3.126 \(\int (d x)^m \cosh ^{-1}(a x)^n \, dx\)

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

[Out]

Unintegrable[(d*x)^m*ArcCosh[a*x]^n, x]

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Rubi [A]  time = 0.0192157, 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 = {} \[ \int (d x)^m \cosh ^{-1}(a x)^n \, dx \]

Verification is Not applicable to the result.

[In]

Int[(d*x)^m*ArcCosh[a*x]^n,x]

[Out]

Defer[Int][(d*x)^m*ArcCosh[a*x]^n, x]

Rubi steps

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

Mathematica [A]  time = 1.39556, size = 0, normalized size = 0. \[ \int (d x)^m \cosh ^{-1}(a x)^n \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(d*x)^m*ArcCosh[a*x]^n,x]

[Out]

Integrate[(d*x)^m*ArcCosh[a*x]^n, x]

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Maple [A]  time = 0.082, size = 0, normalized size = 0. \begin{align*} \int \left ( dx \right ) ^{m} \left ({\rm arccosh} \left (ax\right ) \right ) ^{n}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*x)^m*arccosh(a*x)^n,x)

[Out]

int((d*x)^m*arccosh(a*x)^n,x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate((d*x)^m*arccosh(a*x)^n, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral((d*x)^m*arccosh(a*x)^n, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x)**m*acosh(a*x)**n,x)

[Out]

Integral((d*x)**m*acosh(a*x)**n, 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((d*x)^m*arccosh(a*x)^n,x, algorithm="giac")

[Out]

sage0*x