Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{x \left (1-a^2 x^2\right )^2}{\tanh ^{-1}(a x)^2},x\right ) \]
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Rubi [A] time = 0.0357664, 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 = {} \[ \int \frac{x \left (1-a^2 x^2\right )^2}{\tanh ^{-1}(a x)^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{x \left (1-a^2 x^2\right )^2}{\tanh ^{-1}(a x)^2} \, dx &=\int \frac{x \left (1-a^2 x^2\right )^2}{\tanh ^{-1}(a x)^2} \, dx\\ \end{align*}
Mathematica [A] time = 0.753182, size = 0, normalized size = 0. \[ \int \frac{x \left (1-a^2 x^2\right )^2}{\tanh ^{-1}(a x)^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.379, size = 0, normalized size = 0. \begin{align*} \int{\frac{x \left ( -{a}^{2}{x}^{2}+1 \right ) ^{2}}{ \left ({\it Artanh} \left ( ax \right ) \right ) ^{2}}}\, 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{2 \,{\left (a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x\right )}}{a \log \left (a x + 1\right ) - a \log \left (-a x + 1\right )} + \int -\frac{2 \,{\left (7 \, a^{6} x^{6} - 15 \, a^{4} x^{4} + 9 \, a^{2} x^{2} - 1\right )}}{a \log \left (a x + 1\right ) - a \log \left (-a x + 1\right )}\,{d x} \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^{4} x^{5} - 2 \, a^{2} x^{3} + x}{\operatorname{artanh}\left (a x\right )^{2}}, 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*} \int \frac{x \left (a x - 1\right )^{2} \left (a x + 1\right )^{2}}{\operatorname{atanh}^{2}{\left (a x \right )}}\, dx \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} x^{2} - 1\right )}^{2} x}{\operatorname{artanh}\left (a x\right )^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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