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

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

[Out]

Unintegrable[1/(x*ArcCosh[a*x]), x]

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Rubi [A]  time = 0.0138482, 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 = {} \[ \int \frac{1}{x \cosh ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x*ArcCosh[a*x]),x]

[Out]

Defer[Int][1/(x*ArcCosh[a*x]), x]

Rubi steps

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

Mathematica [A]  time = 0.19446, size = 0, normalized size = 0. \[ \int \frac{1}{x \cosh ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x*ArcCosh[a*x]),x]

[Out]

Integrate[1/(x*ArcCosh[a*x]), x]

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Maple [A]  time = 0.065, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x{\rm arccosh} \left (ax\right )}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x/arccosh(a*x),x)

[Out]

int(1/x/arccosh(a*x),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \operatorname{arcosh}\left (a x\right )}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/arccosh(a*x),x, algorithm="maxima")

[Out]

integrate(1/(x*arccosh(a*x)), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{x \operatorname{arcosh}\left (a x\right )}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/arccosh(a*x),x, algorithm="fricas")

[Out]

integral(1/(x*arccosh(a*x)), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \operatorname{acosh}{\left (a x \right )}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/acosh(a*x),x)

[Out]

Integral(1/(x*acosh(a*x)), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \operatorname{arcosh}\left (a x\right )}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/arccosh(a*x),x, algorithm="giac")

[Out]

integrate(1/(x*arccosh(a*x)), x)