Integrand size = 22, antiderivative size = 22 \[ \int \frac {x^m \arctan (a x)^3}{c+a^2 c x^2} \, dx=\text {Int}\left (\frac {x^m \arctan (a x)^3}{c+a^2 c x^2},x\right ) \]
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Not integrable
Time = 0.05 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {x^m \arctan (a x)^3}{c+a^2 c x^2} \, dx=\int \frac {x^m \arctan (a x)^3}{c+a^2 c x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {x^m \arctan (a x)^3}{c+a^2 c x^2} \, dx \\ \end{align*}
Not integrable
Time = 0.95 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {x^m \arctan (a x)^3}{c+a^2 c x^2} \, dx=\int \frac {x^m \arctan (a x)^3}{c+a^2 c x^2} \, dx \]
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Not integrable
Time = 1.85 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00
\[\int \frac {x^{m} \arctan \left (a x \right )^{3}}{a^{2} c \,x^{2}+c}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {x^m \arctan (a x)^3}{c+a^2 c x^2} \, dx=\int { \frac {x^{m} \arctan \left (a x\right )^{3}}{a^{2} c x^{2} + c} \,d x } \]
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Not integrable
Time = 3.13 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91 \[ \int \frac {x^m \arctan (a x)^3}{c+a^2 c x^2} \, dx=\frac {\int \frac {x^{m} \operatorname {atan}^{3}{\left (a x \right )}}{a^{2} x^{2} + 1}\, dx}{c} \]
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Not integrable
Time = 0.59 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {x^m \arctan (a x)^3}{c+a^2 c x^2} \, dx=\int { \frac {x^{m} \arctan \left (a x\right )^{3}}{a^{2} c x^{2} + c} \,d x } \]
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Not integrable
Time = 136.66 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.14 \[ \int \frac {x^m \arctan (a x)^3}{c+a^2 c x^2} \, dx=\int { \frac {x^{m} \arctan \left (a x\right )^{3}}{a^{2} c x^{2} + c} \,d x } \]
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Not integrable
Time = 0.40 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {x^m \arctan (a x)^3}{c+a^2 c x^2} \, dx=\int \frac {x^m\,{\mathrm {atan}\left (a\,x\right )}^3}{c\,a^2\,x^2+c} \,d x \]
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