3.126 \(\int \frac{x^m}{\sqrt{\sinh ^{-1}(a x)}} \, dx\)

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

[Out]

Unintegrable[x^m/Sqrt[ArcSinh[a*x]], x]

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Rubi [A]  time = 0.013785, 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 = {} \[ \int \frac{x^m}{\sqrt{\sinh ^{-1}(a x)}} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Defer[Int][x^m/Sqrt[ArcSinh[a*x]], x]

Rubi steps

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

Mathematica [A]  time = 1.19762, size = 0, normalized size = 0. \[ \int \frac{x^m}{\sqrt{\sinh ^{-1}(a x)}} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Integrate[x^m/Sqrt[ArcSinh[a*x]], x]

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Maple [A]  time = 0.062, size = 0, normalized size = 0. \begin{align*} \int{{x}^{m}{\frac{1}{\sqrt{{\it Arcsinh} \left ( ax \right ) }}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

Exception raised: UnboundLocalError

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(x**m/sqrt(asinh(a*x)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x^m/sqrt(arcsinh(a*x)), x)