3.132 \(\int \frac{\cosh ^{-1}(a x)^n}{x} \, dx\)

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

[Out]

Unintegrable[ArcCosh[a*x]^n/x, x]

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Rubi [A]  time = 0.017206, 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 = {} \[ \int \frac{\cosh ^{-1}(a x)^n}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Defer[Int][ArcCosh[a*x]^n/x, x]

Rubi steps

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

Mathematica [A]  time = 0.32685, size = 0, normalized size = 0. \[ \int \frac{\cosh ^{-1}(a x)^n}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Integrate[ArcCosh[a*x]^n/x, x]

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Maple [A]  time = 0.053, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\rm arccosh} \left (ax\right ) \right ) ^{n}}{x}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(arccosh(a*x)^n/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(arccosh(a*x)^n/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(acosh(a*x)**n/x, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \mathit{sage}_{0} x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

sage0*x