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

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

[Out]

Unintegrable[1/(x*ArcSinh[a*x]^(3/2)), x]

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Rubi [A]  time = 0.0131123, 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 = {} \[ \int \frac{1}{x \sinh ^{-1}(a x)^{3/2}} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x*ArcSinh[a*x]^(3/2)),x]

[Out]

Defer[Int][1/(x*ArcSinh[a*x]^(3/2)), x]

Rubi steps

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

Mathematica [A]  time = 0.38304, size = 0, normalized size = 0. \[ \int \frac{1}{x \sinh ^{-1}(a x)^{3/2}} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x*ArcSinh[a*x]^(3/2)),x]

[Out]

Integrate[1/(x*ArcSinh[a*x]^(3/2)), x]

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Maple [A]  time = 0.061, 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(1/x/arcsinh(a*x)^(3/2),x)

[Out]

int(1/x/arcsinh(a*x)^(3/2),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \operatorname{arsinh}\left (a x\right )^{\frac{3}{2}}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/arcsinh(a*x)^(3/2),x, algorithm="maxima")

[Out]

integrate(1/(x*arcsinh(a*x)^(3/2)), 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(1/x/arcsinh(a*x)^(3/2),x, algorithm="fricas")

[Out]

Exception raised: UnboundLocalError

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \operatorname{asinh}^{\frac{3}{2}}{\left (a x \right )}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/asinh(a*x)**(3/2),x)

[Out]

Integral(1/(x*asinh(a*x)**(3/2)), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \operatorname{arsinh}\left (a x\right )^{\frac{3}{2}}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/arcsinh(a*x)^(3/2),x, algorithm="giac")

[Out]

integrate(1/(x*arcsinh(a*x)^(3/2)), x)