrt(d + c^2*d*x^2)) - (b*x^5*sqrt(1 + c^2*x^2))/(25*c*sqrt(d + c^2*d*x^2)) + (8*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(15*c^6*d) - (4*x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(15*c^4*d) + (x^4*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(5*c^2*d)]
    @test_int [x^4*(a + b*asinh(c*x))/sqrt(d + c^2*d*x^2), x, 5, (3*b*x^2*sqrt(1 + c^2*x^2))/(16*c^3*sqrt(d + c^2*d*x^2)) - (b*x^4*sqrt(1 + c^2*x^2))/(16*c*sqrt(d + c^2*d*x^2)) - (3*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(8*c^4*d) + (x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(4*c^2*d) + (3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(16*b*c^5*sqrt(d + c^2*d*x^2))]
    @test_int [x^3*(a + b*asinh(c*x))/sqrt(d + c^2*d*x^2), x, 4, (2*b*x*sqrt(1 + c^2*x^2))/(3*c^3*sqrt(d + c^2*d*x^2)) - (b*x^3*sqrt(1 + c^2*x^2))/(9*c*sqrt(d + c^2*d*x^2)) - (2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(3*c^4*d) + (x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(3*c^2*d)]
    @test_int [x^2*(a + b*asinh(c*x))/sqrt(d + c^2*d*x^2), x, 3, -(b*x^2*sqrt(1 + c^2*x^2))/(4*c*sqrt(d + c^2*d*x^2)) + (x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(2*c^2*d) - (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 [x^1*(a + b*asinh(c*x))/sqrt(d + c^2*d*x^2), x, 2, -((b*x*sqrt(1 + c^2*x^2))/(c*sqrt(d + c^2*d*x^2))) + (sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(c^2*d)]
    @test_int [x^0*(a + b*asinh(c*x))/sqrt(d + c^2*d*x^2), 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 [(a + b*asinh(c*x))/(x^1*sqrt(d + c^2*d*x^2)), x, 6, -((2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/sqrt(d + c^2*d*x^2)) - (b*sqrt(1 + c^2*x^2)*PolyLog(2, -ℯ^asinh(c*x)))/sqrt(d + c^2*d*x^2) + (b*sqrt(1 + c^2*x^2)*PolyLog(2, ℯ^asinh(c*x)))/sqrt(d + c^2*d*x^2)]
    @test_int [(a + b*asinh(c*x))/(x^2*sqrt(d + c^2*d*x^2)), x, 2, -((sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(d*x)) + (b*c*sqrt(1 + c^2*x^2)*log(x))/sqrt(d + c^2*d*x^2)]
    @test_int [(a + b*asinh(c*x))/(x^3*sqrt(d + c^2*d*x^2)), x, 8, -((b*c*sqrt(1 + c^2*x^2))/(2*x*sqrt(d + c^2*d*x^2))) - (sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(2*d*x^2) + (c^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/sqrt(d + c^2*d*x^2) + (b*c^2*sqrt(1 + c^2*x^2)*PolyLog(2, -ℯ^asinh(c*x)))/(2*sqrt(d + c^2*d*x^2)) - (b*c^2*sqrt(1 + c^2*x^2)*PolyLog(2, ℯ^asinh(c*x)))/(2*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))/(x^4*sqrt(d + c^2*d*x^2)), x, 4, -(b*c*sqrt(1 + c^2*x^2))/(6*x^2*sqrt(d + c^2*d*x^2)) - (sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(3*d*x^3) + (2*c^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(3*d*x) - (2*b*c^3*sqrt(1 + c^2*x^2)*log(x))/(3*sqrt(d + c^2*d*x^2))]

    @test_int [x^5*(a + b*asinh(c*x))/(d + c^2*d*x^2)^(3/2), x, 5, (5*b*x*sqrt(d + c^2*d*x^2))/(3*c^5*d^2*sqrt(1 + c^2*x^2)) - (b*x^3*sqrt(d + c^2*d*x^2))/(9*c^3*d^2*sqrt(1 + c^2*x^2)) - (a + b*asinh(c*x))/(c^6*d*sqrt(d + c^2*d*x^2)) - (2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(c^6*d^2) + ((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*c^6*d^3) + (b*sqrt(d + c^2*d*x^2)*atan(c*x))/(c^6*d^2*sqrt(1 + c^2*x^2))]
    @test_int [x^4*(a + b*asinh(c*x))/(d + c^2*d*x^2)^(3/2), x, 7, -(b*x^2*sqrt(1 + c^2*x^2))/(4*c^3*d*sqrt(d + c^2*d*x^2)) - (x^3*(a + b*asinh(c*x)))/(c^2*d*sqrt(d + c^2*d*x^2)) + (3*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(2*c^4*d^2) - (3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(4*b*c^5*d*sqrt(d + c^2*d*x^2)) - (b*sqrt(1 + c^2*x^2)*log(1 + c^2*x^2))/(2*c^5*d*sqrt(d + c^2*d*x^2))]
    @test_int [x^3*(a + b*asinh(c*x))/(d + c^2*d*x^2)^(3/2), x, 4, -((b*x*sqrt(d + c^2*d*x^2))/(c^3*d^2*sqrt(1 + c^2*x^2))) + (a + b*asinh(c*x))/(c^4*d*sqrt(d + c^2*d*x^2)) + (sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(c^4*d^2) - (b*sqrt(d + c^2*d*x^2)*atan(c*x))/(c^4*d^2*sqrt(1 + c^2*x^2))]
    @test_int [x^2*(a + b*asinh(c*x))/(d + c^2*d*x^2)^(3/2), x, 3, -((x*(a + b*asinh(c*x)))/(c^2*d*sqrt(d + c^2*d*x^2))) + (sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(2*b*c^3*d*sqrt(d + c^2*d*x^2)) + (b*sqrt(1 + c^2*x^2)*log(1 + c^2*x^2))/(2*c^3*d*sqrt(d + c^2*d*x^2))]
    @test_int [x^1*(a + b*asinh(c*x))/(d + c^2*d*x^2)^(3/2), x, 2, -((a + b*asinh(c*x))/(c^2*d*sqrt(d + c^2*d*x^2))) + (b*sqrt(1 + c^2*x^2)*atan(c*x))/(c^2*d*sqrt(d + c^2*d*x^2))]
    @test_int [x^0*(a + b*asinh(c*x))/(d + c^2*d*x^2)^(3/2), x, 2, (x*(a + b*asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) - (b*sqrt(1 + c^2*x^2)*log(1 + c^2*x^2))/(2*c*d*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))/(x^1*(d + c^2*d*x^2)^(3/2)), x, 8, (a + b*asinh(c*x))/(d*sqrt(d + c^2*d*x^2)) - (b*sqrt(1 + c^2*x^2)*atan(c*x))/(d*sqrt(d + c^2*d*x^2)) - (2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) - (b*sqrt(1 + c^2*x^2)*PolyLog(2, -ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) + (b*sqrt(1 + c^2*x^2)*PolyLog(2, ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))/(x^2*(d + c^2*d*x^2)^(3/2)), x, 5, -((a + b*asinh(c*x))/(d*x*sqrt(d + c^2*d*x^2))) - (2*c^2*x*(a + b*asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) + (b*c*sqrt(d + c^2*d*x^2)*log(x))/(d^2*sqrt(1 + c^2*x^2)) + (b*c*sqrt(d + c^2*d*x^2)*log(1 + c^2*x^2))/(2*d^2*sqrt(1 + c^2*x^2))]
    @test_int [(a + b*asinh(c*x))/(x^3*(d + c^2*d*x^2)^(3/2)), x, 11, -((b*c*sqrt(1 + c^2*x^2))/(2*d*x*sqrt(d + c^2*d*x^2))) - (3*c^2*(a + b*asinh(c*x)))/(2*d*sqrt(d + c^2*d*x^2)) - (a + b*asinh(c*x))/(2*d*x^2*sqrt(d + c^2*d*x^2)) + (b*c^2*sqrt(1 + c^2*x^2)*atan(c*x))/(d*sqrt(d + c^2*d*x^2)) + (3*c^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) + (3*b*c^2*sqrt(1 + c^2*x^2)*PolyLog(2, -ℯ^asinh(c*x)))/(2*d*sqrt(d + c^2*d*x^2)) - (3*b*c^2*sqrt(1 + c^2*x^2)*PolyLog(2, ℯ^asinh(c*x)))/(2*d*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))/(x^4*(d + c^2*d*x^2)^(3/2)), x, 5, -((b*c*sqrt(d + c^2*d*x^2))/(6*d^2*x^2*sqrt(1 + c^2*x^2))) - (a + b*asinh(c*x))/(3*d*x^3*sqrt(d + c^2*d*x^2)) + (4*c^2*(a + b*asinh(c*x)))/(3*d*x*sqrt(d + c^2*d*x^2)) + (8*c^4*x*(a + b*asinh(c*x)))/(3*d*sqrt(d + c^2*d*x^2)) - (5*b*c^3*sqrt(d + c^2*d*x^2)*log(x))/(3*d^2*sqrt(1 + c^2*x^2)) - (b*c^3*sqrt(d + c^2*d*x^2)*log(1 + c^2*x^2))/(2*d^2*sqrt(1 + c^2*x^2))]

    @test_int [x^6*(a + b*asinh(c*x))/(d + c^2*d*x^2)^(5/2), x, 11, -b/(6*c^7*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) - (b*x^2*sqrt(1 + c^2*x^2))/(4*c^5*d^2*sqrt(d + c^2*d*x^2)) - (x^5*(a + b*asinh(c*x)))/(3*c^2*d*(d + c^2*d*x^2)^(3/2)) - (5*x^3*(a + b*asinh(c*x)))/(3*c^4*d^2*sqrt(d + c^2*d*x^2)) + (5*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(2*c^6*d^3) - (5*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(4*b*c^7*d^2*sqrt(d + c^2*d*x^2)) - (7*b*sqrt(1 + c^2*x^2)*log(1 + c^2*x^2))/(6*c^7*d^2*sqrt(d + c^2*d*x^2))]
    @test_int [x^5*(a + b*asinh(c*x))/(d + c^2*d*x^2)^(5/2), x, 5, (b*x*sqrt(d + c^2*d*x^2))/(6*c^5*d^3*(1 + c^2*x^2)^(3/2)) - (b*x*sqrt(d + c^2*d*x^2))/(c^5*d^3*sqrt(1 + c^2*x^2)) - (a + b*asinh(c*x))/(3*c^6*d*(d + c^2*d*x^2)^(3/2)) + (2*(a + b*asinh(c*x)))/(c^6*d^2*sqrt(d + c^2*d*x^2)) + (sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(c^6*d^3) - (11*b*sqrt(d + c^2*d*x^2)*atan(c*x))/(6*c^6*d^3*sqrt(1 + c^2*x^2))]
    @test_int [x^4*(a + b*asinh(c*x))/(d + c^2*d*x^2)^(5/2), x, 7, b/(6*c^5*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) - (x^3*(a + b*asinh(c*x)))/(3*c^2*d*(d + c^2*d*x^2)^(3/2)) - (x*(a + b*asinh(c*x)))/(c^4*d^2*sqrt(d + c^2*d*x^2)) + (sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(2*b*c^5*d^2*sqrt(d + c^2*d*x^2)) + (2*b*sqrt(1 + c^2*x^2)*log(1 + c^2*x^2))/(3*c^5*d^2*sqrt(d + c^2*d*x^2))]
    @test_int [x^3*(a + b*asinh(c*x))/(d + c^2*d*x^2)^(5/2), x, 4, -((b*x*sqrt(d + c^2*d*x^2))/(6*c^3*d^3*(1 + c^2*x^2)^(3/2))) + (a + b*asinh(c*x))/(3*c^4*d*(d + c^2*d*x^2)^(3/2)) - (a + b*asinh(c*x))/(c^4*d^2*sqrt(d + c^2*d*x^2)) + (5*b*sqrt(d + c^2*d*x^2)*atan(c*x))/(6*c^4*d^3*sqrt(1 + c^2*x^2))]
    @test_int [x^2*(a + b*asinh(c*x))/(d + c^2*d*x^2)^(5/2), x, 4, -b/(6*c^3*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) + (x^3*(a + b*asinh(c*x)))/(3*d*(d + c^2*d*x^2)^(3/2)) - (b*sqrt(1 + c^2*x^2)*log(1 + c^2*x^2))/(6*c^3*d^2*sqrt(d + c^2*d*x^2))]
    @test_int [x^1*(a + b*asinh(c*x))/(d + c^2*d*x^2)^(5/2), x, 3, (b*x)/(6*c*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) - (a + b*asinh(c*x))/(3*c^2*d*(d + c^2*d*x^2)^(3/2)) + (b*sqrt(1 + c^2*x^2)*atan(c*x))/(6*c^2*d^2*sqrt(d + c^2*d*x^2))]
    @test_int [x^0*(a + b*asinh(c*x))/(d + c^2*d*x^2)^(5/2), x, 4, b/(6*c*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) + (x*(a + b*asinh(c*x)))/(3*d*(d + c^2*d*x^2)^(3/2)) + (2*x*(a + b*asinh(c*x)))/(3*d^2*sqrt(d + c^2*d*x^2)) - (b*sqrt(1 + c^2*x^2)*log(1 + c^2*x^2))/(3*c*d^2*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))/(x^1*(d + c^2*d*x^2)^(5/2)), x, 11, -((b*c*x)/(6*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2))) + (a + b*asinh(c*x))/(3*d*(d + c^2*d*x^2)^(3/2)) + (a + b*asinh(c*x))/(d^2*sqrt(d + c^2*d*x^2)) - (7*b*sqrt(1 + c^2*x^2)*atan(c*x))/(6*d^2*sqrt(d + c^2*d*x^2)) - (2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2)) - (b*sqrt(1 + c^2*x^2)*PolyLog(2, -ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2)) + (b*sqrt(1 + c^2*x^2)*PolyLog(2, ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))/(x^2*(d + c^2*d*x^2)^(5/2)), x, 5, -((b*c*sqrt(d + c^2*d*x^2))/(6*d^3*(1 + c^2*x^2)^(3/2))) - (a + b*asinh(c*x))/(d*x*(d + c^2*d*x^2)^(3/2)) - (4*c^2*x*(a + b*asinh(c*x)))/(3*d*(d + c^2*d*x^2)^(3/2)) - (8*c^2*x*(a + b*asinh(c*x)))/(3*d^2*sqrt(d + c^2*d*x^2)) + (b*c*sqrt(d + c^2*d*x^2)*log(x))/(d^3*sqrt(1 + c^2*x^2)) + (5*b*c*sqrt(d + c^2*d*x^2)*log(1 + c^2*x^2))/(6*d^3*sqrt(1 + c^2*x^2))]
    @test_int [(a + b*asinh(c*x))/(x^3*(d + c^2*d*x^2)^(5/2)), x, 15, (b*c)/(4*d^2*x*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) + (5*b*c^3*x)/(12*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) - (3*b*c*sqrt(1 + c^2*x^2))/(4*d^2*x*sqrt(d + c^2*d*x^2)) - (5*c^2*(a + b*asinh(c*x)))/(6*d*(d + c^2*d*x^2)^(3/2)) - (a + b*asinh(c*x))/(2*d*x^2*(d + c^2*d*x^2)^(3/2)) - (5*c^2*(a + b*asinh(c*x)))/(2*d^2*sqrt(d + c^2*d*x^2)) + (13*b*c^2*sqrt(1 + c^2*x^2)*atan(c*x))/(6*d^2*sqrt(d + c^2*d*x^2)) + (5*c^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2)) + (5*b*c^2*sqrt(1 + c^2*x^2)*PolyLog(2, -ℯ^asinh(c*x)))/(2*d^2*sqrt(d + c^2*d*x^2)) - (5*b*c^2*sqrt(1 + c^2*x^2)*PolyLog(2, ℯ^asinh(c*x)))/(2*d^2*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))/(x^4*(d + c^2*d*x^2)^(5/2)), x, 5, (b*c^3*sqrt(d + c^2*d*x^2))/(6*d^3*(1 + c^2*x^2)^(3/2)) - (b*c*sqrt(d + c^2*d*x^2))/(6*d^3*x^2*sqrt(1 + c^2*x^2)) - (a + b*asinh(c*x))/(3*d*x^3*(d + c^2*d*x^2)^(3/2)) + (2*c^2*(a + b*asinh(c*x)))/(d*x*(d + c^2*d*x^2)^(3/2)) + (8*c^4*x*(a + b*asinh(c*x)))/(3*d*(d + c^2*d*x^2)^(3/2)) + (16*c^4*x*(a + b*asinh(c*x)))/(3*d^2*sqrt(d + c^2*d*x^2)) - (8*b*c^3*sqrt(d + c^2*d*x^2)*log(x))/(3*d^3*sqrt(1 + c^2*x^2)) - (4*b*c^3*sqrt(d + c^2*d*x^2)*log(1 + c^2*x^2))/(3*d^3*sqrt(1 + c^2*x^2))]

    @test_int [asinh(a*x)/(c + a^2*c*x^2)^(7/2), x, 6, 1/(20*a*c^3*(1 + a^2*x^2)^(3/2)*sqrt(c + a^2*c*x^2)) + 2/(15*a*c^3*sqrt(1 + a^2*x^2)*sqrt(c + a^2*c*x^2)) + (x*asinh(a*x))/(5*c*(c + a^2*c*x^2)^(5/2)) + (4*x*asinh(a*x))/(15*c^2*(c + a^2*c*x^2)^(3/2)) + (8*x*asinh(a*x))/(15*c^3*sqrt(c + a^2*c*x^2)) - (4*sqrt(1 + a^2*x^2)*log(1 + a^2*x^2))/(15*a*c^3*sqrt(c + a^2*c*x^2))]

    @test_int [x^4*asinh(a*x)/sqrt(1 + a^2*x^2), x, 5, (3*x^2)/(16*a^3) - x^4/(16*a) - (3*x*sqrt(1 + a^2*x^2)*asinh(a*x))/(8*a^4) + (x^3*sqrt(1 + a^2*x^2)*asinh(a*x))/(4*a^2) + (3*asinh(a*x)^2)/(16*a^5)]
    @test_int [x^3*asinh(a*x)/sqrt(1 + a^2*x^2), x, 4, (2*x)/(3*a^3) - x^3/(9*a) - (2*sqrt(1 + a^2*x^2)*asinh(a*x))/(3*a^4) + (x^2*sqrt(1 + a^2*x^2)*asinh(a*x))/(3*a^2)]
    @test_int [x^2*asinh(a*x)/sqrt(1 + a^2*x^2), x, 3, -x^2/(4*a) + (x*sqrt(1 + a^2*x^2)*asinh(a*x))/(2*a^2) - asinh(a*x)^2/(4*a^3)]
    @test_int [x^1*asinh(a*x)/sqrt(1 + a^2*x^2), x, 2, -(x/a) + (sqrt(1 + a^2*x^2)*asinh(a*x))/a^2]
    @test_int [x^0*asinh(a*x)/sqrt(1 + a^2*x^2), x, 1, asinh(a*x)^2/(2*a)]
    @test_int [asinh(a*x)/(x^1*sqrt(1 + a^2*x^2)), x, 6, -2*asinh(a*x)*atanh(ℯ^asinh(a*x)) - PolyLog(2, -ℯ^asinh(a*x)) + PolyLog(2, ℯ^asinh(a*x))]
    @test_int [asinh(a*x)/(x^2*sqrt(1 + a^2*x^2)), x, 2, -((sqrt(1 + a^2*x^2)*asinh(a*x))/x) + a*log(x)]
    @test_int [asinh(a*x)/(x^3*sqrt(1 + a^2*x^2)), x, 8, -a/(2*x) - (sqrt(1 + a^2*x^2)*asinh(a*x))/(2*x^2) + a^2*asinh(a*x)*atanh(ℯ^asinh(a*x)) + (a^2*PolyLog(2, -ℯ^asinh(a*x)))/2 - (a^2*PolyLog(2, ℯ^asinh(a*x)))/2]

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

    @test_int [x^m*(d + c^2*d*x^2)^3*(a + b*asinh(c*x)), x, 6, If(13>=8, -((b*c*d^3*(2271 + 1329*m + 284*m^2 + 27*m^3 + m^4)*x^(2 + m)*sqrt(1 + c^2*x^2))/((3 + m)^2*(5 + m)^2*(7 + m)^2)) - (b*c^3*d^3*(9 + m)*(13 + 2*m)*x^(4 + m)*sqrt(1 + c^2*x^2))/((5 + m)^2*(7 + m)^2) - (b*c^5*d^3*x^(6 + m)*sqrt(1 + c^2*x^2))/(7 + m)^2 + (d^3*x^(1 + m)*(a + b*asinh(c*x)))/(1 + m) + (3*c^2*d^3*x^(3 + m)*(a + b*asinh(c*x)))/(3 + m) + (3*c^4*d^3*x^(5 + m)*(a + b*asinh(c*x)))/(5 + m) + (c^6*d^3*x^(7 + m)*(a + b*asinh(c*x)))/(7 + m) - (3*b*c*d^3*(2161 + 1813*m + 455*m^2 + 35*m^3)*x^(2 + m)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, (-c^2)*x^2))/((1 + m)*(2 + m)*(3 + m)^2*(5 + m)^2*(7 + m)^2), -((b*c*d^3*(2271 + 1329*m + 284*m^2 + 27*m^3 + m^4)*x^(2 + m)*sqrt(1 + c^2*x^2))/((7 + m)^2*(15 + 8*m + m^2)^2)) - (b*c^3*d^3*(9 + m)*(13 + 2*m)*x^(4 + m)*sqrt(1 + c^2*x^2))/((5 + m)^2*(7 + m)^2) - (b*c^5*d^3*x^(6 + m)*sqrt(1 + c^2*x^2))/(7 + m)^2 + (d^3*x^(1 + m)*(a + b*asinh(c*x)))/(1 + m) + (3*c^2*d^3*x^(3 + m)*(a + b*asinh(c*x)))/(3 + m) + (3*c^4*d^3*x^(5 + m)*(a + b*asinh(c*x)))/(5 + m) + (c^6*d^3*x^(7 + m)*(a + b*asinh(c*x)))/(7 + m) - (3*b*c*d^3*(2161 + 1813*m + 455*m^2 + 35*m^3)*x^(2 + m)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, (-c^2)*x^2))/((2 + 3*m + m^2)*(105 + 71*m + 15*m^2 + m^3)^2))]
    @test_int [x^m*(d + c^2*d*x^2)^2*(a + b*asinh(c*x)), x, 5, If(13>=8, -((b*c*d^2*(38 + 13*m + m^2)*x^(2 + m)*sqrt(1 + c^2*x^2))/((3 + m)^2*(5 + m)^2)) - (b*c^3*d^2*x^(4 + m)*sqrt(1 + c^2*x^2))/(5 + m)^2 + (d^2*x^(1 + m)*(a + b*asinh(c*x)))/(1 + m) + (2*c^2*d^2*x^(3 + m)*(a + b*asinh(c*x)))/(3 + m) + (c^4*d^2*x^(5 + m)*(a + b*asinh(c*x)))/(5 + m) - (b*c*d^2*(149 + 100*m + 15*m^2)*x^(2 + m)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, (-c^2)*x^2))/((1 + m)*(2 + m)*(3 + m)^2*(5 + m)^2), -((b*c*d^2*(38 + 13*m + m^2)*x^(2 + m)*sqrt(1 + c^2*x^2))/((3 + m)^2*(5 + m)^2)) - (b*c^3*d^2*x^(4 + m)*sqrt(1 + c^2*x^2))/(5 + m)^2 + (d^2*x^(1 + m)*(a + b*asinh(c*x)))/(1 + m) + (2*c^2*d^2*x^(3 + m)*(a + b*asinh(c*x)))/(3 + m) + (c^4*d^2*x^(5 + m)*(a + b*asinh(c*x)))/(5 + m) - (b*c*d^2*(149 + 100*m + 15*m^2)*x^(2 + m)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, (-c^2)*x^2))/((2 + 3*m + m^2)*(15 + 8*m + m^2)^2))]
    @test_int [x^m*(d + c^2*d*x^2)^1*(a + b*asinh(c*x)), x, 4, If(13>=8, -((b*c*d*x^(2 + m)*sqrt(1 + c^2*x^2))/(3 + m)^2) + (d*x^(1 + m)*(a + b*asinh(c*x)))/(1 + m) + (c^2*d*x^(3 + m)*(a + b*asinh(c*x)))/(3 + m) - (b*c*d*(7 + 3*m)*x^(2 + m)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, -(c^2*x^2)))/((1 + m)*(2 + m)*(3 + m)^2), -((b*c*d*x^(2 + m)*sqrt(1 + c^2*x^2))/(3 + m)^2) + (d*x^(1 + m)*(a + b*asinh(c*x)))/(1 + m) + (c^2*d*x^(3 + m)*(a + b*asinh(c*x)))/(3 + m) - (b*c*d*(7 + 3*m)*x^(2 + m)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, (-c^2)*x^2))/((3 + m)^2*(2 + 3*m + m^2)))]
    @test_int [x^m*(a + b*asinh(c*x))/(d + c^2*d*x^2)^1, x, 0, Unintegrable((x^m*(a + b*asinh(c*x)))/(d + c^2*d*x^2), x)]
    @test_int [x^m*(a + b*asinh(c*x))/(d + c^2*d*x^2)^2, x, 2, (x^(1 + m)*(a + b*asinh(c*x)))/(2*d^2*(1 + c^2*x^2)) - (b*c*x^(2 + m)*HypergeometricFunctions._₂F₁(3/2, (2 + m)/2, (4 + m)/2, (-c^2)*x^2))/(2*d^2*(2 + m)) + ((1 - m)*Unintegrable((x^m*(a + b*asinh(c*x)))/(d + c^2*d*x^2), x))/(2*d)]
    @test_int [x^m*(a + b*asinh(c*x))/(d + c^2*d*x^2)^3, x, 4, (x^(1 + m)*(a + b*asinh(c*x)))/(4*d^3*(1 + c^2*x^2)^2) + ((3 - m)*x^(1 + m)*(a + b*asinh(c*x)))/(8*d^3*(1 + c^2*x^2)) - (b*c*(3 - m)*x^(2 + m)*HypergeometricFunctions._₂F₁(3/2, (2 + m)/2, (4 + m)/2, (-c^2)*x^2))/(8*d^3*(2 + m)) - (b*c*x^(2 + m)*HypergeometricFunctions._₂F₁(5/2, (2 + m)/2, (4 + m)/2, (-c^2)*x^2))/(4*d^3*(2 + m)) + ((1 - m)*(3 - m)*Unintegrable((x^m*(a + b*asinh(c*x)))/(d + c^2*d*x^2), x))/(8*d^2)]

    @test_int [x^m*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)), x, 9, If(13>=8, (-15*b*c*d^2*x^(2 + m)*sqrt(d + c^2*d*x^2))/((2 + m)^2*(4 + m)*(6 + m)*sqrt(1 + c^2*x^2)) - (5*b*c*d^2*x^(2 + m)*sqrt(d + c^2*d*x^2))/((6 + m)*(8 + 6*m + m^2)*sqrt(1 + c^2*x^2)) - (b*c*d^2*x^(2 + m)*sqrt(d + c^2*d*x^2))/((12 + 8*m + m^2)*sqrt(1 + c^2*x^2)) - (5*b*c^3*d^2*x^(4 + m)*sqrt(d + c^2*d*x^2))/((4 + m)^2*(6 + m)*sqrt(1 + c^2*x^2)) - (2*b*c^3*d^2*x^(4 + m)*sqrt(d + c^2*d*x^2))/((4 + m)*(6 + m)*sqrt(1 + c^2*x^2)) - (b*c^5*d^2*x^(6 + m)*sqrt(d + c^2*d*x^2))/((6 + m)^2*sqrt(1 + c^2*x^2)) + (15*d^2*x^(1 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((6 + m)*(8 + 6*m + m^2)) + (5*d*x^(1 + m)*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/((4 + m)*(6 + m)) + (x^(1 + m)*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)))/(6 + m) + (15*d^2*x^(1 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, -(c^2*x^2)))/((6 + m)*(8 + 14*m + 7*m^2 + m^3)*sqrt(1 + c^2*x^2)) - (15*b*c*d^2*x^(2 + m)*sqrt(d + c^2*d*x^2)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], -(c^2*x^2)))/((1 + m)*(2 + m)^2*(4 + m)*(6 + m)*sqrt(1 + c^2*x^2)), -((15*b*c*d^2*x^(2 + m)*sqrt(d + c^2*d*x^2))/((2 + m)^2*(4 + m)*(6 + m)*sqrt(1 + c^2*x^2))) - (5*b*c*d^2*x^(2 + m)*sqrt(d + c^2*d*x^2))/((6 + m)*(8 + 6*m + m^2)*sqrt(1 + c^2*x^2)) - (b*c*d^2*x^(2 + m)*sqrt(d + c^2*d*x^2))/((12 + 8*m + m^2)*sqrt(1 + c^2*x^2)) - (5*b*c^3*d^2*x^(4 + m)*sqrt(d + c^2*d*x^2))/((4 + m)^2*(6 + m)*sqrt(1 + c^2*x^2)) - (2*b*c^3*d^2*x^(4 + m)*sqrt(d + c^2*d*x^2))/((4 + m)*(6 + m)*sqrt(1 + c^2*x^2)) - (b*c^5*d^2*x^(6 + m)*sqrt(d + c^2*d*x^2))/((6 + m)^2*sqrt(1 + c^2*x^2)) + (15*d^2*x^(1 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((6 + m)*(8 + 6*m + m^2)) + (5*d*x^(1 + m)*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/((4 + m)*(6 + m)) + (x^(1 + m)*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x)))/(6 + m) + (15*d^2*x^(1 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, (-c^2)*x^2))/((6 + m)*(8 + 14*m + 7*m^2 + m^3)*sqrt(1 + c^2*x^2)) - (15*b*c*d^2*x^(2 + m)*sqrt(d + c^2*d*x^2)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], (-c^2)*x^2))/((2 + m)^2*(6 + m)*(4 + 5*m + m^2)*sqrt(1 + c^2*x^2)))]
    @test_int [x^m*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)), x, 6, If(13>=8, (-3*b*c*d*x^(2 + m)*sqrt(d + c^2*d*x^2))/((2 + m)^2*(4 + m)*sqrt(1 + c^2*x^2)) - (b*c*d*x^(2 + m)*sqrt(d + c^2*d*x^2))/((8 + 6*m + m^2)*sqrt(1 + c^2*x^2)) - (b*c^3*d*x^(4 + m)*sqrt(d + c^2*d*x^2))/((4 + m)^2*sqrt(1 + c^2*x^2)) + (3*d*x^(1 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(8 + 6*m + m^2) + (x^(1 + m)*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/(4 + m) + (3*d*x^(1 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, -(c^2*x^2)))/((8 + 14*m + 7*m^2 + m^3)*sqrt(1 + c^2*x^2)) - (3*b*c*d*x^(2 + m)*sqrt(d + c^2*d*x^2)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], -(c^2*x^2)))/((1 + m)*(2 + m)^2*(4 + m)*sqrt(1 + c^2*x^2)), -((3*b*c*d*x^(2 + m)*sqrt(d + c^2*d*x^2))/((2 + m)^2*(4 + m)*sqrt(1 + c^2*x^2))) - (b*c*d*x^(2 + m)*sqrt(d + c^2*d*x^2))/((8 + 6*m + m^2)*sqrt(1 + c^2*x^2)) - (b*c^3*d*x^(4 + m)*sqrt(d + c^2*d*x^2))/((4 + m)^2*sqrt(1 + c^2*x^2)) + (3*d*x^(1 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(8 + 6*m + m^2) + (x^(1 + m)*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x)))/(4 + m) + (3*d*x^(1 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, (-c^2)*x^2))/((8 + 14*m + 7*m^2 + m^3)*sqrt(1 + c^2*x^2)) - (3*b*c*d*x^(2 + m)*sqrt(d + c^2*d*x^2)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], (-c^2)*x^2))/((2 + m)^2*(4 + 5*m + m^2)*sqrt(1 + c^2*x^2)))]
    @test_int [x^m*(d + c^2*d*x^2)^(1/2)*(a + b*asinh(c*x)), x, 3, -((b*c*x^(2 + m)*sqrt(d + c^2*d*x^2))/((2 + m)^2*sqrt(1 + c^2*x^2))) + (x^(1 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(2 + m) + (x^(1 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, -(c^2*x^2)))/((2 + 3*m + m^2)*sqrt(1 + c^2*x^2)) - (b*c*x^(2 + m)*sqrt(d + c^2*d*x^2)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], -(c^2*x^2)))/((1 + m)*(2 + m)^2*sqrt(1 + c^2*x^2))]
    @test_int [(x^m*(a + b*asinh(c*x)))/(d + c^2*d*x^2)^(1/2), x, 1, (x^(1 + m)*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, -(c^2*x^2)))/((1 + m)*sqrt(d + c^2*d*x^2)) - (b*c*x^(2 + m)*sqrt(1 + c^2*x^2)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], -(c^2*x^2)))/((2 + 3*m + m^2)*sqrt(d + c^2*d*x^2))]
    @test_int [(x^m*(a + b*asinh(c*x)))/(d + c^2*d*x^2)^(3/2), x, 3, (x^(1 + m)*(a + b*asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) - (m*x^(1 + m)*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, (-c^2)*x^2))/(d*(1 + m)*sqrt(d + c^2*d*x^2)) - (b*c*x^(2 + m)*sqrt(1 + c^2*x^2)*HypergeometricFunctions._₂F₁(1, (2 + m)/2, (4 + m)/2, (-c^2)*x^2))/(d*(2 + m)*sqrt(d + c^2*d*x^2)) + (b*c*m*x^(2 + m)*sqrt(1 + c^2*x^2)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], (-c^2)*x^2))/(d*(2 + 3*m + m^2)*sqrt(d + c^2*d*x^2))]
    @test_int [(x^m*(a + b*asinh(c*x)))/(d + c^2*d*x^2)^(5/2), x, 5, (x^(1 + m)*(a + b*asinh(c*x)))/(3*d*(d + c^2*d*x^2)^(3/2)) + ((2 - m)*x^(1 + m)*(a + b*asinh(c*x)))/(3*d^2*sqrt(d + c^2*d*x^2)) - ((2 - m)*m*x^(1 + m)*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, (-c^2)*x^2))/(3*d^2*(1 + m)*sqrt(d + c^2*d*x^2)) - (b*c*(2 - m)*x^(2 + m)*sqrt(1 + c^2*x^2)*HypergeometricFunctions._₂F₁(1, (2 + m)/2, (4 + m)/2, (-c^2)*x^2))/(3*d^2*(2 + m)*sqrt(d + c^2*d*x^2)) - (b*c*x^(2 + m)*sqrt(1 + c^2*x^2)*HypergeometricFunctions._₂F₁(2, (2 + m)/2, (4 + m)/2, (-c^2)*x^2))/(3*d^2*(2 + m)*sqrt(d + c^2*d*x^2)) + (b*c*(2 - m)*m*x^(2 + m)*sqrt(1 + c^2*x^2)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], (-c^2)*x^2))/(3*d^2*(2 + 3*m + m^2)*sqrt(d + c^2*d*x^2))]

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

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

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

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

    @test_int [x^4*(d + c^2*d*x^2)*(a + b*asinh(c*x))^2, x, 11, (304*b^2*d*x)/(3675*c^4) - (152*b^2*d*x^3)/(11025*c^2) + (38*b^2*d*x^5)/6125 + (2*b^2*c^2*d*x^7)/343 - (32*b*d*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(525*c^5) + (16*b*d*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(525*c^3) - (4*b*d*x^4*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(175*c) - (2*b*d*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(21*c^5) + (4*b*d*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x)))/(35*c^5) - (2*b*d*(1 + c^2*x^2)^(7/2)*(a + b*asinh(c*x)))/(49*c^5) + (2*d*x^5*(a + b*asinh(c*x))^2)/35 + (d*x^5*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/7]
    @test_int [x^3*(d + c^2*d*x^2)*(a + b*asinh(c*x))^2, x, 14, -(b^2*d*x^2)/(24*c^2) + (b^2*d*x^4)/72 + (b^2*c^2*d*x^6)/108 + (b*d*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(12*c^3) - (b*d*x^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(18*c) - (b*c*d*x^5*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/18 - (d*(a + b*asinh(c*x))^2)/(24*c^4) + (d*x^4*(a + b*asinh(c*x))^2)/12 + (d*x^4*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/6]
    @test_int [x^2*(d + c^2*d*x^2)*(a + b*asinh(c*x))^2, x, 9, (-52*b^2*d*x)/(225*c^2) + (26*b^2*d*x^3)/675 + (2*b^2*c^2*d*x^5)/125 + (8*b*d*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(45*c^3) - (4*b*d*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(45*c) + (2*b*d*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(15*c^3) - (2*b*d*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x)))/(25*c^3) + (2*d*x^3*(a + b*asinh(c*x))^2)/15 + (d*x^3*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/5]
    @test_int [x^1*(d + c^2*d*x^2)*(a + b*asinh(c*x))^2, x, 7, (5*b^2*d*x^2)/32 + (b^2*c^2*d*x^4)/32 - (3*b*d*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(16*c) - (b*d*x*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(8*c) - (3*d*(a + b*asinh(c*x))^2)/(32*c^2) + (d*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/(4*c^2)]
    @test_int [x^0*(d + c^2*d*x^2)*(a + b*asinh(c*x))^2, x, 6, (14*b^2*d*x)/9 + (2*b^2*c^2*d*x^3)/27 - (4*b*d*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(3*c) - (2*b*d*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(9*c) + (2*d*x*(a + b*asinh(c*x))^2)/3 + (d*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/3]
    @test_int [((d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/x^1, x, 10, (1/4)*b^2*c^2*d*x^2 - (1/2)*b*c*d*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)) - (1/4)*d*(a + b*asinh(c*x))^2 + (1/2)*d*(1 + c^2*x^2)*(a + b*asinh(c*x))^2 + (d*(a + b*asinh(c*x))^3)/(3*b) + d*(a + b*asinh(c*x))^2*log(1 - ℯ^(-2*asinh(c*x))) - b*d*(a + b*asinh(c*x))*PolyLog(2, ℯ^(-2*asinh(c*x))) - (1/2)*b^2*d*PolyLog(3, ℯ^(-2*asinh(c*x)))]
    @test_int [((d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/x^2, x, 12, 2*b^2*c^2*d*x - 2*b*c*d*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)) + 2*c^2*d*x*(a + b*asinh(c*x))^2 - (d*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/x - 4*b*c*d*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)) - 2*b^2*c*d*PolyLog(2, -ℯ^asinh(c*x)) + 2*b^2*c*d*PolyLog(2, ℯ^asinh(c*x))]
    @test_int [((d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/x^3, x, 10, -((b*c*d*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/x) + (1/2)*c^2*d*(a + b*asinh(c*x))^2 - (d*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(2*x^2) + (c^2*d*(a + b*asinh(c*x))^3)/(3*b) + c^2*d*(a + b*asinh(c*x))^2*log(1 - ℯ^(-2*asinh(c*x))) + b^2*c^2*d*log(x) - b*c^2*d*(a + b*asinh(c*x))*PolyLog(2, ℯ^(-2*asinh(c*x))) - (1/2)*b^2*c^2*d*PolyLog(3, ℯ^(-2*asinh(c*x)))]
    @test_int [((d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/x^4, x, 16, -(b^2*c^2*d)/(3*x) - (b*c*d*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(3*x^2) - (2*c^2*d*(a + b*asinh(c*x))^2)/(3*x) - (d*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(3*x^3) - (10*b*c^3*d*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/3 - (5*b^2*c^3*d*PolyLog(2, -ℯ^asinh(c*x)))/3 + (5*b^2*c^3*d*PolyLog(2, ℯ^asinh(c*x)))/3]

    @test_int [x^4*(d + c^2*d*x^2)^2*(a + b*asinh(c*x))^2, x, 16, (4208*b^2*d^2*x)/(99225*c^4) - (2104*b^2*d^2*x^3)/(297675*c^2) + (526*b^2*d^2*x^5)/165375 + (212*b^2*c^2*d^2*x^7)/27783 + (2*b^2*c^4*d^2*x^9)/729 - (128*b*d^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(4725*c^5) + (64*b*d^2*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(4725*c^3) - (16*b*d^2*x^4*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(1575*c) - (8*b*d^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(189*c^5) + (2*b*d^2*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x)))/(315*c^5) + (20*b*d^2*(1 + c^2*x^2)^(7/2)*(a + b*asinh(c*x)))/(441*c^5) - (2*b*d^2*(1 + c^2*x^2)^(9/2)*(a + b*asinh(c*x)))/(81*c^5) + (8*d^2*x^5*(a + b*asinh(c*x))^2)/315 + (4*d^2*x^5*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/63 + (d^2*x^5*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/9]
    @test_int [x^3*(d + c^2*d*x^2)^2*(a + b*asinh(c*x))^2, x, 25, (-73*b^2*d^2*x^2)/(3072*c^2) + (73*b^2*d^2*x^4)/9216 + (43*b^2*c^2*d^2*x^6)/3456 + (b^2*c^4*d^2*x^8)/256 + (73*b*d^2*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(1536*c^3) - (73*b*d^2*x^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2304*c) - (25*b*c*d^2*x^5*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/576 - (b*c*d^2*x^5*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/32 - (73*d^2*(a + b*asinh(c*x))^2)/(3072*c^4) + (d^2*x^4*(a + b*asinh(c*x))^2)/24 + (d^2*x^4*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/12 + (d^2*x^4*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/8]
    @test_int [x^2*(d + c^2*d*x^2)^2*(a + b*asinh(c*x))^2, x, 14, (-1636*b^2*d^2*x)/(11025*c^2) + (818*b^2*d^2*x^3)/33075 + (136*b^2*c^2*d^2*x^5)/6125 + (2*b^2*c^4*d^2*x^7)/343 + (32*b*d^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(315*c^3) - (16*b*d^2*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(315*c) + (8*b*d^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(105*c^3) + (2*b*d^2*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x)))/(175*c^3) - (2*b*d^2*(1 + c^2*x^2)^(7/2)*(a + b*asinh(c*x)))/(49*c^3) + (8*d^2*x^3*(a + b*asinh(c*x))^2)/105 + (4*d^2*x^3*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/35 + (d^2*x^3*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/7]
    @test_int [x^1*(d + c^2*d*x^2)^2*(a + b*asinh(c*x))^2, x, 9, (25*b^2*d^2*x^2)/288 + (5*b^2*c^2*d^2*x^4)/288 + (b^2*d^2*(1 + c^2*x^2)^3)/(108*c^2) - (5*b*d^2*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(48*c) - (5*b*d^2*x*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(72*c) - (b*d^2*x*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x)))/(18*c) - (5*d^2*(a + b*asinh(c*x))^2)/(96*c^2) + (d^2*(1 + c^2*x^2)^3*(a + b*asinh(c*x))^2)/(6*c^2)]
    @test_int [x^0*(d + c^2*d*x^2)^2*(a + b*asinh(c*x))^2, x, 10, (298*b^2*d^2*x)/225 + (76*b^2*c^2*d^2*x^3)/675 + (2*b^2*c^4*d^2*x^5)/125 - (16*b*d^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(15*c) - (8*b*d^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(45*c) - (2*b*d^2*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x)))/(25*c) + (8*d^2*x*(a + b*asinh(c*x))^2)/15 + (4*d^2*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/15 + (d^2*x*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/5]
    @test_int [((d + c^2*d*x^2)^2*(a + b*asinh(c*x))^2)/x^1, x, 17, (13/32)*b^2*c^2*d^2*x^2 + (1/32)*b^2*c^4*d^2*x^4 - (11/16)*b*c*d^2*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)) - (1/8)*b*c*d^2*x*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)) - (11/32)*d^2*(a + b*asinh(c*x))^2 + (1/2)*d^2*(1 + c^2*x^2)*(a + b*asinh(c*x))^2 + (1/4)*d^2*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2 + (d^2*(a + b*asinh(c*x))^3)/(3*b) + d^2*(a + b*asinh(c*x))^2*log(1 - ℯ^(-2*asinh(c*x))) - b*d^2*(a + b*asinh(c*x))*PolyLog(2, ℯ^(-2*asinh(c*x))) - (1/2)*b^2*d^2*PolyLog(3, ℯ^(-2*asinh(c*x)))]
    @test_int [((d + c^2*d*x^2)^2*(a + b*asinh(c*x))^2)/x^2, x, 17, (32*b^2*c^2*d^2*x)/9 + (2*b^2*c^4*d^2*x^3)/27 - (10*b*c*d^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/3 - (2*b*c*d^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/9 + (8*c^2*d^2*x*(a + b*asinh(c*x))^2)/3 + (4*c^2*d^2*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/3 - (d^2*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/x - 4*b*c*d^2*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)) - 2*b^2*c*d^2*PolyLog(2, -ℯ^asinh(c*x)) + 2*b^2*c*d^2*PolyLog(2, ℯ^asinh(c*x))]
    @test_int [((d + c^2*d*x^2)^2*(a + b*asinh(c*x))^2)/x^3, x, 17, (1/4)*b^2*c^4*d^2*x^2 + (1/2)*b*c^3*d^2*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)) - (b*c*d^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/x + (1/4)*c^2*d^2*(a + b*asinh(c*x))^2 + c^2*d^2*(1 + c^2*x^2)*(a + b*asinh(c*x))^2 - (d^2*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/(2*x^2) + (2*c^2*d^2*(a + b*asinh(c*x))^3)/(3*b) + 2*c^2*d^2*(a + b*asinh(c*x))^2*log(1 - ℯ^(-2*asinh(c*x))) + b^2*c^2*d^2*log(x) - 2*b*c^2*d^2*(a + b*asinh(c*x))*PolyLog(2, ℯ^(-2*asinh(c*x))) - b^2*c^2*d^2*PolyLog(3, ℯ^(-2*asinh(c*x)))]
    @test_int [((d + c^2*d*x^2)^2*(a + b*asinh(c*x))^2)/x^4, x, 24, -(b^2*c^2*d^2)/(3*x) + 2*b^2*c^4*d^2*x - (5*b*c^3*d^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/3 - (b*c*d^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*x^2) + (8*c^4*d^2*x*(a + b*asinh(c*x))^2)/3 - (4*c^2*d^2*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(3*x) - (d^2*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/(3*x^3) - (22*b*c^3*d^2*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/3 - (11*b^2*c^3*d^2*PolyLog(2, -ℯ^asinh(c*x)))/3 + (11*b^2*c^3*d^2*PolyLog(2, ℯ^asinh(c*x)))/3]

    @test_int [x^4*(d + c^2*d*x^2)^3*(a + b*asinh(c*x))^2, x, 21, (100976*b^2*d^3*x)/(4002075*c^4) - (50488*b^2*d^3*x^3)/(12006225*c^2) + (12622*b^2*d^3*x^5)/6670125 + (9410*b^2*c^2*d^3*x^7)/1120581 + (182*b^2*c^4*d^3*x^9)/29403 + (2*b^2*c^6*d^3*x^11)/1331 - (256*b*d^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(17325*c^5) + (128*b*d^3*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(17325*c^3) - (32*b*d^3*x^4*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(5775*c) - (16*b*d^3*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(693*c^5) + (4*b*d^3*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x)))/(1155*c^5) - (2*b*d^3*(1 + c^2*x^2)^(7/2)*(a + b*asinh(c*x)))/(1617*c^5) + (8*b*d^3*(1 + c^2*x^2)^(9/2)*(a + b*asinh(c*x)))/(297*c^5) - (2*b*d^3*(1 + c^2*x^2)^(11/2)*(a + b*asinh(c*x)))/(121*c^5) + (16*d^3*x^5*(a + b*asinh(c*x))^2)/1155 + (8*d^3*x^5*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/231 + (2*d^3*x^5*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/33 + (d^3*x^5*(1 + c^2*x^2)^3*(a + b*asinh(c*x))^2)/11]
    @test_int [x^3*(d + c^2*d*x^2)^3*(a + b*asinh(c*x))^2, x, 40, (-79*b^2*d^3*x^2)/(5120*c^2) + (79*b^2*d^3*x^4)/15360 + (401*b^2*c^2*d^3*x^6)/28800 + (57*b^2*c^4*d^3*x^8)/6400 + (b^2*c^6*d^3*x^10)/500 + (79*b*d^3*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2560*c^3) - (79*b*d^3*x^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(3840*c) - (31*b*c*d^3*x^5*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/960 - (b*c*d^3*x^5*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/32 - (b*c*d^3*x^5*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x)))/50 - (79*d^3*(a + b*asinh(c*x))^2)/(5120*c^4) + (d^3*x^4*(a + b*asinh(c*x))^2)/40 + (d^3*x^4*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/20 + (3*d^3*x^4*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/40 + (d^3*x^4*(1 + c^2*x^2)^3*(a + b*asinh(c*x))^2)/10]
    @test_int [x^2*(d + c^2*d*x^2)^3*(a + b*asinh(c*x))^2, x, 19, (-10516*b^2*d^3*x)/(99225*c^2) + (5258*b^2*d^3*x^3)/297675 + (4198*b^2*c^2*d^3*x^5)/165375 + (374*b^2*c^4*d^3*x^7)/27783 + (2*b^2*c^6*d^3*x^9)/729 + (64*b*d^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(945*c^3) - (32*b*d^3*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(945*c) + (16*b*d^3*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(315*c^3) + (4*b*d^3*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x)))/(525*c^3) + (2*b*d^3*(1 + c^2*x^2)^(7/2)*(a + b*asinh(c*x)))/(441*c^3) - (2*b*d^3*(1 + c^2*x^2)^(9/2)*(a + b*asinh(c*x)))/(81*c^3) + (16*d^3*x^3*(a + b*asinh(c*x))^2)/315 + (8*d^3*x^3*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/105 + (2*d^3*x^3*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/21 + (d^3*x^3*(1 + c^2*x^2)^3*(a + b*asinh(c*x))^2)/9]
    @test_int [x^1*(d + c^2*d*x^2)^3*(a + b*asinh(c*x))^2, x, 11, (175*b^2*d^3*x^2)/3072 + (35*b^2*c^2*d^3*x^4)/3072 + (7*b^2*d^3*(1 + c^2*x^2)^3)/(1152*c^2) + (b^2*d^3*(1 + c^2*x^2)^4)/(256*c^2) - (35*b*d^3*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(512*c) - (35*b*d^3*x*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(768*c) - (7*b*d^3*x*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x)))/(192*c) - (b*d^3*x*(1 + c^2*x^2)^(7/2)*(a + b*asinh(c*x)))/(32*c) - (35*d^3*(a + b*asinh(c*x))^2)/(1024*c^2) + (d^3*(1 + c^2*x^2)^4*(a + b*asinh(c*x))^2)/(8*c^2)]
    @test_int [x^0*(d + c^2*d*x^2)^3*(a + b*asinh(c*x))^2, x, 14, (4322*b^2*d^3*x)/3675 + (1514*b^2*c^2*d^3*x^3)/11025 + (234*b^2*c^4*d^3*x^5)/6125 + (2*b^2*c^6*d^3*x^7)/343 - (32*b*d^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(35*c) - (16*b*d^3*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(105*c) - (12*b*d^3*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x)))/(175*c) - (2*b*d^3*(1 + c^2*x^2)^(7/2)*(a + b*asinh(c*x)))/(49*c) + (16*d^3*x*(a + b*asinh(c*x))^2)/35 + (8*d^3*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/35 + (6*d^3*x*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/35 + (d^3*x*(1 + c^2*x^2)^3*(a + b*asinh(c*x))^2)/7]
    @test_int [((d + c^2*d*x^2)^3*(a + b*asinh(c*x))^2)/x^1, x, 26, (71/144)*b^2*c^2*d^3*x^2 + (7/144)*b^2*c^4*d^3*x^4 + (1/108)*b^2*d^3*(1 + c^2*x^2)^3 - (19/24)*b*c*d^3*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)) - (7/36)*b*c*d^3*x*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)) - (1/18)*b*c*d^3*x*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x)) - (19/48)*d^3*(a + b*asinh(c*x))^2 + (1/2)*d^3*(1 + c^2*x^2)*(a + b*asinh(c*x))^2 + (1/4)*d^3*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2 + (1/6)*d^3*(1 + c^2*x^2)^3*(a + b*asinh(c*x))^2 + (d^3*(a + b*asinh(c*x))^3)/(3*b) + d^3*(a + b*asinh(c*x))^2*log(1 - ℯ^(-2*asinh(c*x))) - b*d^3*(a + b*asinh(c*x))*PolyLog(2, ℯ^(-2*asinh(c*x))) - (1/2)*b^2*d^3*PolyLog(3, ℯ^(-2*asinh(c*x)))]
    @test_int [((d + c^2*d*x^2)^3*(a + b*asinh(c*x))^2)/x^2, x, 24, (122*b^2*c^2*d^3*x)/25 + (14*b^2*c^4*d^3*x^3)/75 + (2*b^2*c^6*d^3*x^5)/125 - (22*b*c*d^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/5 - (2*b*c*d^3*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/5 - (2*b*c*d^3*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x)))/25 + (16*c^2*d^3*x*(a + b*asinh(c*x))^2)/5 + (8*c^2*d^3*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/5 + (6*c^2*d^3*x*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/5 - (d^3*(1 + c^2*x^2)^3*(a + b*asinh(c*x))^2)/x - 4*b*c*d^3*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)) - 2*b^2*c*d^3*PolyLog(2, -ℯ^asinh(c*x)) + 2*b^2*c*d^3*PolyLog(2, ℯ^asinh(c*x))]
    @test_int [((d + c^2*d*x^2)^3*(a + b*asinh(c*x))^2)/x^3, x, 28, (21/32)*b^2*c^4*d^3*x^2 + (1/32)*b^2*c^6*d^3*x^4 - (3/16)*b*c^3*d^3*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)) + (7/8)*b*c^3*d^3*x*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)) - (b*c*d^3*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x)))/x - (3/32)*c^2*d^3*(a + b*asinh(c*x))^2 + (3/2)*c^2*d^3*(1 + c^2*x^2)*(a + b*asinh(c*x))^2 + (3/4)*c^2*d^3*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2 - (d^3*(1 + c^2*x^2)^3*(a + b*asinh(c*x))^2)/(2*x^2) + (c^2*d^3*(a + b*asinh(c*x))^3)/b + 3*c^2*d^3*(a + b*asinh(c*x))^2*log(1 - ℯ^(-2*asinh(c*x))) + b^2*c^2*d^3*log(x) - 3*b*c^2*d^3*(a + b*asinh(c*x))*PolyLog(2, ℯ^(-2*asinh(c*x))) - (3/2)*b^2*c^2*d^3*PolyLog(3, ℯ^(-2*asinh(c*x)))]
    @test_int [((d + c^2*d*x^2)^3*(a + b*asinh(c*x))^2)/x^4, x, 31, -(b^2*c^2*d^3)/(3*x) + (50*b^2*c^4*d^3*x)/9 + (2*b^2*c^6*d^3*x^3)/27 - 5*b*c^3*d^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)) + (b*c^3*d^3*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/9 - (b*c*d^3*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x)))/(3*x^2) + (16*c^4*d^3*x*(a + b*asinh(c*x))^2)/3 + (8*c^4*d^3*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/3 - (2*c^2*d^3*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/x - (d^3*(1 + c^2*x^2)^3*(a + b*asinh(c*x))^2)/(3*x^3) - (34*b*c^3*d^3*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/3 - (17*b^2*c^3*d^3*PolyLog(2, -ℯ^asinh(c*x)))/3 + (17*b^2*c^3*d^3*PolyLog(2, ℯ^asinh(c*x)))/3]

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

    @test_int [x^4*(a + b*asinh(c*x))^2/(d + c^2*d*x^2), x, 16, (-22*b^2*x)/(9*c^4*d) + (2*b^2*x^3)/(27*c^2*d) + (22*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(9*c^5*d) - (2*b*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(9*c^3*d) - (x*(a + b*asinh(c*x))^2)/(c^4*d) + (x^3*(a + b*asinh(c*x))^2)/(3*c^2*d) + (2*(a + b*asinh(c*x))^2*atan(ℯ^asinh(c*x)))/(c^5*d) - ((2*im)*b*(a + b*asinh(c*x))*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^5*d) + ((2*im)*b*(a + b*asinh(c*x))*PolyLog(2, im*ℯ^asinh(c*x)))/(c^5*d) + ((2*im)*b^2*PolyLog(3, (-im)*ℯ^asinh(c*x)))/(c^5*d) - ((2*im)*b^2*PolyLog(3, im*ℯ^asinh(c*x)))/(c^5*d)]
    @test_int [x^3*(a + b*asinh(c*x))^2/(d + c^2*d*x^2), x, 10, (b^2*x^2)/(4*c^2*d) - (b*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2*c^3*d) + (a + b*asinh(c*x))^2/(4*c^4*d) + (x^2*(a + b*asinh(c*x))^2)/(2*c^2*d) + (a + b*asinh(c*x))^3/(3*b*c^4*d) - ((a + b*asinh(c*x))^2*log(1 + ℯ^(2*asinh(c*x))))/(c^4*d) - (b*(a + b*asinh(c*x))*PolyLog(2, -ℯ^(2*asinh(c*x))))/(c^4*d) + (b^2*PolyLog(3, -ℯ^(2*asinh(c*x))))/(2*c^4*d)]
    @test_int [x^2*(a + b*asinh(c*x))^2/(d + c^2*d*x^2), x, 11, (2*b^2*x)/(c^2*d) - (2*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c^3*d) + (x*(a + b*asinh(c*x))^2)/(c^2*d) - (2*(a + b*asinh(c*x))^2*atan(ℯ^asinh(c*x)))/(c^3*d) + ((2*im)*b*(a + b*asinh(c*x))*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^3*d) - ((2*im)*b*(a + b*asinh(c*x))*PolyLog(2, im*ℯ^asinh(c*x)))/(c^3*d) - ((2*im)*b^2*PolyLog(3, (-im)*ℯ^asinh(c*x)))/(c^3*d) + ((2*im)*b^2*PolyLog(3, im*ℯ^asinh(c*x)))/(c^3*d)]
    @test_int [x^1*(a + b*asinh(c*x))^2/(d + c^2*d*x^2), x, 6, -(a + b*asinh(c*x))^3/(3*b*c^2*d) + ((a + b*asinh(c*x))^2*log(1 + ℯ^(2*asinh(c*x))))/(c^2*d) + (b*(a + b*asinh(c*x))*PolyLog(2, -ℯ^(2*asinh(c*x))))/(c^2*d) - (b^2*PolyLog(3, -ℯ^(2*asinh(c*x))))/(2*c^2*d)]
    @test_int [x^0*(a + b*asinh(c*x))^2/(d + c^2*d*x^2), x, 8, (2*(a + b*asinh(c*x))^2*atan(ℯ^asinh(c*x)))/(c*d) - ((2*im)*b*(a + b*asinh(c*x))*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c*d) + ((2*im)*b*(a + b*asinh(c*x))*PolyLog(2, im*ℯ^asinh(c*x)))/(c*d) + ((2*im)*b^2*PolyLog(3, (-im)*ℯ^asinh(c*x)))/(c*d) - ((2*im)*b^2*PolyLog(3, im*ℯ^asinh(c*x)))/(c*d)]
    @test_int [(a + b*asinh(c*x))^2/(x^1*(d + c^2*d*x^2)), x, 9, (-2*(a + b*asinh(c*x))^2*atanh(ℯ^(2*asinh(c*x))))/d - (b*(a + b*asinh(c*x))*PolyLog(2, -ℯ^(2*asinh(c*x))))/d + (b*(a + b*asinh(c*x))*PolyLog(2, ℯ^(2*asinh(c*x))))/d + (b^2*PolyLog(3, -ℯ^(2*asinh(c*x))))/(2*d) - (b^2*PolyLog(3, ℯ^(2*asinh(c*x))))/(2*d)]
    @test_int [(a + b*asinh(c*x))^2/(x^2*(d + c^2*d*x^2)), x, 15, -((a + b*asinh(c*x))^2/(d*x)) - (2*c*(a + b*asinh(c*x))^2*atan(ℯ^asinh(c*x)))/d - (4*b*c*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/d - (2*b^2*c*PolyLog(2, -ℯ^asinh(c*x)))/d + ((2*im)*b*c*(a + b*asinh(c*x))*PolyLog(2, (-im)*ℯ^asinh(c*x)))/d - ((2*im)*b*c*(a + b*asinh(c*x))*PolyLog(2, im*ℯ^asinh(c*x)))/d + (2*b^2*c*PolyLog(2, ℯ^asinh(c*x)))/d - ((2*im)*b^2*c*PolyLog(3, (-im)*ℯ^asinh(c*x)))/d + ((2*im)*b^2*c*PolyLog(3, im*ℯ^asinh(c*x)))/d]
    @test_int [(a + b*asinh(c*x))^2/(x^3*(d + c^2*d*x^2)), x, 12, -((b*c*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(d*x)) - (a + b*asinh(c*x))^2/(2*d*x^2) + (2*c^2*(a + b*asinh(c*x))^2*atanh(ℯ^(2*asinh(c*x))))/d + (b^2*c^2*log(x))/d + (b*c^2*(a + b*asinh(c*x))*PolyLog(2, -ℯ^(2*asinh(c*x))))/d - (b*c^2*(a + b*asinh(c*x))*PolyLog(2, ℯ^(2*asinh(c*x))))/d - (b^2*c^2*PolyLog(3, -ℯ^(2*asinh(c*x))))/(2*d) + (b^2*c^2*PolyLog(3, ℯ^(2*asinh(c*x))))/(2*d)]
    @test_int [(a + b*asinh(c*x))^2/(x^4*(d + c^2*d*x^2)), x, 24, -(b^2*c^2)/(3*d*x) - (b*c*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(3*d*x^2) - (a + b*asinh(c*x))^2/(3*d*x^3) + (c^2*(a + b*asinh(c*x))^2)/(d*x) + (2*c^3*(a + b*asinh(c*x))^2*atan(ℯ^asinh(c*x)))/d + (14*b*c^3*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/(3*d) + (7*b^2*c^3*PolyLog(2, -ℯ^asinh(c*x)))/(3*d) - ((2*im)*b*c^3*(a + b*asinh(c*x))*PolyLog(2, (-im)*ℯ^asinh(c*x)))/d + ((2*im)*b*c^3*(a + b*asinh(c*x))*PolyLog(2, im*ℯ^asinh(c*x)))/d - (7*b^2*c^3*PolyLog(2, ℯ^asinh(c*x)))/(3*d) + ((2*im)*b^2*c^3*PolyLog(3, (-im)*ℯ^asinh(c*x)))/d - ((2*im)*b^2*c^3*PolyLog(3, im*ℯ^asinh(c*x)))/d]

    @test_int [x^4*(a + b*asinh(c*x))^2/(d + c^2*d*x^2)^2, x, 15, (2*b^2*x)/(c^4*d^2) + (b*(a + b*asinh(c*x)))/(c^5*d^2*sqrt(1 + c^2*x^2)) - (2*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c^5*d^2) + (3*x*(a + b*asinh(c*x))^2)/(2*c^4*d^2) - (x^3*(a + b*asinh(c*x))^2)/(2*c^2*d^2*(1 + c^2*x^2)) - (3*(a + b*asinh(c*x))^2*atan(ℯ^asinh(c*x)))/(c^5*d^2) - (b^2*atan(c*x))/(c^5*d^2) + ((3*im)*b*(a + b*asinh(c*x))*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^5*d^2) - ((3*im)*b*(a + b*asinh(c*x))*PolyLog(2, im*ℯ^asinh(c*x)))/(c^5*d^2) - ((3*im)*b^2*PolyLog(3, (-im)*ℯ^asinh(c*x)))/(c^5*d^2) + ((3*im)*b^2*PolyLog(3, im*ℯ^asinh(c*x)))/(c^5*d^2)]
    @test_int [x^3*(a + b*asinh(c*x))^2/(d + c^2*d*x^2)^2, x, 10, -((b*x*(a + b*asinh(c*x)))/(c^3*d^2*sqrt(1 + c^2*x^2))) + (a + b*asinh(c*x))^2/(2*c^4*d^2) - (x^2*(a + b*asinh(c*x))^2)/(2*c^2*d^2*(1 + c^2*x^2)) - (a + b*asinh(c*x))^3/(3*b*c^4*d^2) + ((a + b*asinh(c*x))^2*log(1 + ℯ^(2*asinh(c*x))))/(c^4*d^2) + (b^2*log(1 + c^2*x^2))/(2*c^4*d^2) + (b*(a + b*asinh(c*x))*PolyLog(2, -ℯ^(2*asinh(c*x))))/(c^4*d^2) - (b^2*PolyLog(3, -ℯ^(2*asinh(c*x))))/(2*c^4*d^2)]
    @test_int [x^2*(a + b*asinh(c*x))^2/(d + c^2*d*x^2)^2, x, 11, -((b*(a + b*asinh(c*x)))/(c^3*d^2*sqrt(1 + c^2*x^2))) - (x*(a + b*asinh(c*x))^2)/(2*c^2*d^2*(1 + c^2*x^2)) + ((a + b*asinh(c*x))^2*atan(ℯ^asinh(c*x)))/(c^3*d^2) + (b^2*atan(c*x))/(c^3*d^2) - (im*b*(a + b*asinh(c*x))*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^3*d^2) + (im*b*(a + b*asinh(c*x))*PolyLog(2, im*ℯ^asinh(c*x)))/(c^3*d^2) + (im*b^2*PolyLog(3, (-im)*ℯ^asinh(c*x)))/(c^3*d^2) - (im*b^2*PolyLog(3, im*ℯ^asinh(c*x)))/(c^3*d^2)]
    @test_int [x^1*(a + b*asinh(c*x))^2/(d + c^2*d*x^2)^2, x, 3, (b*x*(a + b*asinh(c*x)))/(c*d^2*sqrt(1 + c^2*x^2)) - (a + b*asinh(c*x))^2/(2*c^2*d^2*(1 + c^2*x^2)) - (b^2*log(1 + c^2*x^2))/(2*c^2*d^2)]
    @test_int [x^0*(a + b*asinh(c*x))^2/(d + c^2*d*x^2)^2, x, 11, (b*(a + b*asinh(c*x)))/(c*d^2*sqrt(1 + c^2*x^2)) + (x*(a + b*asinh(c*x))^2)/(2*d^2*(1 + c^2*x^2)) + ((a + b*asinh(c*x))^2*atan(ℯ^asinh(c*x)))/(c*d^2) - (b^2*atan(c*x))/(c*d^2) - (im*b*(a + b*asinh(c*x))*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c*d^2) + (im*b*(a + b*asinh(c*x))*PolyLog(2, im*ℯ^asinh(c*x)))/(c*d^2) + (im*b^2*PolyLog(3, (-im)*ℯ^asinh(c*x)))/(c*d^2) - (im*b^2*PolyLog(3, im*ℯ^asinh(c*x)))/(c*d^2)]
    @test_int [(a + b*asinh(c*x))^2/(x^1*(d + c^2*d*x^2)^2), x, 12, -((b*c*x*(a + b*asinh(c*x)))/(d^2*sqrt(1 + c^2*x^2))) + (a + b*asinh(c*x))^2/(2*d^2*(1 + c^2*x^2)) - (2*(a + b*asinh(c*x))^2*atanh(ℯ^(2*asinh(c*x))))/d^2 + (b^2*log(1 + c^2*x^2))/(2*d^2) - (b*(a + b*asinh(c*x))*PolyLog(2, -ℯ^(2*asinh(c*x))))/d^2 + (b*(a + b*asinh(c*x))*PolyLog(2, ℯ^(2*asinh(c*x))))/d^2 + (b^2*PolyLog(3, -ℯ^(2*asinh(c*x))))/(2*d^2) - (b^2*PolyLog(3, ℯ^(2*asinh(c*x))))/(2*d^2)]
    @test_int [(a + b*asinh(c*x))^2/(x^2*(d + c^2*d*x^2)^2), x, 20, -((b*c*(a + b*asinh(c*x)))/(d^2*sqrt(1 + c^2*x^2))) - (a + b*asinh(c*x))^2/(d^2*x*(1 + c^2*x^2)) - (3*c^2*x*(a + b*asinh(c*x))^2)/(2*d^2*(1 + c^2*x^2)) - (3*c*(a + b*asinh(c*x))^2*atan(ℯ^asinh(c*x)))/d^2 + (b^2*c*atan(c*x))/d^2 - (4*b*c*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/d^2 - (2*b^2*c*PolyLog(2, -ℯ^asinh(c*x)))/d^2 + ((3*im)*b*c*(a + b*asinh(c*x))*PolyLog(2, (-im)*ℯ^asinh(c*x)))/d^2 - ((3*im)*b*c*(a + b*asinh(c*x))*PolyLog(2, im*ℯ^asinh(c*x)))/d^2 + (2*b^2*c*PolyLog(2, ℯ^asinh(c*x)))/d^2 - ((3*im)*b^2*c*PolyLog(3, (-im)*ℯ^asinh(c*x)))/d^2 + ((3*im)*b^2*c*PolyLog(3, im*ℯ^asinh(c*x)))/d^2]
    @test_int [(a + b*asinh(c*x))^2/(x^3*(d + c^2*d*x^2)^2), x, 17, -((b*c*(a + b*asinh(c*x)))/(d^2*x*sqrt(1 + c^2*x^2))) - (c^2*(a + b*asinh(c*x))^2)/(d^2*(1 + c^2*x^2)) - (a + b*asinh(c*x))^2/(2*d^2*x^2*(1 + c^2*x^2)) + (4*c^2*(a + b*asinh(c*x))^2*atanh(ℯ^(2*asinh(c*x))))/d^2 + (b^2*c^2*log(x))/d^2 - (b^2*c^2*log(1 + c^2*x^2))/(2*d^2) + (2*b*c^2*(a + b*asinh(c*x))*PolyLog(2, -ℯ^(2*asinh(c*x))))/d^2 - (2*b*c^2*(a + b*asinh(c*x))*PolyLog(2, ℯ^(2*asinh(c*x))))/d^2 - (b^2*c^2*PolyLog(3, -ℯ^(2*asinh(c*x))))/d^2 + (b^2*c^2*PolyLog(3, ℯ^(2*asinh(c*x))))/d^2]
    @test_int [(a + b*asinh(c*x))^2/(x^4*(d + c^2*d*x^2)^2), x, 32, -(b^2*c^2)/(3*d^2*x) + (2*b*c^3*(a + b*asinh(c*x)))/(3*d^2*sqrt(1 + c^2*x^2)) - (b*c*(a + b*asinh(c*x)))/(3*d^2*x^2*sqrt(1 + c^2*x^2)) - (a + b*asinh(c*x))^2/(3*d^2*x^3*(1 + c^2*x^2)) + (5*c^2*(a + b*asinh(c*x))^2)/(3*d^2*x*(1 + c^2*x^2)) + (5*c^4*x*(a + b*asinh(c*x))^2)/(2*d^2*(1 + c^2*x^2)) + (5*c^3*(a + b*asinh(c*x))^2*atan(ℯ^asinh(c*x)))/d^2 - (b^2*c^3*atan(c*x))/d^2 + (26*b*c^3*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/(3*d^2) + (13*b^2*c^3*PolyLog(2, -ℯ^asinh(c*x)))/(3*d^2) - ((5*im)*b*c^3*(a + b*asinh(c*x))*PolyLog(2, (-im)*ℯ^asinh(c*x)))/d^2 + ((5*im)*b*c^3*(a + b*asinh(c*x))*PolyLog(2, im*ℯ^asinh(c*x)))/d^2 - (13*b^2*c^3*PolyLog(2, ℯ^asinh(c*x)))/(3*d^2) + ((5*im)*b^2*c^3*PolyLog(3, (-im)*ℯ^asinh(c*x)))/d^2 - ((5*im)*b^2*c^3*PolyLog(3, im*ℯ^asinh(c*x)))/d^2]

    @test_int [x^4*(a + b*asinh(c*x))^2/(d + c^2*d*x^2)^3, x, 16, -(b^2*x)/(12*c^4*d^3*(1 + c^2*x^2)) + (b*(a + b*asinh(c*x)))/(6*c^5*d^3*(1 + c^2*x^2)^(3/2)) - (5*b*(a + b*asinh(c*x)))/(4*c^5*d^3*sqrt(1 + c^2*x^2)) - (x^3*(a + b*asinh(c*x))^2)/(4*c^2*d^3*(1 + c^2*x^2)^2) - (3*x*(a + b*asinh(c*x))^2)/(8*c^4*d^3*(1 + c^2*x^2)) + (3*(a + b*asinh(c*x))^2*atan(ℯ^asinh(c*x)))/(4*c^5*d^3) + (7*b^2*atan(c*x))/(6*c^5*d^3) - (((3*im)/4)*b*(a + b*asinh(c*x))*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^5*d^3) + (((3*im)/4)*b*(a + b*asinh(c*x))*PolyLog(2, im*ℯ^asinh(c*x)))/(c^5*d^3) + (((3*im)/4)*b^2*PolyLog(3, (-im)*ℯ^asinh(c*x)))/(c^5*d^3) - (((3*im)/4)*b^2*PolyLog(3, im*ℯ^asinh(c*x)))/(c^5*d^3)]
    @test_int [x^3*(a + b*asinh(c*x))^2/(d + c^2*d*x^2)^3, x, 8, -b^2/(12*c^4*d^3*(1 + c^2*x^2)) + (b*x^3*(a + b*asinh(c*x)))/(6*c*d^3*(1 + c^2*x^2)^(3/2)) + (b*x*(a + b*asinh(c*x)))/(2*c^3*d^3*sqrt(1 + c^2*x^2)) - (a + b*asinh(c*x))^2/(4*c^4*d^3) + (x^4*(a + b*asinh(c*x))^2)/(4*d^3*(1 + c^2*x^2)^2) - (b^2*log(1 + c^2*x^2))/(3*c^4*d^3)]
    @test_int [x^2*(a + b*asinh(c*x))^2/(d + c^2*d*x^2)^3, x, 15, (b^2*x)/(12*c^2*d^3*(1 + c^2*x^2)) - (b*(a + b*asinh(c*x)))/(6*c^3*d^3*(1 + c^2*x^2)^(3/2)) + (b*(a + b*asinh(c*x)))/(4*c^3*d^3*sqrt(1 + c^2*x^2)) - (x*(a + b*asinh(c*x))^2)/(4*c^2*d^3*(1 + c^2*x^2)^2) + (x*(a + b*asinh(c*x))^2)/(8*c^2*d^3*(1 + c^2*x^2)) + ((a + b*asinh(c*x))^2*atan(ℯ^asinh(c*x)))/(4*c^3*d^3) - (b^2*atan(c*x))/(6*c^3*d^3) - ((im/4)*b*(a + b*asinh(c*x))*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^3*d^3) + ((im/4)*b*(a + b*asinh(c*x))*PolyLog(2, im*ℯ^asinh(c*x)))/(c^3*d^3) + ((im/4)*b^2*PolyLog(3, (-im)*ℯ^asinh(c*x)))/(c^3*d^3) - ((im/4)*b^2*PolyLog(3, im*ℯ^asinh(c*x)))/(c^3*d^3)]
    @test_int [x^1*(a + b*asinh(c*x))^2/(d + c^2*d*x^2)^3, x, 5, b^2/(12*c^2*d^3*(1 + c^2*x^2)) + (b*x*(a + b*asinh(c*x)))/(6*c*d^3*(1 + c^2*x^2)^(3/2)) + (b*x*(a + b*asinh(c*x)))/(3*c*d^3*sqrt(1 + c^2*x^2)) - (a + b*asinh(c*x))^2/(4*c^2*d^3*(1 + c^2*x^2)^2) - (b^2*log(1 + c^2*x^2))/(6*c^2*d^3)]
    @test_int [x^0*(a + b*asinh(c*x))^2/(d + c^2*d*x^2)^3, x, 15, -(b^2*x)/(12*d^3*(1 + c^2*x^2)) + (b*(a + b*asinh(c*x)))/(6*c*d^3*(1 + c^2*x^2)^(3/2)) + (3*b*(a + b*asinh(c*x)))/(4*c*d^3*sqrt(1 + c^2*x^2)) + (x*(a + b*asinh(c*x))^2)/(4*d^3*(1 + c^2*x^2)^2) + (3*x*(a + b*asinh(c*x))^2)/(8*d^3*(1 + c^2*x^2)) + (3*(a + b*asinh(c*x))^2*atan(ℯ^asinh(c*x)))/(4*c*d^3) - (5*b^2*atan(c*x))/(6*c*d^3) - (((3*im)/4)*b*(a + b*asinh(c*x))*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c*d^3) + (((3*im)/4)*b*(a + b*asinh(c*x))*PolyLog(2, im*ℯ^asinh(c*x)))/(c*d^3) + (((3*im)/4)*b^2*PolyLog(3, (-im)*ℯ^asinh(c*x)))/(c*d^3) - (((3*im)/4)*b^2*PolyLog(3, im*ℯ^asinh(c*x)))/(c*d^3)]
    @test_int [(a + b*asinh(c*x))^2/(x^1*(d + c^2*d*x^2)^3), x, 17, -b^2/(12*d^3*(1 + c^2*x^2)) - (b*c*x*(a + b*asinh(c*x)))/(6*d^3*(1 + c^2*x^2)^(3/2)) - (4*b*c*x*(a + b*asinh(c*x)))/(3*d^3*sqrt(1 + c^2*x^2)) + (a + b*asinh(c*x))^2/(4*d^3*(1 + c^2*x^2)^2) + (a + b*asinh(c*x))^2/(2*d^3*(1 + c^2*x^2)) - (2*(a + b*asinh(c*x))^2*atanh(ℯ^(2*asinh(c*x))))/d^3 + (2*b^2*log(1 + c^2*x^2))/(3*d^3) - (b*(a + b*asinh(c*x))*PolyLog(2, -ℯ^(2*asinh(c*x))))/d^3 + (b*(a + b*asinh(c*x))*PolyLog(2, ℯ^(2*asinh(c*x))))/d^3 + (b^2*PolyLog(3, -ℯ^(2*asinh(c*x))))/(2*d^3) - (b^2*PolyLog(3, ℯ^(2*asinh(c*x))))/(2*d^3)]
    @test_int [(a + b*asinh(c*x))^2/(x^2*(d + c^2*d*x^2)^3), x, 27, (b^2*c^2*x)/(12*d^3*(1 + c^2*x^2)) - (b*c*(a + b*asinh(c*x)))/(6*d^3*(1 + c^2*x^2)^(3/2)) - (7*b*c*(a + b*asinh(c*x)))/(4*d^3*sqrt(1 + c^2*x^2)) - (a + b*asinh(c*x))^2/(d^3*x*(1 + c^2*x^2)^2) - (5*c^2*x*(a + b*asinh(c*x))^2)/(4*d^3*(1 + c^2*x^2)^2) - (15*c^2*x*(a + b*asinh(c*x))^2)/(8*d^3*(1 + c^2*x^2)) - (15*c*(a + b*asinh(c*x))^2*atan(ℯ^asinh(c*x)))/(4*d^3) + (11*b^2*c*atan(c*x))/(6*d^3) - (4*b*c*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/d^3 - (2*b^2*c*PolyLog(2, -ℯ^asinh(c*x)))/d^3 + (((15*im)/4)*b*c*(a + b*asinh(c*x))*PolyLog(2, (-im)*ℯ^asinh(c*x)))/d^3 - (((15*im)/4)*b*c*(a + b*asinh(c*x))*PolyLog(2, im*ℯ^asinh(c*x)))/d^3 + (2*b^2*c*PolyLog(2, ℯ^asinh(c*x)))/d^3 - (((15*im)/4)*b^2*c*PolyLog(3, (-im)*ℯ^asinh(c*x)))/d^3 + (((15*im)/4)*b^2*c*PolyLog(3, im*ℯ^asinh(c*x)))/d^3]
    @test_int [(a + b*asinh(c*x))^2/(x^3*(d + c^2*d*x^2)^3), x, 23, (b^2*c^2)/(12*d^3*(1 + c^2*x^2)) - (b*c*(a + b*asinh(c*x)))/(d^3*x*(1 + c^2*x^2)^(3/2)) - (5*b*c^3*x*(a + b*asinh(c*x)))/(6*d^3*(1 + c^2*x^2)^(3/2)) + (4*b*c^3*x*(a + b*asinh(c*x)))/(3*d^3*sqrt(1 + c^2*x^2)) - (3*c^2*(a + b*asinh(c*x))^2)/(4*d^3*(1 + c^2*x^2)^2) - (a + b*asinh(c*x))^2/(2*d^3*x^2*(1 + c^2*x^2)^2) - (3*c^2*(a + b*asinh(c*x))^2)/(2*d^3*(1 + c^2*x^2)) + (6*c^2*(a + b*asinh(c*x))^2*atanh(ℯ^(2*asinh(c*x))))/d^3 + (b^2*c^2*log(x))/d^3 - (7*b^2*c^2*log(1 + c^2*x^2))/(6*d^3) + (3*b*c^2*(a + b*asinh(c*x))*PolyLog(2, -ℯ^(2*asinh(c*x))))/d^3 - (3*b*c^2*(a + b*asinh(c*x))*PolyLog(2, ℯ^(2*asinh(c*x))))/d^3 - (3*b^2*c^2*PolyLog(3, -ℯ^(2*asinh(c*x))))/(2*d^3) + (3*b^2*c^2*PolyLog(3, ℯ^(2*asinh(c*x))))/(2*d^3)]
    @test_int [(a + b*asinh(c*x))^2/(x^4*(d + c^2*d*x^2)^3), x, 43, -(b^2*c^2)/(2*d^3*x) + (b^2*c^2)/(6*d^3*x*(1 + c^2*x^2)) + (b^2*c^4*x)/(12*d^3*(1 + c^2*x^2)) - (b*c^3*(a + b*asinh(c*x)))/(6*d^3*(1 + c^2*x^2)^(3/2)) - (b*c*(a + b*asinh(c*x)))/(3*d^3*x^2*(1 + c^2*x^2)^(3/2)) + (29*b*c^3*(a + b*asinh(c*x)))/(12*d^3*sqrt(1 + c^2*x^2)) - (a + b*asinh(c*x))^2/(3*d^3*x^3*(1 + c^2*x^2)^2) + (7*c^2*(a + b*asinh(c*x))^2)/(3*d^3*x*(1 + c^2*x^2)^2) + (35*c^4*x*(a + b*asinh(c*x))^2)/(12*d^3*(1 + c^2*x^2)^2) + (35*c^4*x*(a + b*asinh(c*x))^2)/(8*d^3*(1 + c^2*x^2)) + (35*c^3*(a + b*asinh(c*x))^2*atan(ℯ^asinh(c*x)))/(4*d^3) - (17*b^2*c^3*atan(c*x))/(6*d^3) + (38*b*c^3*(a + b*asinh(c*x))*atanh(ℯ^asinh(c*x)))/(3*d^3) + (19*b^2*c^3*PolyLog(2, -ℯ^asinh(c*x)))/(3*d^3) - (((35*im)/4)*b*c^3*(a + b*asinh(c*x))*PolyLog(2, (-im)*ℯ^asinh(c*x)))/d^3 + (((35*im)/4)*b*c^3*(a + b*asinh(c*x))*PolyLog(2, im*ℯ^asinh(c*x)))/d^3 - (19*b^2*c^3*PolyLog(2, ℯ^asinh(c*x)))/(3*d^3) + (((35*im)/4)*b^2*c^3*PolyLog(3, (-im)*ℯ^asinh(c*x)))/d^3 - (((35*im)/4)*b^2*c^3*PolyLog(3, im*ℯ^asinh(c*x)))/d^3]

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

    @test_int [(pi + pi*c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2, x, 16, (245*b^2*pi^(5/2)*x*sqrt(1 + c^2*x^2))/1152 + (65*b^2*pi^(5/2)*x*(1 + c^2*x^2)^(3/2))/1728 + (1/108)*b^2*pi^(5/2)*x*(1 + c^2*x^2)^(5/2) - (115*b^2*pi^(5/2)*asinh(c*x))/(1152*c) - (5/16)*b*c*pi^(5/2)*x^2*(a + b*asinh(c*x)) - (5*b*pi^(5/2)*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(48*c) - (b*pi^(5/2)*(1 + c^2*x^2)^3*(a + b*asinh(c*x)))/(18*c) + (5/16)*pi^2*x*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x))^2 + (5/24)*pi*x*(pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x))^2 + (1/6)*x*(pi + c^2*pi*x^2)^(5/2)*(a + b*asinh(c*x))^2 + (5*pi^(5/2)*(a + b*asinh(c*x))^3)/(48*b*c)]
    @test_int [(pi + pi*c^2*x^2)^(3/2)*(a + b*asinh(c*x))^2, x, 10, (15/64)*b^2*pi^(3/2)*x*sqrt(1 + c^2*x^2) + (1/32)*b^2*pi^(3/2)*x*(1 + c^2*x^2)^(3/2) - (9*b^2*pi^(3/2)*asinh(c*x))/(64*c) - (3/8)*b*c*pi^(3/2)*x^2*(a + b*asinh(c*x)) - (b*pi^(3/2)*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(8*c) + (3/8)*pi*x*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x))^2 + (1/4)*x*(pi + c^2*pi*x^2)^(3/2)*(a + b*asinh(c*x))^2 + (pi^(3/2)*(a + b*asinh(c*x))^3)/(8*b*c)]
    @test_int [(pi + pi*c^2*x^2)^(1/2)*(a + b*asinh(c*x))^2, x, 5, (1/4)*b^2*sqrt(pi)*x*sqrt(1 + c^2*x^2) - (b^2*sqrt(pi)*asinh(c*x))/(4*c) - (1/2)*b*c*sqrt(pi)*x^2*(a + b*asinh(c*x)) + (1/2)*x*sqrt(pi + c^2*pi*x^2)*(a + b*asinh(c*x))^2 + (sqrt(pi)*(a + b*asinh(c*x))^3)/(6*b*c)]
    @test_int [(a + b*asinh(c*x))^2/(pi + pi*c^2*x^2)^(1/2), x, 1, (a + b*asinh(c*x))^3/(3*b*c*sqrt(pi))]
    @test_int [(a + b*asinh(c*x))^2/(pi + pi*c^2*x^2)^(3/2), x, 6, (a + b*asinh(c*x))^2/(c*pi^(3/2)) + (x*(a + b*asinh(c*x))^2)/(pi*sqrt(pi + c^2*pi*x^2)) - (2*b*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(c*pi^(3/2)) - (b^2*PolyLog(2, -ℯ^(2*asinh(c*x))))/(c*pi^(3/2))]
    @test_int [(a + b*asinh(c*x))^2/(pi + pi*c^2*x^2)^(5/2), x, 9, -((b^2*x)/(3*pi^(5/2)*sqrt(1 + c^2*x^2))) + (b*(a + b*asinh(c*x)))/(3*c*pi^(5/2)*(1 + c^2*x^2)) + (2*(a + b*asinh(c*x))^2)/(3*c*pi^(5/2)) + (x*(a + b*asinh(c*x))^2)/(3*pi*(pi + c^2*pi*x^2)^(3/2)) + (2*x*(a + b*asinh(c*x))^2)/(3*pi^2*sqrt(pi + c^2*pi*x^2)) - (4*b*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(3*c*pi^(5/2)) - (2*b^2*PolyLog(2, -ℯ^(2*asinh(c*x))))/(3*c*pi^(5/2))]

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

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

    @test_int [x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2, x, 14, (-52*b^2*sqrt(d + c^2*d*x^2))/(225*c^4) + (4*a*b*x*sqrt(d + c^2*d*x^2))/(15*c^3*sqrt(1 + c^2*x^2)) - (26*b^2*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2))/(675*c^4) + (2*b^2*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2))/(125*c^4) + (4*b^2*x*sqrt(d + c^2*d*x^2)*asinh(c*x))/(15*c^3*sqrt(1 + c^2*x^2)) - (2*b*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(45*c*sqrt(1 + c^2*x^2)) - (2*b*c*x^5*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(25*sqrt(1 + c^2*x^2)) - (2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(15*c^4) + (x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(15*c^2) + (x^4*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/5]
    @test_int [x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2, x, 10, (b^2*x*sqrt(d + c^2*d*x^2))/(64*c^2) + (b^2*x^3*sqrt(d + c^2*d*x^2))/32 - (b^2*sqrt(d + c^2*d*x^2)*asinh(c*x))/(64*c^3*sqrt(1 + c^2*x^2)) - (b*x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(8*c*sqrt(1 + c^2*x^2)) - (b*c*x^4*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(8*sqrt(1 + c^2*x^2)) + (x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(8*c^2) + (x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/4 - (sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^3)/(24*b*c^3*sqrt(1 + c^2*x^2))]
    @test_int [x^1*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2, x, 5, (4*b^2*sqrt(d + c^2*d*x^2))/(9*c^2) + (2*b^2*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2))/(27*c^2) - (2*b*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(3*c*sqrt(1 + c^2*x^2)) - (2*b*c*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(9*sqrt(1 + c^2*x^2)) + ((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(3*c^2*d)]
    @test_int [sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2, x, 5, (b^2*x*sqrt(d + c^2*d*x^2))/4 - (b^2*sqrt(d + c^2*d*x^2)*asinh(c*x))/(4*c*sqrt(1 + c^2*x^2)) - (b*c*x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(2*sqrt(1 + c^2*x^2)) + (x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/2 + (sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^3)/(6*b*c*sqrt(1 + c^2*x^2))]
    @test_int [(sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/x^1, x, 12, 2*b^2*sqrt(d + c^2*d*x^2) - (2*a*b*c*x*sqrt(d + c^2*d*x^2))/sqrt(1 + c^2*x^2) - (2*b^2*c*x*sqrt(d + c^2*d*x^2)*asinh(c*x))/sqrt(1 + c^2*x^2) + sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2 - (2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2*atanh(ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (2*b*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*PolyLog(2, -ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) + (2*b*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*PolyLog(2, ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) + (2*b^2*sqrt(d + c^2*d*x^2)*PolyLog(3, -ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (2*b^2*sqrt(d + c^2*d*x^2)*PolyLog(3, ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2)]
    @test_int [(sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/x^2, x, 7, -((sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/x) + (c*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/sqrt(1 + c^2*x^2) + (c*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^3)/(3*b*sqrt(1 + c^2*x^2)) + (2*b*c*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*log(1 - ℯ^(-2*asinh(c*x))))/sqrt(1 + c^2*x^2) - (b^2*c*sqrt(d + c^2*d*x^2)*PolyLog(2, ℯ^(-2*asinh(c*x))))/sqrt(1 + c^2*x^2)]
    @test_int [(sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/x^3, x, 13, -((b*c*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(x*sqrt(1 + c^2*x^2))) - (sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*x^2) - (c^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2*atanh(ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (b^2*c^2*sqrt(d + c^2*d*x^2)*atanh(sqrt(1 + c^2*x^2)))/sqrt(1 + c^2*x^2) - (b*c^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*PolyLog(2, -ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) + (b*c^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*PolyLog(2, ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) + (b^2*c^2*sqrt(d + c^2*d*x^2)*PolyLog(3, -ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (b^2*c^2*sqrt(d + c^2*d*x^2)*PolyLog(3, ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2)]
    @test_int [(sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/x^4, x, 9, -((b^2*c^2*sqrt(d + c^2*d*x^2))/(3*x)) + (b^2*c^3*sqrt(d + c^2*d*x^2)*asinh(c*x))/(3*sqrt(1 + c^2*x^2)) - (b*c*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(3*x^2) + (c^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(3*sqrt(1 + c^2*x^2)) - ((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(3*d*x^3) + (2*b*c^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*log(1 - ℯ^(-2*asinh(c*x))))/(3*sqrt(1 + c^2*x^2)) - (b^2*c^3*sqrt(d + c^2*d*x^2)*PolyLog(2, ℯ^(-2*asinh(c*x))))/(3*sqrt(1 + c^2*x^2))]

    @test_int [x^3*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2, x, 20, (-304*b^2*d*sqrt(d + c^2*d*x^2))/(3675*c^4) + (4*a*b*d*x*sqrt(d + c^2*d*x^2))/(35*c^3*sqrt(1 + c^2*x^2)) - (152*b^2*d*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2))/(11025*c^4) - (38*b^2*d*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2))/(6125*c^4) + (2*b^2*d*(1 + c^2*x^2)^3*sqrt(d + c^2*d*x^2))/(343*c^4) + (4*b^2*d*x*sqrt(d + c^2*d*x^2)*asinh(c*x))/(35*c^3*sqrt(1 + c^2*x^2)) - (2*b*d*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(105*c*sqrt(1 + c^2*x^2)) - (16*b*c*d*x^5*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(175*sqrt(1 + c^2*x^2)) - (2*b*c^3*d*x^7*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(49*sqrt(1 + c^2*x^2)) - (2*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(35*c^4) + (d*x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(35*c^2) + (3*d*x^4*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/35 + (x^4*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/7]
    @test_int [x^2*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2, x, 17, (-7*b^2*d*x*sqrt(d + c^2*d*x^2))/(1152*c^2) + (43*b^2*d*x^3*sqrt(d + c^2*d*x^2))/1728 + (b^2*c^2*d*x^5*sqrt(d + c^2*d*x^2))/108 + (7*b^2*d*sqrt(d + c^2*d*x^2)*asinh(c*x))/(1152*c^3*sqrt(1 + c^2*x^2)) - (b*d*x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(16*c*sqrt(1 + c^2*x^2)) - (7*b*c*d*x^4*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(48*sqrt(1 + c^2*x^2)) - (b*c^3*d*x^6*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(18*sqrt(1 + c^2*x^2)) + (d*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(16*c^2) + (d*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/8 + (x^3*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/6 - (d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^3)/(48*b*c^3*sqrt(1 + c^2*x^2))]
    @test_int [x*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2, x, 6, (16*b^2*d*sqrt(d + c^2*d*x^2))/(75*c^2) + (8*b^2*d*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2))/(225*c^2) + (2*b^2*d*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2))/(125*c^2) - (2*b*d*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(5*c*sqrt(1 + c^2*x^2)) - (4*b*c*d*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(15*sqrt(1 + c^2*x^2)) - (2*b*c^3*d*x^5*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(25*sqrt(1 + c^2*x^2)) + ((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2)/(5*c^2*d)]
    @test_int [(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2, x, 10, (15/64)*b^2*d*x*sqrt(d + c^2*d*x^2) + (1/32)*b^2*d*x*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2) - (9*b^2*d*sqrt(d + c^2*d*x^2)*asinh(c*x))/(64*c*sqrt(1 + c^2*x^2)) - (3*b*c*d*x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(8*sqrt(1 + c^2*x^2)) - (b*d*(1 + c^2*x^2)^(3/2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(8*c) + (3/8)*d*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2 + (1/4)*x*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2 + (d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^3)/(8*b*c*sqrt(1 + c^2*x^2))]
    @test_int [((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/x, x, 17, (22*b^2*d*sqrt(d + c^2*d*x^2))/9 - (2*a*b*c*d*x*sqrt(d + c^2*d*x^2))/sqrt(1 + c^2*x^2) + (2*b^2*d*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2))/27 - (2*b^2*c*d*x*sqrt(d + c^2*d*x^2)*asinh(c*x))/sqrt(1 + c^2*x^2) - (2*b*c*d*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(3*sqrt(1 + c^2*x^2)) - (2*b*c^3*d*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(9*sqrt(1 + c^2*x^2)) + d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2 + ((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/3 - (2*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2*atanh(ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (2*b*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*PolyLog(2, -ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) + (2*b*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*PolyLog(2, ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) + (2*b^2*d*sqrt(d + c^2*d*x^2)*PolyLog(3, -ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (2*b^2*d*sqrt(d + c^2*d*x^2)*PolyLog(3, ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2)]
    @test_int [((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/x^2, x, 14, (1/4)*b^2*c^2*d*x*sqrt(d + c^2*d*x^2) - (5*b^2*c*d*sqrt(d + c^2*d*x^2)*asinh(c*x))/(4*sqrt(1 + c^2*x^2)) - (3*b*c^3*d*x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(2*sqrt(1 + c^2*x^2)) + b*c*d*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (3/2)*c^2*d*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2 + (c*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/sqrt(1 + c^2*x^2) - ((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/x + (c*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^3)/(2*b*sqrt(1 + c^2*x^2)) + (2*b*c*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*log(1 - ℯ^(-2*asinh(c*x))))/sqrt(1 + c^2*x^2) - (b^2*c*d*sqrt(d + c^2*d*x^2)*PolyLog(2, ℯ^(-2*asinh(c*x))))/sqrt(1 + c^2*x^2)]
    @test_int [((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/x^3, x, 18, 2*b^2*c^2*d*sqrt(d + c^2*d*x^2) - (3*a*b*c^3*d*x*sqrt(d + c^2*d*x^2))/sqrt(1 + c^2*x^2) - (3*b^2*c^3*d*x*sqrt(d + c^2*d*x^2)*asinh(c*x))/sqrt(1 + c^2*x^2) - (b*c*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(x*sqrt(1 + c^2*x^2)) + (b*c^3*d*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/sqrt(1 + c^2*x^2) + (3*c^2*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/2 - ((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(2*x^2) - (3*c^2*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2*atanh(ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (b^2*c^2*d*sqrt(d + c^2*d*x^2)*atanh(sqrt(1 + c^2*x^2)))/sqrt(1 + c^2*x^2) - (3*b*c^2*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*PolyLog(2, -ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) + (3*b*c^2*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*PolyLog(2, ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) + (3*b^2*c^2*d*sqrt(d + c^2*d*x^2)*PolyLog(3, -ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (3*b^2*c^2*d*sqrt(d + c^2*d*x^2)*PolyLog(3, ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2)]
    @test_int [((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/x^4, x, 16, -((b^2*c^2*d*sqrt(d + c^2*d*x^2))/(3*x)) + (b^2*c^3*d*sqrt(d + c^2*d*x^2)*asinh(c*x))/(3*sqrt(1 + c^2*x^2)) - (b*c*d*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(3*x^2) - (c^2*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/x + (4*c^3*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(3*sqrt(1 + c^2*x^2)) - ((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(3*x^3) + (c^3*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^3)/(3*b*sqrt(1 + c^2*x^2)) + (8*b*c^3*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*log(1 - ℯ^(-2*asinh(c*x))))/(3*sqrt(1 + c^2*x^2)) - (4*b^2*c^3*d*sqrt(d + c^2*d*x^2)*PolyLog(2, ℯ^(-2*asinh(c*x))))/(3*sqrt(1 + c^2*x^2))]

    @test_int [x^3*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2, x, 27, (-160*b^2*d^2*sqrt(d + c^2*d*x^2))/(3969*c^4) + (4*a*b*d^2*x*sqrt(d + c^2*d*x^2))/(63*c^3*sqrt(1 + c^2*x^2)) - (80*b^2*d^2*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2))/(11907*c^4) - (4*b^2*d^2*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2))/(1323*c^4) - (50*b^2*d^2*(1 + c^2*x^2)^3*sqrt(d + c^2*d*x^2))/(27783*c^4) + (2*b^2*d^2*(1 + c^2*x^2)^4*sqrt(d + c^2*d*x^2))/(729*c^4) + (4*b^2*d^2*x*sqrt(d + c^2*d*x^2)*asinh(c*x))/(63*c^3*sqrt(1 + c^2*x^2)) - (2*b*d^2*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(189*c*sqrt(1 + c^2*x^2)) - (2*b*c*d^2*x^5*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(21*sqrt(1 + c^2*x^2)) - (38*b*c^3*d^2*x^7*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(441*sqrt(1 + c^2*x^2)) - (2*b*c^5*d^2*x^9*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(81*sqrt(1 + c^2*x^2)) - (2*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(63*c^4) + (d^2*x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(63*c^2) + (d^2*x^4*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/21 + (5*d*x^4*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/63 + (x^4*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2)/9]
    @test_int [x^2*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2, x, 25, (-359*b^2*d^2*x*sqrt(d + c^2*d*x^2))/(36864*c^2) + (1079*b^2*d^2*x^3*sqrt(d + c^2*d*x^2))/55296 + (209*b^2*c^2*d^2*x^5*sqrt(d + c^2*d*x^2))/13824 + (b^2*c^4*d^2*x^7*sqrt(d + c^2*d*x^2))/256 + (359*b^2*d^2*sqrt(d + c^2*d*x^2)*asinh(c*x))/(36864*c^3*sqrt(1 + c^2*x^2)) - (5*b*d^2*x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(128*c*sqrt(1 + c^2*x^2)) - (59*b*c*d^2*x^4*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(384*sqrt(1 + c^2*x^2)) - (17*b*c^3*d^2*x^6*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(144*sqrt(1 + c^2*x^2)) - (b*c^5*d^2*x^8*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(32*sqrt(1 + c^2*x^2)) + (5*d^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(128*c^2) + (5*d^2*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/64 + (5*d*x^3*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/48 + (x^3*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2)/8 - (5*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^3)/(384*b*c^3*sqrt(1 + c^2*x^2))]
    @test_int [x*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2, x, 6, (32*b^2*d^2*sqrt(d + c^2*d*x^2))/(245*c^2) + (16*b^2*d^2*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2))/(735*c^2) + (12*b^2*d^2*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2))/(1225*c^2) + (2*b^2*d^2*(1 + c^2*x^2)^3*sqrt(d + c^2*d*x^2))/(343*c^2) - (2*b*d^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(7*c*sqrt(1 + c^2*x^2)) - (2*b*c*d^2*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(7*sqrt(1 + c^2*x^2)) - (6*b*c^3*d^2*x^5*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(35*sqrt(1 + c^2*x^2)) - (2*b*c^5*d^2*x^7*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(49*sqrt(1 + c^2*x^2)) + ((d + c^2*d*x^2)^(7/2)*(a + b*asinh(c*x))^2)/(7*c^2*d)]
    @test_int [(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2, x, 16, (245*b^2*d^2*x*sqrt(d + c^2*d*x^2))/1152 + (65*b^2*d^2*x*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2))/1728 + (b^2*d^2*x*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2))/108 - (115*b^2*d^2*sqrt(d + c^2*d*x^2)*asinh(c*x))/(1152*c*sqrt(1 + c^2*x^2)) - (5*b*c*d^2*x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(16*sqrt(1 + c^2*x^2)) - (5*b*d^2*(1 + c^2*x^2)^(3/2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(48*c) - (b*d^2*(1 + c^2*x^2)^(5/2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(18*c) + (5*d^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/16 + (5*d*x*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/24 + (x*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2)/6 + (5*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^3)/(48*b*c*sqrt(1 + c^2*x^2))]
    @test_int [((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2)/x, x, 23, (598*b^2*d^2*sqrt(d + c^2*d*x^2))/225 - (2*a*b*c*d^2*x*sqrt(d + c^2*d*x^2))/sqrt(1 + c^2*x^2) + (74*b^2*d^2*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2))/675 + (2*b^2*d^2*(1 + c^2*x^2)^2*sqrt(d + c^2*d*x^2))/125 - (2*b^2*c*d^2*x*sqrt(d + c^2*d*x^2)*asinh(c*x))/sqrt(1 + c^2*x^2) - (16*b*c*d^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(15*sqrt(1 + c^2*x^2)) - (22*b*c^3*d^2*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(45*sqrt(1 + c^2*x^2)) - (2*b*c^5*d^2*x^5*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(25*sqrt(1 + c^2*x^2)) + d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2 + (d*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/3 + ((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2)/5 - (2*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2*atanh(ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (2*b*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*PolyLog(2, -ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) + (2*b*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*PolyLog(2, ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) + (2*b^2*d^2*sqrt(d + c^2*d*x^2)*PolyLog(3, -ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (2*b^2*d^2*sqrt(d + c^2*d*x^2)*PolyLog(3, ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2)]
    @test_int [((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2)/x^2, x, 23, (31/64)*b^2*c^2*d^2*x*sqrt(d + c^2*d*x^2) + (1/32)*b^2*c^2*d^2*x*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2) - (89*b^2*c*d^2*sqrt(d + c^2*d*x^2)*asinh(c*x))/(64*sqrt(1 + c^2*x^2)) - (15*b*c^3*d^2*x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(8*sqrt(1 + c^2*x^2)) + b*c*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) - (1/8)*b*c*d^2*(1 + c^2*x^2)^(3/2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) + (15/8)*c^2*d^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2 + (c*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/sqrt(1 + c^2*x^2) + (5/4)*c^2*d*x*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2 - ((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2)/x + (5*c*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^3)/(8*b*sqrt(1 + c^2*x^2)) + (2*b*c*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*log(1 - ℯ^(-2*asinh(c*x))))/sqrt(1 + c^2*x^2) - (b^2*c*d^2*sqrt(d + c^2*d*x^2)*PolyLog(2, ℯ^(-2*asinh(c*x))))/sqrt(1 + c^2*x^2)]
    @test_int [((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2)/x^3, x, 25, (40*b^2*c^2*d^2*sqrt(d + c^2*d*x^2))/9 - (5*a*b*c^3*d^2*x*sqrt(d + c^2*d*x^2))/sqrt(1 + c^2*x^2) + (2*b^2*c^2*d^2*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2))/27 - (5*b^2*c^3*d^2*x*sqrt(d + c^2*d*x^2)*asinh(c*x))/sqrt(1 + c^2*x^2) - (b*c*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(x*sqrt(1 + c^2*x^2)) + (b*c^3*d^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(3*sqrt(1 + c^2*x^2)) - (2*b*c^5*d^2*x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(9*sqrt(1 + c^2*x^2)) + (5*c^2*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/2 + (5*c^2*d*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/6 - ((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2)/(2*x^2) - (5*c^2*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2*atanh(ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (b^2*c^2*d^2*sqrt(d + c^2*d*x^2)*atanh(sqrt(1 + c^2*x^2)))/sqrt(1 + c^2*x^2) - (5*b*c^2*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*PolyLog(2, -ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) + (5*b*c^2*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*PolyLog(2, ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) + (5*b^2*c^2*d^2*sqrt(d + c^2*d*x^2)*PolyLog(3, -ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2) - (5*b^2*c^2*d^2*sqrt(d + c^2*d*x^2)*PolyLog(3, ℯ^asinh(c*x)))/sqrt(1 + c^2*x^2)]
    @test_int [((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2)/x^4, x, 27, (7/12)*b^2*c^4*d^2*x*sqrt(d + c^2*d*x^2) - (b^2*c^2*d^2*(1 + c^2*x^2)*sqrt(d + c^2*d*x^2))/(3*x) - (23*b^2*c^3*d^2*sqrt(d + c^2*d*x^2)*asinh(c*x))/(12*sqrt(1 + c^2*x^2)) - (5*b*c^5*d^2*x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(2*sqrt(1 + c^2*x^2)) + (7/3)*b*c^3*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)) - (b*c*d^2*(1 + c^2*x^2)^(3/2)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/(3*x^2) + (5/2)*c^4*d^2*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2 + (7*c^3*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(3*sqrt(1 + c^2*x^2)) - (5*c^2*d*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(3*x) - ((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2)/(3*x^3) + (5*c^3*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^3)/(6*b*sqrt(1 + c^2*x^2)) + (14*b*c^3*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))*log(1 - ℯ^(-2*asinh(c*x))))/(3*sqrt(1 + c^2*x^2)) - (7*b^2*c^3*d^2*sqrt(d + c^2*d*x^2)*PolyLog(2, ℯ^(-2*asinh(c*x))))/(3*sqrt(1 + c^2*x^2))]

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

    @test_int [(x^4*asinh(a*x)^2)/sqrt(1 + a^2*x^2), x, 10, (-15*x*sqrt(1 + a^2*x^2))/(64*a^4) + (x^3*sqrt(1 + a^2*x^2))/(32*a^2) + (15*asinh(a*x))/(64*a^5) + (3*x^2*asinh(a*x))/(8*a^3) - (x^4*asinh(a*x))/(8*a) - (3*x*sqrt(1 + a^2*x^2)*asinh(a*x)^2)/(8*a^4) + (x^3*sqrt(1 + a^2*x^2)*asinh(a*x)^2)/(4*a^2) + asinh(a*x)^3/(8*a^5)]
    @test_int [(x^3*asinh(a*x)^2)/sqrt(1 + a^2*x^2), x, 8, (-14*sqrt(1 + a^2*x^2))/(9*a^4) + (2*(1 + a^2*x^2)^(3/2))/(27*a^4) + (4*x*asinh(a*x))/(3*a^3) - (2*x^3*asinh(a*x))/(9*a) - (2*sqrt(1 + a^2*x^2)*asinh(a*x)^2)/(3*a^4) + (x^2*sqrt(1 + a^2*x^2)*asinh(a*x)^2)/(3*a^2)]
    @test_int [(x^2*asinh(a*x)^2)/sqrt(1 + a^2*x^2), x, 5, (x*sqrt(1 + a^2*x^2))/(4*a^2) - asinh(a*x)/(4*a^3) - (x^2*asinh(a*x))/(2*a) + (x*sqrt(1 + a^2*x^2)*asinh(a*x)^2)/(2*a^2) - asinh(a*x)^3/(6*a^3)]
    @test_int [(x*asinh(a*x)^2)/sqrt(1 + a^2*x^2), x, 3, (2*sqrt(1 + a^2*x^2))/a^2 - (2*x*asinh(a*x))/a + (sqrt(1 + a^2*x^2)*asinh(a*x)^2)/a^2]
    @test_int [asinh(a*x)^2/sqrt(1 + a^2*x^2), x, 1, asinh(a*x)^3/(3*a)]
    @test_int [asinh(a*x)^2/(x*sqrt(1 + a^2*x^2)), x, 8, -2*asinh(a*x)^2*atanh(ℯ^asinh(a*x)) - 2*asinh(a*x)*PolyLog(2, -ℯ^asinh(a*x)) + 2*asinh(a*x)*PolyLog(2, ℯ^asinh(a*x)) + 2*PolyLog(3, -ℯ^asinh(a*x)) - 2*PolyLog(3, ℯ^asinh(a*x))]
    @test_int [asinh(a*x)^2/(x^2*sqrt(1 + a^2*x^2)), x, 6, -(a*asinh(a*x)^2) - (sqrt(1 + a^2*x^2)*asinh(a*x)^2)/x + 2*a*asinh(a*x)*log(1 - ℯ^(2*asinh(a*x))) + a*PolyLog(2, ℯ^(2*asinh(a*x)))]
    @test_int [asinh(a*x)^2/(x^3*sqrt(1 + a^2*x^2)), x, 13, -((a*asinh(a*x))/x) - (sqrt(1 + a^2*x^2)*asinh(a*x)^2)/(2*x^2) + a^2*asinh(a*x)^2*atanh(ℯ^asinh(a*x)) - a^2*atanh(sqrt(1 + a^2*x^2)) + a^2*asinh(a*x)*PolyLog(2, -ℯ^asinh(a*x)) - a^2*asinh(a*x)*PolyLog(2, ℯ^asinh(a*x)) - a^2*PolyLog(3, -ℯ^asinh(a*x)) + a^2*PolyLog(3, ℯ^asinh(a*x))]

    @test_int [(x^5*(a + b*asinh(c*x))^2)/sqrt(d + c^2*d*x^2), x, 14, -((16*a*b*x*sqrt(1 + c^2*x^2))/(15*c^5*sqrt(d + c^2*d*x^2))) + (298*b^2*(1 + c^2*x^2))/(225*c^6*sqrt(d + c^2*d*x^2)) - (76*b^2*(1 + c^2*x^2)^2)/(675*c^6*sqrt(d + c^2*d*x^2)) + (2*b^2*(1 + c^2*x^2)^3)/(125*c^6*sqrt(d + c^2*d*x^2)) - (16*b^2*x*sqrt(1 + c^2*x^2)*asinh(c*x))/(15*c^5*sqrt(d + c^2*d*x^2)) + (8*b*x^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(45*c^3*sqrt(d + c^2*d*x^2)) - (2*b*x^5*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(25*c*sqrt(d + c^2*d*x^2)) + (8*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(15*c^6*d) - (4*x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(15*c^4*d) + (x^4*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(5*c^2*d)]
    @test_int [(x^4*(a + b*asinh(c*x))^2)/sqrt(d + c^2*d*x^2), x, 10, -((15*b^2*x*(1 + c^2*x^2))/(64*c^4*sqrt(d + c^2*d*x^2))) + (b^2*x^3*(1 + c^2*x^2))/(32*c^2*sqrt(d + c^2*d*x^2)) + (15*b^2*sqrt(1 + c^2*x^2)*asinh(c*x))/(64*c^5*sqrt(d + c^2*d*x^2)) + (3*b*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(8*c^3*sqrt(d + c^2*d*x^2)) - (b*x^4*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(8*c*sqrt(d + c^2*d*x^2)) - (3*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(8*c^4*d) + (x^3*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(4*c^2*d) + (sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^3)/(8*b*c^5*sqrt(d + c^2*d*x^2))]
    @test_int [(x^3*(a + b*asinh(c*x))^2)/sqrt(d + c^2*d*x^2), x, 9, (4*a*b*x*sqrt(1 + c^2*x^2))/(3*c^3*sqrt(d + c^2*d*x^2)) - (14*b^2*(1 + c^2*x^2))/(9*c^4*sqrt(d + c^2*d*x^2)) + (2*b^2*(1 + c^2*x^2)^2)/(27*c^4*sqrt(d + c^2*d*x^2)) + (4*b^2*x*sqrt(1 + c^2*x^2)*asinh(c*x))/(3*c^3*sqrt(d + c^2*d*x^2)) - (2*b*x^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(9*c*sqrt(d + c^2*d*x^2)) - (2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(3*c^4*d) + (x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(3*c^2*d)]
    @test_int [(x^2*(a + b*asinh(c*x))^2)/sqrt(d + c^2*d*x^2), x, 5, (b^2*x*(1 + c^2*x^2))/(4*c^2*sqrt(d + c^2*d*x^2)) - (b^2*sqrt(1 + c^2*x^2)*asinh(c*x))/(4*c^3*sqrt(d + c^2*d*x^2)) - (b*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2*c*sqrt(d + c^2*d*x^2)) + (x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*c^2*d) - (sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^3)/(6*b*c^3*sqrt(d + c^2*d*x^2))]
    @test_int [(x*(a + b*asinh(c*x))^2)/sqrt(d + c^2*d*x^2), x, 4, (-2*a*b*x*sqrt(1 + c^2*x^2))/(c*sqrt(d + c^2*d*x^2)) + (2*b^2*(1 + c^2*x^2))/(c^2*sqrt(d + c^2*d*x^2)) - (2*b^2*x*sqrt(1 + c^2*x^2)*asinh(c*x))/(c*sqrt(d + c^2*d*x^2)) + (sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(c^2*d)]
    @test_int [(a + b*asinh(c*x))^2/sqrt(d + c^2*d*x^2), x, 1, (sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^3)/(3*b*c*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))^2/(x*sqrt(d + c^2*d*x^2)), x, 8, (-2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2*atanh(ℯ^asinh(c*x)))/sqrt(d + c^2*d*x^2) - (2*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*PolyLog(2, -ℯ^asinh(c*x)))/sqrt(d + c^2*d*x^2) + (2*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*PolyLog(2, ℯ^asinh(c*x)))/sqrt(d + c^2*d*x^2) + (2*b^2*sqrt(1 + c^2*x^2)*PolyLog(3, -ℯ^asinh(c*x)))/sqrt(d + c^2*d*x^2) - (2*b^2*sqrt(1 + c^2*x^2)*PolyLog(3, ℯ^asinh(c*x)))/sqrt(d + c^2*d*x^2)]
    @test_int [(a + b*asinh(c*x))^2/(x^2*sqrt(d + c^2*d*x^2)), x, 6, (c*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/sqrt(d + c^2*d*x^2) - (sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(d*x) + (2*b*c*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*log(1 - ℯ^(-2*asinh(c*x))))/sqrt(d + c^2*d*x^2) - (b^2*c*sqrt(1 + c^2*x^2)*PolyLog(2, ℯ^(-2*asinh(c*x))))/sqrt(d + c^2*d*x^2)]
    @test_int [(a + b*asinh(c*x))^2/(x^3*sqrt(d + c^2*d*x^2)), x, 13, -((b*c*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(x*sqrt(d + c^2*d*x^2))) - (sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*d*x^2) + (c^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2*atanh(ℯ^asinh(c*x)))/sqrt(d + c^2*d*x^2) - (b^2*c^2*sqrt(1 + c^2*x^2)*atanh(sqrt(1 + c^2*x^2)))/sqrt(d + c^2*d*x^2) + (b*c^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*PolyLog(2, -ℯ^asinh(c*x)))/sqrt(d + c^2*d*x^2) - (b*c^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*PolyLog(2, ℯ^asinh(c*x)))/sqrt(d + c^2*d*x^2) - (b^2*c^2*sqrt(1 + c^2*x^2)*PolyLog(3, -ℯ^asinh(c*x)))/sqrt(d + c^2*d*x^2) + (b^2*c^2*sqrt(1 + c^2*x^2)*PolyLog(3, ℯ^asinh(c*x)))/sqrt(d + c^2*d*x^2)]
    @test_int [(a + b*asinh(c*x))^2/(x^4*sqrt(d + c^2*d*x^2)), x, 9, -((b^2*c^2*(1 + c^2*x^2))/(3*x*sqrt(d + c^2*d*x^2))) - (b*c*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(3*x^2*sqrt(d + c^2*d*x^2)) - (2*c^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(3*sqrt(d + c^2*d*x^2)) - (sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(3*d*x^3) + (2*c^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(3*d*x) - (4*b*c^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*log(1 - ℯ^(-2*asinh(c*x))))/(3*sqrt(d + c^2*d*x^2)) + (2*b^2*c^3*sqrt(1 + c^2*x^2)*PolyLog(2, ℯ^(-2*asinh(c*x))))/(3*sqrt(d + c^2*d*x^2))]

    @test_int [(x^5*(a + b*asinh(c*x))^2)/(d + c^2*d*x^2)^(3/2), x, 22, (16*a*b*x*sqrt(1 + c^2*x^2))/(3*c^5*d*sqrt(d + c^2*d*x^2)) - (32*b^2*(1 + c^2*x^2))/(9*c^6*d*sqrt(d + c^2*d*x^2)) + (2*b^2*(1 + c^2*x^2)^2)/(27*c^6*d*sqrt(d + c^2*d*x^2)) + (16*b^2*x*sqrt(1 + c^2*x^2)*asinh(c*x))/(3*c^5*d*sqrt(d + c^2*d*x^2)) - (2*b*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c^5*d*sqrt(d + c^2*d*x^2)) - (2*b*x^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(9*c^3*d*sqrt(d + c^2*d*x^2)) - (x^4*(a + b*asinh(c*x))^2)/(c^2*d*sqrt(d + c^2*d*x^2)) - (8*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(3*c^6*d^2) + (4*x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(3*c^4*d^2) + (4*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c^6*d*sqrt(d + c^2*d*x^2)) - (2*im*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^6*d*sqrt(d + c^2*d*x^2)) + (2*im*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, im*ℯ^asinh(c*x)))/(c^6*d*sqrt(d + c^2*d*x^2))]
    @test_int [(x^4*(a + b*asinh(c*x))^2)/(d + c^2*d*x^2)^(3/2), x, 14, (b^2*x*(1 + c^2*x^2))/(4*c^4*d*sqrt(d + c^2*d*x^2)) - (b^2*sqrt(1 + c^2*x^2)*asinh(c*x))/(4*c^5*d*sqrt(d + c^2*d*x^2)) - (b*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2*c^3*d*sqrt(d + c^2*d*x^2)) - (x^3*(a + b*asinh(c*x))^2)/(c^2*d*sqrt(d + c^2*d*x^2)) + (sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c^5*d*sqrt(d + c^2*d*x^2)) + (3*x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2*c^4*d^2) - (sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^3)/(2*b*c^5*d*sqrt(d + c^2*d*x^2)) - (2*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(c^5*d*sqrt(d + c^2*d*x^2)) - (b^2*sqrt(1 + c^2*x^2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(c^5*d*sqrt(d + c^2*d*x^2))]
    @test_int [(x^3*(a + b*asinh(c*x))^2)/(d + c^2*d*x^2)^(3/2), x, 13, (-4*a*b*x*sqrt(1 + c^2*x^2))/(c^3*d*sqrt(d + c^2*d*x^2)) + (2*b^2*(1 + c^2*x^2))/(c^4*d*sqrt(d + c^2*d*x^2)) - (4*b^2*x*sqrt(1 + c^2*x^2)*asinh(c*x))/(c^3*d*sqrt(d + c^2*d*x^2)) + (2*b*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c^3*d*sqrt(d + c^2*d*x^2)) - (x^2*(a + b*asinh(c*x))^2)/(c^2*d*sqrt(d + c^2*d*x^2)) + (2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(c^4*d^2) - (4*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c^4*d*sqrt(d + c^2*d*x^2)) + ((2*im)*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^4*d*sqrt(d + c^2*d*x^2)) - ((2*im)*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, im*ℯ^asinh(c*x)))/(c^4*d*sqrt(d + c^2*d*x^2))]
    @test_int [(x^2*(a + b*asinh(c*x))^2)/(d + c^2*d*x^2)^(3/2), x, 7, -((x*(a + b*asinh(c*x))^2)/(c^2*d*sqrt(d + c^2*d*x^2))) - (sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c^3*d*sqrt(d + c^2*d*x^2)) + (sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^3)/(3*b*c^3*d*sqrt(d + c^2*d*x^2)) + (2*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(c^3*d*sqrt(d + c^2*d*x^2)) + (b^2*sqrt(1 + c^2*x^2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(c^3*d*sqrt(d + c^2*d*x^2))]
    @test_int [(x*(a + b*asinh(c*x))^2)/(d + c^2*d*x^2)^(3/2), x, 7, -((a + b*asinh(c*x))^2/(c^2*d*sqrt(d + c^2*d*x^2))) + (4*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c^2*d*sqrt(d + c^2*d*x^2)) - ((2*im)*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^2*d*sqrt(d + c^2*d*x^2)) + ((2*im)*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, im*ℯ^asinh(c*x)))/(c^2*d*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))^2/(d + c^2*d*x^2)^(3/2), x, 6, (x*(a + b*asinh(c*x))^2)/(d*sqrt(d + c^2*d*x^2)) + (sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*d*sqrt(d + c^2*d*x^2)) - (2*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(c*d*sqrt(d + c^2*d*x^2)) - (b^2*sqrt(1 + c^2*x^2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(c*d*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))^2/(x*(d + c^2*d*x^2)^(3/2)), x, 15, (a + b*asinh(c*x))^2/(d*sqrt(d + c^2*d*x^2)) - (4*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) - (2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2*atanh(ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) - (2*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*PolyLog(2, -ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) + ((2*im)*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) - ((2*im)*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, im*ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) + (2*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*PolyLog(2, ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) + (2*b^2*sqrt(1 + c^2*x^2)*PolyLog(3, -ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) - (2*b^2*sqrt(1 + c^2*x^2)*PolyLog(3, ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))^2/(x^2*(d + c^2*d*x^2)^(3/2)), x, 14, -((a + b*asinh(c*x))^2/(d*x*sqrt(d + c^2*d*x^2))) - (2*c^2*x*(a + b*asinh(c*x))^2)/(d*sqrt(d + c^2*d*x^2)) - (2*c*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(d*sqrt(d + c^2*d*x^2)) - (4*b*c*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atanh(ℯ^(2*asinh(c*x))))/(d*sqrt(d + c^2*d*x^2)) + (4*b*c*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(d*sqrt(d + c^2*d*x^2)) + (b^2*c*sqrt(1 + c^2*x^2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(d*sqrt(d + c^2*d*x^2)) + (b^2*c*sqrt(1 + c^2*x^2)*PolyLog(2, ℯ^(2*asinh(c*x))))/(d*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))^2/(x^3*(d + c^2*d*x^2)^(3/2)), x, 26, -((b*c*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(d*x*sqrt(d + c^2*d*x^2))) - (3*c^2*(a + b*asinh(c*x))^2)/(2*d*sqrt(d + c^2*d*x^2)) - (a + b*asinh(c*x))^2/(2*d*x^2*sqrt(d + c^2*d*x^2)) + (4*b*c^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) + (3*c^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2*atanh(ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) - (b^2*c^2*sqrt(1 + c^2*x^2)*atanh(sqrt(1 + c^2*x^2)))/(d*sqrt(d + c^2*d*x^2)) + (3*b*c^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*PolyLog(2, -ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) - ((2*im)*b^2*c^2*sqrt(1 + c^2*x^2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) + ((2*im)*b^2*c^2*sqrt(1 + c^2*x^2)*PolyLog(2, im*ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) - (3*b*c^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*PolyLog(2, ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) - (3*b^2*c^2*sqrt(1 + c^2*x^2)*PolyLog(3, -ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2)) + (3*b^2*c^2*sqrt(1 + c^2*x^2)*PolyLog(3, ℯ^asinh(c*x)))/(d*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))^2/(x^4*(d + c^2*d*x^2)^(3/2)), x, 24, -(b^2*c^2*(1 + c^2*x^2))/(3*d*x*sqrt(d + c^2*d*x^2)) - (b*c*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(3*d*x^2*sqrt(d + c^2*d*x^2)) - (a + b*asinh(c*x))^2/(3*d*x^3*sqrt(d + c^2*d*x^2)) + (4*c^2*(a + b*asinh(c*x))^2)/(3*d*x*sqrt(d + c^2*d*x^2)) + (8*c^4*x*(a + b*asinh(c*x))^2)/(3*d*sqrt(d + c^2*d*x^2)) + (8*c^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(3*d*sqrt(d + c^2*d*x^2)) + (20*b*c^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atanh(ℯ^(2*asinh(c*x))))/(3*d*sqrt(d + c^2*d*x^2)) - (16*b*c^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(3*d*sqrt(d + c^2*d*x^2)) - (b^2*c^3*sqrt(1 + c^2*x^2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(d*sqrt(d + c^2*d*x^2)) - (5*b^2*c^3*sqrt(1 + c^2*x^2)*PolyLog(2, ℯ^(2*asinh(c*x))))/(3*d*sqrt(d + c^2*d*x^2))]

    @test_int [(x^5*(a + b*asinh(c*x))^2)/(d + c^2*d*x^2)^(5/2), x, 26, b^2/(3*c^6*d^2*sqrt(d + c^2*d*x^2)) - (16*a*b*x*sqrt(1 + c^2*x^2))/(3*c^5*d^2*sqrt(d + c^2*d*x^2)) + (2*b^2*(1 + c^2*x^2))/(c^6*d^2*sqrt(d + c^2*d*x^2)) - (16*b^2*x*sqrt(1 + c^2*x^2)*asinh(c*x))/(3*c^5*d^2*sqrt(d + c^2*d*x^2)) - (b*x^3*(a + b*asinh(c*x)))/(3*c^3*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) + (11*b*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(3*c^5*d^2*sqrt(d + c^2*d*x^2)) - (x^4*(a + b*asinh(c*x))^2)/(3*c^2*d*(d + c^2*d*x^2)^(3/2)) - (4*x^2*(a + b*asinh(c*x))^2)/(3*c^4*d^2*sqrt(d + c^2*d*x^2)) + (8*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(3*c^6*d^3) - (22*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(3*c^6*d^2*sqrt(d + c^2*d*x^2)) + (((11*im)/3)*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^6*d^2*sqrt(d + c^2*d*x^2)) - (((11*im)/3)*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, im*ℯ^asinh(c*x)))/(c^6*d^2*sqrt(d + c^2*d*x^2))]
    @test_int [(x^4*(a + b*asinh(c*x))^2)/(d + c^2*d*x^2)^(5/2), x, 16, -(b^2*x)/(3*c^4*d^2*sqrt(d + c^2*d*x^2)) + (b^2*sqrt(1 + c^2*x^2)*asinh(c*x))/(3*c^5*d^2*sqrt(d + c^2*d*x^2)) - (b*x^2*(a + b*asinh(c*x)))/(3*c^3*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) - (x^3*(a + b*asinh(c*x))^2)/(3*c^2*d*(d + c^2*d*x^2)^(3/2)) - (x*(a + b*asinh(c*x))^2)/(c^4*d^2*sqrt(d + c^2*d*x^2)) - (4*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(3*c^5*d^2*sqrt(d + c^2*d*x^2)) + (sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^3)/(3*b*c^5*d^2*sqrt(d + c^2*d*x^2)) + (8*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(3*c^5*d^2*sqrt(d + c^2*d*x^2)) + (4*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(3*c^5*d^2*sqrt(d + c^2*d*x^2))]
    @test_int [(x^3*(a + b*asinh(c*x))^2)/(d + c^2*d*x^2)^(5/2), x, 16, -b^2/(3*c^4*d^2*sqrt(d + c^2*d*x^2)) - (b*x*(a + b*asinh(c*x)))/(3*c^3*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) - (x^2*(a + b*asinh(c*x))^2)/(3*c^2*d*(d + c^2*d*x^2)^(3/2)) - (2*(a + b*asinh(c*x))^2)/(3*c^4*d^2*sqrt(d + c^2*d*x^2)) + (10*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(3*c^4*d^2*sqrt(d + c^2*d*x^2)) - (((5*im)/3)*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^4*d^2*sqrt(d + c^2*d*x^2)) + (((5*im)/3)*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, im*ℯ^asinh(c*x)))/(c^4*d^2*sqrt(d + c^2*d*x^2))]
    @test_int [(x^2*(a + b*asinh(c*x))^2)/(d + c^2*d*x^2)^(5/2), x, 9, (b^2*x)/(3*c^2*d^2*sqrt(d + c^2*d*x^2)) - (b^2*sqrt(1 + c^2*x^2)*asinh(c*x))/(3*c^3*d^2*sqrt(d + c^2*d*x^2)) + (b*x^2*(a + b*asinh(c*x)))/(3*c*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) + (x^3*(a + b*asinh(c*x))^2)/(3*d*(d + c^2*d*x^2)^(3/2)) + (sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(3*c^3*d^2*sqrt(d + c^2*d*x^2)) - (2*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(3*c^3*d^2*sqrt(d + c^2*d*x^2)) - (b^2*sqrt(1 + c^2*x^2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(3*c^3*d^2*sqrt(d + c^2*d*x^2))]
    @test_int [(x*(a + b*asinh(c*x))^2)/(d + c^2*d*x^2)^(5/2), x, 9, b^2/(3*c^2*d^2*sqrt(d + c^2*d*x^2)) + (b*x*(a + b*asinh(c*x)))/(3*c*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) - (a + b*asinh(c*x))^2/(3*c^2*d*(d + c^2*d*x^2)^(3/2)) + (2*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(3*c^2*d^2*sqrt(d + c^2*d*x^2)) - ((im/3)*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c^2*d^2*sqrt(d + c^2*d*x^2)) + ((im/3)*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, im*ℯ^asinh(c*x)))/(c^2*d^2*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))^2/(d + c^2*d*x^2)^(5/2), x, 9, -(b^2*x)/(3*d^2*sqrt(d + c^2*d*x^2)) + (b*(a + b*asinh(c*x)))/(3*c*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) + (x*(a + b*asinh(c*x))^2)/(3*d*(d + c^2*d*x^2)^(3/2)) + (2*x*(a + b*asinh(c*x))^2)/(3*d^2*sqrt(d + c^2*d*x^2)) + (2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(3*c*d^2*sqrt(d + c^2*d*x^2)) - (4*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(3*c*d^2*sqrt(d + c^2*d*x^2)) - (2*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(3*c*d^2*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))^2/(x*(d + c^2*d*x^2)^(5/2)), x, 24, -b^2/(3*d^2*sqrt(d + c^2*d*x^2)) - (b*c*x*(a + b*asinh(c*x)))/(3*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) + (a + b*asinh(c*x))^2/(3*d*(d + c^2*d*x^2)^(3/2)) + (a + b*asinh(c*x))^2/(d^2*sqrt(d + c^2*d*x^2)) - (14*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(3*d^2*sqrt(d + c^2*d*x^2)) - (2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2*atanh(ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2)) - (2*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*PolyLog(2, -ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2)) + (((7*im)/3)*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2)) - (((7*im)/3)*b^2*sqrt(1 + c^2*x^2)*PolyLog(2, im*ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2)) + (2*b*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*PolyLog(2, ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2)) + (2*b^2*sqrt(1 + c^2*x^2)*PolyLog(3, -ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2)) - (2*b^2*sqrt(1 + c^2*x^2)*PolyLog(3, ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))^2/(x^2*(d + c^2*d*x^2)^(5/2)), x, 19, (b^2*c^2*x)/(3*d^2*sqrt(d + c^2*d*x^2)) - (b*c*(a + b*asinh(c*x)))/(3*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) - (a + b*asinh(c*x))^2/(d*x*(d + c^2*d*x^2)^(3/2)) - (4*c^2*x*(a + b*asinh(c*x))^2)/(3*d*(d + c^2*d*x^2)^(3/2)) - (8*c^2*x*(a + b*asinh(c*x))^2)/(3*d^2*sqrt(d + c^2*d*x^2)) - (8*c*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(3*d^2*sqrt(d + c^2*d*x^2)) - (4*b*c*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atanh(ℯ^(2*asinh(c*x))))/(d^2*sqrt(d + c^2*d*x^2)) + (16*b*c*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(3*d^2*sqrt(d + c^2*d*x^2)) + (5*b^2*c*sqrt(1 + c^2*x^2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(3*d^2*sqrt(d + c^2*d*x^2)) + (b^2*c*sqrt(1 + c^2*x^2)*PolyLog(2, ℯ^(2*asinh(c*x))))/(d^2*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))^2/(x^3*(d + c^2*d*x^2)^(5/2)), x, 38, (b^2*c^2)/(3*d^2*sqrt(d + c^2*d*x^2)) - (b*c*(a + b*asinh(c*x)))/(d^2*x*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) - (2*b*c^3*x*(a + b*asinh(c*x)))/(3*d^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) - (5*c^2*(a + b*asinh(c*x))^2)/(6*d*(d + c^2*d*x^2)^(3/2)) - (a + b*asinh(c*x))^2/(2*d*x^2*(d + c^2*d*x^2)^(3/2)) - (5*c^2*(a + b*asinh(c*x))^2)/(2*d^2*sqrt(d + c^2*d*x^2)) + (26*b*c^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(3*d^2*sqrt(d + c^2*d*x^2)) + (5*c^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2*atanh(ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2)) - (b^2*c^2*sqrt(1 + c^2*x^2)*atanh(sqrt(1 + c^2*x^2)))/(d^2*sqrt(d + c^2*d*x^2)) + (5*b*c^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*PolyLog(2, -ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2)) - (((13*im)/3)*b^2*c^2*sqrt(1 + c^2*x^2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2)) + (((13*im)/3)*b^2*c^2*sqrt(1 + c^2*x^2)*PolyLog(2, im*ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2)) - (5*b*c^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*PolyLog(2, ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2)) - (5*b^2*c^2*sqrt(1 + c^2*x^2)*PolyLog(3, -ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2)) + (5*b^2*c^2*sqrt(1 + c^2*x^2)*PolyLog(3, ℯ^asinh(c*x)))/(d^2*sqrt(d + c^2*d*x^2))]
    @test_int [(a + b*asinh(c*x))^2/(x^4*(d + c^2*d*x^2)^(5/2)), x, 32, -(b^2*c^2)/(3*d^2*x*sqrt(d + c^2*d*x^2)) - (2*b^2*c^4*x)/(3*d^2*sqrt(d + c^2*d*x^2)) - (b*c*(a + b*asinh(c*x)))/(3*d^2*x^2*sqrt(1 + c^2*x^2)*sqrt(d + c^2*d*x^2)) - (a + b*asinh(c*x))^2/(3*d*x^3*(d + c^2*d*x^2)^(3/2)) + (2*c^2*(a + b*asinh(c*x))^2)/(d*x*(d + c^2*d*x^2)^(3/2)) + (8*c^4*x*(a + b*asinh(c*x))^2)/(3*d*(d + c^2*d*x^2)^(3/2)) + (16*c^4*x*(a + b*asinh(c*x))^2)/(3*d^2*sqrt(d + c^2*d*x^2)) + (16*c^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(3*d^2*sqrt(d + c^2*d*x^2)) + (32*b*c^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*atanh(ℯ^(2*asinh(c*x))))/(3*d^2*sqrt(d + c^2*d*x^2)) - (32*b*c^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(3*d^2*sqrt(d + c^2*d*x^2)) - (8*b^2*c^3*sqrt(1 + c^2*x^2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(3*d^2*sqrt(d + c^2*d*x^2)) - (8*b^2*c^3*sqrt(1 + c^2*x^2)*PolyLog(2, ℯ^(2*asinh(c*x))))/(3*d^2*sqrt(d + c^2*d*x^2))]

    @test_int [asinh(a*x)^2/(c + a^2*c*x^2)^(7/2), x, 13, -x/(3*c^3*sqrt(c + a^2*c*x^2)) - x/(30*c^3*(1 + a^2*x^2)*sqrt(c + a^2*c*x^2)) + asinh(a*x)/(10*a*c^3*(1 + a^2*x^2)^(3/2)*sqrt(c + a^2*c*x^2)) + (4*asinh(a*x))/(15*a*c^3*sqrt(1 + a^2*x^2)*sqrt(c + a^2*c*x^2)) + (x*asinh(a*x)^2)/(5*c*(c + a^2*c*x^2)^(5/2)) + (4*x*asinh(a*x)^2)/(15*c^2*(c + a^2*c*x^2)^(3/2)) + (8*x*asinh(a*x)^2)/(15*c^3*sqrt(c + a^2*c*x^2)) + (8*sqrt(1 + a^2*x^2)*asinh(a*x)^2)/(15*a*c^3*sqrt(c + a^2*c*x^2)) - (16*sqrt(1 + a^2*x^2)*asinh(a*x)*log(1 + ℯ^(2*asinh(a*x))))/(15*a*c^3*sqrt(c + a^2*c*x^2)) - (8*sqrt(1 + a^2*x^2)*PolyLog(2, -ℯ^(2*asinh(a*x))))/(15*a*c^3*sqrt(c + a^2*c*x^2))]

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

    @test_int [x^m*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2, x, 12, If(13>=8, (10*b^2*c^2*d^2*x^(3 + m)*sqrt(d + c^2*d*x^2))/((4 + m)^3*(6 + m)) + (2*b^2*c^2*d^2*(52 + 15*m + m^2)*x^(3 + m)*sqrt(d + c^2*d*x^2))/((4 + m)^2*(6 + m)^3) + (2*b^2*c^4*d^2*x^(5 + m)*sqrt(d + c^2*d*x^2))/(6 + m)^3 - (30*b*c*d^2*x^(2 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((2 + m)^2*(4 + m)*(6 + m)*sqrt(1 + c^2*x^2)) - (10*b*c*d^2*x^(2 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((6 + m)*(8 + 6*m + m^2)*sqrt(1 + c^2*x^2)) - (2*b*c*d^2*x^(2 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((12 + 8*m + m^2)*sqrt(1 + c^2*x^2)) - (10*b*c^3*d^2*x^(4 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((4 + m)^2*(6 + m)*sqrt(1 + c^2*x^2)) - (4*b*c^3*d^2*x^(4 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((4 + m)*(6 + m)*sqrt(1 + c^2*x^2)) - (2*b*c^5*d^2*x^(6 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((6 + m)^2*sqrt(1 + c^2*x^2)) + (15*d^2*x^(1 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/((6 + m)*(8 + 6*m + m^2)) + (5*d*x^(1 + m)*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/((4 + m)*(6 + m)) + (x^(1 + m)*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2)/(6 + m) + (30*b^2*c^2*d^2*x^(3 + m)*sqrt(d + c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, (-c^2)*x^2))/((2 + m)^2*(3 + m)*(4 + m)*(6 + m)*sqrt(1 + c^2*x^2)) + (10*b^2*c^2*d^2*(10 + 3*m)*x^(3 + m)*sqrt(d + c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, (-c^2)*x^2))/((2 + m)*(3 + m)*(4 + m)^3*(6 + m)*sqrt(1 + c^2*x^2)) + (2*b^2*c^2*d^2*(264 + 130*m + 15*m^2)*x^(3 + m)*sqrt(d + c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, (-c^2)*x^2))/((2 + m)*(3 + m)*(4 + m)^2*(6 + m)^3*sqrt(1 + c^2*x^2)) + (15*d^3*Unintegrable((x^m*(a + b*asinh(c*x))^2)/sqrt(d + c^2*d*x^2), x))/((6 + m)*(8 + 6*m + m^2)), (10*b^2*c^2*d^2*x^(3 + m)*sqrt(d + c^2*d*x^2))/((4 + m)^3*(6 + m)) + (2*b^2*c^2*d^2*(52 + 15*m + m^2)*x^(3 + m)*sqrt(d + c^2*d*x^2))/((4 + m)^2*(6 + m)^3) + (2*b^2*c^4*d^2*x^(5 + m)*sqrt(d + c^2*d*x^2))/(6 + m)^3 - (30*b*c*d^2*x^(2 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((2 + m)^2*(4 + m)*(6 + m)*sqrt(1 + c^2*x^2)) - (10*b*c*d^2*x^(2 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((6 + m)*(8 + 6*m + m^2)*sqrt(1 + c^2*x^2)) - (2*b*c*d^2*x^(2 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((12 + 8*m + m^2)*sqrt(1 + c^2*x^2)) - (10*b*c^3*d^2*x^(4 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((4 + m)^2*(6 + m)*sqrt(1 + c^2*x^2)) - (4*b*c^3*d^2*x^(4 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((4 + m)*(6 + m)*sqrt(1 + c^2*x^2)) - (2*b*c^5*d^2*x^(6 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((6 + m)^2*sqrt(1 + c^2*x^2)) + (15*d^2*x^(1 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/((6 + m)*(8 + 6*m + m^2)) + (5*d*x^(1 + m)*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/((4 + m)*(6 + m)) + (x^(1 + m)*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^2)/(6 + m) + (10*b^2*c^2*d^2*(10 + 3*m)*x^(3 + m)*sqrt(d + c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, (-c^2)*x^2))/((4 + m)^3*(6 + m)*(6 + 5*m + m^2)*sqrt(1 + c^2*x^2)) + (30*b^2*c^2*d^2*x^(3 + m)*sqrt(d + c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, (-c^2)*x^2))/((2 + m)^2*(6 + m)*(12 + 7*m + m^2)*sqrt(1 + c^2*x^2)) + (2*b^2*c^2*d^2*(264 + 130*m + 15*m^2)*x^(3 + m)*sqrt(d + c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, (-c^2)*x^2))/((4 + m)^2*(6 + m)^3*(6 + 5*m + m^2)*sqrt(1 + c^2*x^2)) + (15*d^3*Unintegrable((x^m*(a + b*asinh(c*x))^2)/sqrt(d + c^2*d*x^2), x))/((6 + m)*(8 + 6*m + m^2)))]
    @test_int [x^m*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2, x, 7, If(13>=8, (2*b^2*c^2*d*x^(3 + m)*sqrt(d + c^2*d*x^2))/(4 + m)^3 - (6*b*c*d*x^(2 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((2 + m)^2*(4 + m)*sqrt(1 + c^2*x^2)) - (2*b*c*d*x^(2 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((8 + 6*m + m^2)*sqrt(1 + c^2*x^2)) - (2*b*c^3*d*x^(4 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((4 + m)^2*sqrt(1 + c^2*x^2)) + (3*d*x^(1 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(8 + 6*m + m^2) + (x^(1 + m)*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(4 + m) + (6*b^2*c^2*d*x^(3 + m)*sqrt(d + c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, (-c^2)*x^2))/((2 + m)^2*(3 + m)*(4 + m)*sqrt(1 + c^2*x^2)) + (2*b^2*c^2*d*(10 + 3*m)*x^(3 + m)*sqrt(d + c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, (-c^2)*x^2))/((2 + m)*(3 + m)*(4 + m)^3*sqrt(1 + c^2*x^2)) + (3*d^2*Unintegrable((x^m*(a + b*asinh(c*x))^2)/sqrt(d + c^2*d*x^2), x))/(8 + 6*m + m^2), (2*b^2*c^2*d*x^(3 + m)*sqrt(d + c^2*d*x^2))/(4 + m)^3 - (6*b*c*d*x^(2 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((2 + m)^2*(4 + m)*sqrt(1 + c^2*x^2)) - (2*b*c*d*x^(2 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((8 + 6*m + m^2)*sqrt(1 + c^2*x^2)) - (2*b*c^3*d*x^(4 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((4 + m)^2*sqrt(1 + c^2*x^2)) + (3*d*x^(1 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(8 + 6*m + m^2) + (x^(1 + m)*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(4 + m) + (2*b^2*c^2*d*(10 + 3*m)*x^(3 + m)*sqrt(d + c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, (-c^2)*x^2))/((4 + m)^3*(6 + 5*m + m^2)*sqrt(1 + c^2*x^2)) + (6*b^2*c^2*d*x^(3 + m)*sqrt(d + c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, (-c^2)*x^2))/((2 + m)^2*(12 + 7*m + m^2)*sqrt(1 + c^2*x^2)) + (3*d^2*Unintegrable((x^m*(a + b*asinh(c*x))^2)/sqrt(d + c^2*d*x^2), x))/(8 + 6*m + m^2))]
    @test_int [x^m*(d + c^2*d*x^2)^(1/2)*(a + b*asinh(c*x))^2, x, 3, -((2*b*c*x^(2 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x)))/((2 + m)^2*sqrt(1 + c^2*x^2))) + (x^(1 + m)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^2)/(2 + m) + (2*b^2*c^2*x^(3 + m)*sqrt(d + c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, (-c^2)*x^2))/((2 + m)^2*(3 + m)*sqrt(1 + c^2*x^2)) + (d*Unintegrable((x^m*(a + b*asinh(c*x))^2)/sqrt(d + c^2*d*x^2), x))/(2 + m)]
    @test_int [x^m*(a + b*asinh(c*x))^2/(d + c^2*d*x^2)^(1/2), x, 0, Unintegrable((x^m*(a + b*asinh(c*x))^2)/sqrt(d + c^2*d*x^2), x)]
    @test_int [x^m*(a + b*asinh(c*x))^2/(d + c^2*d*x^2)^(3/2), x, 0, Unintegrable((x^m*(a + b*asinh(c*x))^2)/(d + c^2*d*x^2)^(3/2), x)]
    @test_int [x^m*(a + b*asinh(c*x))^2/(d + c^2*d*x^2)^(5/2), x, 0, Unintegrable((x^m*(a + b*asinh(c*x))^2)/(d + c^2*d*x^2)^(5/2), x)]

    @test_int [(x^m*asinh(a*x)^2)/sqrt(1 + a^2*x^2), x, 0, Unintegrable((x^m*asinh(a*x)^2)/sqrt(1 + a^2*x^2), x)]

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

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

    @test_int [(c + a^2*c*x^2)^3*asinh(a*x)^3, x, 24, (-413312*c^3*sqrt(1 + a^2*x^2))/(128625*a) - (30256*c^3*(1 + a^2*x^2)^(3/2))/(385875*a) - (2664*c^3*(1 + a^2*x^2)^(5/2))/(214375*a) - (6*c^3*(1 + a^2*x^2)^(7/2))/(2401*a) + (4322*c^3*x*asinh(a*x))/1225 + (1514*a^2*c^3*x^3*asinh(a*x))/3675 + (702*a^4*c^3*x^5*asinh(a*x))/6125 + (6*a^6*c^3*x^7*asinh(a*x))/343 - (48*c^3*sqrt(1 + a^2*x^2)*asinh(a*x)^2)/(35*a) - (8*c^3*(1 + a^2*x^2)^(3/2)*asinh(a*x)^2)/(35*a) - (18*c^3*(1 + a^2*x^2)^(5/2)*asinh(a*x)^2)/(175*a) - (3*c^3*(1 + a^2*x^2)^(7/2)*asinh(a*x)^2)/(49*a) + (16*c^3*x*asinh(a*x)^3)/35 + (8*c^3*x*(1 + a^2*x^2)*asinh(a*x)^3)/35 + (6*c^3*x*(1 + a^2*x^2)^2*asinh(a*x)^3)/35 + (c^3*x*(1 + a^2*x^2)^3*asinh(a*x)^3)/7]
    @test_int [(c + a^2*c*x^2)^2*asinh(a*x)^3, x, 17, (-4144*c^2*sqrt(1 + a^2*x^2))/(1125*a) - (272*c^2*(1 + a^2*x^2)^(3/2))/(3375*a) - (6*c^2*(1 + a^2*x^2)^(5/2))/(625*a) + (298*c^2*x*asinh(a*x))/75 + (76*a^2*c^2*x^3*asinh(a*x))/225 + (6*a^4*c^2*x^5*asinh(a*x))/125 - (8*c^2*sqrt(1 + a^2*x^2)*asinh(a*x)^2)/(5*a) - (4*c^2*(1 + a^2*x^2)^(3/2)*asinh(a*x)^2)/(15*a) - (3*c^2*(1 + a^2*x^2)^(5/2)*asinh(a*x)^2)/(25*a) + (8*c^2*x*asinh(a*x)^3)/15 + (4*c^2*x*(1 + a^2*x^2)*asinh(a*x)^3)/15 + (c^2*x*(1 + a^2*x^2)^2*asinh(a*x)^3)/5]
    @test_int [(c + a^2*c*x^2)*asinh(a*x)^3, x, 10, (-40*c*sqrt(1 + a^2*x^2))/(9*a) - (2*c*(1 + a^2*x^2)^(3/2))/(27*a) + (14*c*x*asinh(a*x))/3 + (2*a^2*c*x^3*asinh(a*x))/9 - (2*c*sqrt(1 + a^2*x^2)*asinh(a*x)^2)/a - (c*(1 + a^2*x^2)^(3/2)*asinh(a*x)^2)/(3*a) + (2*c*x*asinh(a*x)^3)/3 + (c*x*(1 + a^2*x^2)*asinh(a*x)^3)/3]
    @test_int [asinh(a*x)^3/(c + a^2*c*x^2), x, 10, (2*asinh(a*x)^3*atan(ℯ^asinh(a*x)))/(a*c) - ((3*im)*asinh(a*x)^2*PolyLog(2, (-im)*ℯ^asinh(a*x)))/(a*c) + ((3*im)*asinh(a*x)^2*PolyLog(2, im*ℯ^asinh(a*x)))/(a*c) + ((6*im)*asinh(a*x)*PolyLog(3, (-im)*ℯ^asinh(a*x)))/(a*c) - ((6*im)*asinh(a*x)*PolyLog(3, im*ℯ^asinh(a*x)))/(a*c) - ((6*im)*PolyLog(4, (-im)*ℯ^asinh(a*x)))/(a*c) + ((6*im)*PolyLog(4, im*ℯ^asinh(a*x)))/(a*c)]
    @test_int [asinh(a*x)^3/(c + a^2*c*x^2)^2, x, 18, (3*asinh(a*x)^2)/(2*a*c^2*sqrt(1 + a^2*x^2)) + (x*asinh(a*x)^3)/(2*c^2*(1 + a^2*x^2)) - (6*asinh(a*x)*atan(ℯ^asinh(a*x)))/(a*c^2) + (asinh(a*x)^3*atan(ℯ^asinh(a*x)))/(a*c^2) + ((3*im)*PolyLog(2, (-im)*ℯ^asinh(a*x)))/(a*c^2) - (((3*im)/2)*asinh(a*x)^2*PolyLog(2, (-im)*ℯ^asinh(a*x)))/(a*c^2) - ((3*im)*PolyLog(2, im*ℯ^asinh(a*x)))/(a*c^2) + (((3*im)/2)*asinh(a*x)^2*PolyLog(2, im*ℯ^asinh(a*x)))/(a*c^2) + ((3*im)*asinh(a*x)*PolyLog(3, (-im)*ℯ^asinh(a*x)))/(a*c^2) - ((3*im)*asinh(a*x)*PolyLog(3, im*ℯ^asinh(a*x)))/(a*c^2) - ((3*im)*PolyLog(4, (-im)*ℯ^asinh(a*x)))/(a*c^2) + ((3*im)*PolyLog(4, im*ℯ^asinh(a*x)))/(a*c^2)]
    @test_int [asinh(a*x)^3/(c + a^2*c*x^2)^3, x, 28, -1/(4*a*c^3*sqrt(1 + a^2*x^2)) - (x*asinh(a*x))/(4*c^3*(1 + a^2*x^2)) + asinh(a*x)^2/(4*a*c^3*(1 + a^2*x^2)^(3/2)) + (9*asinh(a*x)^2)/(8*a*c^3*sqrt(1 + a^2*x^2)) + (x*asinh(a*x)^3)/(4*c^3*(1 + a^2*x^2)^2) + (3*x*asinh(a*x)^3)/(8*c^3*(1 + a^2*x^2)) - (5*asinh(a*x)*atan(ℯ^asinh(a*x)))/(a*c^3) + (3*asinh(a*x)^3*atan(ℯ^asinh(a*x)))/(4*a*c^3) + (((5*im)/2)*PolyLog(2, (-im)*ℯ^asinh(a*x)))/(a*c^3) - (((9*im)/8)*asinh(a*x)^2*PolyLog(2, (-im)*ℯ^asinh(a*x)))/(a*c^3) - (((5*im)/2)*PolyLog(2, im*ℯ^asinh(a*x)))/(a*c^3) + (((9*im)/8)*asinh(a*x)^2*PolyLog(2, im*ℯ^asinh(a*x)))/(a*c^3) + (((9*im)/4)*asinh(a*x)*PolyLog(3, (-im)*ℯ^asinh(a*x)))/(a*c^3) - (((9*im)/4)*asinh(a*x)*PolyLog(3, im*ℯ^asinh(a*x)))/(a*c^3) - (((9*im)/4)*PolyLog(4, (-im)*ℯ^asinh(a*x)))/(a*c^3) + (((9*im)/4)*PolyLog(4, im*ℯ^asinh(a*x)))/(a*c^3)]

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

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

    @test_int [(c + a^2*c*x^2)^(5/2)*asinh(a*x)^3, x, 24, (-865*a*c^2*x^2*sqrt(c + a^2*c*x^2))/(2304*sqrt(1 + a^2*x^2)) - (65*a^3*c^2*x^4*sqrt(c + a^2*c*x^2))/(2304*sqrt(1 + a^2*x^2)) - (c^2*(1 + a^2*x^2)^(5/2)*sqrt(c + a^2*c*x^2))/(216*a) + (245*c^2*x*sqrt(c + a^2*c*x^2)*asinh(a*x))/384 + (65*c^2*x*(1 + a^2*x^2)*sqrt(c + a^2*c*x^2)*asinh(a*x))/576 + (c^2*x*(1 + a^2*x^2)^2*sqrt(c + a^2*c*x^2)*asinh(a*x))/36 - (115*c^2*sqrt(c + a^2*c*x^2)*asinh(a*x)^2)/(768*a*sqrt(1 + a^2*x^2)) - (15*a*c^2*x^2*sqrt(c + a^2*c*x^2)*asinh(a*x)^2)/(32*sqrt(1 + a^2*x^2)) - (5*c^2*(1 + a^2*x^2)^(3/2)*sqrt(c + a^2*c*x^2)*asinh(a*x)^2)/(32*a) - (c^2*(1 + a^2*x^2)^(5/2)*sqrt(c + a^2*c*x^2)*asinh(a*x)^2)/(12*a) + (5*c^2*x*sqrt(c + a^2*c*x^2)*asinh(a*x)^3)/16 + (5*c*x*(c + a^2*c*x^2)^(3/2)*asinh(a*x)^3)/24 + (x*(c + a^2*c*x^2)^(5/2)*asinh(a*x)^3)/6 + (5*c^2*sqrt(c + a^2*c*x^2)*asinh(a*x)^4)/(64*a*sqrt(1 + a^2*x^2))]
    @test_int [(c + a^2*c*x^2)^(3/2)*asinh(a*x)^3, x, 14, (-51*a*c*x^2*sqrt(c + a^2*c*x^2))/(128*sqrt(1 + a^2*x^2)) - (3*a^3*c*x^4*sqrt(c + a^2*c*x^2))/(128*sqrt(1 + a^2*x^2)) + (45*c*x*sqrt(c + a^2*c*x^2)*asinh(a*x))/64 + (3*c*x*(1 + a^2*x^2)*sqrt(c + a^2*c*x^2)*asinh(a*x))/32 - (27*c*sqrt(c + a^2*c*x^2)*asinh(a*x)^2)/(128*a*sqrt(1 + a^2*x^2)) - (9*a*c*x^2*sqrt(c + a^2*c*x^2)*asinh(a*x)^2)/(16*sqrt(1 + a^2*x^2)) - (3*c*(1 + a^2*x^2)^(3/2)*sqrt(c + a^2*c*x^2)*asinh(a*x)^2)/(16*a) + (3*c*x*sqrt(c + a^2*c*x^2)*asinh(a*x)^3)/8 + (x*(c + a^2*c*x^2)^(3/2)*asinh(a*x)^3)/4 + (3*c*sqrt(c + a^2*c*x^2)*asinh(a*x)^4)/(32*a*sqrt(1 + a^2*x^2))]
    @test_int [sqrt(c + a^2*c*x^2)*asinh(a*x)^3, x, 6, (-3*a*x^2*sqrt(c + a^2*c*x^2))/(8*sqrt(1 + a^2*x^2)) + (3*x*sqrt(c + a^2*c*x^2)*asinh(a*x))/4 - (3*sqrt(c + a^2*c*x^2)*asinh(a*x)^2)/(8*a*sqrt(1 + a^2*x^2)) - (3*a*x^2*sqrt(c + a^2*c*x^2)*asinh(a*x)^2)/(4*sqrt(1 + a^2*x^2)) + (x*sqrt(c + a^2*c*x^2)*asinh(a*x)^3)/2 + (sqrt(c + a^2*c*x^2)*asinh(a*x)^4)/(8*a*sqrt(1 + a^2*x^2))]

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

    @test_int [asinh(a*x)^3/sqrt(c + a^2*c*x^2), x, 1, (sqrt(1 + a^2*x^2)*asinh(a*x)^4)/(4*a*sqrt(c + a^2*c*x^2))]
    @test_int [asinh(a*x)^3/(c + a^2*c*x^2)^(3/2), x, 7, (x*asinh(a*x)^3)/(c*sqrt(c + a^2*c*x^2)) + (sqrt(1 + a^2*x^2)*asinh(a*x)^3)/(a*c*sqrt(c + a^2*c*x^2)) - (3*sqrt(1 + a^2*x^2)*asinh(a*x)^2*log(1 + ℯ^(2*asinh(a*x))))/(a*c*sqrt(c + a^2*c*x^2)) - (3*sqrt(1 + a^2*x^2)*asinh(a*x)*PolyLog(2, -ℯ^(2*asinh(a*x))))/(a*c*sqrt(c + a^2*c*x^2)) + (3*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(2*asinh(a*x))))/(2*a*c*sqrt(c + a^2*c*x^2))]
    @test_int [asinh(a*x)^3/(c + a^2*c*x^2)^(5/2), x, 11, -((x*asinh(a*x))/(c^2*sqrt(c + a^2*c*x^2))) + asinh(a*x)^2/(2*a*c^2*sqrt(1 + a^2*x^2)*sqrt(c + a^2*c*x^2)) + (x*asinh(a*x)^3)/(3*c*(c + a^2*c*x^2)^(3/2)) + (2*x*asinh(a*x)^3)/(3*c^2*sqrt(c + a^2*c*x^2)) + (2*sqrt(1 + a^2*x^2)*asinh(a*x)^3)/(3*a*c^2*sqrt(c + a^2*c*x^2)) - (2*sqrt(1 + a^2*x^2)*asinh(a*x)^2*log(1 + ℯ^(2*asinh(a*x))))/(a*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(1 + a^2*x^2)*log(1 + a^2*x^2))/(2*a*c^2*sqrt(c + a^2*c*x^2)) - (2*sqrt(1 + a^2*x^2)*asinh(a*x)*PolyLog(2, -ℯ^(2*asinh(a*x))))/(a*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(2*asinh(a*x))))/(a*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [asinh(a*x)^3/(c + a^2*c*x^2)^(7/2), x, 17, -1/(20*a*c^3*sqrt(1 + a^2*x^2)*sqrt(c + a^2*c*x^2)) - (x*asinh(a*x))/(c^3*sqrt(c + a^2*c*x^2)) - (x*asinh(a*x))/(10*c^3*(1 + a^2*x^2)*sqrt(c + a^2*c*x^2)) + (3*asinh(a*x)^2)/(20*a*c^3*(1 + a^2*x^2)^(3/2)*sqrt(c + a^2*c*x^2)) + (2*asinh(a*x)^2)/(5*a*c^3*sqrt(1 + a^2*x^2)*sqrt(c + a^2*c*x^2)) + (x*asinh(a*x)^3)/(5*c*(c + a^2*c*x^2)^(5/2)) + (4*x*asinh(a*x)^3)/(15*c^2*(c + a^2*c*x^2)^(3/2)) + (8*x*asinh(a*x)^3)/(15*c^3*sqrt(c + a^2*c*x^2)) + (8*sqrt(1 + a^2*x^2)*asinh(a*x)^3)/(15*a*c^3*sqrt(c + a^2*c*x^2)) - (8*sqrt(1 + a^2*x^2)*asinh(a*x)^2*log(1 + ℯ^(2*asinh(a*x))))/(5*a*c^3*sqrt(c + a^2*c*x^2)) + (sqrt(1 + a^2*x^2)*log(1 + a^2*x^2))/(2*a*c^3*sqrt(c + a^2*c*x^2)) - (8*sqrt(1 + a^2*x^2)*asinh(a*x)*PolyLog(2, -ℯ^(2*asinh(a*x))))/(5*a*c^3*sqrt(c + a^2*c*x^2)) + (4*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(2*asinh(a*x))))/(5*a*c^3*sqrt(c + a^2*c*x^2))]

    @test_int [(x^m*asinh(a*x)^3)/sqrt(1 + a^2*x^2), x, 0, Unintegrable((x^m*asinh(a*x)^3)/sqrt(1 + a^2*x^2), x)]

    @test_int [(x^4*asinh(a*x)^3)/sqrt(1 + a^2*x^2), x, 13, (45*x^2)/(128*a^3) - (3*x^4)/(128*a) - (45*x*sqrt(1 + a^2*x^2)*asinh(a*x))/(64*a^4) + (3*x^3*sqrt(1 + a^2*x^2)*asinh(a*x))/(32*a^2) + (45*asinh(a*x)^2)/(128*a^5) + (9*x^2*asinh(a*x)^2)/(16*a^3) - (3*x^4*asinh(a*x)^2)/(16*a) - (3*x*sqrt(1 + a^2*x^2)*asinh(a*x)^3)/(8*a^4) + (x^3*sqrt(1 + a^2*x^2)*asinh(a*x)^3)/(4*a^2) + (3*asinh(a*x)^4)/(32*a^5)]
    @test_int [(x^3*asinh(a*x)^3)/sqrt(1 + a^2*x^2), x, 10, (40*x)/(9*a^3) - (2*x^3)/(27*a) - (40*sqrt(1 + a^2*x^2)*asinh(a*x))/(9*a^4) + (2*x^2*sqrt(1 + a^2*x^2)*asinh(a*x))/(9*a^2) + (2*x*asinh(a*x)^2)/a^3 - (x^3*asinh(a*x)^2)/(3*a) - (2*sqrt(1 + a^2*x^2)*asinh(a*x)^3)/(3*a^4) + (x^2*sqrt(1 + a^2*x^2)*asinh(a*x)^3)/(3*a^2)]
    @test_int [(x^2*asinh(a*x)^3)/sqrt(1 + a^2*x^2), x, 6, (-3*x^2)/(8*a) + (3*x*sqrt(1 + a^2*x^2)*asinh(a*x))/(4*a^2) - (3*asinh(a*x)^2)/(8*a^3) - (3*x^2*asinh(a*x)^2)/(4*a) + (x*sqrt(1 + a^2*x^2)*asinh(a*x)^3)/(2*a^2) - asinh(a*x)^4/(8*a^3)]
    @test_int [(x*asinh(a*x)^3)/sqrt(1 + a^2*x^2), x, 4, (-6*x)/a + (6*sqrt(1 + a^2*x^2)*asinh(a*x))/a^2 - (3*x*asinh(a*x)^2)/a + (sqrt(1 + a^2*x^2)*asinh(a*x)^3)/a^2]
    @test_int [asinh(a*x)^3/sqrt(1 + a^2*x^2), x, 1, asinh(a*x)^4/(4*a)]
    @test_int [asinh(a*x)^3/(x*sqrt(1 + a^2*x^2)), x, 10, -2*asinh(a*x)^3*atanh(ℯ^asinh(a*x)) - 3*asinh(a*x)^2*PolyLog(2, -ℯ^asinh(a*x)) + 3*asinh(a*x)^2*PolyLog(2, ℯ^asinh(a*x)) + 6*asinh(a*x)*PolyLog(3, -ℯ^asinh(a*x)) - 6*asinh(a*x)*PolyLog(3, ℯ^asinh(a*x)) - 6*PolyLog(4, -ℯ^asinh(a*x)) + 6*PolyLog(4, ℯ^asinh(a*x))]
    @test_int [asinh(a*x)^3/(x^2*sqrt(1 + a^2*x^2)), x, 7, -(a*asinh(a*x)^3) - (sqrt(1 + a^2*x^2)*asinh(a*x)^3)/x + 3*a*asinh(a*x)^2*log(1 - ℯ^(2*asinh(a*x))) + 3*a*asinh(a*x)*PolyLog(2, ℯ^(2*asinh(a*x))) - (3*a*PolyLog(3, ℯ^(2*asinh(a*x))))/2]
    @test_int [asinh(a*x)^3/(x^3*sqrt(1 + a^2*x^2)), x, 18, (-3*a*asinh(a*x)^2)/(2*x) - (sqrt(1 + a^2*x^2)*asinh(a*x)^3)/(2*x^2) - 6*a^2*asinh(a*x)*atanh(ℯ^asinh(a*x)) + a^2*asinh(a*x)^3*atanh(ℯ^asinh(a*x)) - 3*a^2*PolyLog(2, -ℯ^asinh(a*x)) + (3*a^2*asinh(a*x)^2*PolyLog(2, -ℯ^asinh(a*x)))/2 + 3*a^2*PolyLog(2, ℯ^asinh(a*x)) - (3*a^2*asinh(a*x)^2*PolyLog(2, ℯ^asinh(a*x)))/2 - 3*a^2*asinh(a*x)*PolyLog(3, -ℯ^asinh(a*x)) + 3*a^2*asinh(a*x)*PolyLog(3, ℯ^asinh(a*x)) + 3*a^2*PolyLog(4, -ℯ^asinh(a*x)) - 3*a^2*PolyLog(4, ℯ^asinh(a*x))]

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

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

    @test_int [(c + a^2*c*x^2)^3/asinh(a*x), x, 7, (35*c^3*CoshIntegral(asinh(a*x)))/(64*a) + (21*c^3*CoshIntegral(3*asinh(a*x)))/(64*a) + (7*c^3*CoshIntegral(5*asinh(a*x)))/(64*a) + (c^3*CoshIntegral(7*asinh(a*x)))/(64*a)]
    @test_int [(c + a^2*c*x^2)^2/asinh(a*x), x, 6, (5*c^2*CoshIntegral(asinh(a*x)))/(8*a) + (5*c^2*CoshIntegral(3*asinh(a*x)))/(16*a) + (c^2*CoshIntegral(5*asinh(a*x)))/(16*a)]
    @test_int [(c + a^2*c*x^2)^1/asinh(a*x), x, 5, (3*c*CoshIntegral(asinh(a*x)))/(4*a) + (c*CoshIntegral(3*asinh(a*x)))/(4*a)]
    @test_int [1/((c + a^2*c*x^2)^1*asinh(a*x)), x, 0, Unintegrable(1/((c + a^2*c*x^2)*asinh(a*x)), x)]
    @test_int [1/((c + a^2*c*x^2)^2*asinh(a*x)), x, 0, Unintegrable(1/((c + a^2*c*x^2)^2*asinh(a*x)), x)]

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

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

    @test_int [(x^4*sqrt(1 + c^2*x^2))/(a + b*asinh(c*x)), x, 12, -((cosh((2*a)/b)*CoshIntegral((2*(a + b*asinh(c*x)))/b))/(32*b*c^5)) - (cosh((4*a)/b)*CoshIntegral((4*(a + b*asinh(c*x)))/b))/(16*b*c^5) + (cosh((6*a)/b)*CoshIntegral((6*(a + b*asinh(c*x)))/b))/(32*b*c^5) + log(a + b*asinh(c*x))/(16*b*c^5) + (sinh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(32*b*c^5) + (sinh((4*a)/b)*SinhIntegral((4*(a + b*asinh(c*x)))/b))/(16*b*c^5) - (sinh((6*a)/b)*SinhIntegral((6*(a + b*asinh(c*x)))/b))/(32*b*c^5)]
    @test_int [(x^3*sqrt(1 + c^2*x^2))/(a + b*asinh(c*x)), x, 12, (CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(8*b*c^4) + (CoshIntegral((3*(a + b*asinh(c*x)))/b)*sinh((3*a)/b))/(16*b*c^4) - (CoshIntegral((5*(a + b*asinh(c*x)))/b)*sinh((5*a)/b))/(16*b*c^4) - (cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(8*b*c^4) - (cosh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(16*b*c^4) + (cosh((5*a)/b)*SinhIntegral((5*(a + b*asinh(c*x)))/b))/(16*b*c^4)]
    @test_int [(x^2*sqrt(1 + c^2*x^2))/(a + b*asinh(c*x)), x, 6, (cosh((4*a)/b)*CoshIntegral((4*(a + b*asinh(c*x)))/b))/(8*b*c^3) - log(a + b*asinh(c*x))/(8*b*c^3) - (sinh((4*a)/b)*SinhIntegral((4*(a + b*asinh(c*x)))/b))/(8*b*c^3)]
    @test_int [(x*sqrt(1 + c^2*x^2))/(a + b*asinh(c*x)), x, 9, -((CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(4*b*c^2)) - (CoshIntegral((3*(a + b*asinh(c*x)))/b)*sinh((3*a)/b))/(4*b*c^2) + (cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(4*b*c^2) + (cosh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(4*b*c^2)]
    @test_int [sqrt(1 + c^2*x^2)/(a + b*asinh(c*x)), x, 6, (cosh((2*a)/b)*CoshIntegral((2*(a + b*asinh(c*x)))/b))/(2*b*c) + log(a + b*asinh(c*x))/(2*b*c) - (sinh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(2*b*c)]
    @test_int [sqrt(1 + c^2*x^2)/(x*(a + b*asinh(c*x))), x, 6, -((CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/b) + (cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/b + Unintegrable(1/(x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x)]
    @test_int [sqrt(1 + c^2*x^2)/(x^2*(a + b*asinh(c*x))), x, 3, (c*log(a + b*asinh(c*x)))/b + Unintegrable(1/(x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x)]
    @test_int [sqrt(1 + c^2*x^2)/(x^3*(a + b*asinh(c*x))), x, 0, Unintegrable(sqrt(1 + c^2*x^2)/(x^3*(a + b*asinh(c*x))), x)]
    @test_int [sqrt(1 + c^2*x^2)/(x^4*(a + b*asinh(c*x))), x, 0, Unintegrable(sqrt(1 + c^2*x^2)/(x^4*(a + b*asinh(c*x))), x)]

    @test_int [(x^3*(1 + c^2*x^2)^(3/2))/(a + b*asinh(c*x)), x, 15, (3*CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(64*b*c^4) + (3*CoshIntegral((3*(a + b*asinh(c*x)))/b)*sinh((3*a)/b))/(64*b*c^4) - (CoshIntegral((5*(a + b*asinh(c*x)))/b)*sinh((5*a)/b))/(64*b*c^4) - (CoshIntegral((7*(a + b*asinh(c*x)))/b)*sinh((7*a)/b))/(64*b*c^4) - (3*cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(64*b*c^4) - (3*cosh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(64*b*c^4) + (cosh((5*a)/b)*SinhIntegral((5*(a + b*asinh(c*x)))/b))/(64*b*c^4) + (cosh((7*a)/b)*SinhIntegral((7*(a + b*asinh(c*x)))/b))/(64*b*c^4)]
    @test_int [(x^2*(1 + c^2*x^2)^(3/2))/(a + b*asinh(c*x)), x, 12, -((cosh((2*a)/b)*CoshIntegral((2*(a + b*asinh(c*x)))/b))/(32*b*c^3)) + (cosh((4*a)/b)*CoshIntegral((4*(a + b*asinh(c*x)))/b))/(16*b*c^3) + (cosh((6*a)/b)*CoshIntegral((6*(a + b*asinh(c*x)))/b))/(32*b*c^3) - log(a + b*asinh(c*x))/(16*b*c^3) + (sinh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(32*b*c^3) - (sinh((4*a)/b)*SinhIntegral((4*(a + b*asinh(c*x)))/b))/(16*b*c^3) - (sinh((6*a)/b)*SinhIntegral((6*(a + b*asinh(c*x)))/b))/(32*b*c^3)]
    @test_int [(x*(1 + c^2*x^2)^(3/2))/(a + b*asinh(c*x)), x, 12, -((CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(8*b*c^2)) - (3*CoshIntegral((3*(a + b*asinh(c*x)))/b)*sinh((3*a)/b))/(16*b*c^2) - (CoshIntegral((5*(a + b*asinh(c*x)))/b)*sinh((5*a)/b))/(16*b*c^2) + (cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(8*b*c^2) + (3*cosh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(16*b*c^2) + (cosh((5*a)/b)*SinhIntegral((5*(a + b*asinh(c*x)))/b))/(16*b*c^2)]
    @test_int [(1 + c^2*x^2)^(3/2)/(a + b*asinh(c*x)), x, 9, (cosh((2*a)/b)*CoshIntegral((2*(a + b*asinh(c*x)))/b))/(2*b*c) + (cosh((4*a)/b)*CoshIntegral((4*(a + b*asinh(c*x)))/b))/(8*b*c) + (3*log(a + b*asinh(c*x)))/(8*b*c) - (sinh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(2*b*c) - (sinh((4*a)/b)*SinhIntegral((4*(a + b*asinh(c*x)))/b))/(8*b*c)]
    @test_int [(1 + c^2*x^2)^(3/2)/(x*(a + b*asinh(c*x))), x, 15, -((5*CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(4*b)) - (CoshIntegral((3*(a + b*asinh(c*x)))/b)*sinh((3*a)/b))/(4*b) + (5*cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(4*b) + (cosh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(4*b) + Unintegrable(1/(x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x)]
    @test_int [(1 + c^2*x^2)^(3/2)/(x^2*(a + b*asinh(c*x))), x, 9, (c*cosh((2*a)/b)*CoshIntegral((2*(a + b*asinh(c*x)))/b))/(2*b) + (3*c*log(a + b*asinh(c*x)))/(2*b) - (c*sinh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(2*b) + Unintegrable(1/(x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x)]
    @test_int [(1 + c^2*x^2)^(3/2)/(x^3*(a + b*asinh(c*x))), x, 0, Unintegrable((1 + c^2*x^2)^(3/2)/(x^3*(a + b*asinh(c*x))), x)]
    @test_int [(1 + c^2*x^2)^(3/2)/(x^4*(a + b*asinh(c*x))), x, 0, Unintegrable((1 + c^2*x^2)^(3/2)/(x^4*(a + b*asinh(c*x))), x)]

    @test_int [(x^3*(1 + c^2*x^2)^(5/2))/(a + b*asinh(c*x)), x, 15, (3*CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(128*b*c^4) + (CoshIntegral((3*(a + b*asinh(c*x)))/b)*sinh((3*a)/b))/(32*b*c^4) - (3*CoshIntegral((7*(a + b*asinh(c*x)))/b)*sinh((7*a)/b))/(256*b*c^4) - (CoshIntegral((9*(a + b*asinh(c*x)))/b)*sinh((9*a)/b))/(256*b*c^4) - (3*cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(128*b*c^4) - (cosh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(32*b*c^4) + (3*cosh((7*a)/b)*SinhIntegral((7*(a + b*asinh(c*x)))/b))/(256*b*c^4) + (cosh((9*a)/b)*SinhIntegral((9*(a + b*asinh(c*x)))/b))/(256*b*c^4)]
    @test_int [(x^2*(1 + c^2*x^2)^(5/2))/(a + b*asinh(c*x)), x, 15, -((cosh((2*a)/b)*CoshIntegral((2*(a + b*asinh(c*x)))/b))/(32*b*c^3)) + (cosh((4*a)/b)*CoshIntegral((4*(a + b*asinh(c*x)))/b))/(32*b*c^3) + (cosh((6*a)/b)*CoshIntegral((6*(a + b*asinh(c*x)))/b))/(32*b*c^3) + (cosh((8*a)/b)*CoshIntegral((8*(a + b*asinh(c*x)))/b))/(128*b*c^3) - (5*log(a + b*asinh(c*x)))/(128*b*c^3) + (sinh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(32*b*c^3) - (sinh((4*a)/b)*SinhIntegral((4*(a + b*asinh(c*x)))/b))/(32*b*c^3) - (sinh((6*a)/b)*SinhIntegral((6*(a + b*asinh(c*x)))/b))/(32*b*c^3) - (sinh((8*a)/b)*SinhIntegral((8*(a + b*asinh(c*x)))/b))/(128*b*c^3)]
    @test_int [(x*(1 + c^2*x^2)^(5/2))/(a + b*asinh(c*x)), x, 15, -((5*CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(64*b*c^2)) - (9*CoshIntegral((3*(a + b*asinh(c*x)))/b)*sinh((3*a)/b))/(64*b*c^2) - (5*CoshIntegral((5*(a + b*asinh(c*x)))/b)*sinh((5*a)/b))/(64*b*c^2) - (CoshIntegral((7*(a + b*asinh(c*x)))/b)*sinh((7*a)/b))/(64*b*c^2) + (5*cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(64*b*c^2) + (9*cosh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(64*b*c^2) + (5*cosh((5*a)/b)*SinhIntegral((5*(a + b*asinh(c*x)))/b))/(64*b*c^2) + (cosh((7*a)/b)*SinhIntegral((7*(a + b*asinh(c*x)))/b))/(64*b*c^2)]
    @test_int [(1 + c^2*x^2)^(5/2)/(a + b*asinh(c*x)), x, 12, (15*cosh((2*a)/b)*CoshIntegral((2*(a + b*asinh(c*x)))/b))/(32*b*c) + (3*cosh((4*a)/b)*CoshIntegral((4*(a + b*asinh(c*x)))/b))/(16*b*c) + (cosh((6*a)/b)*CoshIntegral((6*(a + b*asinh(c*x)))/b))/(32*b*c) + (5*log(a + b*asinh(c*x)))/(16*b*c) - (15*sinh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(32*b*c) - (3*sinh((4*a)/b)*SinhIntegral((4*(a + b*asinh(c*x)))/b))/(16*b*c) - (sinh((6*a)/b)*SinhIntegral((6*(a + b*asinh(c*x)))/b))/(32*b*c)]
    @test_int [(1 + c^2*x^2)^(5/2)/(x*(a + b*asinh(c*x))), x, 27, -((11*CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(8*b)) - (7*CoshIntegral((3*(a + b*asinh(c*x)))/b)*sinh((3*a)/b))/(16*b) - (CoshIntegral((5*(a + b*asinh(c*x)))/b)*sinh((5*a)/b))/(16*b) + (11*cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(8*b) + (7*cosh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(16*b) + (cosh((5*a)/b)*SinhIntegral((5*(a + b*asinh(c*x)))/b))/(16*b) + Unintegrable(1/(x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x)]
    @test_int [(1 + c^2*x^2)^(5/2)/(x^2*(a + b*asinh(c*x))), x, 18, (c*cosh((2*a)/b)*CoshIntegral((2*(a + b*asinh(c*x)))/b))/b + (c*cosh((4*a)/b)*CoshIntegral((4*(a + b*asinh(c*x)))/b))/(8*b) + (15*c*log(a + b*asinh(c*x)))/(8*b) - (c*sinh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/b - (c*sinh((4*a)/b)*SinhIntegral((4*(a + b*asinh(c*x)))/b))/(8*b) + Unintegrable(1/(x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x)]
    @test_int [(1 + c^2*x^2)^(5/2)/(x^3*(a + b*asinh(c*x))), x, 0, Unintegrable((1 + c^2*x^2)^(5/2)/(x^3*(a + b*asinh(c*x))), x)]
    @test_int [(1 + c^2*x^2)^(5/2)/(x^4*(a + b*asinh(c*x))), x, 0, Unintegrable((1 + c^2*x^2)^(5/2)/(x^4*(a + b*asinh(c*x))), x)]

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

    @test_int [x^4/(sqrt(1 + a^2*x^2)*asinh(a*x)), x, 5, -CoshIntegral(2*asinh(a*x))/(2*a^5) + CoshIntegral(4*asinh(a*x))/(8*a^5) + (3*log(asinh(a*x)))/(8*a^5)]
    @test_int [x^3/(sqrt(1 + a^2*x^2)*asinh(a*x)), x, 5, (-3*SinhIntegral(asinh(a*x)))/(4*a^4) + SinhIntegral(3*asinh(a*x))/(4*a^4)]
    @test_int [x^2/(sqrt(1 + a^2*x^2)*asinh(a*x)), x, 4, CoshIntegral(2*asinh(a*x))/(2*a^3) - log(asinh(a*x))/(2*a^3)]
    @test_int [x^2/(sqrt(1 + a^2*x^2)*asinh(a*x)), x, 4, CoshIntegral(2*asinh(a*x))/(2*a^3) - log(asinh(a*x))/(2*a^3)]
    @test_int [x/(sqrt(1 + a^2*x^2)*asinh(a*x)), x, 2, SinhIntegral(asinh(a*x))/a^2]
    @test_int [1/(sqrt(1 + a^2*x^2)*asinh(a*x)), x, 1, log(asinh(a*x))/a]
    @test_int [1/(x*sqrt(1 + a^2*x^2)*asinh(a*x)), x, 0, Unintegrable(1/(x*sqrt(1 + a^2*x^2)*asinh(a*x)), x)]
    @test_int [1/(x^2*sqrt(1 + a^2*x^2)*asinh(a*x)), x, 0, Unintegrable(1/(x^2*sqrt(1 + a^2*x^2)*asinh(a*x)), x)]

    @test_int [x^5/(sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x, 12, -((5*CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(8*b*c^6)) + (5*CoshIntegral((3*(a + b*asinh(c*x)))/b)*sinh((3*a)/b))/(16*b*c^6) - (CoshIntegral((5*(a + b*asinh(c*x)))/b)*sinh((5*a)/b))/(16*b*c^6) + (5*cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(8*b*c^6) - (5*cosh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(16*b*c^6) + (cosh((5*a)/b)*SinhIntegral((5*(a + b*asinh(c*x)))/b))/(16*b*c^6)]
    @test_int [x^4/(sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x, 9, -((cosh((2*a)/b)*CoshIntegral((2*(a + b*asinh(c*x)))/b))/(2*b*c^5)) + (cosh((4*a)/b)*CoshIntegral((4*(a + b*asinh(c*x)))/b))/(8*b*c^5) + (3*log(a + b*asinh(c*x)))/(8*b*c^5) + (sinh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(2*b*c^5) - (sinh((4*a)/b)*SinhIntegral((4*(a + b*asinh(c*x)))/b))/(8*b*c^5)]
    @test_int [x^3/(sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x, 9, (3*CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(4*b*c^4) - (CoshIntegral((3*(a + b*asinh(c*x)))/b)*sinh((3*a)/b))/(4*b*c^4) - (3*cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(4*b*c^4) + (cosh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(4*b*c^4)]
    @test_int [x^2/(sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x, 6, (cosh((2*a)/b)*CoshIntegral((2*(a + b*asinh(c*x)))/b))/(2*b*c^3) - log(a + b*asinh(c*x))/(2*b*c^3) - (sinh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(2*b*c^3)]
    @test_int [x/(sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x, 4, -((CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(b*c^2)) + (cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(b*c^2)]
    @test_int [1/(sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x, 1, log(a + b*asinh(c*x))/(b*c)]
    @test_int [1/(x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x, 0, Unintegrable(1/(x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x)]
    @test_int [1/(x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x, 0, Unintegrable(1/(x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x)]

    @test_int [x^2/((1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))), x, 0, Unintegrable(x^2/((1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))), x)]
    @test_int [x/((1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))), x, 0, Unintegrable(x/((1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))), x)]
    @test_int [1/((1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))), x, 0, Unintegrable(1/((1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))), x)]
    @test_int [1/(x*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))), x, 0, Unintegrable(1/(x*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))), x)]
    @test_int [1/(x^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))), x, 0, Unintegrable(1/(x^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))), x)]

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

    @test_int [x^m*(1 + c^2*x^2)^(5/2)/(a + b*asinh(c*x)), x, 0, Unintegrable((x^m*(1 + c^2*x^2)^(5/2))/(a + b*asinh(c*x)), x)]
    @test_int [x^m*(1 + c^2*x^2)^(3/2)/(a + b*asinh(c*x)), x, 0, Unintegrable((x^m*(1 + c^2*x^2)^(3/2))/(a + b*asinh(c*x)), x)]
    @test_int [x^m*(1 + c^2*x^2)^(1/2)/(a + b*asinh(c*x)), x, 0, Unintegrable((x^m*sqrt(1 + c^2*x^2))/(a + b*asinh(c*x)), x)]
    @test_int [x^m/((1 + c^2*x^2)^(1/2)*(a + b*asinh(c*x))), x, 0, Unintegrable(x^m/(sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))), x)]
    @test_int [x^m/((1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))), x, 0, Unintegrable(x^m/((1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))), x)]

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

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

    @test_int [(c + a^2*c*x^2)^3/asinh(a*x)^2, x, 8, -((c^3*(1 + a^2*x^2)^(7/2))/(a*asinh(a*x))) + (35*c^3*SinhIntegral(asinh(a*x)))/(64*a) + (63*c^3*SinhIntegral(3*asinh(a*x)))/(64*a) + (35*c^3*SinhIntegral(5*asinh(a*x)))/(64*a) + (7*c^3*SinhIntegral(7*asinh(a*x)))/(64*a)]
    @test_int [(c + a^2*c*x^2)^2/asinh(a*x)^2, x, 7, -((c^2*(1 + a^2*x^2)^(5/2))/(a*asinh(a*x))) + (5*c^2*SinhIntegral(asinh(a*x)))/(8*a) + (15*c^2*SinhIntegral(3*asinh(a*x)))/(16*a) + (5*c^2*SinhIntegral(5*asinh(a*x)))/(16*a)]
    @test_int [(c + a^2*c*x^2)/asinh(a*x)^2, x, 6, -((c*(1 + a^2*x^2)^(3/2))/(a*asinh(a*x))) + (3*c*SinhIntegral(asinh(a*x)))/(4*a) + (3*c*SinhIntegral(3*asinh(a*x)))/(4*a)]
    @test_int [1/((c + a^2*c*x^2)*asinh(a*x)^2), x, 1, -(1/(a*c*sqrt(1 + a^2*x^2)*asinh(a*x))) - (a*Unintegrable(x/((1 + a^2*x^2)^(3/2)*asinh(a*x)), x))/c]
    @test_int [1/((c + a^2*c*x^2)^2*asinh(a*x)^2), x, 1, -(1/(a*c^2*(1 + a^2*x^2)^(3/2)*asinh(a*x))) - (3*a*Unintegrable(x/((1 + a^2*x^2)^(5/2)*asinh(a*x)), x))/c^2]

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

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

    @test_int [(x^3*sqrt(1 + c^2*x^2))/(a + b*asinh(c*x))^2, x, 22, -((x^3*(1 + c^2*x^2))/(b*c*(a + b*asinh(c*x)))) - (cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(8*b^2*c^4) - (3*cosh((3*a)/b)*CoshIntegral((3*(a + b*asinh(c*x)))/b))/(16*b^2*c^4) + (5*cosh((5*a)/b)*CoshIntegral((5*(a + b*asinh(c*x)))/b))/(16*b^2*c^4) + (sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(8*b^2*c^4) + (3*sinh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(16*b^2*c^4) - (5*sinh((5*a)/b)*SinhIntegral((5*(a + b*asinh(c*x)))/b))/(16*b^2*c^4)]
    @test_int [(x^2*sqrt(1 + c^2*x^2))/(a + b*asinh(c*x))^2, x, 16, -((x^2*(1 + c^2*x^2))/(b*c*(a + b*asinh(c*x)))) - (CoshIntegral((4*(a + b*asinh(c*x)))/b)*sinh((4*a)/b))/(2*b^2*c^3) + (cosh((4*a)/b)*SinhIntegral((4*(a + b*asinh(c*x)))/b))/(2*b^2*c^3)]
    @test_int [(x*sqrt(1 + c^2*x^2))/(a + b*asinh(c*x))^2, x, 14, -((x*(1 + c^2*x^2))/(b*c*(a + b*asinh(c*x)))) + (cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(4*b^2*c^2) + (3*cosh((3*a)/b)*CoshIntegral((3*(a + b*asinh(c*x)))/b))/(4*b^2*c^2) - (sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(4*b^2*c^2) - (3*sinh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(4*b^2*c^2)]
    @test_int [sqrt(1 + c^2*x^2)/(a + b*asinh(c*x))^2, x, 7, -((1 + c^2*x^2)/(b*c*(a + b*asinh(c*x)))) - (CoshIntegral((2*(a + b*asinh(c*x)))/b)*sinh((2*a)/b))/(b^2*c) + (cosh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(b^2*c)]
    @test_int [sqrt(1 + c^2*x^2)/(x*(a + b*asinh(c*x))^2), x, 5, -((1 + c^2*x^2)/(b*c*x*(a + b*asinh(c*x)))) + (cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/b^2 - (sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/b^2 - Unintegrable(1/(x^2*(a + b*asinh(c*x))), x)/(b*c)]
    @test_int [sqrt(1 + c^2*x^2)/(x^2*(a + b*asinh(c*x))^2), x, 1, -((1 + c^2*x^2)/(b*c*x^2*(a + b*asinh(c*x)))) - (2*Unintegrable(1/(x^3*(a + b*asinh(c*x))), x))/(b*c)]
    @test_int [sqrt(1 + c^2*x^2)/(x^3*(a + b*asinh(c*x))^2), x, 0, Unintegrable(sqrt(1 + c^2*x^2)/(x^3*(a + b*asinh(c*x))^2), x)]
    @test_int [sqrt(1 + c^2*x^2)/(x^4*(a + b*asinh(c*x))^2), x, 0, Unintegrable(sqrt(1 + c^2*x^2)/(x^4*(a + b*asinh(c*x))^2), x)]

    @test_int [(x^3*(1 + c^2*x^2)^(3/2))/(a + b*asinh(c*x))^2, x, 28, -((x^3*(1 + c^2*x^2)^2)/(b*c*(a + b*asinh(c*x)))) - (3*cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(64*b^2*c^4) - (9*cosh((3*a)/b)*CoshIntegral((3*(a + b*asinh(c*x)))/b))/(64*b^2*c^4) + (5*cosh((5*a)/b)*CoshIntegral((5*(a + b*asinh(c*x)))/b))/(64*b^2*c^4) + (7*cosh((7*a)/b)*CoshIntegral((7*(a + b*asinh(c*x)))/b))/(64*b^2*c^4) + (3*sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(64*b^2*c^4) + (9*sinh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(64*b^2*c^4) - (5*sinh((5*a)/b)*SinhIntegral((5*(a + b*asinh(c*x)))/b))/(64*b^2*c^4) - (7*sinh((7*a)/b)*SinhIntegral((7*(a + b*asinh(c*x)))/b))/(64*b^2*c^4)]
    @test_int [(x^2*(1 + c^2*x^2)^(3/2))/(a + b*asinh(c*x))^2, x, 19, -((x^2*(1 + c^2*x^2)^2)/(b*c*(a + b*asinh(c*x)))) + (CoshIntegral((2*(a + b*asinh(c*x)))/b)*sinh((2*a)/b))/(16*b^2*c^3) - (CoshIntegral((4*(a + b*asinh(c*x)))/b)*sinh((4*a)/b))/(4*b^2*c^3) - (3*CoshIntegral((6*(a + b*asinh(c*x)))/b)*sinh((6*a)/b))/(16*b^2*c^3) - (cosh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(16*b^2*c^3) + (cosh((4*a)/b)*SinhIntegral((4*(a + b*asinh(c*x)))/b))/(4*b^2*c^3) + (3*cosh((6*a)/b)*SinhIntegral((6*(a + b*asinh(c*x)))/b))/(16*b^2*c^3)]
    @test_int [(x*(1 + c^2*x^2)^(3/2))/(a + b*asinh(c*x))^2, x, 22, -((x*(1 + c^2*x^2)^2)/(b*c*(a + b*asinh(c*x)))) + (cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(8*b^2*c^2) + (9*cosh((3*a)/b)*CoshIntegral((3*(a + b*asinh(c*x)))/b))/(16*b^2*c^2) + (5*cosh((5*a)/b)*CoshIntegral((5*(a + b*asinh(c*x)))/b))/(16*b^2*c^2) - (sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(8*b^2*c^2) - (9*sinh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(16*b^2*c^2) - (5*sinh((5*a)/b)*SinhIntegral((5*(a + b*asinh(c*x)))/b))/(16*b^2*c^2)]
    @test_int [(1 + c^2*x^2)^(3/2)/(a + b*asinh(c*x))^2, x, 10, -((1 + c^2*x^2)^2/(b*c*(a + b*asinh(c*x)))) - (CoshIntegral((2*(a + b*asinh(c*x)))/b)*sinh((2*a)/b))/(b^2*c) - (CoshIntegral((4*(a + b*asinh(c*x)))/b)*sinh((4*a)/b))/(2*b^2*c) + (cosh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(b^2*c) + (cosh((4*a)/b)*SinhIntegral((4*(a + b*asinh(c*x)))/b))/(2*b^2*c)]
    @test_int [(1 + c^2*x^2)^(3/2)/(x*(a + b*asinh(c*x))^2), x, 10, -((1 + c^2*x^2)^2/(b*c*x*(a + b*asinh(c*x)))) + (9*cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(4*b^2) + (3*cosh((3*a)/b)*CoshIntegral((3*(a + b*asinh(c*x)))/b))/(4*b^2) - (9*sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(4*b^2) - (3*sinh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(4*b^2) - Unintegrable((1 + c^2*x^2)/(x^2*(a + b*asinh(c*x))), x)/(b*c)]
    @test_int [(1 + c^2*x^2)^(3/2)/(x^2*(a + b*asinh(c*x))^2), x, 1, -((1 + c^2*x^2)^2/(b*c*x^2*(a + b*asinh(c*x)))) - (2*Unintegrable((1 + c^2*x^2)/(x^3*(a + b*asinh(c*x))), x))/(b*c) + (2*c*Unintegrable((1 + c^2*x^2)/(x*(a + b*asinh(c*x))), x))/b]
    @test_int [(1 + c^2*x^2)^(3/2)/(x^3*(a + b*asinh(c*x))^2), x, 0, Unintegrable((1 + c^2*x^2)^(3/2)/(x^3*(a + b*asinh(c*x))^2), x)]
    @test_int [(1 + c^2*x^2)^(3/2)/(x^4*(a + b*asinh(c*x))^2), x, 1, -((1 + c^2*x^2)^2/(b*c*x^4*(a + b*asinh(c*x)))) - (4*Unintegrable((1 + c^2*x^2)/(x^5*(a + b*asinh(c*x))), x))/(b*c)]

    @test_int [(x^3*(1 + c^2*x^2)^(5/2))/(a + b*asinh(c*x))^2, x, 34, -((x^3*(1 + c^2*x^2)^3)/(b*c*(a + b*asinh(c*x)))) - (3*cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(128*b^2*c^4) - (3*cosh((3*a)/b)*CoshIntegral((3*(a + b*asinh(c*x)))/b))/(32*b^2*c^4) + (21*cosh((7*a)/b)*CoshIntegral((7*(a + b*asinh(c*x)))/b))/(256*b^2*c^4) + (9*cosh((9*a)/b)*CoshIntegral((9*(a + b*asinh(c*x)))/b))/(256*b^2*c^4) + (3*sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(128*b^2*c^4) + (3*sinh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(32*b^2*c^4) - (21*sinh((7*a)/b)*SinhIntegral((7*(a + b*asinh(c*x)))/b))/(256*b^2*c^4) - (9*sinh((9*a)/b)*SinhIntegral((9*(a + b*asinh(c*x)))/b))/(256*b^2*c^4)]
    @test_int [(x^2*(1 + c^2*x^2)^(5/2))/(a + b*asinh(c*x))^2, x, 28, -((x^2*(1 + c^2*x^2)^3)/(b*c*(a + b*asinh(c*x)))) + (CoshIntegral((2*(a + b*asinh(c*x)))/b)*sinh((2*a)/b))/(16*b^2*c^3) - (CoshIntegral((4*(a + b*asinh(c*x)))/b)*sinh((4*a)/b))/(8*b^2*c^3) - (3*CoshIntegral((6*(a + b*asinh(c*x)))/b)*sinh((6*a)/b))/(16*b^2*c^3) - (CoshIntegral((8*(a + b*asinh(c*x)))/b)*sinh((8*a)/b))/(16*b^2*c^3) - (cosh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(16*b^2*c^3) + (cosh((4*a)/b)*SinhIntegral((4*(a + b*asinh(c*x)))/b))/(8*b^2*c^3) + (3*cosh((6*a)/b)*SinhIntegral((6*(a + b*asinh(c*x)))/b))/(16*b^2*c^3) + (cosh((8*a)/b)*SinhIntegral((8*(a + b*asinh(c*x)))/b))/(16*b^2*c^3)]
    @test_int [(x*(1 + c^2*x^2)^(5/2))/(a + b*asinh(c*x))^2, x, 28, -((x*(1 + c^2*x^2)^3)/(b*c*(a + b*asinh(c*x)))) + (5*cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(64*b^2*c^2) + (27*cosh((3*a)/b)*CoshIntegral((3*(a + b*asinh(c*x)))/b))/(64*b^2*c^2) + (25*cosh((5*a)/b)*CoshIntegral((5*(a + b*asinh(c*x)))/b))/(64*b^2*c^2) + (7*cosh((7*a)/b)*CoshIntegral((7*(a + b*asinh(c*x)))/b))/(64*b^2*c^2) - (5*sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(64*b^2*c^2) - (27*sinh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(64*b^2*c^2) - (25*sinh((5*a)/b)*SinhIntegral((5*(a + b*asinh(c*x)))/b))/(64*b^2*c^2) - (7*sinh((7*a)/b)*SinhIntegral((7*(a + b*asinh(c*x)))/b))/(64*b^2*c^2)]
    @test_int [(1 + c^2*x^2)^(5/2)/(a + b*asinh(c*x))^2, x, 13, -((1 + c^2*x^2)^3/(b*c*(a + b*asinh(c*x)))) - (15*CoshIntegral((2*(a + b*asinh(c*x)))/b)*sinh((2*a)/b))/(16*b^2*c) - (3*CoshIntegral((4*(a + b*asinh(c*x)))/b)*sinh((4*a)/b))/(4*b^2*c) - (3*CoshIntegral((6*(a + b*asinh(c*x)))/b)*sinh((6*a)/b))/(16*b^2*c) + (15*cosh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(16*b^2*c) + (3*cosh((4*a)/b)*SinhIntegral((4*(a + b*asinh(c*x)))/b))/(4*b^2*c) + (3*cosh((6*a)/b)*SinhIntegral((6*(a + b*asinh(c*x)))/b))/(16*b^2*c)]
    @test_int [(1 + c^2*x^2)^(5/2)/(x*(a + b*asinh(c*x))^2), x, 13, -((1 + c^2*x^2)^3/(b*c*x*(a + b*asinh(c*x)))) + (25*cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(8*b^2) + (25*cosh((3*a)/b)*CoshIntegral((3*(a + b*asinh(c*x)))/b))/(16*b^2) + (5*cosh((5*a)/b)*CoshIntegral((5*(a + b*asinh(c*x)))/b))/(16*b^2) - (25*sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(8*b^2) - (25*sinh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(16*b^2) - (5*sinh((5*a)/b)*SinhIntegral((5*(a + b*asinh(c*x)))/b))/(16*b^2) - Unintegrable((1 + c^2*x^2)^2/(x^2*(a + b*asinh(c*x))), x)/(b*c)]
    @test_int [(1 + c^2*x^2)^(5/2)/(x^2*(a + b*asinh(c*x))^2), x, 1, -((1 + c^2*x^2)^3/(b*c*x^2*(a + b*asinh(c*x)))) - (2*Unintegrable((1 + c^2*x^2)^2/(x^3*(a + b*asinh(c*x))), x))/(b*c) + (4*c*Unintegrable((1 + c^2*x^2)^2/(x*(a + b*asinh(c*x))), x))/b]
    @test_int [(1 + c^2*x^2)^(5/2)/(x^3*(a + b*asinh(c*x))^2), x, 0, Unintegrable((1 + c^2*x^2)^(5/2)/(x^3*(a + b*asinh(c*x))^2), x)]
    @test_int [(1 + c^2*x^2)^(5/2)/(x^4*(a + b*asinh(c*x))^2), x, 0, Unintegrable((1 + c^2*x^2)^(5/2)/(x^4*(a + b*asinh(c*x))^2), x)]

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

    @test_int [x^5/(sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2), x, 13, -(x^5/(b*c*(a + b*asinh(c*x)))) + (5*cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(8*b^2*c^6) - (15*cosh((3*a)/b)*CoshIntegral((3*(a + b*asinh(c*x)))/b))/(16*b^2*c^6) + (5*cosh((5*a)/b)*CoshIntegral((5*(a + b*asinh(c*x)))/b))/(16*b^2*c^6) - (5*sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(8*b^2*c^6) + (15*sinh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(16*b^2*c^6) - (5*sinh((5*a)/b)*SinhIntegral((5*(a + b*asinh(c*x)))/b))/(16*b^2*c^6)]
    @test_int [x^4/(sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2), x, 10, -(x^4/(b*c*(a + b*asinh(c*x)))) + (CoshIntegral((2*(a + b*asinh(c*x)))/b)*sinh((2*a)/b))/(b^2*c^5) - (CoshIntegral((4*(a + b*asinh(c*x)))/b)*sinh((4*a)/b))/(2*b^2*c^5) - (cosh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(b^2*c^5) + (cosh((4*a)/b)*SinhIntegral((4*(a + b*asinh(c*x)))/b))/(2*b^2*c^5)]
    @test_int [x^3/(sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2), x, 10, -(x^3/(b*c*(a + b*asinh(c*x)))) - (3*cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(4*b^2*c^4) + (3*cosh((3*a)/b)*CoshIntegral((3*(a + b*asinh(c*x)))/b))/(4*b^2*c^4) + (3*sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(4*b^2*c^4) - (3*sinh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(4*b^2*c^4)]
    @test_int [x^2/(sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2), x, 7, -(x^2/(b*c*(a + b*asinh(c*x)))) - (CoshIntegral((2*(a + b*asinh(c*x)))/b)*sinh((2*a)/b))/(b^2*c^3) + (cosh((2*a)/b)*SinhIntegral((2*(a + b*asinh(c*x)))/b))/(b^2*c^3)]
    @test_int [x/(sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2), x, 5, -(x/(b*c*(a + b*asinh(c*x)))) + (cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(b^2*c^2) - (sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(b^2*c^2)]
    @test_int [1/(sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2), x, 1, -(1/(b*c*(a + b*asinh(c*x))))]
    @test_int [1/(x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2), x, 1, -(1/(b*c*x*(a + b*asinh(c*x)))) - Unintegrable(1/(x^2*(a + b*asinh(c*x))), x)/(b*c)]
    @test_int [1/(x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2), x, 1, -(1/(b*c*x^2*(a + b*asinh(c*x)))) - (2*Unintegrable(1/(x^3*(a + b*asinh(c*x))), x))/(b*c)]

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

    @test_int [x^3/((1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2), x, 0, Unintegrable(x^3/((1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2), x)]
    @test_int [x^2/((1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2), x, 0, Unintegrable(x^2/((1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2), x)]
    @test_int [x/((1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2), x, 0, Unintegrable(x/((1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2), x)]
    @test_int [1/((1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2), x, 1, -(1/(b*c*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))) - (4*c*Unintegrable(x/((1 + c^2*x^2)^3*(a + b*asinh(c*x))), x))/b]
    @test_int [1/(x*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2), x, 0, Unintegrable(1/(x*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2), x)]
    @test_int [1/(x^2*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2), x, 0, Unintegrable(1/(x^2*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2), x)]

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

    @test_int [(x^m*(1 + c^2*x^2)^(5/2))/(a + b*asinh(c*x))^2, x, 0, Unintegrable((x^m*(1 + c^2*x^2)^(5/2))/(a + b*asinh(c*x))^2, x)]
    @test_int [(x^m*(1 + c^2*x^2)^(3/2))/(a + b*asinh(c*x))^2, x, 0, Unintegrable((x^m*(1 + c^2*x^2)^(3/2))/(a + b*asinh(c*x))^2, x)]
    @test_int [(x^m*(1 + c^2*x^2)^(1/2))/(a + b*asinh(c*x))^2, x, 0, Unintegrable((x^m*sqrt(1 + c^2*x^2))/(a + b*asinh(c*x))^2, x)]
    @test_int [x^m/((1 + c^2*x^2)^(1/2)*(a + b*asinh(c*x))^2), x, 1, -(x^m/(b*c*(a + b*asinh(c*x)))) + (m*Unintegrable(x^(-1 + m)/(a + b*asinh(c*x)), x))/(b*c)]
    @test_int [x^m/((1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^2), x, 0, Unintegrable(x^m/((1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^2), x)]
    @test_int [x^m/((1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2), x, 0, Unintegrable(x^m/((1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2), x)]

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

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

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

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

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

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

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

    @test_int [(x^3*(d + c^2*d*x^2))/(a + b*asinh(c*x))^(3/2), x, 27, (-2*d*x^3*(1 + c^2*x^2)^(3/2))/(b*c*sqrt(a + b*asinh(c*x))) - (3*d*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^4) + (d*ℯ^((6*a)/b)*sqrt((3*pi)/2)*erf((sqrt(6)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^4) - (3*d*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^4*ℯ^((2*a)/b)) + (d*sqrt((3*pi)/2)*erfi((sqrt(6)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^4*ℯ^((6*a)/b))]
    @test_int [(x^2*(d + c^2*d*x^2))/(a + b*asinh(c*x))^(3/2), x, 32, (-2*d*x^2*(1 + c^2*x^2)^(3/2))/(b*c*sqrt(a + b*asinh(c*x))) + (d*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(8*b^(3/2)*c^3) - (d*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^3) - (d*ℯ^((5*a)/b)*sqrt(5*pi)*erf((sqrt(5)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^3) - (d*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(8*b^(3/2)*c^3*ℯ^(a/b)) + (d*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^3*ℯ^((3*a)/b)) + (d*sqrt(5*pi)*erfi((sqrt(5)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^3*ℯ^((5*a)/b))]
    @test_int [(x*(d + c^2*d*x^2))/(a + b*asinh(c*x))^(3/2), x, 17, (-2*d*x*(1 + c^2*x^2)^(3/2))/(b*c*sqrt(a + b*asinh(c*x))) + (d*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(4*b^(3/2)*c^2) + (d*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(2*b^(3/2)*c^2) + (d*sqrt(pi)*erfi((2*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(4*b^(3/2)*c^2*ℯ^((4*a)/b)) + (d*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(2*b^(3/2)*c^2*ℯ^((2*a)/b))]
    @test_int [(d + c^2*d*x^2)/(a + b*asinh(c*x))^(3/2), x, 14, (-2*d*(1 + c^2*x^2)^(3/2))/(b*c*sqrt(a + b*asinh(c*x))) - (3*d*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(4*b^(3/2)*c) - (d*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(4*b^(3/2)*c) + (3*d*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(4*b^(3/2)*c*ℯ^(a/b)) + (d*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(4*b^(3/2)*c*ℯ^((3*a)/b))]
    @test_int [(d + c^2*d*x^2)/(x*(a + b*asinh(c*x))^(3/2)), x, 12, (-2*d*(1 + c^2*x^2)^(3/2))/(b*c*x*sqrt(a + b*asinh(c*x))) + (d*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/b^(3/2) + (d*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(b^(3/2)*ℯ^((2*a)/b)) - (2*d*Unintegrable(1/(x^2*sqrt(1 + c^2*x^2)*sqrt(a + b*asinh(c*x))), x))/(b*c)]

    @test_int [(x^3*(d + c^2*d*x^2)^2)/(a + b*asinh(c*x))^(3/2), x, 32, (-2*d^2*x^3*(1 + c^2*x^2)^(5/2))/(b*c*sqrt(a + b*asinh(c*x))) - (d^2*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(32*b^(3/2)*c^4) - (3*d^2*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(32*b^(3/2)*c^4) + (d^2*ℯ^((8*a)/b)*sqrt(pi/2)*erf((2*sqrt(2)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(32*b^(3/2)*c^4) + (d^2*ℯ^((6*a)/b)*sqrt((3*pi)/2)*erf((sqrt(6)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(32*b^(3/2)*c^4) - (d^2*sqrt(pi)*erfi((2*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(32*b^(3/2)*c^4*ℯ^((4*a)/b)) - (3*d^2*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(32*b^(3/2)*c^4*ℯ^((2*a)/b)) + (d^2*sqrt(pi/2)*erfi((2*sqrt(2)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(32*b^(3/2)*c^4*ℯ^((8*a)/b)) + (d^2*sqrt((3*pi)/2)*erfi((sqrt(6)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(32*b^(3/2)*c^4*ℯ^((6*a)/b))]
    @test_int [(x^2*(d + c^2*d*x^2)^2)/(a + b*asinh(c*x))^(3/2), x, 42, (-2*d^2*x^2*(1 + c^2*x^2)^(5/2))/(b*c*sqrt(a + b*asinh(c*x))) + (5*d^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(64*b^(3/2)*c^3) - (d^2*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(64*b^(3/2)*c^3) - (3*d^2*ℯ^((5*a)/b)*sqrt(5*pi)*erf((sqrt(5)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(64*b^(3/2)*c^3) - (d^2*ℯ^((7*a)/b)*sqrt(7*pi)*erf((sqrt(7)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(64*b^(3/2)*c^3) - (5*d^2*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(64*b^(3/2)*c^3*ℯ^(a/b)) + (d^2*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(64*b^(3/2)*c^3*ℯ^((3*a)/b)) + (3*d^2*sqrt(5*pi)*erfi((sqrt(5)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(64*b^(3/2)*c^3*ℯ^((5*a)/b)) + (d^2*sqrt(7*pi)*erfi((sqrt(7)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(64*b^(3/2)*c^3*ℯ^((7*a)/b))]
    @test_int [(x*(d + c^2*d*x^2)^2)/(a + b*asinh(c*x))^(3/2), x, 32, (-2*d^2*x*(1 + c^2*x^2)^(5/2))/(b*c*sqrt(a + b*asinh(c*x))) + (d^2*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(4*b^(3/2)*c^2) + (5*d^2*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^2) + (d^2*ℯ^((6*a)/b)*sqrt((3*pi)/2)*erf((sqrt(6)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^2) + (d^2*sqrt(pi)*erfi((2*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(4*b^(3/2)*c^2*ℯ^((4*a)/b)) + (5*d^2*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^2*ℯ^((2*a)/b)) + (d^2*sqrt((3*pi)/2)*erfi((sqrt(6)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^2*ℯ^((6*a)/b))]
    @test_int [(d + c^2*d*x^2)^2/(a + b*asinh(c*x))^(3/2), x, 19, (-2*d^2*(1 + c^2*x^2)^(5/2))/(b*c*sqrt(a + b*asinh(c*x))) - (5*d^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(8*b^(3/2)*c) - (5*d^2*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(16*b^(3/2)*c) - (d^2*ℯ^((5*a)/b)*sqrt(5*pi)*erf((sqrt(5)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(16*b^(3/2)*c) + (5*d^2*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(8*b^(3/2)*c*ℯ^(a/b)) + (5*d^2*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(16*b^(3/2)*c*ℯ^((3*a)/b)) + (d^2*sqrt(5*pi)*erfi((sqrt(5)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(16*b^(3/2)*c*ℯ^((5*a)/b))]
    @test_int [(d + c^2*d*x^2)^2/(x*(a + b*asinh(c*x))^(3/2)), x, 25, (-2*d^2*(1 + c^2*x^2)^(5/2))/(b*c*x*sqrt(a + b*asinh(c*x))) + (d^2*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(4*b^(3/2)) - (d^2*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(2*b^(3/2)) + (d^2*ℯ^((2*a)/b)*sqrt(2*pi)*erf((sqrt(2)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/b^(3/2) + (d^2*sqrt(pi)*erfi((2*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(4*b^(3/2)*ℯ^((4*a)/b)) - (d^2*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(2*b^(3/2)*ℯ^((2*a)/b)) + (d^2*sqrt(2*pi)*erfi((sqrt(2)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(b^(3/2)*ℯ^((2*a)/b)) - (2*d^2*Unintegrable(1/(x^2*sqrt(1 + c^2*x^2)*sqrt(a + b*asinh(c*x))), x))/(b*c)]

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

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

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

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

    @test_int [(c + a^2*c*x^2)^(3/2)*sqrt(asinh(a*x)), x, 24, (3*c*x*sqrt(c + a^2*c*x^2)*sqrt(asinh(a*x)))/8 + (x*(c + a^2*c*x^2)^(3/2)*sqrt(asinh(a*x)))/4 + (c*sqrt(c + a^2*c*x^2)*asinh(a*x)^(3/2))/(4*a*sqrt(1 + a^2*x^2)) + (c*sqrt(pi)*sqrt(c + a^2*c*x^2)*erf(2*sqrt(asinh(a*x))))/(256*a*sqrt(1 + a^2*x^2)) + (c*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erf(sqrt(2)*sqrt(asinh(a*x))))/(16*a*sqrt(1 + a^2*x^2)) - (c*sqrt(pi)*sqrt(c + a^2*c*x^2)*erfi(2*sqrt(asinh(a*x))))/(256*a*sqrt(1 + a^2*x^2)) - (c*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erfi(sqrt(2)*sqrt(asinh(a*x))))/(16*a*sqrt(1 + a^2*x^2))]
    @test_int [sqrt(c + a^2*c*x^2)*sqrt(asinh(a*x)), x, 10, (x*sqrt(c + a^2*c*x^2)*sqrt(asinh(a*x)))/2 + (sqrt(c + a^2*c*x^2)*asinh(a*x)^(3/2))/(3*a*sqrt(1 + a^2*x^2)) + (sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erf(sqrt(2)*sqrt(asinh(a*x))))/(16*a*sqrt(1 + a^2*x^2)) - (sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erfi(sqrt(2)*sqrt(asinh(a*x))))/(16*a*sqrt(1 + a^2*x^2))]
    @test_int [sqrt(asinh(a*x))/sqrt(c + a^2*c*x^2), x, 1, (2*sqrt(1 + a^2*x^2)*asinh(a*x)^(3/2))/(3*a*sqrt(c + a^2*c*x^2))]
    @test_int [sqrt(asinh(a*x))/(c + a^2*c*x^2)^(3/2), x, 1, (x*sqrt(asinh(a*x)))/(c*sqrt(c + a^2*c*x^2)) - (a*sqrt(1 + a^2*x^2)*Unintegrable(x/((1 + a^2*x^2)*sqrt(asinh(a*x))), x))/(2*c*sqrt(c + a^2*c*x^2))]
    @test_int [sqrt(asinh(a*x))/(c + a^2*c*x^2)^(5/2), x, 2, (x*sqrt(asinh(a*x)))/(3*c*(c + a^2*c*x^2)^(3/2)) + (2*x*sqrt(asinh(a*x)))/(3*c^2*sqrt(c + a^2*c*x^2)) - (a*sqrt(1 + a^2*x^2)*Unintegrable(x/((1 + a^2*x^2)^2*sqrt(asinh(a*x))), x))/(6*c^2*sqrt(c + a^2*c*x^2)) - (a*sqrt(1 + a^2*x^2)*Unintegrable(x/((1 + a^2*x^2)*sqrt(asinh(a*x))), x))/(3*c^2*sqrt(c + a^2*c*x^2))]

    @test_int [(c + a^2*c*x^2)^(3/2)*asinh(a*x)^(3/2), x, 26, (-27*c*sqrt(c + a^2*c*x^2)*sqrt(asinh(a*x)))/(256*a*sqrt(1 + a^2*x^2)) - (9*a*c*x^2*sqrt(c + a^2*c*x^2)*sqrt(asinh(a*x)))/(32*sqrt(1 + a^2*x^2)) - (3*c*(1 + a^2*x^2)^(3/2)*sqrt(c + a^2*c*x^2)*sqrt(asinh(a*x)))/(32*a) + (3*c*x*sqrt(c + a^2*c*x^2)*asinh(a*x)^(3/2))/8 + (x*(c + a^2*c*x^2)^(3/2)*asinh(a*x)^(3/2))/4 + (3*c*sqrt(c + a^2*c*x^2)*asinh(a*x)^(5/2))/(20*a*sqrt(1 + a^2*x^2)) + (3*c*sqrt(pi)*sqrt(c + a^2*c*x^2)*erf(2*sqrt(asinh(a*x))))/(2048*a*sqrt(1 + a^2*x^2)) + (3*c*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erf(sqrt(2)*sqrt(asinh(a*x))))/(64*a*sqrt(1 + a^2*x^2)) + (3*c*sqrt(pi)*sqrt(c + a^2*c*x^2)*erfi(2*sqrt(asinh(a*x))))/(2048*a*sqrt(1 + a^2*x^2)) + (3*c*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erfi(sqrt(2)*sqrt(asinh(a*x))))/(64*a*sqrt(1 + a^2*x^2))]
    @test_int [sqrt(c + a^2*c*x^2)*asinh(a*x)^(3/2), x, 11, (-3*sqrt(c + a^2*c*x^2)*sqrt(asinh(a*x)))/(16*a*sqrt(1 + a^2*x^2)) - (3*a*x^2*sqrt(c + a^2*c*x^2)*sqrt(asinh(a*x)))/(8*sqrt(1 + a^2*x^2)) + (x*sqrt(c + a^2*c*x^2)*asinh(a*x)^(3/2))/2 + (sqrt(c + a^2*c*x^2)*asinh(a*x)^(5/2))/(5*a*sqrt(1 + a^2*x^2)) + (3*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erf(sqrt(2)*sqrt(asinh(a*x))))/(64*a*sqrt(1 + a^2*x^2)) + (3*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erfi(sqrt(2)*sqrt(asinh(a*x))))/(64*a*sqrt(1 + a^2*x^2))]
    @test_int [asinh(a*x)^(3/2)/sqrt(c + a^2*c*x^2), x, 1, (2*sqrt(1 + a^2*x^2)*asinh(a*x)^(5/2))/(5*a*sqrt(c + a^2*c*x^2))]
    @test_int [asinh(a*x)^(3/2)/(c + a^2*c*x^2)^(3/2), x, 1, (x*asinh(a*x)^(3/2))/(c*sqrt(c + a^2*c*x^2)) - (3*a*sqrt(1 + a^2*x^2)*Unintegrable((x*sqrt(asinh(a*x)))/(1 + a^2*x^2), x))/(2*c*sqrt(c + a^2*c*x^2))]

    @test_int [(c + a^2*c*x^2)^(3/2)*asinh(a*x)^(5/2), x, 39, (225*c*x*sqrt(c + a^2*c*x^2)*sqrt(asinh(a*x)))/512 + (15*c*x*(1 + a^2*x^2)*sqrt(c + a^2*c*x^2)*sqrt(asinh(a*x)))/256 - (45*c*sqrt(c + a^2*c*x^2)*asinh(a*x)^(3/2))/(256*a*sqrt(1 + a^2*x^2)) - (15*a*c*x^2*sqrt(c + a^2*c*x^2)*asinh(a*x)^(3/2))/(32*sqrt(1 + a^2*x^2)) - (5*c*(1 + a^2*x^2)^(3/2)*sqrt(c + a^2*c*x^2)*asinh(a*x)^(3/2))/(32*a) + (3*c*x*sqrt(c + a^2*c*x^2)*asinh(a*x)^(5/2))/8 + (x*(c + a^2*c*x^2)^(3/2)*asinh(a*x)^(5/2))/4 + (3*c*sqrt(c + a^2*c*x^2)*asinh(a*x)^(7/2))/(28*a*sqrt(1 + a^2*x^2)) + (15*c*sqrt(pi)*sqrt(c + a^2*c*x^2)*erf(2*sqrt(asinh(a*x))))/(16384*a*sqrt(1 + a^2*x^2)) + (15*c*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erf(sqrt(2)*sqrt(asinh(a*x))))/(256*a*sqrt(1 + a^2*x^2)) - (15*c*sqrt(pi)*sqrt(c + a^2*c*x^2)*erfi(2*sqrt(asinh(a*x))))/(16384*a*sqrt(1 + a^2*x^2)) - (15*c*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erfi(sqrt(2)*sqrt(asinh(a*x))))/(256*a*sqrt(1 + a^2*x^2))]
    @test_int [sqrt(c + a^2*c*x^2)*asinh(a*x)^(5/2), x, 13, (15*x*sqrt(c + a^2*c*x^2)*sqrt(asinh(a*x)))/32 - (5*sqrt(c + a^2*c*x^2)*asinh(a*x)^(3/2))/(16*a*sqrt(1 + a^2*x^2)) - (5*a*x^2*sqrt(c + a^2*c*x^2)*asinh(a*x)^(3/2))/(8*sqrt(1 + a^2*x^2)) + (x*sqrt(c + a^2*c*x^2)*asinh(a*x)^(5/2))/2 + (sqrt(c + a^2*c*x^2)*asinh(a*x)^(7/2))/(7*a*sqrt(1 + a^2*x^2)) + (15*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erf(sqrt(2)*sqrt(asinh(a*x))))/(256*a*sqrt(1 + a^2*x^2)) - (15*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erfi(sqrt(2)*sqrt(asinh(a*x))))/(256*a*sqrt(1 + a^2*x^2))]
    @test_int [asinh(a*x)^(5/2)/sqrt(c + a^2*c*x^2), x, 1, (2*sqrt(1 + a^2*x^2)*asinh(a*x)^(7/2))/(7*a*sqrt(c + a^2*c*x^2))]
    @test_int [asinh(a*x)^(5/2)/(c + a^2*c*x^2)^(3/2), x, 1, (x*asinh(a*x)^(5/2))/(c*sqrt(c + a^2*c*x^2)) - (5*a*sqrt(1 + a^2*x^2)*Unintegrable((x*asinh(a*x)^(3/2))/(1 + a^2*x^2), x))/(2*c*sqrt(c + a^2*c*x^2))]

    @test_int [(a^2 + x^2)^(3/2)*sqrt(asinh(x/a)), x, 24, (3*a^2*x*sqrt(a^2 + x^2)*sqrt(asinh(x/a)))/8 + (x*(a^2 + x^2)^(3/2)*sqrt(asinh(x/a)))/4 + (a^3*sqrt(a^2 + x^2)*asinh(x/a)^(3/2))/(4*sqrt(1 + x^2/a^2)) + (a^3*sqrt(pi)*sqrt(a^2 + x^2)*erf(2*sqrt(asinh(x/a))))/(256*sqrt(1 + x^2/a^2)) + (a^3*sqrt(pi/2)*sqrt(a^2 + x^2)*erf(sqrt(2)*sqrt(asinh(x/a))))/(16*sqrt(1 + x^2/a^2)) - (a^3*sqrt(pi)*sqrt(a^2 + x^2)*erfi(2*sqrt(asinh(x/a))))/(256*sqrt(1 + x^2/a^2)) - (a^3*sqrt(pi/2)*sqrt(a^2 + x^2)*erfi(sqrt(2)*sqrt(asinh(x/a))))/(16*sqrt(1 + x^2/a^2))]
    @test_int [sqrt(a^2 + x^2)*sqrt(asinh(x/a)), x, 10, (x*sqrt(a^2 + x^2)*sqrt(asinh(x/a)))/2 + (a*sqrt(a^2 + x^2)*asinh(x/a)^(3/2))/(3*sqrt(1 + x^2/a^2)) + (a*sqrt(pi/2)*sqrt(a^2 + x^2)*erf(sqrt(2)*sqrt(asinh(x/a))))/(16*sqrt(1 + x^2/a^2)) - (a*sqrt(pi/2)*sqrt(a^2 + x^2)*erfi(sqrt(2)*sqrt(asinh(x/a))))/(16*sqrt(1 + x^2/a^2))]
    @test_int [sqrt(asinh(x/a))/sqrt(a^2 + x^2), x, 1, (2*a*sqrt(1 + x^2/a^2)*asinh(x/a)^(3/2))/(3*sqrt(a^2 + x^2))]
    @test_int [sqrt(asinh(x/a))/(a^2 + x^2)^(3/2), x, 1, (x*sqrt(asinh(x/a)))/(a^2*sqrt(a^2 + x^2)) - (sqrt(1 + x^2/a^2)*Unintegrable(x/((1 + x^2/a^2)*sqrt(asinh(x/a))), x))/(2*a^3*sqrt(a^2 + x^2))]
    @test_int [sqrt(asinh(x/a))/(a^2 + x^2)^(5/2), x, 2, (x*sqrt(asinh(x/a)))/(3*a^2*(a^2 + x^2)^(3/2)) + (2*x*sqrt(asinh(x/a)))/(3*a^4*sqrt(a^2 + x^2)) - (sqrt(1 + x^2/a^2)*Unintegrable(x/((1 + x^2/a^2)^2*sqrt(asinh(x/a))), x))/(6*a^5*sqrt(a^2 + x^2)) - (sqrt(1 + x^2/a^2)*Unintegrable(x/((1 + x^2/a^2)*sqrt(asinh(x/a))), x))/(3*a^5*sqrt(a^2 + x^2))]

    @test_int [(a^2 + x^2)^(3/2)*asinh(x/a)^(3/2), x, 26, (-27*a^3*sqrt(a^2 + x^2)*sqrt(asinh(x/a)))/(256*sqrt(1 + x^2/a^2)) - (9*a*x^2*sqrt(a^2 + x^2)*sqrt(asinh(x/a)))/(32*sqrt(1 + x^2/a^2)) - (3*(a^2 + x^2)^(5/2)*sqrt(asinh(x/a)))/(32*a*sqrt(1 + x^2/a^2)) + (3*a^2*x*sqrt(a^2 + x^2)*asinh(x/a)^(3/2))/8 + (x*(a^2 + x^2)^(3/2)*asinh(x/a)^(3/2))/4 + (3*a^3*sqrt(a^2 + x^2)*asinh(x/a)^(5/2))/(20*sqrt(1 + x^2/a^2)) + (3*a^3*sqrt(pi)*sqrt(a^2 + x^2)*erf(2*sqrt(asinh(x/a))))/(2048*sqrt(1 + x^2/a^2)) + (3*a^3*sqrt(pi/2)*sqrt(a^2 + x^2)*erf(sqrt(2)*sqrt(asinh(x/a))))/(64*sqrt(1 + x^2/a^2)) + (3*a^3*sqrt(pi)*sqrt(a^2 + x^2)*erfi(2*sqrt(asinh(x/a))))/(2048*sqrt(1 + x^2/a^2)) + (3*a^3*sqrt(pi/2)*sqrt(a^2 + x^2)*erfi(sqrt(2)*sqrt(asinh(x/a))))/(64*sqrt(1 + x^2/a^2))]
    @test_int [sqrt(a^2 + x^2)*asinh(x/a)^(3/2), x, 11, (-3*a*sqrt(a^2 + x^2)*sqrt(asinh(x/a)))/(16*sqrt(1 + x^2/a^2)) - (3*x^2*sqrt(a^2 + x^2)*sqrt(asinh(x/a)))/(8*a*sqrt(1 + x^2/a^2)) + (x*sqrt(a^2 + x^2)*asinh(x/a)^(3/2))/2 + (a*sqrt(a^2 + x^2)*asinh(x/a)^(5/2))/(5*sqrt(1 + x^2/a^2)) + (3*a*sqrt(pi/2)*sqrt(a^2 + x^2)*erf(sqrt(2)*sqrt(asinh(x/a))))/(64*sqrt(1 + x^2/a^2)) + (3*a*sqrt(pi/2)*sqrt(a^2 + x^2)*erfi(sqrt(2)*sqrt(asinh(x/a))))/(64*sqrt(1 + x^2/a^2))]
    @test_int [asinh(x/a)^(3/2)/sqrt(a^2 + x^2), x, 1, (2*a*sqrt(1 + x^2/a^2)*asinh(x/a)^(5/2))/(5*sqrt(a^2 + x^2))]
    @test_int [asinh(x/a)^(3/2)/(a^2 + x^2)^(3/2), x, 1, (x*asinh(x/a)^(3/2))/(a^2*sqrt(a^2 + x^2)) - (3*sqrt(1 + x^2/a^2)*Unintegrable((x*sqrt(asinh(x/a)))/(1 + x^2/a^2), x))/(2*a^3*sqrt(a^2 + x^2))]

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

    @test_int [x/(sqrt(1 + x^2)*sqrt(asinh(x))), x, 6, -(sqrt(pi)*erf(sqrt(asinh(x))))/2 + (sqrt(pi)*erfi(sqrt(asinh(x))))/2]

    @test_int [(c + a^2*c*x^2)^(5/2)/sqrt(asinh(a*x)), x, 18, (5*c^2*sqrt(c + a^2*c*x^2)*sqrt(asinh(a*x)))/(8*a*sqrt(1 + a^2*x^2)) + (3*c^2*sqrt(pi)*sqrt(c + a^2*c*x^2)*erf(2*sqrt(asinh(a*x))))/(64*a*sqrt(1 + a^2*x^2)) + (15*c^2*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erf(sqrt(2)*sqrt(asinh(a*x))))/(64*a*sqrt(1 + a^2*x^2)) + (c^2*sqrt(pi/6)*sqrt(c + a^2*c*x^2)*erf(sqrt(6)*sqrt(asinh(a*x))))/(64*a*sqrt(1 + a^2*x^2)) + (3*c^2*sqrt(pi)*sqrt(c + a^2*c*x^2)*erfi(2*sqrt(asinh(a*x))))/(64*a*sqrt(1 + a^2*x^2)) + (15*c^2*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erfi(sqrt(2)*sqrt(asinh(a*x))))/(64*a*sqrt(1 + a^2*x^2)) + (c^2*sqrt(pi/6)*sqrt(c + a^2*c*x^2)*erfi(sqrt(6)*sqrt(asinh(a*x))))/(64*a*sqrt(1 + a^2*x^2))]
    @test_int [(c + a^2*c*x^2)^(3/2)/sqrt(asinh(a*x)), x, 13, (3*c*sqrt(c + a^2*c*x^2)*sqrt(asinh(a*x)))/(4*a*sqrt(1 + a^2*x^2)) + (c*sqrt(pi)*sqrt(c + a^2*c*x^2)*erf(2*sqrt(asinh(a*x))))/(32*a*sqrt(1 + a^2*x^2)) + (c*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erf(sqrt(2)*sqrt(asinh(a*x))))/(4*a*sqrt(1 + a^2*x^2)) + (c*sqrt(pi)*sqrt(c + a^2*c*x^2)*erfi(2*sqrt(asinh(a*x))))/(32*a*sqrt(1 + a^2*x^2)) + (c*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erfi(sqrt(2)*sqrt(asinh(a*x))))/(4*a*sqrt(1 + a^2*x^2))]
    @test_int [sqrt(c + a^2*c*x^2)/sqrt(asinh(a*x)), x, 8, (sqrt(c + a^2*c*x^2)*sqrt(asinh(a*x)))/(a*sqrt(1 + a^2*x^2)) + (sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erf(sqrt(2)*sqrt(asinh(a*x))))/(4*a*sqrt(1 + a^2*x^2)) + (sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erfi(sqrt(2)*sqrt(asinh(a*x))))/(4*a*sqrt(1 + a^2*x^2))]
    @test_int [1/(sqrt(c + a^2*c*x^2)*sqrt(asinh(a*x))), x, 1, (2*sqrt(1 + a^2*x^2)*sqrt(asinh(a*x)))/(a*sqrt(c + a^2*c*x^2))]
    @test_int [1/((c + a^2*c*x^2)^(3/2)*sqrt(asinh(a*x))), x, 0, Unintegrable(1/((c + a^2*c*x^2)^(3/2)*sqrt(asinh(a*x))), x)]
    @test_int [1/((c + a^2*c*x^2)^(5/2)*sqrt(asinh(a*x))), x, 0, Unintegrable(1/((c + a^2*c*x^2)^(5/2)*sqrt(asinh(a*x))), x)]

    @test_int [(c + a^2*c*x^2)^(5/2)/asinh(a*x)^(3/2), x, 19, -((2*sqrt(1 + a^2*x^2)*(c + a^2*c*x^2)^(5/2))/(a*sqrt(asinh(a*x)))) - (3*c^2*sqrt(pi)*sqrt(c + a^2*c*x^2)*erf(2*sqrt(asinh(a*x))))/(8*a*sqrt(1 + a^2*x^2)) - (15*c^2*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erf(sqrt(2)*sqrt(asinh(a*x))))/(16*a*sqrt(1 + a^2*x^2)) - (c^2*sqrt((3*pi)/2)*sqrt(c + a^2*c*x^2)*erf(sqrt(6)*sqrt(asinh(a*x))))/(16*a*sqrt(1 + a^2*x^2)) + (3*c^2*sqrt(pi)*sqrt(c + a^2*c*x^2)*erfi(2*sqrt(asinh(a*x))))/(8*a*sqrt(1 + a^2*x^2)) + (15*c^2*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erfi(sqrt(2)*sqrt(asinh(a*x))))/(16*a*sqrt(1 + a^2*x^2)) + (c^2*sqrt((3*pi)/2)*sqrt(c + a^2*c*x^2)*erfi(sqrt(6)*sqrt(asinh(a*x))))/(16*a*sqrt(1 + a^2*x^2))]
    @test_int [(c + a^2*c*x^2)^(3/2)/asinh(a*x)^(3/2), x, 14, -((2*sqrt(1 + a^2*x^2)*(c + a^2*c*x^2)^(3/2))/(a*sqrt(asinh(a*x)))) - (c*sqrt(pi)*sqrt(c + a^2*c*x^2)*erf(2*sqrt(asinh(a*x))))/(4*a*sqrt(1 + a^2*x^2)) - (c*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erf(sqrt(2)*sqrt(asinh(a*x))))/(a*sqrt(1 + a^2*x^2)) + (c*sqrt(pi)*sqrt(c + a^2*c*x^2)*erfi(2*sqrt(asinh(a*x))))/(4*a*sqrt(1 + a^2*x^2)) + (c*sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erfi(sqrt(2)*sqrt(asinh(a*x))))/(a*sqrt(1 + a^2*x^2))]
    @test_int [sqrt(c + a^2*c*x^2)/asinh(a*x)^(3/2), x, 9, (-2*sqrt(1 + a^2*x^2)*sqrt(c + a^2*c*x^2))/(a*sqrt(asinh(a*x))) - (sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erf(sqrt(2)*sqrt(asinh(a*x))))/(a*sqrt(1 + a^2*x^2)) + (sqrt(pi/2)*sqrt(c + a^2*c*x^2)*erfi(sqrt(2)*sqrt(asinh(a*x))))/(a*sqrt(1 + a^2*x^2))]
    @test_int [1/(sqrt(c + a^2*c*x^2)*asinh(a*x)^(3/2)), x, 1, (-2*sqrt(1 + a^2*x^2))/(a*sqrt(c + a^2*c*x^2)*sqrt(asinh(a*x)))]
    @test_int [1/((c + a^2*c*x^2)^(3/2)*asinh(a*x)^(3/2)), x, 1, -((2*sqrt(1 + a^2*x^2))/(a*(c + a^2*c*x^2)^(3/2)*sqrt(asinh(a*x)))) - (4*a*sqrt(1 + a^2*x^2)*Unintegrable(x/((1 + a^2*x^2)^2*sqrt(asinh(a*x))), x))/(c*sqrt(c + a^2*c*x^2))]
    @test_int [1/((c + a^2*c*x^2)^(5/2)*asinh(a*x)^(3/2)), x, 1, -((2*sqrt(1 + a^2*x^2))/(a*(c + a^2*c*x^2)^(5/2)*sqrt(asinh(a*x)))) - (8*a*sqrt(1 + a^2*x^2)*Unintegrable(x/((1 + a^2*x^2)^3*sqrt(asinh(a*x))), x))/(c^2*sqrt(c + a^2*c*x^2))]

    @test_int [(c + a^2*c*x^2)^(3/2)/asinh(a*x)^(5/2), x, 18, -((2*sqrt(1 + a^2*x^2)*(c + a^2*c*x^2)^(3/2))/(3*a*asinh(a*x)^(3/2))) - (16*c*x*(1 + a^2*x^2)*sqrt(c + a^2*c*x^2))/(3*sqrt(asinh(a*x))) + (2*c*sqrt(pi)*sqrt(c + a^2*c*x^2)*erf(2*sqrt(asinh(a*x))))/(3*a*sqrt(1 + a^2*x^2)) + (2*c*sqrt(2*pi)*sqrt(c + a^2*c*x^2)*erf(sqrt(2)*sqrt(asinh(a*x))))/(3*a*sqrt(1 + a^2*x^2)) + (2*c*sqrt(pi)*sqrt(c + a^2*c*x^2)*erfi(2*sqrt(asinh(a*x))))/(3*a*sqrt(1 + a^2*x^2)) + (2*c*sqrt(2*pi)*sqrt(c + a^2*c*x^2)*erfi(sqrt(2)*sqrt(asinh(a*x))))/(3*a*sqrt(1 + a^2*x^2))]
    @test_int [sqrt(c + a^2*c*x^2)/asinh(a*x)^(5/2), x, 7, (-2*sqrt(1 + a^2*x^2)*sqrt(c + a^2*c*x^2))/(3*a*asinh(a*x)^(3/2)) - (8*x*sqrt(c + a^2*c*x^2))/(3*sqrt(asinh(a*x))) + (2*sqrt(2*pi)*sqrt(c + a^2*c*x^2)*erf(sqrt(2)*sqrt(asinh(a*x))))/(3*a*sqrt(1 + a^2*x^2)) + (2*sqrt(2*pi)*sqrt(c + a^2*c*x^2)*erfi(sqrt(2)*sqrt(asinh(a*x))))/(3*a*sqrt(1 + a^2*x^2))]
    @test_int [1/(sqrt(c + a^2*c*x^2)*asinh(a*x)^(5/2)), x, 1, (-2*sqrt(1 + a^2*x^2))/(3*a*sqrt(c + a^2*c*x^2)*asinh(a*x)^(3/2))]
    @test_int [1/((c + a^2*c*x^2)^(3/2)*asinh(a*x)^(5/2)), x, 1, -((2*sqrt(1 + a^2*x^2))/(3*a*(c + a^2*c*x^2)^(3/2)*asinh(a*x)^(3/2))) - (4*a*sqrt(1 + a^2*x^2)*Unintegrable(x/((1 + a^2*x^2)^2*asinh(a*x)^(3/2)), x))/(3*c*sqrt(c + a^2*c*x^2))]
    @test_int [1/((c + a^2*c*x^2)^(5/2)*asinh(a*x)^(5/2)), x, 1, -((2*sqrt(1 + a^2*x^2))/(3*a*(c + a^2*c*x^2)^(5/2)*asinh(a*x)^(3/2))) - (8*a*sqrt(1 + a^2*x^2)*Unintegrable(x/((1 + a^2*x^2)^3*asinh(a*x)^(3/2)), x))/(3*c^2*sqrt(c + a^2*c*x^2))]

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

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

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

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

    @test_int [x^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n, x, 6, -(sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^(1 + n))/(8*b*c^3*(1 + n)*sqrt(1 + c^2*x^2)) + (sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-4*(a + b*asinh(c*x)))/b))/(2^(2*(3 + n))*c^3*ℯ^((4*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) - (ℯ^((4*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (4*(a + b*asinh(c*x)))/b))/(2^(2*(3 + n))*c^3*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n)]
    @test_int [x*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n, x, 9, (3^(-1 - n)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-3*(a + b*asinh(c*x)))/b))/(8*c^2*ℯ^((3*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) + (sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, -((a + b*asinh(c*x))/b)))/(8*c^2*ℯ^(a/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) + (ℯ^(a/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (a + b*asinh(c*x))/b))/(8*c^2*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n) + (3^(-1 - n)*ℯ^((3*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (3*(a + b*asinh(c*x)))/b))/(8*c^2*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n)]
    @test_int [sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n, x, 6, (sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^(1 + n))/(2*b*c*(1 + n)*sqrt(1 + c^2*x^2)) + (2^(-3 - n)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-2*(a + b*asinh(c*x)))/b))/(c*ℯ^((2*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) - (2^(-3 - n)*ℯ^((2*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (2*(a + b*asinh(c*x)))/b))/(c*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n)]
    @test_int [(sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n)/x, x, 6, (d*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, -((a + b*asinh(c*x))/b)))/(ℯ^(a/b)*(-((a + b*asinh(c*x))/b))^n*(2*sqrt(d + c^2*d*x^2))) + (d*ℯ^(a/b)*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (a + b*asinh(c*x))/b))/(((a + b*asinh(c*x))/b)^n*(2*sqrt(d + c^2*d*x^2))) + d*Unintegrable((a + b*asinh(c*x))^n/(x*sqrt(d + c^2*d*x^2)), x)]
    @test_int [(sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n)/x^2, x, 3, (c*d*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^(1 + n))/(b*(1 + n)*sqrt(d + c^2*d*x^2)) + d*Unintegrable((a + b*asinh(c*x))^n/(x^2*sqrt(d + c^2*d*x^2)), x)]

    @test_int [x^2*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^n, x, 12, -(d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^(1 + n))/(16*b*c^3*(1 + n)*sqrt(1 + c^2*x^2)) + (2^(-7 - n)*3^(-1 - n)*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-6*(a + b*asinh(c*x)))/b))/(c^3*ℯ^((6*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) + (2^(-7 - 2*n)*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-4*(a + b*asinh(c*x)))/b))/(c^3*ℯ^((4*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) - (2^(-7 - n)*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-2*(a + b*asinh(c*x)))/b))/(c^3*ℯ^((2*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) + (2^(-7 - n)*d*ℯ^((2*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (2*(a + b*asinh(c*x)))/b))/(c^3*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n) - (2^(-7 - 2*n)*d*ℯ^((4*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (4*(a + b*asinh(c*x)))/b))/(c^3*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n) - (2^(-7 - n)*3^(-1 - n)*d*ℯ^((6*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (6*(a + b*asinh(c*x)))/b))/(c^3*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n)]
    @test_int [x*(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^n, x, 12, (5^(-1 - n)*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-5*(a + b*asinh(c*x)))/b))/(32*c^2*ℯ^((5*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) + (d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-3*(a + b*asinh(c*x)))/b))/(32*3^n*c^2*ℯ^((3*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) + (d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, -((a + b*asinh(c*x))/b)))/(16*c^2*ℯ^(a/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) + (d*ℯ^(a/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (a + b*asinh(c*x))/b))/(16*c^2*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n) + (d*ℯ^((3*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (3*(a + b*asinh(c*x)))/b))/(32*3^n*c^2*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n) + (5^(-1 - n)*d*ℯ^((5*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (5*(a + b*asinh(c*x)))/b))/(32*c^2*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n)]
    @test_int [(d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^n, x, 9, (3*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^(1 + n))/(8*b*c*(1 + n)*sqrt(1 + c^2*x^2)) + (d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-4*(a + b*asinh(c*x)))/b))/(2^(2*(3 + n))*c*ℯ^((4*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) + (2^(-3 - n)*d*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-2*(a + b*asinh(c*x)))/b))/(c*ℯ^((2*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) - (2^(-3 - n)*d*ℯ^((2*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (2*(a + b*asinh(c*x)))/b))/(c*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n) - (d*ℯ^((4*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (4*(a + b*asinh(c*x)))/b))/(2^(2*(3 + n))*c*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n)]
    @test_int [((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^n)/x, x, 15, (1/(8*sqrt(d + c^2*d*x^2)))*((3^(-1 - n)*d^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, -((3*(a + b*asinh(c*x)))/b)))/(ℯ^((3*a)/b)*(-((a + b*asinh(c*x))/b))^n)) + (5*d^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, -((a + b*asinh(c*x))/b)))/(ℯ^(a/b)*(-((a + b*asinh(c*x))/b))^n*(8*sqrt(d + c^2*d*x^2))) + (5*d^2*ℯ^(a/b)*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (a + b*asinh(c*x))/b))/(((a + b*asinh(c*x))/b)^n*(8*sqrt(d + c^2*d*x^2))) + (1/(8*sqrt(d + c^2*d*x^2)))*((3^(-1 - n)*d^2*ℯ^((3*a)/b)*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (3*(a + b*asinh(c*x)))/b))/((a + b*asinh(c*x))/b)^n) + d^2*Unintegrable((a + b*asinh(c*x))^n/(x*sqrt(d + c^2*d*x^2)), x)]
    @test_int [((d + c^2*d*x^2)^(3/2)*(a + b*asinh(c*x))^n)/x^2, x, 9, (3*c*d^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^(1 + n))/(2*b*(1 + n)*sqrt(d + c^2*d*x^2)) + (1/sqrt(d + c^2*d*x^2))*((2^(-3 - n)*c*d^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, -((2*(a + b*asinh(c*x)))/b)))/(ℯ^((2*a)/b)*(-((a + b*asinh(c*x))/b))^n)) - (1/sqrt(d + c^2*d*x^2))*((2^(-3 - n)*c*d^2*ℯ^((2*a)/b)*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (2*(a + b*asinh(c*x)))/b))/((a + b*asinh(c*x))/b)^n) + d^2*Unintegrable((a + b*asinh(c*x))^n/(x^2*sqrt(d + c^2*d*x^2)), x)]

    @test_int [x^2*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^n, x, 15, (-5*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^(1 + n))/(128*b*c^3*(1 + n)*sqrt(1 + c^2*x^2)) + (2^(-11 - 3*n)*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-8*(a + b*asinh(c*x)))/b))/(c^3*ℯ^((8*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) + (2^(-7 - n)*3^(-1 - n)*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-6*(a + b*asinh(c*x)))/b))/(c^3*ℯ^((6*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) + (d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-4*(a + b*asinh(c*x)))/b))/(2^(2*(4 + n))*c^3*ℯ^((4*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) - (2^(-7 - n)*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-2*(a + b*asinh(c*x)))/b))/(c^3*ℯ^((2*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) + (2^(-7 - n)*d^2*ℯ^((2*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (2*(a + b*asinh(c*x)))/b))/(c^3*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n) - (d^2*ℯ^((4*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (4*(a + b*asinh(c*x)))/b))/(2^(2*(4 + n))*c^3*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n) - (2^(-7 - n)*3^(-1 - n)*d^2*ℯ^((6*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (6*(a + b*asinh(c*x)))/b))/(c^3*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n) - (2^(-11 - 3*n)*d^2*ℯ^((8*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (8*(a + b*asinh(c*x)))/b))/(c^3*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n)]
    @test_int [x*(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^n, x, 15, (7^(-1 - n)*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-7*(a + b*asinh(c*x)))/b))/(128*c^2*ℯ^((7*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) + (d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-5*(a + b*asinh(c*x)))/b))/(128*5^n*c^2*ℯ^((5*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) + (3^(1 - n)*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-3*(a + b*asinh(c*x)))/b))/(128*c^2*ℯ^((3*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) + (5*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, -((a + b*asinh(c*x))/b)))/(128*c^2*ℯ^(a/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) + (5*d^2*ℯ^(a/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (a + b*asinh(c*x))/b))/(128*c^2*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n) + (3^(1 - n)*d^2*ℯ^((3*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (3*(a + b*asinh(c*x)))/b))/(128*c^2*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n) + (d^2*ℯ^((5*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (5*(a + b*asinh(c*x)))/b))/(128*5^n*c^2*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n) + (7^(-1 - n)*d^2*ℯ^((7*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (7*(a + b*asinh(c*x)))/b))/(128*c^2*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n)]
    @test_int [(d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^n, x, 12, (5*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^(1 + n))/(16*b*c*(1 + n)*sqrt(1 + c^2*x^2)) + (2^(-7 - n)*3^(-1 - n)*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-6*(a + b*asinh(c*x)))/b))/(c*ℯ^((6*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) + (3*2^(-7 - 2*n)*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-4*(a + b*asinh(c*x)))/b))/(c*ℯ^((4*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) + (15*2^(-7 - n)*d^2*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (-2*(a + b*asinh(c*x)))/b))/(c*ℯ^((2*a)/b)*sqrt(1 + c^2*x^2)*(-((a + b*asinh(c*x))/b))^n) - (15*2^(-7 - n)*d^2*ℯ^((2*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (2*(a + b*asinh(c*x)))/b))/(c*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n) - (3*2^(-7 - 2*n)*d^2*ℯ^((4*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (4*(a + b*asinh(c*x)))/b))/(c*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n) - (2^(-7 - n)*3^(-1 - n)*d^2*ℯ^((6*a)/b)*sqrt(d + c^2*d*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (6*(a + b*asinh(c*x)))/b))/(c*sqrt(1 + c^2*x^2)*((a + b*asinh(c*x))/b)^n)]
    @test_int [((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^n)/x, x, 27, (1/(32*sqrt(d + c^2*d*x^2)))*((5^(-1 - n)*d^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, -((5*(a + b*asinh(c*x)))/b)))/(ℯ^((5*a)/b)*(-((a + b*asinh(c*x))/b))^n)) - (1/(32*sqrt(d + c^2*d*x^2)))*((5*3^(-1 - n)*d^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, -((3*(a + b*asinh(c*x)))/b)))/(ℯ^((3*a)/b)*(-((a + b*asinh(c*x))/b))^n)) + (1/(8*sqrt(d + c^2*d*x^2)))*((d^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, -((3*(a + b*asinh(c*x)))/b)))/(3^n*ℯ^((3*a)/b)*(-((a + b*asinh(c*x))/b))^n)) + (11*d^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, -((a + b*asinh(c*x))/b)))/(ℯ^(a/b)*(-((a + b*asinh(c*x))/b))^n*(16*sqrt(d + c^2*d*x^2))) + (11*d^3*ℯ^(a/b)*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (a + b*asinh(c*x))/b))/(((a + b*asinh(c*x))/b)^n*(16*sqrt(d + c^2*d*x^2))) - (1/(32*sqrt(d + c^2*d*x^2)))*((5*3^(-1 - n)*d^3*ℯ^((3*a)/b)*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (3*(a + b*asinh(c*x)))/b))/((a + b*asinh(c*x))/b)^n) + (d^3*ℯ^((3*a)/b)*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (3*(a + b*asinh(c*x)))/b))/(3^n*((a + b*asinh(c*x))/b)^n*(8*sqrt(d + c^2*d*x^2))) + (1/(32*sqrt(d + c^2*d*x^2)))*((5^(-1 - n)*d^3*ℯ^((5*a)/b)*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (5*(a + b*asinh(c*x)))/b))/((a + b*asinh(c*x))/b)^n) + d^3*Unintegrable((a + b*asinh(c*x))^n/(x*sqrt(d + c^2*d*x^2)), x)]
    @test_int [((d + c^2*d*x^2)^(5/2)*(a + b*asinh(c*x))^n)/x^2, x, 18, (15*c*d^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^(1 + n))/(8*b*(1 + n)*sqrt(d + c^2*d*x^2)) + (1/sqrt(d + c^2*d*x^2))*((c*d^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, -((4*(a + b*asinh(c*x)))/b)))/(2^(2*(3 + n))*ℯ^((4*a)/b)*(-((a + b*asinh(c*x))/b))^n)) + (1/sqrt(d + c^2*d*x^2))*((2^(-2 - n)*c*d^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, -((2*(a + b*asinh(c*x)))/b)))/(ℯ^((2*a)/b)*(-((a + b*asinh(c*x))/b))^n)) - (1/sqrt(d + c^2*d*x^2))*((2^(-2 - n)*c*d^3*ℯ^((2*a)/b)*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (2*(a + b*asinh(c*x)))/b))/((a + b*asinh(c*x))/b)^n) - (1/sqrt(d + c^2*d*x^2))*((c*d^3*ℯ^((4*a)/b)*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^n*Gamma(1 + n, (4*(a + b*asinh(c*x)))/b))/(2^(2*(3 + n))*((a + b*asinh(c*x))/b)^n)) + d^3*Unintegrable((a + b*asinh(c*x))^n/(x^2*sqrt(d + c^2*d*x^2)), x)]

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

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

    @test_int [(x^3*asinh(a*x)^n)/sqrt(1 + a^2*x^2), x, 9, (3^(-1 - n)*asinh(a*x)^n*Gamma(1 + n, -3*asinh(a*x)))/(8*a^4*(-asinh(a*x))^n) - (3*asinh(a*x)^n*Gamma(1 + n, -asinh(a*x)))/(8*a^4*(-asinh(a*x))^n) - (3*Gamma(1 + n, asinh(a*x)))/(8*a^4) + (3^(-1 - n)*Gamma(1 + n, 3*asinh(a*x)))/(8*a^4)]
    @test_int [(x^2*asinh(a*x)^n)/sqrt(1 + a^2*x^2), x, 6, -asinh(a*x)^(1 + n)/(2*a^3*(1 + n)) + (2^(-3 - n)*asinh(a*x)^n*Gamma(1 + n, -2*asinh(a*x)))/(a^3*(-asinh(a*x))^n) - (2^(-3 - n)*Gamma(1 + n, 2*asinh(a*x)))/a^3]
    @test_int [(x*asinh(a*x)^n)/sqrt(1 + a^2*x^2), x, 4, (asinh(a*x)^n*Gamma(1 + n, -asinh(a*x)))/(2*a^2*(-asinh(a*x))^n) + Gamma(1 + n, asinh(a*x))/(2*a^2)]
    @test_int [asinh(a*x)^n/sqrt(1 + a^2*x^2), x, 1, asinh(a*x)^(1 + n)/(a*(1 + n))]
    @test_int [asinh(a*x)^n/(x*sqrt(1 + a^2*x^2)), x, 0, Unintegrable(asinh(a*x)^n/(x*sqrt(1 + a^2*x^2)), x)]
    @test_int [asinh(a*x)^n/(x^2*sqrt(1 + a^2*x^2)), x, 0, Unintegrable(asinh(a*x)^n/(x^2*sqrt(1 + a^2*x^2)), x)]

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

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(d+e*x)^(p/2)*(f+g*x)^(q/2)*(a+b*asinh(c*x))^1*with*e*f+d*g=0*and*c^2*d^2+e^2=0=#

    #= ::Subsubsection::Closed:: =#
    #=q>0=#

    @test_int [(d + im*c*d*x)^(5/2)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)), x, 13, (((-2*im)/3)*b*d^2*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/sqrt(1 + c^2*x^2) - (3*b*c*d^2*x^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/(16*sqrt(1 + c^2*x^2)) - (((2*im)/9)*b*c^2*d^2*x^3*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/sqrt(1 + c^2*x^2) + (b*c^3*d^2*x^4*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/(16*sqrt(1 + c^2*x^2)) + (3*d^2*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/8 - (c^2*d^2*x^3*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/4 + (((2*im)/3)*d^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(1 + c^2*x^2)*(a + b*asinh(c*x)))/c + (5*d^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2)/(16*b*c*sqrt(1 + c^2*x^2))]
    @test_int [(d + im*c*d*x)^(3/2)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)), x, 8, ((-im/3)*b*d*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/sqrt(1 + c^2*x^2) - (b*c*d*x^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/(4*sqrt(1 + c^2*x^2)) - ((im/9)*b*c^2*d*x^3*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/sqrt(1 + c^2*x^2) + (d*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/2 + ((im/3)*d*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(1 + c^2*x^2)*(a + b*asinh(c*x)))/c + (d*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2)/(4*b*c*sqrt(1 + c^2*x^2))]
    @test_int [sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)), x, 4, -(b*c*x^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/(4*sqrt(1 + c^2*x^2)) + (x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/2 + (sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2)/(4*b*c*sqrt(1 + c^2*x^2))]
    @test_int [(sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/sqrt(d + im*c*d*x), x, 6, (im*b*f*x*sqrt(1 + c^2*x^2))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (im*f*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (f*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(2*b*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))]
    @test_int [(sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/(d + im*c*d*x)^(3/2), x, 8, ((2*im)*f^2*(1 - im*c*x)*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (f^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(2*b*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (2*b*f^2*(1 + c^2*x^2)^(3/2)*log(im - c*x))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [(sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/(d + im*c*d*x)^(5/2), x, 6, (((2*im)/3)*b*f^3*(1 + c^2*x^2)^(5/2))/(c*(im - c*x)*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + ((im/3)*f^3*(1 - im*c*x)^3*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (b*f^3*(1 + c^2*x^2)^(5/2)*log(im - c*x))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]

    @test_int [(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)), x, 12, ((-im/5)*b*d*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/(1 + c^2*x^2)^(3/2) - (5*b*c*d*x^2*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/(16*(1 + c^2*x^2)^(3/2)) - (((2*im)/15)*b*c^2*d*x^3*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/(1 + c^2*x^2)^(3/2) - (b*c^3*d*x^4*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/(16*(1 + c^2*x^2)^(3/2)) - ((im/25)*b*c^4*d*x^5*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/(1 + c^2*x^2)^(3/2) + (d*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/4 + (3*d*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/(8*(1 + c^2*x^2)) + ((im/5)*d*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(1 + c^2*x^2)*(a + b*asinh(c*x)))/c + (3*d*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^2)/(16*b*c*(1 + c^2*x^2)^(3/2))]
    @test_int [(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)), x, 7, (-5*b*c*x^2*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/(16*(1 + c^2*x^2)^(3/2)) - (b*c^3*x^4*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/(16*(1 + c^2*x^2)^(3/2)) + (x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/4 + (3*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/(8*(1 + c^2*x^2)) + (3*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^2)/(16*b*c*(1 + c^2*x^2)^(3/2))]
    @test_int [sqrt(d + im*c*d*x)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)), x, 8, ((im/3)*b*f*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/sqrt(1 + c^2*x^2) - (b*c*f*x^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/(4*sqrt(1 + c^2*x^2)) + ((im/9)*b*c^2*f*x^3*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/sqrt(1 + c^2*x^2) + (f*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/2 - ((im/3)*f*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(1 + c^2*x^2)*(a + b*asinh(c*x)))/c + (f*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2)/(4*b*c*sqrt(1 + c^2*x^2))]
    @test_int [((f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/sqrt(d + im*c*d*x), x, 9, ((2*im)*b*f^2*x*sqrt(1 + c^2*x^2))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (b*c*f^2*x^2*sqrt(1 + c^2*x^2))/(4*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - ((2*im)*f^2*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (f^2*x*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (3*f^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(4*b*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))]
    @test_int [((f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/(d + im*c*d*x)^(3/2), x, 10, ((-im)*b*f^3*x*(1 + c^2*x^2)^(3/2))/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + ((4*im)*f^3*(1 - im*c*x)*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (im*f^3*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (3*f^3*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(2*b*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (4*b*f^3*(1 + c^2*x^2)^(3/2)*log(im - c*x))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [((f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/(d + im*c*d*x)^(5/2), x, 9, (((4*im)/3)*b*f^4*(1 + c^2*x^2)^(5/2))/(c*(im - c*x)*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (b*f^4*(1 + c^2*x^2)^(5/2)*asinh(c*x)^2)/(2*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (((2*im)/3)*f^4*(1 - im*c*x)^3*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - ((2*im)*f^4*(1 - im*c*x)*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (f^4*(1 + c^2*x^2)^(5/2)*asinh(c*x)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (8*b*f^4*(1 + c^2*x^2)^(5/2)*log(im - c*x))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]

    @test_int [(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)*(a + b*asinh(c*x)), x, 9, (-25*b*c*x^2*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))/(96*(1 + c^2*x^2)^(5/2)) - (5*b*c^3*x^4*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))/(96*(1 + c^2*x^2)^(5/2)) - (b*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)*sqrt(1 + c^2*x^2))/(36*c) + (x*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)*(a + b*asinh(c*x)))/6 + (5*x*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)*(a + b*asinh(c*x)))/(16*(1 + c^2*x^2)^2) + (5*x*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)*(a + b*asinh(c*x)))/(24*(1 + c^2*x^2)) + (5*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)*(a + b*asinh(c*x))^2)/(32*b*c*(1 + c^2*x^2)^(5/2))]
    @test_int [(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(5/2)*(a + b*asinh(c*x)), x, 12, ((im/5)*b*f*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/(1 + c^2*x^2)^(3/2) - (5*b*c*f*x^2*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/(16*(1 + c^2*x^2)^(3/2)) + (((2*im)/15)*b*c^2*f*x^3*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/(1 + c^2*x^2)^(3/2) - (b*c^3*f*x^4*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/(16*(1 + c^2*x^2)^(3/2)) + ((im/25)*b*c^4*f*x^5*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/(1 + c^2*x^2)^(3/2) + (f*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/4 + (3*f*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/(8*(1 + c^2*x^2)) - ((im/5)*f*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(1 + c^2*x^2)*(a + b*asinh(c*x)))/c + (3*f*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^2)/(16*b*c*(1 + c^2*x^2)^(3/2))]
    @test_int [sqrt(d + im*c*d*x)*(f - im*c*f*x)^(5/2)*(a + b*asinh(c*x)), x, 13, (((2*im)/3)*b*f^2*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/sqrt(1 + c^2*x^2) - (3*b*c*f^2*x^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/(16*sqrt(1 + c^2*x^2)) + (((2*im)/9)*b*c^2*f^2*x^3*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/sqrt(1 + c^2*x^2) + (b*c^3*f^2*x^4*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/(16*sqrt(1 + c^2*x^2)) + (3*f^2*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/8 - (c^2*f^2*x^3*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/4 - (((2*im)/3)*f^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(1 + c^2*x^2)*(a + b*asinh(c*x)))/c + (5*f^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2)/(16*b*c*sqrt(1 + c^2*x^2))]
    @test_int [((f - im*c*f*x)^(5/2)*(a + b*asinh(c*x)))/sqrt(d + im*c*d*x), x, 13, (((11*im)/3)*b*f^3*x*sqrt(1 + c^2*x^2))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (3*b*c*f^3*x^2*sqrt(1 + c^2*x^2))/(4*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - ((im/9)*b*c^2*f^3*x^3*sqrt(1 + c^2*x^2))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (((11*im)/3)*f^3*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (3*f^3*x*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + ((im/3)*c*f^3*x^2*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (5*f^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(4*b*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))]
    @test_int [((f - im*c*f*x)^(5/2)*(a + b*asinh(c*x)))/(d + im*c*d*x)^(3/2), x, 7, (((-3*im)/2)*b*f^4*x*(1 + c^2*x^2)^(3/2))/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (b*c*f^4*x^2*(1 + c^2*x^2)^(3/2))/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (5*b*f^4*(1 - im*c*x)^2*(1 + c^2*x^2)^(3/2))/(4*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (15*b*f^4*(1 + c^2*x^2)^(3/2)*asinh(c*x)^2)/(4*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + ((2*im)*f^4*(1 - im*c*x)^3*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (((15*im)/2)*f^4*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (((5*im)/2)*f^4*(1 - im*c*x)*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (15*f^4*(1 + c^2*x^2)^(3/2)*asinh(c*x)*(a + b*asinh(c*x)))/(2*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (8*b*f^4*(1 + c^2*x^2)^(3/2)*log(im - c*x))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [((f - im*c*f*x)^(5/2)*(a + b*asinh(c*x)))/(d + im*c*d*x)^(5/2), x, 10, (im*b*f^5*x*(1 + c^2*x^2)^(5/2))/((d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (((8*im)/3)*b*f^5*(1 + c^2*x^2)^(5/2))/(c*(im - c*x)*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (5*b*f^5*(1 + c^2*x^2)^(5/2)*asinh(c*x)^2)/(2*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (((2*im)/3)*f^5*(1 - im*c*x)^4*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (((10*im)/3)*f^5*(1 - im*c*x)^2*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - ((5*im)*f^5*(1 + c^2*x^2)^3*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (5*f^5*(1 + c^2*x^2)^(5/2)*asinh(c*x)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (28*b*f^5*(1 + c^2*x^2)^(5/2)*log(im - c*x))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]

    #= ::Subsubsection::Closed:: =#
    #=q<0=#

    @test_int [((d + im*c*d*x)^(5/2)*(a + b*asinh(c*x)))/sqrt(f - im*c*f*x), x, 13, (((-11*im)/3)*b*d^3*x*sqrt(1 + c^2*x^2))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (3*b*c*d^3*x^2*sqrt(1 + c^2*x^2))/(4*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + ((im/9)*b*c^2*d^3*x^3*sqrt(1 + c^2*x^2))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (((11*im)/3)*d^3*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (3*d^3*x*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - ((im/3)*c*d^3*x^2*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (5*d^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(4*b*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))]
    @test_int [((d + im*c*d*x)^(3/2)*(a + b*asinh(c*x)))/sqrt(f - im*c*f*x), x, 9, ((-2*im)*b*d^2*x*sqrt(1 + c^2*x^2))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (b*c*d^2*x^2*sqrt(1 + c^2*x^2))/(4*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + ((2*im)*d^2*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (d^2*x*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (3*d^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(4*b*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))]
    @test_int [(sqrt(d + im*c*d*x)*(a + b*asinh(c*x)))/sqrt(f - im*c*f*x), x, 6, ((-im)*b*d*x*sqrt(1 + c^2*x^2))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (im*d*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (d*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(2*b*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))]
    @test_int [(a + b*asinh(c*x))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)), x, 2, (sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(2*b*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))]
    @test_int [(a + b*asinh(c*x))/((d + im*c*d*x)^(3/2)*sqrt(f - im*c*f*x)), x, 5, (f*(im + c*x)*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (b*f*(1 + c^2*x^2)^(3/2)*log(im - c*x))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [(a + b*asinh(c*x))/((d + im*c*d*x)^(5/2)*sqrt(f - im*c*f*x)), x, 8, ((im/3)*b*f^2*(1 + c^2*x^2)^(5/2))/(c*(im - c*x)*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (((2*im)/3)*f^2*(1 - im*c*x)*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (f^2*x*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - ((im/3)*b*f^2*(1 + c^2*x^2)^(5/2)*atan(c*x))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (b*f^2*(1 + c^2*x^2)^(5/2)*log(1 + c^2*x^2))/(6*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]

    @test_int [((d + im*c*d*x)^(5/2)*(a + b*asinh(c*x)))/(f - im*c*f*x)^(3/2), x, 7, (((3*im)/2)*b*d^4*x*(1 + c^2*x^2)^(3/2))/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (b*c*d^4*x^2*(1 + c^2*x^2)^(3/2))/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (5*b*d^4*(1 + im*c*x)^2*(1 + c^2*x^2)^(3/2))/(4*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (15*b*d^4*(1 + c^2*x^2)^(3/2)*asinh(c*x)^2)/(4*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - ((2*im)*d^4*(1 + im*c*x)^3*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (((15*im)/2)*d^4*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (((5*im)/2)*d^4*(1 + im*c*x)*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (15*d^4*(1 + c^2*x^2)^(3/2)*asinh(c*x)*(a + b*asinh(c*x)))/(2*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (8*b*d^4*(1 + c^2*x^2)^(3/2)*log(im + c*x))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [((d + im*c*d*x)^(3/2)*(a + b*asinh(c*x)))/(f - im*c*f*x)^(3/2), x, 10, (im*b*d^3*x*(1 + c^2*x^2)^(3/2))/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - ((4*im)*d^3*(1 + im*c*x)*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (im*d^3*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (3*d^3*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(2*b*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (4*b*d^3*(1 + c^2*x^2)^(3/2)*log(im + c*x))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [(sqrt(d + im*c*d*x)*(a + b*asinh(c*x)))/(f - im*c*f*x)^(3/2), x, 8, ((-2*im)*d^2*(1 + im*c*x)*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (d^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(2*b*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (2*b*d^2*(1 + c^2*x^2)^(3/2)*log(im + c*x))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [(a + b*asinh(c*x))/(sqrt(d + im*c*d*x)*(f - im*c*f*x)^(3/2)), x, 5, -((d*(im - c*x)*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))) - (b*d*(1 + c^2*x^2)^(3/2)*log(im + c*x))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [(a + b*asinh(c*x))/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)), x, 3, (x*(1 + c^2*x^2)*(a + b*asinh(c*x)))/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (b*(1 + c^2*x^2)^(3/2)*log(1 + c^2*x^2))/(2*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [(a + b*asinh(c*x))/((d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(3/2)), x, 8, ((im/6)*b*f*(1 + c^2*x^2)^(5/2))/(c*(im - c*x)*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (f*(im + c*x)*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (2*f*x*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - ((im/6)*b*f*(1 + c^2*x^2)^(5/2)*atan(c*x))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (b*f*(1 + c^2*x^2)^(5/2)*log(1 + c^2*x^2))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]

    @test_int [((d + im*c*d*x)^(5/2)*(a + b*asinh(c*x)))/(f - im*c*f*x)^(5/2), x, 10, ((-im)*b*d^5*x*(1 + c^2*x^2)^(5/2))/((d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (((8*im)/3)*b*d^5*(1 + c^2*x^2)^(5/2))/(c*(im + c*x)*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (5*b*d^5*(1 + c^2*x^2)^(5/2)*asinh(c*x)^2)/(2*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (((2*im)/3)*d^5*(1 + im*c*x)^4*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (((10*im)/3)*d^5*(1 + im*c*x)^2*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + ((5*im)*d^5*(1 + c^2*x^2)^3*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (5*d^5*(1 + c^2*x^2)^(5/2)*asinh(c*x)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (28*b*d^5*(1 + c^2*x^2)^(5/2)*log(im + c*x))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]
    @test_int [((d + im*c*d*x)^(3/2)*(a + b*asinh(c*x)))/(f - im*c*f*x)^(5/2), x, 9, (((4*im)/3)*b*d^4*(1 + c^2*x^2)^(5/2))/(c*(im + c*x)*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (b*d^4*(1 + c^2*x^2)^(5/2)*asinh(c*x)^2)/(2*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (((2*im)/3)*d^4*(1 + im*c*x)^3*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + ((2*im)*d^4*(1 + im*c*x)*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (d^4*(1 + c^2*x^2)^(5/2)*asinh(c*x)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (8*b*d^4*(1 + c^2*x^2)^(5/2)*log(im + c*x))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]
    @test_int [(sqrt(d + im*c*d*x)*(a + b*asinh(c*x)))/(f - im*c*f*x)^(5/2), x, 6, (((2*im)/3)*b*d^3*(1 + c^2*x^2)^(5/2))/(c*(im + c*x)*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - ((im/3)*d^3*(1 + im*c*x)^3*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (b*d^3*(1 + c^2*x^2)^(5/2)*log(im + c*x))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]
    @test_int [(a + b*asinh(c*x))/(sqrt(d + im*c*d*x)*(f - im*c*f*x)^(5/2)), x, 8, ((im/3)*b*d^2*(1 + c^2*x^2)^(5/2))/(c*(im + c*x)*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (((2*im)/3)*d^2*(1 + im*c*x)*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (d^2*x*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + ((im/3)*b*d^2*(1 + c^2*x^2)^(5/2)*atan(c*x))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (b*d^2*(1 + c^2*x^2)^(5/2)*log(1 + c^2*x^2))/(6*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]
    @test_int [(a + b*asinh(c*x))/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(5/2)), x, 8, ((im/6)*b*d*(1 + c^2*x^2)^(5/2))/(c*(im + c*x)*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (d*(im - c*x)*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (2*d*x*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + ((im/6)*b*d*(1 + c^2*x^2)^(5/2)*atan(c*x))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (b*d*(1 + c^2*x^2)^(5/2)*log(1 + c^2*x^2))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]
    @test_int [(a + b*asinh(c*x))/((d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)), x, 5, (b*(1 + c^2*x^2)^(3/2))/(6*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (x*(1 + c^2*x^2)*(a + b*asinh(c*x)))/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (2*x*(1 + c^2*x^2)^2*(a + b*asinh(c*x)))/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (b*(1 + c^2*x^2)^(5/2)*log(1 + c^2*x^2))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(d+e*x)^(p/2)*(f+g*x)^(q/2)*(a+b*asinh(c*x))^2*with*e*f+d*g=0*and*c^2*d^2+e^2=0=#

    #= ::Subsubsection::Closed:: =#
    #=q>0=#

    @test_int [(d + im*c*d*x)^(5/2)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2, x, 23, (((8*im)/9)*b^2*d^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/c + (15*b^2*d^2*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/64 - (b^2*c^2*d^2*x^3*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/32 + (((4*im)/27)*b^2*d^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(1 + c^2*x^2))/c - (15*b^2*d^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*asinh(c*x))/(64*c*sqrt(1 + c^2*x^2)) - (((4*im)/3)*b*d^2*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/sqrt(1 + c^2*x^2) - (3*b*c*d^2*x^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/(8*sqrt(1 + c^2*x^2)) - (((4*im)/9)*b*c^2*d^2*x^3*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/sqrt(1 + c^2*x^2) + (b*c^3*d^2*x^4*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/(8*sqrt(1 + c^2*x^2)) + (3*d^2*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2)/8 - (c^2*d^2*x^3*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2)/4 + (((2*im)/3)*d^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/c + (5*d^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^3)/(24*b*c*sqrt(1 + c^2*x^2))]
    @test_int [(d + im*c*d*x)^(3/2)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2, x, 13, (((4*im)/9)*b^2*d*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/c + (b^2*d*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/4 + (((2*im)/27)*b^2*d*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(1 + c^2*x^2))/c - (b^2*d*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*asinh(c*x))/(4*c*sqrt(1 + c^2*x^2)) - (((2*im)/3)*b*d*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/sqrt(1 + c^2*x^2) - (b*c*d*x^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/(2*sqrt(1 + c^2*x^2)) - (((2*im)/9)*b*c^2*d*x^3*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/sqrt(1 + c^2*x^2) + (d*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2)/2 + ((im/3)*d*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/c + (d*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^3)/(6*b*c*sqrt(1 + c^2*x^2))]
    @test_int [sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2, x, 6, (b^2*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/4 - (b^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*asinh(c*x))/(4*c*sqrt(1 + c^2*x^2)) - (b*c*x^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/(2*sqrt(1 + c^2*x^2)) + (x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2)/2 + (sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^3)/(6*b*c*sqrt(1 + c^2*x^2))]
    @test_int [(sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2)/sqrt(d + im*c*d*x), x, 8, ((2*im)*a*b*f*x*sqrt(1 + c^2*x^2))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - ((2*im)*b^2*f*(1 + c^2*x^2))/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + ((2*im)*b^2*f*x*sqrt(1 + c^2*x^2)*asinh(c*x))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (im*f*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (f*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^3)/(3*b*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))]
    @test_int [(sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2)/(d + im*c*d*x)^(3/2), x, 19, ((2*im)*f^2*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (2*f^2*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (2*f^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (f^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^3)/(3*b*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - ((8*im)*b*f^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (4*b*f^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (4*b^2*f^2*(1 + c^2*x^2)^(3/2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (4*b^2*f^2*(1 + c^2*x^2)^(3/2)*PolyLog(2, im*ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (2*b^2*f^2*(1 + c^2*x^2)^(3/2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [(sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2)/(d + im*c*d*x)^(5/2), x, 20, -(f^3*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2)/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (((4*im)/3)*b^2*f^3*(1 + c^2*x^2)^(5/2)*cot(pi/4 + (im/2)*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - ((im/3)*f^3*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2*cot(pi/4 + (im/2)*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (2*b*f^3*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*csc(pi/4 + (im/2)*asinh(c*x))^2)/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + ((im/3)*f^3*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2*cot(pi/4 + (im/2)*asinh(c*x))*csc(pi/4 + (im/2)*asinh(c*x))^2)/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (4*b*f^3*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*log(1 + im*ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (4*b^2*f^3*(1 + c^2*x^2)^(5/2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]

    @test_int [(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^2, x, 19, (((8*im)/225)*b^2*d*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/c + (b^2*d*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/32 + (((16*im)/75)*b^2*d*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/(c*(1 + c^2*x^2)) + (15*b^2*d*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/(64*(1 + c^2*x^2)) + (((2*im)/125)*b^2*d*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(1 + c^2*x^2))/c - (9*b^2*d*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*asinh(c*x))/(64*c*(1 + c^2*x^2)^(3/2)) - (((2*im)/5)*b*d*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/(1 + c^2*x^2)^(3/2) - (3*b*c*d*x^2*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/(8*(1 + c^2*x^2)^(3/2)) - (((4*im)/15)*b*c^2*d*x^3*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/(1 + c^2*x^2)^(3/2) - (((2*im)/25)*b*c^4*d*x^5*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/(1 + c^2*x^2)^(3/2) - (b*d*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(8*c) + (d*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^2)/4 + (3*d*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^2)/(8*(1 + c^2*x^2)) + ((im/5)*d*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/c + (d*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^3)/(8*b*c*(1 + c^2*x^2)^(3/2))]
    @test_int [(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^2, x, 11, (b^2*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/32 + (15*b^2*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/(64*(1 + c^2*x^2)) - (9*b^2*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*asinh(c*x))/(64*c*(1 + c^2*x^2)^(3/2)) - (3*b*c*x^2*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/(8*(1 + c^2*x^2)^(3/2)) - (b*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(8*c) + (x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^2)/4 + (3*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^2)/(8*(1 + c^2*x^2)) + ((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^3)/(8*b*c*(1 + c^2*x^2)^(3/2))]
    @test_int [sqrt(d + im*c*d*x)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^2, x, 13, (((-4*im)/9)*b^2*f*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/c + (b^2*f*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/4 - (((2*im)/27)*b^2*f*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(1 + c^2*x^2))/c - (b^2*f*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*asinh(c*x))/(4*c*sqrt(1 + c^2*x^2)) + (((2*im)/3)*b*f*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/sqrt(1 + c^2*x^2) - (b*c*f*x^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/(2*sqrt(1 + c^2*x^2)) + (((2*im)/9)*b*c^2*f*x^3*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/sqrt(1 + c^2*x^2) + (f*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2)/2 - ((im/3)*f*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/c + (f*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^3)/(6*b*c*sqrt(1 + c^2*x^2))]
    @test_int [((f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^2)/sqrt(d + im*c*d*x), x, 11, ((-4*im)*b^2*f^2*(1 + c^2*x^2))/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (b^2*f^2*x*(1 + c^2*x^2))/(4*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (b^2*f^2*sqrt(1 + c^2*x^2)*asinh(c*x))/(4*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + ((4*im)*b*f^2*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (b*c*f^2*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - ((2*im)*f^2*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (f^2*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (f^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^3)/(2*b*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))]
    @test_int [((f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^2)/(d + im*c*d*x)^(3/2), x, 23, ((-2*im)*a*b*f^3*x*(1 + c^2*x^2)^(3/2))/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + ((2*im)*b^2*f^3*(1 + c^2*x^2)^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - ((2*im)*b^2*f^3*x*(1 + c^2*x^2)^(3/2)*asinh(c*x))/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + ((4*im)*f^3*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (4*f^3*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (4*f^3*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (im*f^3*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (f^3*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^3)/(b*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - ((16*im)*b*f^3*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (8*b*f^3*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (8*b^2*f^3*(1 + c^2*x^2)^(3/2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (8*b^2*f^3*(1 + c^2*x^2)^(3/2)*PolyLog(2, im*ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (4*b^2*f^3*(1 + c^2*x^2)^(3/2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [((f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^2)/(d + im*c*d*x)^(5/2), x, 21, (-8*f^4*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2)/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (f^4*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^3)/(3*b*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (((8*im)/3)*b^2*f^4*(1 + c^2*x^2)^(5/2)*cot(pi/4 + (im/2)*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (((8*im)/3)*f^4*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2*cot(pi/4 + (im/2)*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (4*b*f^4*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*csc(pi/4 + (im/2)*asinh(c*x))^2)/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (((2*im)/3)*f^4*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2*cot(pi/4 + (im/2)*asinh(c*x))*csc(pi/4 + (im/2)*asinh(c*x))^2)/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (32*b*f^4*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*log(1 + im*ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (32*b^2*f^4*(1 + c^2*x^2)^(5/2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]

    @test_int [(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)*(a + b*asinh(c*x))^2, x, 17, (b^2*x*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))/108 + (245*b^2*x*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))/(1152*(1 + c^2*x^2)^2) + (65*b^2*x*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))/(1728*(1 + c^2*x^2)) - (115*b^2*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)*asinh(c*x))/(1152*c*(1 + c^2*x^2)^(5/2)) - (5*b*c*x^2*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)*(a + b*asinh(c*x)))/(16*(1 + c^2*x^2)^(5/2)) - (5*b*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)*(a + b*asinh(c*x)))/(48*c*sqrt(1 + c^2*x^2)) - (b*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(18*c) + (x*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)*(a + b*asinh(c*x))^2)/6 + (5*x*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)*(a + b*asinh(c*x))^2)/(16*(1 + c^2*x^2)^2) + (5*x*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)*(a + b*asinh(c*x))^2)/(24*(1 + c^2*x^2)) + (5*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)*(a + b*asinh(c*x))^3)/(48*b*c*(1 + c^2*x^2)^(5/2))]
    @test_int [(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(5/2)*(a + b*asinh(c*x))^2, x, 19, (((-8*im)/225)*b^2*f*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/c + (b^2*f*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/32 - (((16*im)/75)*b^2*f*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/(c*(1 + c^2*x^2)) + (15*b^2*f*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))/(64*(1 + c^2*x^2)) - (((2*im)/125)*b^2*f*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(1 + c^2*x^2))/c - (9*b^2*f*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*asinh(c*x))/(64*c*(1 + c^2*x^2)^(3/2)) + (((2*im)/5)*b*f*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/(1 + c^2*x^2)^(3/2) - (3*b*c*f*x^2*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/(8*(1 + c^2*x^2)^(3/2)) + (((4*im)/15)*b*c^2*f*x^3*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/(1 + c^2*x^2)^(3/2) + (((2*im)/25)*b*c^4*f*x^5*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x)))/(1 + c^2*x^2)^(3/2) - (b*f*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(8*c) + (f*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^2)/4 + (3*f*x*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^2)/(8*(1 + c^2*x^2)) - ((im/5)*f*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/c + (f*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)*(a + b*asinh(c*x))^3)/(8*b*c*(1 + c^2*x^2)^(3/2))]
    @test_int [sqrt(d + im*c*d*x)*(f - im*c*f*x)^(5/2)*(a + b*asinh(c*x))^2, x, 23, (((-8*im)/9)*b^2*f^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/c + (15*b^2*f^2*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/64 - (b^2*c^2*f^2*x^3*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))/32 - (((4*im)/27)*b^2*f^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(1 + c^2*x^2))/c - (15*b^2*f^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*asinh(c*x))/(64*c*sqrt(1 + c^2*x^2)) + (((4*im)/3)*b*f^2*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/sqrt(1 + c^2*x^2) - (3*b*c*f^2*x^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/(8*sqrt(1 + c^2*x^2)) + (((4*im)/9)*b*c^2*f^2*x^3*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/sqrt(1 + c^2*x^2) + (b*c^3*f^2*x^4*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x)))/(8*sqrt(1 + c^2*x^2)) + (3*f^2*x*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2)/8 - (c^2*f^2*x^3*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^2)/4 - (((2*im)/3)*f^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/c + (5*f^2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)*(a + b*asinh(c*x))^3)/(24*b*c*sqrt(1 + c^2*x^2))]
    @test_int [((f - im*c*f*x)^(5/2)*(a + b*asinh(c*x))^2)/sqrt(d + im*c*d*x), x, 17, (((-68*im)/9)*b^2*f^3*(1 + c^2*x^2))/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (3*b^2*f^3*x*(1 + c^2*x^2))/(4*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (((2*im)/27)*b^2*f^3*(1 + c^2*x^2)^2)/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (3*b^2*f^3*sqrt(1 + c^2*x^2)*asinh(c*x))/(4*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (((22*im)/3)*b*f^3*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (3*b*c*f^3*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (((2*im)/9)*b*c^2*f^3*x^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (((11*im)/3)*f^3*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (3*f^3*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + ((im/3)*c*f^3*x^2*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (5*f^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^3)/(6*b*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))]
    @test_int [((f - im*c*f*x)^(5/2)*(a + b*asinh(c*x))^2)/(d + im*c*d*x)^(3/2), x, 28, ((-8*im)*a*b*f^4*x*(1 + c^2*x^2)^(3/2))/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + ((8*im)*b^2*f^4*(1 + c^2*x^2)^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (b^2*f^4*x*(1 + c^2*x^2)^2)/(4*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (b^2*f^4*(1 + c^2*x^2)^(3/2)*asinh(c*x))/(4*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - ((8*im)*b^2*f^4*x*(1 + c^2*x^2)^(3/2)*asinh(c*x))/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (b*c*f^4*x^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(2*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + ((8*im)*f^4*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (8*f^4*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (8*f^4*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + ((4*im)*f^4*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (f^4*x*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/(2*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (5*f^4*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^3)/(2*b*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - ((32*im)*b*f^4*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (16*b*f^4*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (16*b^2*f^4*(1 + c^2*x^2)^(3/2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (16*b^2*f^4*(1 + c^2*x^2)^(3/2)*PolyLog(2, im*ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (8*b^2*f^4*(1 + c^2*x^2)^(3/2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [((f - im*c*f*x)^(5/2)*(a + b*asinh(c*x))^2)/(d + im*c*d*x)^(5/2), x, 25, ((2*im)*a*b*f^5*x*(1 + c^2*x^2)^(5/2))/((d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - ((2*im)*b^2*f^5*(1 + c^2*x^2)^3)/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + ((2*im)*b^2*f^5*x*(1 + c^2*x^2)^(5/2)*asinh(c*x))/((d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (28*f^5*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2)/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (im*f^5*(1 + c^2*x^2)^3*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (5*f^5*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^3)/(3*b*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (((16*im)/3)*b^2*f^5*(1 + c^2*x^2)^(5/2)*cot(pi/4 + (im/2)*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (((28*im)/3)*f^5*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2*cot(pi/4 + (im/2)*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (8*b*f^5*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*csc(pi/4 + (im/2)*asinh(c*x))^2)/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (((4*im)/3)*f^5*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2*cot(pi/4 + (im/2)*asinh(c*x))*csc(pi/4 + (im/2)*asinh(c*x))^2)/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (112*b*f^5*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*log(1 + im*ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (112*b^2*f^5*(1 + c^2*x^2)^(5/2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]

    #= ::Subsubsection::Closed:: =#
    #=q<0=#

    @test_int [((d + im*c*d*x)^(5/2)*(a + b*asinh(c*x))^2)/sqrt(f - im*c*f*x), x, 17, (((68*im)/9)*b^2*d^3*(1 + c^2*x^2))/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (3*b^2*d^3*x*(1 + c^2*x^2))/(4*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (((2*im)/27)*b^2*d^3*(1 + c^2*x^2)^2)/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (3*b^2*d^3*sqrt(1 + c^2*x^2)*asinh(c*x))/(4*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (((22*im)/3)*b*d^3*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (3*b*c*d^3*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (((2*im)/9)*b*c^2*d^3*x^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (((11*im)/3)*d^3*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (3*d^3*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - ((im/3)*c*d^3*x^2*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (5*d^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^3)/(6*b*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))]
    @test_int [((d + im*c*d*x)^(3/2)*(a + b*asinh(c*x))^2)/sqrt(f - im*c*f*x), x, 11, ((4*im)*b^2*d^2*(1 + c^2*x^2))/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (b^2*d^2*x*(1 + c^2*x^2))/(4*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (b^2*d^2*sqrt(1 + c^2*x^2)*asinh(c*x))/(4*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - ((4*im)*b*d^2*x*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (b*c*d^2*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + ((2*im)*d^2*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - (d^2*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(2*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (d^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^3)/(2*b*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))]
    @test_int [(sqrt(d + im*c*d*x)*(a + b*asinh(c*x))^2)/sqrt(f - im*c*f*x), x, 8, ((-2*im)*a*b*d*x*sqrt(1 + c^2*x^2))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + ((2*im)*b^2*d*(1 + c^2*x^2))/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) - ((2*im)*b^2*d*x*sqrt(1 + c^2*x^2)*asinh(c*x))/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (im*d*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)) + (d*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^3)/(3*b*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))]
    @test_int [(a + b*asinh(c*x))^2/(sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x)), x, 2, (sqrt(1 + c^2*x^2)*(a + b*asinh(c*x))^3)/(3*b*c*sqrt(d + im*c*d*x)*sqrt(f - im*c*f*x))]
    @test_int [(a + b*asinh(c*x))^2/((d + im*c*d*x)^(3/2)*sqrt(f - im*c*f*x)), x, 16, (im*f*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (f*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (f*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - ((4*im)*b*f*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (2*b*f*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (2*b^2*f*(1 + c^2*x^2)^(3/2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (2*b^2*f*(1 + c^2*x^2)^(3/2)*PolyLog(2, im*ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (b^2*f*(1 + c^2*x^2)^(3/2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [(a + b*asinh(c*x))^2/((d + im*c*d*x)^(5/2)*sqrt(f - im*c*f*x)), x, 30, (((-2*im)/3)*b^2*f^2*(1 + c^2*x^2)^2)/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (2*b^2*f^2*x*(1 + c^2*x^2)^2)/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (b^2*f^2*(1 + c^2*x^2)^(5/2)*asinh(c*x))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (b*f^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (((2*im)/3)*b*f^2*x*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/((d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (b*c*f^2*x^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (((2*im)/3)*f^2*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (f^2*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (c^2*f^2*x^3*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (2*f^2*x*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (f^2*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2)/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (((4*im)/3)*b*f^2*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (2*b*f^2*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (2*b^2*f^2*(1 + c^2*x^2)^(5/2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (2*b^2*f^2*(1 + c^2*x^2)^(5/2)*PolyLog(2, im*ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (b^2*f^2*(1 + c^2*x^2)^(5/2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]

    @test_int [((d + im*c*d*x)^(5/2)*(a + b*asinh(c*x))^2)/(f - im*c*f*x)^(3/2), x, 28, ((8*im)*a*b*d^4*x*(1 + c^2*x^2)^(3/2))/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - ((8*im)*b^2*d^4*(1 + c^2*x^2)^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (b^2*d^4*x*(1 + c^2*x^2)^2)/(4*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (b^2*d^4*(1 + c^2*x^2)^(3/2)*asinh(c*x))/(4*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + ((8*im)*b^2*d^4*x*(1 + c^2*x^2)^(3/2)*asinh(c*x))/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (b*c*d^4*x^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(2*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - ((8*im)*d^4*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (8*d^4*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (8*d^4*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - ((4*im)*d^4*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (d^4*x*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/(2*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (5*d^4*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^3)/(2*b*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + ((32*im)*b*d^4*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (16*b*d^4*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (16*b^2*d^4*(1 + c^2*x^2)^(3/2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (16*b^2*d^4*(1 + c^2*x^2)^(3/2)*PolyLog(2, im*ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (8*b^2*d^4*(1 + c^2*x^2)^(3/2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [((d + im*c*d*x)^(3/2)*(a + b*asinh(c*x))^2)/(f - im*c*f*x)^(3/2), x, 23, ((2*im)*a*b*d^3*x*(1 + c^2*x^2)^(3/2))/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - ((2*im)*b^2*d^3*(1 + c^2*x^2)^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + ((2*im)*b^2*d^3*x*(1 + c^2*x^2)^(3/2)*asinh(c*x))/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - ((4*im)*d^3*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (4*d^3*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (4*d^3*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (im*d^3*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (d^3*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^3)/(b*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + ((16*im)*b*d^3*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (8*b*d^3*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (8*b^2*d^3*(1 + c^2*x^2)^(3/2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (8*b^2*d^3*(1 + c^2*x^2)^(3/2)*PolyLog(2, im*ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (4*b^2*d^3*(1 + c^2*x^2)^(3/2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [(sqrt(d + im*c*d*x)*(a + b*asinh(c*x))^2)/(f - im*c*f*x)^(3/2), x, 19, ((-2*im)*d^2*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (2*d^2*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (2*d^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (d^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^3)/(3*b*c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + ((8*im)*b*d^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (4*b*d^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (4*b^2*d^2*(1 + c^2*x^2)^(3/2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (4*b^2*d^2*(1 + c^2*x^2)^(3/2)*PolyLog(2, im*ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (2*b^2*d^2*(1 + c^2*x^2)^(3/2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [(a + b*asinh(c*x))^2/(sqrt(d + im*c*d*x)*(f - im*c*f*x)^(3/2)), x, 16, ((-im)*d*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (d*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (d*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + ((4*im)*b*d*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (2*b*d*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + (2*b^2*d*(1 + c^2*x^2)^(3/2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (2*b^2*d*(1 + c^2*x^2)^(3/2)*PolyLog(2, im*ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (b^2*d*(1 + c^2*x^2)^(3/2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [(a + b*asinh(c*x))^2/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)), x, 7, (x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) + ((1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (2*b*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2)) - (b^2*(1 + c^2*x^2)^(3/2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(c*(d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(3/2))]
    @test_int [(a + b*asinh(c*x))^2/((d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(3/2)), x, 21, ((-im/3)*b^2*f*(1 + c^2*x^2)^2)/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (b^2*f*x*(1 + c^2*x^2)^2)/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (b*f*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - ((im/3)*b*f*x*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/((d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + ((im/3)*f*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (f*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (2*f*x*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (2*f*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2)/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (((2*im)/3)*b*f*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (4*b*f*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (b^2*f*(1 + c^2*x^2)^(5/2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (b^2*f*(1 + c^2*x^2)^(5/2)*PolyLog(2, im*ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (2*b^2*f*(1 + c^2*x^2)^(5/2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]

    @test_int [((d + im*c*d*x)^(5/2)*(a + b*asinh(c*x))^2)/(f - im*c*f*x)^(5/2), x, 25, ((-2*im)*a*b*d^5*x*(1 + c^2*x^2)^(5/2))/((d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + ((2*im)*b^2*d^5*(1 + c^2*x^2)^3)/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - ((2*im)*b^2*d^5*x*(1 + c^2*x^2)^(5/2)*asinh(c*x))/((d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (28*d^5*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2)/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (im*d^5*(1 + c^2*x^2)^3*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (5*d^5*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^3)/(3*b*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (112*b*d^5*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*log(1 + im/ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (112*b^2*d^5*(1 + c^2*x^2)^(5/2)*PolyLog(2, (-im)/ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (8*b*d^5*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*sec(pi/4 + (im/2)*asinh(c*x))^2)/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (((16*im)/3)*b^2*d^5*(1 + c^2*x^2)^(5/2)*tan(pi/4 + (im/2)*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (((28*im)/3)*d^5*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2*tan(pi/4 + (im/2)*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (((4*im)/3)*d^5*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2*sec(pi/4 + (im/2)*asinh(c*x))^2*tan(pi/4 + (im/2)*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]
    @test_int [((d + im*c*d*x)^(3/2)*(a + b*asinh(c*x))^2)/(f - im*c*f*x)^(5/2), x, 21, (8*d^4*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2)/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (d^4*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^3)/(3*b*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (32*b*d^4*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*log(1 + im/ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (32*b^2*d^4*(1 + c^2*x^2)^(5/2)*PolyLog(2, (-im)/ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (4*b*d^4*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*sec(pi/4 + (im/2)*asinh(c*x))^2)/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (((8*im)/3)*b^2*d^4*(1 + c^2*x^2)^(5/2)*tan(pi/4 + (im/2)*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (((8*im)/3)*d^4*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2*tan(pi/4 + (im/2)*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (((2*im)/3)*d^4*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2*sec(pi/4 + (im/2)*asinh(c*x))^2*tan(pi/4 + (im/2)*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]
    @test_int [(sqrt(d + im*c*d*x)*(a + b*asinh(c*x))^2)/(f - im*c*f*x)^(5/2), x, 20, (d^3*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2)/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (4*b*d^3*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*log(1 + im/ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (4*b^2*d^3*(1 + c^2*x^2)^(5/2)*PolyLog(2, (-im)/ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (2*b*d^3*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*sec(pi/4 + (im/2)*asinh(c*x))^2)/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (((4*im)/3)*b^2*d^3*(1 + c^2*x^2)^(5/2)*tan(pi/4 + (im/2)*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + ((im/3)*d^3*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2*tan(pi/4 + (im/2)*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - ((im/3)*d^3*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2*sec(pi/4 + (im/2)*asinh(c*x))^2*tan(pi/4 + (im/2)*asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]
    @test_int [(a + b*asinh(c*x))^2/(sqrt(d + im*c*d*x)*(f - im*c*f*x)^(5/2)), x, 30, (((2*im)/3)*b^2*d^2*(1 + c^2*x^2)^2)/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (2*b^2*d^2*x*(1 + c^2*x^2)^2)/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (b^2*d^2*(1 + c^2*x^2)^(5/2)*asinh(c*x))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (b*d^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (((2*im)/3)*b*d^2*x*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/((d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (b*c*d^2*x^2*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (((2*im)/3)*d^2*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (d^2*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (c^2*d^2*x^3*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (2*d^2*x*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (d^2*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2)/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (((4*im)/3)*b*d^2*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (2*b*d^2*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (2*b^2*d^2*(1 + c^2*x^2)^(5/2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (2*b^2*d^2*(1 + c^2*x^2)^(5/2)*PolyLog(2, im*ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (b^2*d^2*(1 + c^2*x^2)^(5/2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]
    @test_int [(a + b*asinh(c*x))^2/((d + im*c*d*x)^(3/2)*(f - im*c*f*x)^(5/2)), x, 21, ((im/3)*b^2*d*(1 + c^2*x^2)^2)/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (b^2*d*x*(1 + c^2*x^2)^2)/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (b*d*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + ((im/3)*b*d*x*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/((d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - ((im/3)*d*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (d*x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (2*d*x*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (2*d*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2)/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (((2*im)/3)*b*d*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*atan(ℯ^asinh(c*x)))/(c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (4*b*d*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (b^2*d*(1 + c^2*x^2)^(5/2)*PolyLog(2, (-im)*ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (b^2*d*(1 + c^2*x^2)^(5/2)*PolyLog(2, im*ℯ^asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (2*b^2*d*(1 + c^2*x^2)^(5/2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]
    @test_int [(a + b*asinh(c*x))^2/((d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)), x, 10, -(b^2*x*(1 + c^2*x^2)^2)/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (b*(1 + c^2*x^2)^(3/2)*(a + b*asinh(c*x)))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (x*(1 + c^2*x^2)*(a + b*asinh(c*x))^2)/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (2*x*(1 + c^2*x^2)^2*(a + b*asinh(c*x))^2)/(3*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) + (2*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))^2)/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (4*b*(1 + c^2*x^2)^(5/2)*(a + b*asinh(c*x))*log(1 + ℯ^(2*asinh(c*x))))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2)) - (2*b^2*(1 + c^2*x^2)^(5/2)*PolyLog(2, -ℯ^(2*asinh(c*x))))/(3*c*(d + im*c*d*x)^(5/2)*(f - im*c*f*x)^(5/2))]

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

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

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

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

    @test_int [(d + e*x^2)^4*(a + b*asinh(c*x)), x, 5, -((b*(315*c^8*d^4 - 420*c^6*d^3*e + 378*c^4*d^2*e^2 - 180*c^2*d*e^3 + 35*e^4)*sqrt(1 + c^2*x^2))/(315*c^9)) - (4*b*e*(105*c^6*d^3 - 189*c^4*d^2*e + 135*c^2*d*e^2 - 35*e^3)*(1 + c^2*x^2)^(3/2))/(945*c^9) - (2*b*e^2*(63*c^4*d^2 - 90*c^2*d*e + 35*e^2)*(1 + c^2*x^2)^(5/2))/(525*c^9) - (4*b*(9*c^2*d - 7*e)*e^3*(1 + c^2*x^2)^(7/2))/(441*c^9) - (b*e^4*(1 + c^2*x^2)^(9/2))/(81*c^9) + d^4*x*(a + b*asinh(c*x)) + (4/3)*d^3*e*x^3*(a + b*asinh(c*x)) + (6/5)*d^2*e^2*x^5*(a + b*asinh(c*x)) + (4/7)*d*e^3*x^7*(a + b*asinh(c*x)) + (1/9)*e^4*x^9*(a + b*asinh(c*x))]
    @test_int [(d + e*x^2)^3*(a + b*asinh(c*x)), x, 5, -((b*(35*c^6*d^3 - 35*c^4*d^2*e + 21*c^2*d*e^2 - 5*e^3)*sqrt(1 + c^2*x^2))/(35*c^7)) - (b*e*(35*c^4*d^2 - 42*c^2*d*e + 15*e^2)*(1 + c^2*x^2)^(3/2))/(105*c^7) - (3*b*(7*c^2*d - 5*e)*e^2*(1 + c^2*x^2)^(5/2))/(175*c^7) - (b*e^3*(1 + c^2*x^2)^(7/2))/(49*c^7) + d^3*x*(a + b*asinh(c*x)) + d^2*e*x^3*(a + b*asinh(c*x)) + (3/5)*d*e^2*x^5*(a + b*asinh(c*x)) + (1/7)*e^3*x^7*(a + b*asinh(c*x))]
    @test_int [(d + e*x^2)^2*(a + b*asinh(c*x)), x, 5, -(b*(15*c^4*d^2 - 10*c^2*d*e + 3*e^2)*sqrt(1 + c^2*x^2))/(15*c^5) - (2*b*(5*c^2*d - 3*e)*e*(1 + c^2*x^2)^(3/2))/(45*c^5) - (b*e^2*(1 + c^2*x^2)^(5/2))/(25*c^5) + d^2*x*(a + b*asinh(c*x)) + (2*d*e*x^3*(a + b*asinh(c*x)))/3 + (e^2*x^5*(a + b*asinh(c*x)))/5]
    @test_int [(d + e*x^2)*(a + b*asinh(c*x)), x, 4, -(b*(3*c^2*d - e)*sqrt(1 + c^2*x^2))/(3*c^3) - (b*e*(1 + c^2*x^2)^(3/2))/(9*c^3) + d*x*(a + b*asinh(c*x)) + (e*x^3*(a + b*asinh(c*x)))/3]
    @test_int [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^2), x, 18, ((a + b*asinh(c*x))*log(1 - (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d + e))))/(2*sqrt(-d)*sqrt(e)) - ((a + b*asinh(c*x))*log(1 + (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d + e))))/(2*sqrt(-d)*sqrt(e)) + ((a + b*asinh(c*x))*log(1 - (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d + e))))/(2*sqrt(-d)*sqrt(e)) - ((a + b*asinh(c*x))*log(1 + (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d + e))))/(2*sqrt(-d)*sqrt(e)) - (b*PolyLog(2, -((sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d + e)))))/(2*sqrt(-d)*sqrt(e)) + (b*PolyLog(2, (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d + e))))/(2*sqrt(-d)*sqrt(e)) - (b*PolyLog(2, -((sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d + e)))))/(2*sqrt(-d)*sqrt(e)) + (b*PolyLog(2, (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d + e))))/(2*sqrt(-d)*sqrt(e))]
    @test_int [(a + b*asinh(c*x))/(d + e*x^2)^2, x, 26, -((a + b*asinh(c*x))/(4*d*sqrt(e)*(sqrt(-d) - sqrt(e)*x))) + (a + b*asinh(c*x))/(4*d*sqrt(e)*(sqrt(-d) + sqrt(e)*x)) - (b*c*atan((sqrt(e) - c^2*sqrt(-d)*x)/(sqrt(c^2*d - e)*sqrt(1 + c^2*x^2))))/(4*d*sqrt(c^2*d - e)*sqrt(e)) - (b*c*atan((sqrt(e) + c^2*sqrt(-d)*x)/(sqrt(c^2*d - e)*sqrt(1 + c^2*x^2))))/(4*d*sqrt(c^2*d - e)*sqrt(e)) - ((a + b*asinh(c*x))*log(1 - (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d + e))))/(4*(-d)^(3/2)*sqrt(e)) + ((a + b*asinh(c*x))*log(1 + (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d + e))))/(4*(-d)^(3/2)*sqrt(e)) - ((a + b*asinh(c*x))*log(1 - (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d + e))))/(4*(-d)^(3/2)*sqrt(e)) + ((a + b*asinh(c*x))*log(1 + (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d + e))))/(4*(-d)^(3/2)*sqrt(e)) + (b*PolyLog(2, -((sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d + e)))))/(4*(-d)^(3/2)*sqrt(e)) - (b*PolyLog(2, (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d + e))))/(4*(-d)^(3/2)*sqrt(e)) + (b*PolyLog(2, -((sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d + e)))))/(4*(-d)^(3/2)*sqrt(e)) - (b*PolyLog(2, (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d + e))))/(4*(-d)^(3/2)*sqrt(e))]

    @test_int [(d + e*x^2)^3*(a + b*asinh(c*x))^2, x, 26, 2*b^2*d^3*x - (4*b^2*d^2*e*x)/(3*c^2) + (16*b^2*d*e^2*x)/(25*c^4) - (32*b^2*e^3*x)/(245*c^6) + (2*b^2*d^2*e*x^3)/9 - (8*b^2*d*e^2*x^3)/(75*c^2) + (16*b^2*e^3*x^3)/(735*c^4) + (6*b^2*d*e^2*x^5)/125 - (12*b^2*e^3*x^5)/(1225*c^2) + (2*b^2*e^3*x^7)/343 - (2*b*d^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/c + (4*b*d^2*e*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(3*c^3) - (16*b*d*e^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(25*c^5) + (32*b*e^3*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(245*c^7) - (2*b*d^2*e*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(3*c) + (8*b*d*e^2*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(25*c^3) - (16*b*e^3*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(245*c^5) - (6*b*d*e^2*x^4*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(25*c) + (12*b*e^3*x^4*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(245*c^3) - (2*b*e^3*x^6*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(49*c) + d^3*x*(a + b*asinh(c*x))^2 + d^2*e*x^3*(a + b*asinh(c*x))^2 + (3*d*e^2*x^5*(a + b*asinh(c*x))^2)/5 + (e^3*x^7*(a + b*asinh(c*x))^2)/7]
    @test_int [(d + e*x^2)^2*(a + b*asinh(c*x))^2, x, 17, 2*b^2*d^2*x - (8*b^2*d*e*x)/(9*c^2) + (16*b^2*e^2*x)/(75*c^4) + (4*b^2*d*e*x^3)/27 - (8*b^2*e^2*x^3)/(225*c^2) + (2*b^2*e^2*x^5)/125 - (2*b*d^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/c + (8*b*d*e*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(9*c^3) - (16*b*e^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(75*c^5) - (4*b*d*e*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(9*c) + (8*b*e^2*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(75*c^3) - (2*b*e^2*x^4*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(25*c) + d^2*x*(a + b*asinh(c*x))^2 + (2*d*e*x^3*(a + b*asinh(c*x))^2)/3 + (e^2*x^5*(a + b*asinh(c*x))^2)/5]
    @test_int [(d + e*x^2)^1*(a + b*asinh(c*x))^2, x, 10, 2*b^2*d*x - (4*b^2*e*x)/(9*c^2) + (2*b^2*e*x^3)/27 - (2*b*d*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/c + (4*b*e*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(9*c^3) - (2*b*e*x^2*sqrt(1 + c^2*x^2)*(a + b*asinh(c*x)))/(9*c) + d*x*(a + b*asinh(c*x))^2 + (e*x^3*(a + b*asinh(c*x))^2)/3]
    @test_int [(d + e*x^2)^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^2), x, 22, ((a + b*asinh(c*x))^2*log(1 - (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d + e))))/(2*sqrt(-d)*sqrt(e)) - ((a + b*asinh(c*x))^2*log(1 + (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d + e))))/(2*sqrt(-d)*sqrt(e)) + ((a + b*asinh(c*x))^2*log(1 - (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d + e))))/(2*sqrt(-d)*sqrt(e)) - ((a + b*asinh(c*x))^2*log(1 + (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d + e))))/(2*sqrt(-d)*sqrt(e)) - (b*(a + b*asinh(c*x))*PolyLog(2, -((sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d + e)))))/(sqrt(-d)*sqrt(e)) + (b*(a + b*asinh(c*x))*PolyLog(2, (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d + e))))/(sqrt(-d)*sqrt(e)) - (b*(a + b*asinh(c*x))*PolyLog(2, -((sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d + e)))))/(sqrt(-d)*sqrt(e)) + (b*(a + b*asinh(c*x))*PolyLog(2, (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d + e))))/(sqrt(-d)*sqrt(e)) + (b^2*PolyLog(3, -((sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d + e)))))/(sqrt(-d)*sqrt(e)) - (b^2*PolyLog(3, (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d + e))))/(sqrt(-d)*sqrt(e)) + (b^2*PolyLog(3, -((sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d + e)))))/(sqrt(-d)*sqrt(e)) - (b^2*PolyLog(3, (sqrt(e)*ℯ^asinh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d + e))))/(sqrt(-d)*sqrt(e))]

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

    @test_int [(d + e*x^2)^3/(a + b*asinh(c*x)), x, 42, (d^3*cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(b*c) - (3*d^2*e*cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(4*b*c^3) + (3*d*e^2*cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(8*b*c^5) - (5*e^3*cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(64*b*c^7) + (3*d^2*e*cosh((3*a)/b)*CoshIntegral((3*(a + b*asinh(c*x)))/b))/(4*b*c^3) - (9*d*e^2*cosh((3*a)/b)*CoshIntegral((3*(a + b*asinh(c*x)))/b))/(16*b*c^5) + (9*e^3*cosh((3*a)/b)*CoshIntegral((3*(a + b*asinh(c*x)))/b))/(64*b*c^7) + (3*d*e^2*cosh((5*a)/b)*CoshIntegral((5*(a + b*asinh(c*x)))/b))/(16*b*c^5) - (5*e^3*cosh((5*a)/b)*CoshIntegral((5*(a + b*asinh(c*x)))/b))/(64*b*c^7) + (e^3*cosh((7*a)/b)*CoshIntegral((7*(a + b*asinh(c*x)))/b))/(64*b*c^7) - (d^3*sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(b*c) + (3*d^2*e*sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(4*b*c^3) - (3*d*e^2*sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(8*b*c^5) + (5*e^3*sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(64*b*c^7) - (3*d^2*e*sinh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(4*b*c^3) + (9*d*e^2*sinh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(16*b*c^5) - (9*e^3*sinh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(64*b*c^7) - (3*d*e^2*sinh((5*a)/b)*SinhIntegral((5*(a + b*asinh(c*x)))/b))/(16*b*c^5) + (5*e^3*sinh((5*a)/b)*SinhIntegral((5*(a + b*asinh(c*x)))/b))/(64*b*c^7) - (e^3*sinh((7*a)/b)*SinhIntegral((7*(a + b*asinh(c*x)))/b))/(64*b*c^7)]
    @test_int [(d + e*x^2)^2/(a + b*asinh(c*x)), x, 27, (d^2*cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(b*c) - (d*e*cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(2*b*c^3) + (e^2*cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(8*b*c^5) + (d*e*cosh((3*a)/b)*CoshIntegral((3*(a + b*asinh(c*x)))/b))/(2*b*c^3) - (3*e^2*cosh((3*a)/b)*CoshIntegral((3*(a + b*asinh(c*x)))/b))/(16*b*c^5) + (e^2*cosh((5*a)/b)*CoshIntegral((5*(a + b*asinh(c*x)))/b))/(16*b*c^5) - (d^2*sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(b*c) + (d*e*sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(2*b*c^3) - (e^2*sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(8*b*c^5) - (d*e*sinh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(2*b*c^3) + (3*e^2*sinh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(16*b*c^5) - (e^2*sinh((5*a)/b)*SinhIntegral((5*(a + b*asinh(c*x)))/b))/(16*b*c^5)]
    @test_int [(d + e*x^2)^1/(a + b*asinh(c*x)), x, 15, (d*cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(b*c) - (e*cosh(a/b)*CoshIntegral((a + b*asinh(c*x))/b))/(4*b*c^3) + (e*cosh((3*a)/b)*CoshIntegral((3*(a + b*asinh(c*x)))/b))/(4*b*c^3) - (d*sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(b*c) + (e*sinh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(4*b*c^3) - (e*sinh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(4*b*c^3)]
    @test_int [(d + e*x^2)^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^2)^1*(a + b*asinh(c*x))), x, 0, Unintegrable(1/((d + e*x^2)*(a + b*asinh(c*x))), x)]
    @test_int [1/((d + e*x^2)^2*(a + b*asinh(c*x))), x, 0, Unintegrable(1/((d + e*x^2)^2*(a + b*asinh(c*x))), x)]

    @test_int [(d + e*x^2)^2/(a + b*asinh(c*x))^2, x, 26, -((d^2*sqrt(1 + c^2*x^2))/(b*c*(a + b*asinh(c*x)))) - (2*d*e*x^2*sqrt(1 + c^2*x^2))/(b*c*(a + b*asinh(c*x))) - (e^2*x^4*sqrt(1 + c^2*x^2))/(b*c*(a + b*asinh(c*x))) - (d^2*CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(b^2*c) + (d*e*CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(2*b^2*c^3) - (e^2*CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(8*b^2*c^5) - (3*d*e*CoshIntegral((3*(a + b*asinh(c*x)))/b)*sinh((3*a)/b))/(2*b^2*c^3) + (9*e^2*CoshIntegral((3*(a + b*asinh(c*x)))/b)*sinh((3*a)/b))/(16*b^2*c^5) - (5*e^2*CoshIntegral((5*(a + b*asinh(c*x)))/b)*sinh((5*a)/b))/(16*b^2*c^5) + (d^2*cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(b^2*c) - (d*e*cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(2*b^2*c^3) + (e^2*cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(8*b^2*c^5) + (3*d*e*cosh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(2*b^2*c^3) - (9*e^2*cosh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(16*b^2*c^5) + (5*e^2*cosh((5*a)/b)*SinhIntegral((5*(a + b*asinh(c*x)))/b))/(16*b^2*c^5)]
    @test_int [(d + e*x^2)^1/(a + b*asinh(c*x))^2, x, 15, -((d*sqrt(1 + c^2*x^2))/(b*c*(a + b*asinh(c*x)))) - (e*x^2*sqrt(1 + c^2*x^2))/(b*c*(a + b*asinh(c*x))) - (d*CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(b^2*c) + (e*CoshIntegral((a + b*asinh(c*x))/b)*sinh(a/b))/(4*b^2*c^3) - (3*e*CoshIntegral((3*(a + b*asinh(c*x)))/b)*sinh((3*a)/b))/(4*b^2*c^3) + (d*cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(b^2*c) - (e*cosh(a/b)*SinhIntegral((a + b*asinh(c*x))/b))/(4*b^2*c^3) + (3*e*cosh((3*a)/b)*SinhIntegral((3*(a + b*asinh(c*x)))/b))/(4*b^2*c^3)]
    @test_int [(d + e*x^2)^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^2)^1*(a + b*asinh(c*x))^2), x, 0, Unintegrable(1/((d + e*x^2)*(a + b*asinh(c*x))^2), x)]
    @test_int [1/((d + e*x^2)^2*(a + b*asinh(c*x))^2), x, 0, Unintegrable(1/((d + e*x^2)^2*(a + b*asinh(c*x))^2), x)]

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

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

    @test_int [(d + e*x^2)^2*sqrt(a + b*asinh(c*x)), x, 42, d^2*x*sqrt(a + b*asinh(c*x)) + (2*d*e*x^3*sqrt(a + b*asinh(c*x)))/3 + (e^2*x^5*sqrt(a + b*asinh(c*x)))/5 + (sqrt(b)*d^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(4*c) - (sqrt(b)*d*e*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(8*c^3) + (sqrt(b)*e^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(32*c^5) + (sqrt(b)*d*e*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(24*c^3) - (sqrt(b)*e^2*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(64*c^5) + (sqrt(b)*e^2*ℯ^((5*a)/b)*sqrt(pi/5)*erf((sqrt(5)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(320*c^5) - (sqrt(b)*d^2*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(4*c*ℯ^(a/b)) + (sqrt(b)*d*e*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(8*c^3*ℯ^(a/b)) - (sqrt(b)*e^2*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(32*c^5*ℯ^(a/b)) - (sqrt(b)*d*e*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(24*c^3*ℯ^((3*a)/b)) + (sqrt(b)*e^2*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(64*c^5*ℯ^((3*a)/b)) - (sqrt(b)*e^2*sqrt(pi/5)*erfi((sqrt(5)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(320*c^5*ℯ^((5*a)/b))]
    @test_int [(d + e*x^2)*sqrt(a + b*asinh(c*x)), x, 23, d*x*sqrt(a + b*asinh(c*x)) + (e*x^3*sqrt(a + b*asinh(c*x)))/3 + (sqrt(b)*d*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(4*c) - (sqrt(b)*e*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(16*c^3) + (sqrt(b)*e*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(48*c^3) - (sqrt(b)*d*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(4*c*ℯ^(a/b)) + (sqrt(b)*e*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(16*c^3*ℯ^(a/b)) - (sqrt(b)*e*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(48*c^3*ℯ^((3*a)/b))]
    @test_int [sqrt(a + b*asinh(c*x)), x, 7, x*sqrt(a + b*asinh(c*x)) + (sqrt(b)*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(4*c) - (sqrt(b)*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(4*c*ℯ^(a/b))]
    @test_int [sqrt(a + b*asinh(c*x))/(d + e*x^2), x, 0, Unintegrable(sqrt(a + b*asinh(c*x))/(d + e*x^2), x)]
    @test_int [sqrt(a + b*asinh(c*x))/(d + e*x^2)^2, x, 0, Unintegrable(sqrt(a + b*asinh(c*x))/(d + e*x^2)^2, x)]

    @test_int [(d + e*x^2)*(a + b*asinh(c*x))^(3/2), x, 32, (-3*b*d*sqrt(1 + c^2*x^2)*sqrt(a + b*asinh(c*x)))/(2*c) + (b*e*sqrt(1 + c^2*x^2)*sqrt(a + b*asinh(c*x)))/(3*c^3) - (b*e*x^2*sqrt(1 + c^2*x^2)*sqrt(a + b*asinh(c*x)))/(6*c) + d*x*(a + b*asinh(c*x))^(3/2) + (e*x^3*(a + b*asinh(c*x))^(3/2))/3 + (3*b^(3/2)*d*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(8*c) - (3*b^(3/2)*e*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(32*c^3) + (b^(3/2)*e*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(96*c^3) + (3*b^(3/2)*d*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(8*c*ℯ^(a/b)) - (3*b^(3/2)*e*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(32*c^3*ℯ^(a/b)) + (b^(3/2)*e*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(96*c^3*ℯ^((3*a)/b))]
    @test_int [(a + b*asinh(c*x))^(3/2), x, 8, (-3*b*sqrt(1 + c^2*x^2)*sqrt(a + b*asinh(c*x)))/(2*c) + x*(a + b*asinh(c*x))^(3/2) + (3*b^(3/2)*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(8*c) + (3*b^(3/2)*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(8*c*ℯ^(a/b))]
    @test_int [(a + b*asinh(c*x))^(3/2)/(d + e*x^2), x, 0, Unintegrable((a + b*asinh(c*x))^(3/2)/(d + e*x^2), x)]
    @test_int [(a + b*asinh(c*x))^(3/2)/(d + e*x^2)^2, x, 0, Unintegrable((a + b*asinh(c*x))^(3/2)/(d + e*x^2)^2, x)]

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

    @test_int [(d + e*x^2)^2/sqrt(a + b*asinh(c*x)), x, 39, (d^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(2*sqrt(b)*c) - (d*e*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(4*sqrt(b)*c^3) + (e^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(16*sqrt(b)*c^5) + (d*e*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(4*sqrt(b)*c^3) - (e^2*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(32*sqrt(b)*c^5) + (e^2*ℯ^((5*a)/b)*sqrt(pi/5)*erf((sqrt(5)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(32*sqrt(b)*c^5) + (d^2*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(2*sqrt(b)*c*ℯ^(a/b)) - (d*e*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(4*sqrt(b)*c^3*ℯ^(a/b)) + (e^2*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(16*sqrt(b)*c^5*ℯ^(a/b)) + (d*e*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(4*sqrt(b)*c^3*ℯ^((3*a)/b)) - (e^2*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(32*sqrt(b)*c^5*ℯ^((3*a)/b)) + (e^2*sqrt(pi/5)*erfi((sqrt(5)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(32*sqrt(b)*c^5*ℯ^((5*a)/b))]
    @test_int [(d + e*x^2)/sqrt(a + b*asinh(c*x)), x, 21, (d*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(2*sqrt(b)*c) - (e*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(8*sqrt(b)*c^3) + (e*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(8*sqrt(b)*c^3) + (d*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(2*sqrt(b)*c*ℯ^(a/b)) - (e*sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(8*sqrt(b)*c^3*ℯ^(a/b)) + (e*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*asinh(c*x)))/sqrt(b)))/(8*sqrt(b)*c^3*ℯ^((3*a)/b))]
    @test_int [1/sqrt(a + b*asinh(c*x)), x, 6, (ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*asinh(c*x))/sqrt(b)))/(2*sqrt(b)*c) + (sqrt(pi)*erfi(sqrt(a + b*asinh(c*x))/sqrt(b)))/(2*sqrt(b)*c*ℯ^(a/b))]
    @test_int [1/((d + e*x^2)*sqrt(a + b*asinh(c*x))), x, 0, Unintegrable(1/((d + e*x^2)*sqrt(a + b*asinh(c*x))), x)]
    @test_int [1/((d + e*x^2)^2*sqrt(a + b*asinh(c*x))), x, 0, Unintegrable(1/((d + e*x^2)^2*sqrt(a + b*asinh(c*x))), x)]

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

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

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

    @test_int [sqrt(d + e*x^2)*(a + b*asinh(c*x)), x, 0, Unintegrable(sqrt(d + e*x^2)*(a + b*asinh(c*x)), x)]
    @test_int [(a + b*asinh(c*x))/sqrt(d + e*x^2), x, 0, Unintegrable((a + b*asinh(c*x))/sqrt(d + e*x^2), x)]
    @test_int [(a + b*asinh(c*x))/(d + e*x^2)^(3/2), x, 6, (x*(a + b*asinh(c*x)))/(d*sqrt(d + e*x^2)) - (b*atanh((sqrt(e)*sqrt(1 + c^2*x^2))/(c*sqrt(d + e*x^2))))/(d*sqrt(e))]
    @test_int [(a + b*asinh(c*x))/(d + e*x^2)^(5/2), x, 7, -(b*c*sqrt(1 + c^2*x^2))/(3*d*(c^2*d - e)*sqrt(d + e*x^2)) + (x*(a + b*asinh(c*x)))/(3*d*(d + e*x^2)^(3/2)) + (2*x*(a + b*asinh(c*x)))/(3*d^2*sqrt(d + e*x^2)) - (2*b*atanh((sqrt(e)*sqrt(1 + c^2*x^2))/(c*sqrt(d + e*x^2))))/(3*d^2*sqrt(e))]
    @test_int [(a + b*asinh(c*x))/(d + e*x^2)^(7/2), x, 8, -((b*c*sqrt(1 + c^2*x^2))/(15*d*(c^2*d - e)*(d + e*x^2)^(3/2))) - (2*b*c*(3*c^2*d - 2*e)*sqrt(1 + c^2*x^2))/(15*d^2*(c^2*d - e)^2*sqrt(d + e*x^2)) + (x*(a + b*asinh(c*x)))/(5*d*(d + e*x^2)^(5/2)) + (4*x*(a + b*asinh(c*x)))/(15*d^2*(d + e*x^2)^(3/2)) + (8*x*(a + b*asinh(c*x)))/(15*d^3*sqrt(d + e*x^2)) - (8*b*atanh((sqrt(e)*sqrt(1 + c^2*x^2))/(c*sqrt(d + e*x^2))))/(15*d^3*sqrt(e))]

    @test_int [sqrt(d + e*x^2)*(a + b*asinh(c*x))^2, x, 0, Unintegrable(sqrt(d + e*x^2)*(a + b*asinh(c*x))^2, x)]
    @test_int [(a + b*asinh(c*x))^2/sqrt(d + e*x^2), x, 0, Unintegrable((a + b*asinh(c*x))^2/sqrt(d + e*x^2), x)]
    @test_int [(a + b*asinh(c*x))^2/(d + e*x^2)^(3/2), x, 0, Unintegrable((a + b*asinh(c*x))^2/(d + e*x^2)^(3/2), x)]
    @test_int [(a + b*asinh(c*x))^2/(d + e*x^2)^(5/2), x, 0, Unintegrable((a + b*asinh(c*x))^2/(d + e*x^2)^(5/2), x)]

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

    @test_int [sqrt(d + e*x^2)/(a + b*asinh(c*x)), x, 0, Unintegrable(sqrt(d + e*x^2)/(a + b*asinh(c*x)), x)]
    @test_int [1/(sqrt(d + e*x^2)*(a + b*asinh(c*x))), x, 0, Unintegrable(1/(sqrt(d + e*x^2)*(a + b*asinh(c*x))), x)]
    @test_int [1/((d + e*x^2)^(3/2)*(a + b*asinh(c*x))), x, 0, Unintegrable(1/((d + e*x^2)^(3/2)*(a + b*asinh(c*x))), x)]
    @test_int [1/((d + e*x^2)^(5/2)*(a + b*asinh(c*x))), x, 0, Unintegrable(1/((d + e*x^2)^(5/2)*(a + b*asinh(c*x))), x)]

    @test_int [sqrt(d + e*x^2)/(a + b*asinh(c*x))^2, x, 0, Unintegrable(sqrt(d + e*x^2)/(a + b*asinh(c*x))^2, x)]
    @test_int [1/(sqrt(d + e*x^2)*(a + b*asinh(c*x))^2), x, 0, Unintegrable(1/(sqrt(d + e*x^2)*(a + b*asinh(c*x))^2), x)]
    @test_int [1/((d + e*x^2)^(3/2)*(a + b*asinh(c*x))^2), x, 0, Unintegrable(1/((d + e*x^2)^(3/2)*(a + b*asinh(c*x))^2), x)]
    @test_int [1/((d + e*x^2)^(5/2)*(a + b*asinh(c*x))^2), x, 0, Unintegrable(1/((d + e*x^2)^(5/2)*(a + b*asinh(c*x))^2), x)]
    end

max_stars_repo_path: test/7 Inverse hyperbolic functions/7.1 Inverse hyperbolic sine/7.1.4 (f x)^m (d+e x^2)^p (a+b arcsinh(c x))^n.jl