Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{a^2 c x^2+c}{x \tan ^{-1}(a x)^3},x\right ) \]
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Rubi [A] time = 0.0320454, 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 = {} \[ \int \frac{c+a^2 c x^2}{x \tan ^{-1}(a x)^3} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{c+a^2 c x^2}{x \tan ^{-1}(a x)^3} \, dx &=\int \frac{c+a^2 c x^2}{x \tan ^{-1}(a x)^3} \, dx\\ \end{align*}
Mathematica [A] time = 1.50604, size = 0, normalized size = 0. \[ \int \frac{c+a^2 c x^2}{x \tan ^{-1}(a x)^3} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.96, size = 0, normalized size = 0. \begin{align*} \int{\frac{{a}^{2}c{x}^{2}+c}{x \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^{5} c x^{5} + 2 \, a^{3} c x^{3} - 2 \, c x^{2}{\left (\int \frac{6 \, a^{6} x^{3}}{\arctan \left (a x\right )}\,{d x} + \int \frac{5 \, a^{4} x}{\arctan \left (a x\right )}\,{d x} + \int \frac{1}{x^{3} \arctan \left (a x\right )}\,{d x}\right )} \arctan \left (a x\right )^{2} + a c x +{\left (3 \, a^{6} c x^{6} + 5 \, a^{4} c x^{4} + a^{2} c x^{2} - c\right )} \arctan \left (a x\right )}{2 \, a^{2} x^{2} \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^{2} c x^{2} + c}{x \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 \left (\int \frac{1}{x \operatorname{atan}^{3}{\left (a x \right )}}\, dx + \int \frac{a^{2} x}{\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{a^{2} c x^{2} + c}{x \arctan \left (a x\right )^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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