Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{x^m \tan ^{-1}(a x)}{\left (a^2 c x^2+c\right )^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0498953, 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 = {} \[ \int \frac{x^m \tan ^{-1}(a x)}{\left (c+a^2 c x^2\right )^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{x^m \tan ^{-1}(a x)}{\left (c+a^2 c x^2\right )^2} \, dx &=\int \frac{x^m \tan ^{-1}(a x)}{\left (c+a^2 c x^2\right )^2} \, dx\\ \end{align*}
Mathematica [A] time = 0.604582, size = 0, normalized size = 0. \[ \int \frac{x^m \tan ^{-1}(a x)}{\left (c+a^2 c x^2\right )^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 1.122, size = 0, normalized size = 0. \begin{align*} \int{\frac{{x}^{m}\arctan \left ( ax \right ) }{ \left ({a}^{2}c{x}^{2}+c \right ) ^{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{x^{m} \arctan \left (a x\right )}{{\left (a^{2} c x^{2} + c\right )}^{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{x^{m} \arctan \left (a x\right )}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{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*} \frac{\int \frac{x^{m} \operatorname{atan}{\left (a x \right )}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}} \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} \arctan \left (a x\right )}{{\left (a^{2} c x^{2} + c\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]