Optimal. Leaf size=21 \[ a^2 \text{CannotIntegrate}\left (\frac{e^{\sin ^{-1}(a x)^2}}{a^2 x^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.07802, 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 = {} \[ \int \frac{e^{\sin ^{-1}(a x)^2}}{x^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{e^{\sin ^{-1}(a x)^2}}{x^2} \, dx &=\frac{\operatorname{Subst}\left (\int a^2 e^{x^2} \cot (x) \csc (x) \, dx,x,\sin ^{-1}(a x)\right )}{a}\\ &=a \operatorname{Subst}\left (\int e^{x^2} \cot (x) \csc (x) \, dx,x,\sin ^{-1}(a x)\right )\\ \end{align*}
Mathematica [A] time = 1.62852, size = 0, normalized size = 0. \[ \int \frac{e^{\sin ^{-1}(a x)^2}}{x^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.007, size = 0, normalized size = 0. \begin{align*} \int{\frac{{{\rm e}^{ \left ( \arcsin \left ( ax \right ) \right ) ^{2}}}}{{x}^{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{e^{\left (\arcsin \left (a x\right )^{2}\right )}}{x^{2}}\,{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{e^{\left (\arcsin \left (a x\right )^{2}\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{e^{\operatorname{asin}^{2}{\left (a x \right )}}}{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{e^{\left (\arcsin \left (a x\right )^{2}\right )}}{x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]