3.50 \(\int \frac{1}{x^2 \sinh ^{-1}(a x)} \, dx\)

Optimal. Leaf size=12 \[ \text{Unintegrable}\left (\frac{1}{x^2 \sinh ^{-1}(a x)},x\right ) \]

[Out]

Unintegrable[1/(x^2*ArcSinh[a*x]), x]

________________________________________________________________________________________

Rubi [A]  time = 0.0149415, 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 = {} \[ \int \frac{1}{x^2 \sinh ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x^2*ArcSinh[a*x]),x]

[Out]

Defer[Int][1/(x^2*ArcSinh[a*x]), x]

Rubi steps

\begin{align*} \int \frac{1}{x^2 \sinh ^{-1}(a x)} \, dx &=\int \frac{1}{x^2 \sinh ^{-1}(a x)} \, dx\\ \end{align*}

Mathematica [A]  time = 0.803094, size = 0, normalized size = 0. \[ \int \frac{1}{x^2 \sinh ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x^2*ArcSinh[a*x]),x]

[Out]

Integrate[1/(x^2*ArcSinh[a*x]), x]

________________________________________________________________________________________

Maple [A]  time = 0.086, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{{x}^{2}{\it Arcsinh} \left ( ax \right ) }}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^2/arcsinh(a*x),x)

[Out]

int(1/x^2/arcsinh(a*x),x)

________________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x^{2} \operatorname{arsinh}\left (a x\right )}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arcsinh(a*x),x, algorithm="maxima")

[Out]

integrate(1/(x^2*arcsinh(a*x)), x)

________________________________________________________________________________________

Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{x^{2} \operatorname{arsinh}\left (a x\right )}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arcsinh(a*x),x, algorithm="fricas")

[Out]

integral(1/(x^2*arcsinh(a*x)), x)

________________________________________________________________________________________

Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x^{2} \operatorname{asinh}{\left (a x \right )}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**2/asinh(a*x),x)

[Out]

Integral(1/(x**2*asinh(a*x)), x)

________________________________________________________________________________________

Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x^{2} \operatorname{arsinh}\left (a x\right )}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arcsinh(a*x),x, algorithm="giac")

[Out]

integrate(1/(x^2*arcsinh(a*x)), x)