Optimal. Leaf size=22 \[ -\frac {1}{6 x^6}+\frac {1}{6} \log \left (x^6+1\right )-\log (x) \]
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Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {266, 44} \[ -\frac {1}{6 x^6}+\frac {1}{6} \log \left (x^6+1\right )-\log (x) \]
Antiderivative was successfully verified.
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Rule 44
Rule 266
Rubi steps
\begin {align*} \int \frac {1}{x^7 \left (1+x^6\right )} \, dx &=\frac {1}{6} \operatorname {Subst}\left (\int \frac {1}{x^2 (1+x)} \, dx,x,x^6\right )\\ &=\frac {1}{6} \operatorname {Subst}\left (\int \left (\frac {1}{x^2}-\frac {1}{x}+\frac {1}{1+x}\right ) \, dx,x,x^6\right )\\ &=-\frac {1}{6 x^6}-\log (x)+\frac {1}{6} \log \left (1+x^6\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 22, normalized size = 1.00 \[ -\frac {1}{6 x^6}+\frac {1}{6} \log \left (x^6+1\right )-\log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.87, size = 24, normalized size = 1.09 \[ \frac {x^{6} \log \left (x^{6} + 1\right ) - 6 \, x^{6} \log \relax (x) - 1}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 25, normalized size = 1.14 \[ \frac {x^{6} - 1}{6 \, x^{6}} + \frac {1}{6} \, \log \left (x^{6} + 1\right ) - \frac {1}{6} \, \log \left (x^{6}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 32, normalized size = 1.45 \[ -\ln \relax (x )+\frac {\ln \left (x^{2}+1\right )}{6}+\frac {\ln \left (x^{4}-x^{2}+1\right )}{6}-\frac {1}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.98, size = 20, normalized size = 0.91 \[ -\frac {1}{6 \, x^{6}} + \frac {1}{6} \, \log \left (x^{6} + 1\right ) - \frac {1}{6} \, \log \left (x^{6}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 18, normalized size = 0.82 \[ \frac {\ln \left (x^6+1\right )}{6}-\ln \relax (x)-\frac {1}{6\,x^6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 17, normalized size = 0.77 \[ - \log {\relax (x )} + \frac {\log {\left (x^{6} + 1 \right )}}{6} - \frac {1}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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