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

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

[Out]

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

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Rubi [A]  time = 0.0141627, 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 = {} \[ \int x^m \sinh ^{-1}(a x)^{3/2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Defer[Int][x^m*ArcSinh[a*x]^(3/2), x]

Rubi steps

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

Mathematica [A]  time = 1.05965, size = 0, normalized size = 0. \[ \int x^m \sinh ^{-1}(a x)^{3/2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Integrate[x^m*ArcSinh[a*x]^(3/2), x]

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Maple [A]  time = 0.058, size = 0, normalized size = 0. \begin{align*} \int{x}^{m} \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(x^m*arcsinh(a*x)^(3/2),x)

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int x^{m} \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(x^m*arcsinh(a*x)^(3/2),x, algorithm="maxima")

[Out]

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

[Out]

Exception raised: UnboundLocalError

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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Giac [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out