3.2.22 \(\int \frac {x^m}{\sinh ^{-1}(a x)^2} \, dx\) [122]

Optimal. Leaf size=13 \[ \text {Int}\left (\frac {x^m}{\sinh ^{-1}(a x)^2},x\right ) \]

[Out]

Unintegrable(x^m/arcsinh(a*x)^2,x)

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Rubi [A]
time = 0.01, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {x^m}{\sinh ^{-1}(a x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[x^m/ArcSinh[a*x]^2,x]

[Out]

Defer[Int][x^m/ArcSinh[a*x]^2, x]

Rubi steps

\begin {align*} \int \frac {x^m}{\sinh ^{-1}(a x)^2} \, dx &=\int \frac {x^m}{\sinh ^{-1}(a x)^2} \, dx\\ \end {align*}

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Mathematica [A]
time = 0.43, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^m}{\sinh ^{-1}(a x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[x^m/ArcSinh[a*x]^2,x]

[Out]

Integrate[x^m/ArcSinh[a*x]^2, x]

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Maple [A]
time = 2.90, size = 0, normalized size = 0.00 \[\int \frac {x^{m}}{\arcsinh \left (a x \right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^m/arcsinh(a*x)^2,x)

[Out]

int(x^m/arcsinh(a*x)^2,x)

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m/arcsinh(a*x)^2,x, algorithm="maxima")

[Out]

-((a^2*x^2 + 1)^(3/2)*x^m + (a^3*x^3 + a*x)*x^m)/((a^3*x^2 + sqrt(a^2*x^2 + 1)*a^2*x + a)*log(a*x + sqrt(a^2*x
^2 + 1))) + integrate(((a^3*(m + 1)*x^3 + a*(m - 1)*x)*(a^2*x^2 + 1)*x^m + (2*a^4*(m + 1)*x^4 + a^2*(3*m + 1)*
x^2 + m)*sqrt(a^2*x^2 + 1)*x^m + (a^5*(m + 1)*x^5 + 2*a^3*(m + 1)*x^3 + a*(m + 1)*x)*x^m)/((a^5*x^5 + (a^2*x^2
+ 1)*a^3*x^3 + 2*a^3*x^3 + a*x + 2*(a^4*x^4 + a^2*x^2)*sqrt(a^2*x^2 + 1))*log(a*x + sqrt(a^2*x^2 + 1))), x)

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m/arcsinh(a*x)^2,x, algorithm="fricas")

[Out]

integral(x^m/arcsinh(a*x)^2, x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^{m}}{\operatorname {asinh}^{2}{\left (a x \right )}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**m/asinh(a*x)**2,x)

[Out]

Integral(x**m/asinh(a*x)**2, x)

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m/arcsinh(a*x)^2,x, algorithm="giac")

[Out]

integrate(x^m/arcsinh(a*x)^2, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.08 \begin {gather*} \int \frac {x^m}{{\mathrm {asinh}\left (a\,x\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^m/asinh(a*x)^2,x)

[Out]

int(x^m/asinh(a*x)^2, x)

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