Integrand size = 22, antiderivative size = 22 \[ \int \frac {x^m \left (c+a^2 c x^2\right )^3}{\arctan (a x)^2} \, dx=\text {Int}\left (\frac {x^m \left (c+a^2 c x^2\right )^3}{\arctan (a x)^2},x\right ) \]
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Not integrable
Time = 0.04 (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 = {} \[ \int \frac {x^m \left (c+a^2 c x^2\right )^3}{\arctan (a x)^2} \, dx=\int \frac {x^m \left (c+a^2 c x^2\right )^3}{\arctan (a x)^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {x^m \left (c+a^2 c x^2\right )^3}{\arctan (a x)^2} \, dx \\ \end{align*}
Not integrable
Time = 0.59 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {x^m \left (c+a^2 c x^2\right )^3}{\arctan (a x)^2} \, dx=\int \frac {x^m \left (c+a^2 c x^2\right )^3}{\arctan (a x)^2} \, dx \]
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Timed out.
hanged
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Not integrable
Time = 0.25 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.18 \[ \int \frac {x^m \left (c+a^2 c x^2\right )^3}{\arctan (a x)^2} \, dx=\int { \frac {{\left (a^{2} c x^{2} + c\right )}^{3} x^{m}}{\arctan \left (a x\right )^{2}} \,d x } \]
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Not integrable
Time = 14.04 (sec) , antiderivative size = 73, normalized size of antiderivative = 3.32 \[ \int \frac {x^m \left (c+a^2 c x^2\right )^3}{\arctan (a x)^2} \, dx=c^{3} \left (\int \frac {x^{m}}{\operatorname {atan}^{2}{\left (a x \right )}}\, dx + \int \frac {3 a^{2} x^{2} x^{m}}{\operatorname {atan}^{2}{\left (a x \right )}}\, dx + \int \frac {3 a^{4} x^{4} x^{m}}{\operatorname {atan}^{2}{\left (a x \right )}}\, dx + \int \frac {a^{6} x^{6} x^{m}}{\operatorname {atan}^{2}{\left (a x \right )}}\, dx\right ) \]
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Not integrable
Time = 0.65 (sec) , antiderivative size = 177, normalized size of antiderivative = 8.05 \[ \int \frac {x^m \left (c+a^2 c x^2\right )^3}{\arctan (a x)^2} \, dx=\int { \frac {{\left (a^{2} c x^{2} + c\right )}^{3} x^{m}}{\arctan \left (a x\right )^{2}} \,d x } \]
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Not integrable
Time = 174.27 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.14 \[ \int \frac {x^m \left (c+a^2 c x^2\right )^3}{\arctan (a x)^2} \, dx=\int { \frac {{\left (a^{2} c x^{2} + c\right )}^{3} x^{m}}{\arctan \left (a x\right )^{2}} \,d x } \]
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Not integrable
Time = 0.42 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {x^m \left (c+a^2 c x^2\right )^3}{\arctan (a x)^2} \, dx=\int \frac {x^m\,{\left (c\,a^2\,x^2+c\right )}^3}{{\mathrm {atan}\left (a\,x\right )}^2} \,d x \]
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