3.119 \(\int \frac{x^m}{\cosh ^{-1}(a x)} \, dx\)

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

[Out]

Unintegrable[x^m/ArcCosh[a*x], x]

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Rubi [A]  time = 0.0229181, 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 = {} \[ \int \frac{x^m}{\cosh ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

Int[x^m/ArcCosh[a*x],x]

[Out]

Defer[Int][x^m/ArcCosh[a*x], x]

Rubi steps

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

Mathematica [A]  time = 1.30103, size = 0, normalized size = 0. \[ \int \frac{x^m}{\cosh ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[x^m/ArcCosh[a*x],x]

[Out]

Integrate[x^m/ArcCosh[a*x], x]

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Maple [A]  time = 0.485, size = 0, normalized size = 0. \begin{align*} \int{\frac{{x}^{m}}{{\rm arccosh} \left (ax\right )}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^m/arccosh(a*x),x)

[Out]

int(x^m/arccosh(a*x),x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m/arccosh(a*x),x, algorithm="maxima")

[Out]

integrate(x^m/arccosh(a*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m/arccosh(a*x),x, algorithm="fricas")

[Out]

integral(x^m/arccosh(a*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**m/acosh(a*x),x)

[Out]

Integral(x**m/acosh(a*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m/arccosh(a*x),x, algorithm="giac")

[Out]

integrate(x^m/arccosh(a*x), x)