Optimal. Leaf size=12 \[ -\frac{1}{6} \log \left (1-x^6\right ) \]
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Rubi [A] time = 0.0025075, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {260} \[ -\frac{1}{6} \log \left (1-x^6\right ) \]
Antiderivative was successfully verified.
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Rule 260
Rubi steps
\begin{align*} \int \frac{x^5}{1-x^6} \, dx &=-\frac{1}{6} \log \left (1-x^6\right )\\ \end{align*}
Mathematica [A] time = 0.002893, size = 12, normalized size = 1. \[ -\frac{1}{6} \log \left (1-x^6\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 18, normalized size = 1.5 \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 [A] time = 0.979428, size = 11, normalized size = 0.92 \begin{align*} -\frac{1}{6} \, \log \left (x^{6} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40847, size = 26, normalized size = 2.17 \begin{align*} -\frac{1}{6} \, \log \left (x^{6} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.086711, size = 8, normalized size = 0.67 \begin{align*} - \frac{\log{\left (x^{6} - 1 \right )}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18427, size = 12, normalized size = 1. \begin{align*} -\frac{1}{6} \, \log \left ({\left | x^{6} - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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