Optimal. Leaf size=21 \[ \text{Unintegrable}\left (\frac{\left (a^2 c x^2+c\right )^3}{\tan ^{-1}(a x)^3},x\right ) \]
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Rubi [A] time = 0.0218144, 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 = {} \[ \int \frac{\left (c+a^2 c x^2\right )^3}{\tan ^{-1}(a x)^3} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\left (c+a^2 c x^2\right )^3}{\tan ^{-1}(a x)^3} \, dx &=\int \frac{\left (c+a^2 c x^2\right )^3}{\tan ^{-1}(a x)^3} \, dx\\ \end{align*}
Mathematica [A] time = 1.1501, size = 0, normalized size = 0. \[ \int \frac{\left (c+a^2 c x^2\right )^3}{\tan ^{-1}(a x)^3} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 1.2, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({a}^{2}c{x}^{2}+c \right ) ^{3}}{ \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{a^{8} c^{3} x^{8} + 4 \, a^{6} c^{3} x^{6} + 6 \, a^{4} c^{3} x^{4} + 4 \, a^{2} c^{3} x^{2} - 8 \, a \arctan \left (a x\right )^{2} \int \frac{9 \, a^{8} c^{3} x^{8} + 28 \, a^{6} c^{3} x^{6} + 30 \, a^{4} c^{3} x^{4} + 12 \, a^{2} c^{3} x^{2} + c^{3}}{\arctan \left (a x\right )}\,{d x} + c^{3} + 8 \,{\left (a^{9} c^{3} x^{9} + 4 \, a^{7} c^{3} x^{7} + 6 \, a^{5} c^{3} x^{5} + 4 \, a^{3} c^{3} x^{3} + a c^{3} x\right )} \arctan \left (a x\right )}{2 \, a \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{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}{\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*} c^{3} \left (\int \frac{3 a^{2} x^{2}}{\operatorname{atan}^{3}{\left (a x \right )}}\, dx + \int \frac{3 a^{4} x^{4}}{\operatorname{atan}^{3}{\left (a x \right )}}\, dx + \int \frac{a^{6} x^{6}}{\operatorname{atan}^{3}{\left (a x \right )}}\, dx + \int \frac{1}{\operatorname{atan}^{3}{\left (a x \right )}}\, dx\right ) \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{{\left (a^{2} c x^{2} + c\right )}^{3}}{\arctan \left (a x\right )^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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