3.135 \(\int \frac{\sinh ^{-1}(a x)^n}{x^2} \, dx\)

Optimal. Leaf size=12 \[ \text{Unintegrable}\left (\frac{\sinh ^{-1}(a x)^n}{x^2},x\right ) \]

[Out]

Unintegrable[ArcSinh[a*x]^n/x^2, x]

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Rubi [A]  time = 0.0164332, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\sinh ^{-1}(a x)^n}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Defer[Int][ArcSinh[a*x]^n/x^2, x]

Rubi steps

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

Mathematica [A]  time = 0.895444, size = 0, normalized size = 0. \[ \int \frac{\sinh ^{-1}(a x)^n}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Integrate[ArcSinh[a*x]^n/x^2, x]

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Maple [A]  time = 0.053, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\it Arcsinh} \left ( ax \right ) \right ) ^{n}}{{x}^{2}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{arsinh}\left (a x\right )^{n}}{x^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(arcsinh(a*x)^n/x^2, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\operatorname{arsinh}\left (a x\right )^{n}}{x^{2}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(arcsinh(a*x)^n/x^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(asinh(a*x)**n/x**2, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{arsinh}\left (a x\right )^{n}}{x^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(arcsinh(a*x)^n/x^2, x)