3.85 \(\int \frac{\sinh ^{-1}(a x)^{3/2}}{x} \, dx\)

Optimal. Leaf size=14 \[ \text{Unintegrable}\left (\frac{\sinh ^{-1}(a x)^{3/2}}{x},x\right ) \]

[Out]

Unintegrable[ArcSinh[a*x]^(3/2)/x, x]

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Rubi [A]  time = 0.0149503, 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 = {} \[ \int \frac{\sinh ^{-1}(a x)^{3/2}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[ArcSinh[a*x]^(3/2)/x,x]

[Out]

Defer[Int][ArcSinh[a*x]^(3/2)/x, x]

Rubi steps

\begin{align*} \int \frac{\sinh ^{-1}(a x)^{3/2}}{x} \, dx &=\int \frac{\sinh ^{-1}(a x)^{3/2}}{x} \, dx\\ \end{align*}

Mathematica [A]  time = 0.315237, size = 0, normalized size = 0. \[ \int \frac{\sinh ^{-1}(a x)^{3/2}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[ArcSinh[a*x]^(3/2)/x,x]

[Out]

Integrate[ArcSinh[a*x]^(3/2)/x, x]

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Maple [A]  time = 0.058, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x} \left ({\it Arcsinh} \left ( ax \right ) \right ) ^{{\frac{3}{2}}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(arcsinh(a*x)^(3/2)/x,x)

[Out]

int(arcsinh(a*x)^(3/2)/x,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{arsinh}\left (a x\right )^{\frac{3}{2}}}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(arcsinh(a*x)^(3/2)/x,x, algorithm="maxima")

[Out]

integrate(arcsinh(a*x)^(3/2)/x, x)

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Fricas [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(arcsinh(a*x)^(3/2)/x,x, algorithm="fricas")

[Out]

Exception raised: UnboundLocalError

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{asinh}^{\frac{3}{2}}{\left (a x \right )}}{x}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(asinh(a*x)**(3/2)/x,x)

[Out]

Integral(asinh(a*x)**(3/2)/x, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{arsinh}\left (a x\right )^{\frac{3}{2}}}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(arcsinh(a*x)^(3/2)/x,x, algorithm="giac")

[Out]

integrate(arcsinh(a*x)^(3/2)/x, x)