Optimal. Leaf size=26 \[ \text{Unintegrable}\left (\frac{x^m}{\left (a^2 c x^2+c\right ) \sqrt{\tan ^{-1}(a x)}},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0677465, 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 = {} \[ \int \frac{x^m}{\left (c+a^2 c x^2\right ) \sqrt{\tan ^{-1}(a x)}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{x^m}{\left (c+a^2 c x^2\right ) \sqrt{\tan ^{-1}(a x)}} \, dx &=\int \frac{x^m}{\left (c+a^2 c x^2\right ) \sqrt{\tan ^{-1}(a x)}} \, dx\\ \end{align*}
Mathematica [A] time = 0.602541, size = 0, normalized size = 0. \[ \int \frac{x^m}{\left (c+a^2 c x^2\right ) \sqrt{\tan ^{-1}(a x)}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.566, size = 0, normalized size = 0. \begin{align*} \int{\frac{{x}^{m}}{{a}^{2}c{x}^{2}+c}{\frac{1}{\sqrt{\arctan \left ( ax \right ) }}}}\, 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: RuntimeError} \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{x^{m}}{{\left (a^{2} c x^{2} + c\right )} \sqrt{\arctan \left (a x\right )}}, 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*} \frac{\int \frac{x^{m}}{a^{2} x^{2} \sqrt{\operatorname{atan}{\left (a x \right )}} + \sqrt{\operatorname{atan}{\left (a x \right )}}}\, dx}{c} \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{x^{m}}{{\left (a^{2} c x^{2} + c\right )} \sqrt{\arctan \left (a x\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]