Optimal. Leaf size=19 \[ \text{Unintegrable}\left (\frac{1-a^2 x^2}{\tanh ^{-1}(a x)^3},x\right ) \]
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Rubi [A] time = 0.0132488, 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 = {} \[ \int \frac{1-a^2 x^2}{\tanh ^{-1}(a x)^3} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1-a^2 x^2}{\tanh ^{-1}(a x)^3} \, dx &=\int \frac{1-a^2 x^2}{\tanh ^{-1}(a x)^3} \, dx\\ \end{align*}
Mathematica [A] time = 1.14183, size = 0, normalized size = 0. \[ \int \frac{1-a^2 x^2}{\tanh ^{-1}(a x)^3} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.237, size = 0, normalized size = 0. \begin{align*} \int{\frac{-{a}^{2}{x}^{2}+1}{ \left ({\it Artanh} \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{2 \,{\left (a^{4} x^{4} - 2 \, a^{2} x^{2} - 2 \,{\left (a^{5} x^{5} - 2 \, a^{3} x^{3} + a x\right )} \log \left (a x + 1\right ) + 2 \,{\left (a^{5} x^{5} - 2 \, a^{3} x^{3} + a x\right )} \log \left (-a x + 1\right ) + 1\right )}}{a \log \left (a x + 1\right )^{2} - 2 \, a \log \left (a x + 1\right ) \log \left (-a x + 1\right ) + a \log \left (-a x + 1\right )^{2}} + \int -\frac{4 \,{\left (5 \, a^{4} x^{4} - 6 \, a^{2} x^{2} + 1\right )}}{\log \left (a x + 1\right ) - \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^{2} x^{2} - 1}{\operatorname{artanh}\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*} - \int \frac{a^{2} x^{2}}{\operatorname{atanh}^{3}{\left (a x \right )}}\, dx - \int - \frac{1}{\operatorname{atanh}^{3}{\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{a^{2} x^{2} - 1}{\operatorname{artanh}\left (a x\right )^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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