Optimal. Leaf size=25 \[ \text{Unintegrable}\left (\frac{1}{x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0995991, 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 = {} \[ \int \frac{1}{x \sqrt{1+a^2 x^2} \sinh ^{-1}(a x)} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{1}{x \sqrt{1+a^2 x^2} \sinh ^{-1}(a x)} \, dx &=\int \frac{1}{x \sqrt{1+a^2 x^2} \sinh ^{-1}(a x)} \, dx\\ \end{align*}
Mathematica [A] time = 1.05339, size = 0, normalized size = 0. \[ \int \frac{1}{x \sqrt{1+a^2 x^2} \sinh ^{-1}(a x)} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.078, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x{\it Arcsinh} \left ( ax \right ) }{\frac{1}{\sqrt{{a}^{2}{x}^{2}+1}}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\sqrt{a^{2} x^{2} + 1} x \operatorname{arsinh}\left (a x\right )}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\sqrt{a^{2} x^{2} + 1}}{{\left (a^{2} x^{3} + x\right )} \operatorname{arsinh}\left (a x\right )}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \sqrt{a^{2} x^{2} + 1} \operatorname{asinh}{\left (a x \right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\sqrt{a^{2} x^{2} + 1} x \operatorname{arsinh}\left (a x\right )}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]