3.123 \(\int x^m \sqrt{\cosh ^{-1}(a x)} \, dx\)

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

[Out]

Unintegrable[x^m*Sqrt[ArcCosh[a*x]], x]

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Rubi [A]  time = 0.0156938, 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 = {} \[ \int x^m \sqrt{\cosh ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Defer[Int][x^m*Sqrt[ArcCosh[a*x]], x]

Rubi steps

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

Mathematica [A]  time = 2.16921, size = 0, normalized size = 0. \[ \int x^m \sqrt{\cosh ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Integrate[x^m*Sqrt[ArcCosh[a*x]], x]

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Maple [A]  time = 0.067, size = 0, normalized size = 0. \begin{align*} \int{x}^{m}\sqrt{{\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)^(1/2),x)

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int x^{m} \sqrt{\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)^(1/2),x, algorithm="maxima")

[Out]

integrate(x^m*sqrt(arccosh(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*arccosh(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 x^{m} \sqrt{\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)**(1/2),x)

[Out]

Integral(x**m*sqrt(acosh(a*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(x^m*arccosh(a*x)^(1/2),x, algorithm="giac")

[Out]

sage0*x