Optimal. Leaf size=8 \[ \frac{1}{3} \tanh ^{-1}\left (x^3\right ) \]
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Rubi [A] time = 0.0037426, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {275, 206} \[ \frac{1}{3} \tanh ^{-1}\left (x^3\right ) \]
Antiderivative was successfully verified.
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Rule 275
Rule 206
Rubi steps
\begin{align*} \int \frac{x^2}{1-x^6} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{1}{1-x^2} \, dx,x,x^3\right )\\ &=\frac{1}{3} \tanh ^{-1}\left (x^3\right )\\ \end{align*}
Mathematica [B] time = 0.003339, size = 23, normalized size = 2.88 \[ \frac{1}{6} \log \left (x^3+1\right )-\frac{1}{6} \log \left (1-x^3\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.002, size = 18, normalized size = 2.3 \begin{align*} -{\frac{\ln \left ({x}^{3}-1 \right ) }{6}}+{\frac{\ln \left ({x}^{3}+1 \right ) }{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.981056, size = 23, normalized size = 2.88 \begin{align*} \frac{1}{6} \, \log \left (x^{3} + 1\right ) - \frac{1}{6} \, \log \left (x^{3} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.39459, size = 50, normalized size = 6.25 \begin{align*} \frac{1}{6} \, \log \left (x^{3} + 1\right ) - \frac{1}{6} \, \log \left (x^{3} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.097713, size = 15, normalized size = 1.88 \begin{align*} - \frac{\log{\left (x^{3} - 1 \right )}}{6} + \frac{\log{\left (x^{3} + 1 \right )}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.17161, size = 26, normalized size = 3.25 \begin{align*} \frac{1}{6} \, \log \left ({\left | x^{3} + 1 \right |}\right ) - \frac{1}{6} \, \log \left ({\left | x^{3} - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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