Optimal. Leaf size=15 \[ \log (x)-\frac {1}{3} \log \left (1-x^6\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {446, 72} \[ \log (x)-\frac {1}{3} \log \left (1-x^6\right ) \]
Antiderivative was successfully verified.
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Rule 72
Rule 446
Rubi steps
\begin {align*} \int \frac {1+x^6}{x \left (1-x^6\right )} \, dx &=\frac {1}{6} \operatorname {Subst}\left (\int \frac {1+x}{(1-x) x} \, dx,x,x^6\right )\\ &=\frac {1}{6} \operatorname {Subst}\left (\int \left (-\frac {2}{-1+x}+\frac {1}{x}\right ) \, dx,x,x^6\right )\\ &=\log (x)-\frac {1}{3} \log \left (1-x^6\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 1.00 \[ \log (x)-\frac {1}{3} \log \left (1-x^6\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 11, normalized size = 0.73 \[ -\frac {1}{3} \, \log \left (x^{6} - 1\right ) + \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 16, normalized size = 1.07 \[ \frac {1}{6} \, \log \left (x^{6}\right ) - \frac {1}{3} \, \log \left ({\left | x^{6} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.05, size = 36, normalized size = 2.40 \[ \ln \relax (x )-\frac {\ln \left (x -1\right )}{3}-\frac {\ln \left (x +1\right )}{3}-\frac {\ln \left (x^{2}-x +1\right )}{3}-\frac {\ln \left (x^{2}+x +1\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 15, normalized size = 1.00 \[ -\frac {1}{3} \, \log \left (x^{6} - 1\right ) + \frac {1}{6} \, \log \left (x^{6}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 11, normalized size = 0.73 \[ \ln \relax (x)-\frac {\ln \left (x^6-1\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 10, normalized size = 0.67 \[ \log {\relax (x )} - \frac {\log {\left (x^{6} - 1 \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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