Optimal. Leaf size=24 \[ \text{Unintegrable}\left (\sqrt{d+e x^2} \left (a+b \sin ^{-1}(c x)\right )^2,x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0371079, 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 = {} \[ \int \sqrt{d+e x^2} \left (a+b \sin ^{-1}(c x)\right )^2 \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \sqrt{d+e x^2} \left (a+b \sin ^{-1}(c x)\right )^2 \, dx &=\int \sqrt{d+e x^2} \left (a+b \sin ^{-1}(c x)\right )^2 \, dx\\ \end{align*}
Mathematica [A] time = 16.879, size = 0, normalized size = 0. \[ \int \sqrt{d+e x^2} \left (a+b \sin ^{-1}(c x)\right )^2 \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.379, size = 0, normalized size = 0. \begin{align*} \int \sqrt{e{x}^{2}+d} \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(-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 ({\left (b^{2} \arcsin \left (c x\right )^{2} + 2 \, a b \arcsin \left (c x\right ) + a^{2}\right )} \sqrt{e x^{2} + d}, 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 \left (a + b \operatorname{asin}{\left (c x \right )}\right )^{2} \sqrt{d + e 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 \sqrt{e x^{2} + d}{\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]