Optimal. Leaf size=24 \[ \text{Unintegrable}\left (\frac{x^m \tan ^{-1}(a x)^3}{a^2 c x^2+c},x\right ) \]
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Rubi [A] time = 0.0645185, 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 = {} \[ \int \frac{x^m \tan ^{-1}(a x)^3}{c+a^2 c x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{x^m \tan ^{-1}(a x)^3}{c+a^2 c x^2} \, dx &=\int \frac{x^m \tan ^{-1}(a x)^3}{c+a^2 c x^2} \, dx\\ \end{align*}
Mathematica [A] time = 0.864707, size = 0, normalized size = 0. \[ \int \frac{x^m \tan ^{-1}(a x)^3}{c+a^2 c x^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.443, size = 0, normalized size = 0. \begin{align*} \int{\frac{{x}^{m} \left ( \arctan \left ( ax \right ) \right ) ^{3}}{{a}^{2}c{x}^{2}+c}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{m} \arctan \left (a x\right )^{3}}{a^{2} c x^{2} + c}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{x^{m} \arctan \left (a x\right )^{3}}{a^{2} c x^{2} + c}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \frac{\int \frac{x^{m} \operatorname{atan}^{3}{\left (a x \right )}}{a^{2} x^{2} + 1}\, dx}{c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{m} \arctan \left (a x\right )^{3}}{a^{2} c x^{2} + c}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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