Optimal. Leaf size=25 \[ \text{Unintegrable}\left (\frac{\sqrt{d+e x^2} \left (a+b \text{csch}^{-1}(c x)\right )}{x^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0898209, 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 = {} \[ \int \frac{\sqrt{d+e x^2} \left (a+b \text{csch}^{-1}(c x)\right )}{x^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{\sqrt{d+e x^2} \left (a+b \text{csch}^{-1}(c x)\right )}{x^2} \, dx &=\int \frac{\sqrt{d+e x^2} \left (a+b \text{csch}^{-1}(c x)\right )}{x^2} \, dx\\ \end{align*}
Mathematica [A] time = 1.70099, size = 0, normalized size = 0. \[ \int \frac{\sqrt{d+e x^2} \left (a+b \text{csch}^{-1}(c x)\right )}{x^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.449, size = 0, normalized size = 0. \begin{align*} \int{\frac{a+b{\rm arccsch} \left (cx\right )}{{x}^{2}}\sqrt{e{x}^{2}+d}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \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{e x^{2} + d}{\left (b \operatorname{arcsch}\left (c x\right ) + a\right )}}{x^{2}}, 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{\left (a + b \operatorname{acsch}{\left (c x \right )}\right ) \sqrt{d + e x^{2}}}{x^{2}}\, 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{\sqrt{e x^{2} + d}{\left (b \operatorname{arcsch}\left (c x\right ) + a\right )}}{x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]