Optimal. Leaf size=24 \[ \text{Unintegrable}\left (\frac{x^m}{\left (a^2 c x^2+c\right )^2 \tan ^{-1}(a x)^3},x\right ) \]
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Rubi [A] time = 0.0667678, 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 = {} \[ \int \frac{x^m}{\left (c+a^2 c x^2\right )^2 \tan ^{-1}(a x)^3} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{x^m}{\left (c+a^2 c x^2\right )^2 \tan ^{-1}(a x)^3} \, dx &=\int \frac{x^m}{\left (c+a^2 c x^2\right )^2 \tan ^{-1}(a x)^3} \, dx\\ \end{align*}
Mathematica [A] time = 0.492035, size = 0, normalized size = 0. \[ \int \frac{x^m}{\left (c+a^2 c x^2\right )^2 \tan ^{-1}(a x)^3} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 1.17, size = 0, normalized size = 0. \begin{align*} \int{\frac{{x}^{m}}{ \left ({a}^{2}c{x}^{2}+c \right ) ^{2} \left ( \arctan \left ( ax \right ) \right ) ^{3}}}\, 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*} \frac{{\left (a^{4} c^{2} x^{3} + a^{2} c^{2} x\right )} \arctan \left (a x\right )^{2} \int \frac{{\left ({\left (a^{4} m^{2} - 3 \, a^{4} m + 2 \, a^{4}\right )} x^{4} + 2 \,{\left (a^{2} m^{2} - 2 \, a^{2} m - a^{2}\right )} x^{2} + m^{2} - m\right )} x^{m}}{{\left (a^{6} c^{2} x^{6} + 2 \, a^{4} c^{2} x^{4} + a^{2} c^{2} x^{2}\right )} \arctan \left (a x\right )}\,{d x} - a x x^{m} -{\left ({\left (a^{2} m - 2 \, a^{2}\right )} x^{2} + m\right )} x^{m} \arctan \left (a x\right )}{2 \,{\left (a^{4} c^{2} x^{3} + a^{2} c^{2} x\right )} \arctan \left (a x\right )^{2}} \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}}{{\left (a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right )} \arctan \left (a x\right )^{3}}, 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}}{a^{4} x^{4} \operatorname{atan}^{3}{\left (a x \right )} + 2 a^{2} x^{2} \operatorname{atan}^{3}{\left (a x \right )} + \operatorname{atan}^{3}{\left (a x \right )}}\, dx}{c^{2}} \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}}{{\left (a^{2} c x^{2} + c\right )}^{2} \arctan \left (a x\right )^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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