Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{1}{\left (d+e x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0340797, 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 = {} \[ \int \frac{1}{\left (d+e x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{1}{\left (d+e x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2} \, dx &=\int \frac{1}{\left (d+e x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2} \, dx\\ \end{align*}
Mathematica [A] time = 20.5259, size = 0, normalized size = 0. \[ \int \frac{1}{\left (d+e x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.688, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( e{x}^{2}+d \right ) \left ( a+b\arcsin \left ( cx \right ) \right ) ^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [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]
________________________________________________________________________________________
Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{a^{2} e x^{2} + a^{2} d +{\left (b^{2} e x^{2} + b^{2} d\right )} \arcsin \left (c x\right )^{2} + 2 \,{\left (a b e x^{2} + a b d\right )} \arcsin \left (c x\right )}, 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{1}{{\left (e x^{2} + d\right )}{\left (b \arcsin \left (c x\right ) + a\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]