Optimal. Leaf size=16 \[ \frac{1}{3} \tanh ^{-1}\left (x^3\right )-\frac{1}{3 x^3} \]
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Rubi [A] time = 0.0068052, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231, Rules used = {275, 325, 206} \[ \frac{1}{3} \tanh ^{-1}\left (x^3\right )-\frac{1}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 275
Rule 325
Rule 206
Rubi steps
\begin{align*} \int \frac{1}{x^4 \left (1-x^6\right )} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{1}{x^2 \left (1-x^2\right )} \, dx,x,x^3\right )\\ &=-\frac{1}{3 x^3}+\frac{1}{3} \operatorname{Subst}\left (\int \frac{1}{1-x^2} \, dx,x,x^3\right )\\ &=-\frac{1}{3 x^3}+\frac{1}{3} \tanh ^{-1}\left (x^3\right )\\ \end{align*}
Mathematica [A] time = 0.0040312, size = 30, normalized size = 1.88 \[ -\frac{1}{3 x^3}-\frac{1}{6} \log \left (1-x^3\right )+\frac{1}{6} \log \left (x^3+1\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.008, size = 39, normalized size = 2.4 \begin{align*} -{\frac{1}{3\,{x}^{3}}}+{\frac{\ln \left ({x}^{2}-x+1 \right ) }{6}}+{\frac{\ln \left ( 1+x \right ) }{6}}-{\frac{\ln \left ( -1+x \right ) }{6}}-{\frac{\ln \left ({x}^{2}+x+1 \right ) }{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.985231, size = 30, normalized size = 1.88 \begin{align*} -\frac{1}{3 \, x^{3}} + \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 = 1.61879, size = 69, normalized size = 4.31 \begin{align*} \frac{x^{3} \log \left (x^{3} + 1\right ) - x^{3} \log \left (x^{3} - 1\right ) - 2}{6 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.123865, size = 22, normalized size = 1.38 \begin{align*} - \frac{\log{\left (x^{3} - 1 \right )}}{6} + \frac{\log{\left (x^{3} + 1 \right )}}{6} - \frac{1}{3 x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17975, size = 32, normalized size = 2. \begin{align*} -\frac{1}{3 \, x^{3}} + \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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