Optimal. Leaf size=29 \[ \text{Unintegrable}\left (\frac{\left (c^2 x^2+1\right )^{5/2}}{x^4 \left (a+b \sinh ^{-1}(c x)\right )},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.140862, 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 = {} \[ \int \frac{\left (1+c^2 x^2\right )^{5/2}}{x^4 \left (a+b \sinh ^{-1}(c x)\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{\left (1+c^2 x^2\right )^{5/2}}{x^4 \left (a+b \sinh ^{-1}(c x)\right )} \, dx &=\int \frac{\left (1+c^2 x^2\right )^{5/2}}{x^4 \left (a+b \sinh ^{-1}(c x)\right )} \, dx\\ \end{align*}
Mathematica [A] time = 0.898547, size = 0, normalized size = 0. \[ \int \frac{\left (1+c^2 x^2\right )^{5/2}}{x^4 \left (a+b \sinh ^{-1}(c x)\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.429, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{{x}^{4} \left ( a+b{\it Arcsinh} \left ( cx \right ) \right ) } \left ({c}^{2}{x}^{2}+1 \right ) ^{{\frac{5}{2}}}}\, 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{{\left (c^{2} x^{2} + 1\right )}^{\frac{5}{2}}}{{\left (b \operatorname{arsinh}\left (c x\right ) + a\right )} x^{4}}\,{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{{\left (c^{4} x^{4} + 2 \, c^{2} x^{2} + 1\right )} \sqrt{c^{2} x^{2} + 1}}{b x^{4} \operatorname{arsinh}\left (c x\right ) + a x^{4}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \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{{\left (c^{2} x^{2} + 1\right )}^{\frac{5}{2}}}{{\left (b \operatorname{arsinh}\left (c x\right ) + a\right )} x^{4}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]