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 = 0.0104281, antiderivative size = 22, normalized size of antiderivative = 1., 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 266
Rule 44
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*}
Mathematica [A] time = 0.0034667, size = 22, normalized size = 1. \[ -\frac{1}{6 x^6}+\frac{1}{6} \log \left (x^6+1\right )-\log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 32, normalized size = 1.5 \begin{align*}{\frac{\ln \left ({x}^{2}+1 \right ) }{6}}-{\frac{1}{6\,{x}^{6}}}-\ln \left ( x \right ) +{\frac{\ln \left ({x}^{4}-{x}^{2}+1 \right ) }{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.19439, size = 27, normalized size = 1.23 \begin{align*} -\frac{1}{6 \, x^{6}} + \frac{1}{6} \, \log \left (x^{6} + 1\right ) - \frac{1}{6} \, \log \left (x^{6}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.46069, size = 63, normalized size = 2.86 \begin{align*} \frac{x^{6} \log \left (x^{6} + 1\right ) - 6 \, x^{6} \log \left (x\right ) - 1}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.129262, size = 17, normalized size = 0.77 \begin{align*} - \log{\left (x \right )} + \frac{\log{\left (x^{6} + 1 \right )}}{6} - \frac{1}{6 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20296, size = 34, normalized size = 1.55 \begin{align*} \frac{x^{6} - 1}{6 \, x^{6}} + \frac{1}{6} \, \log \left (x^{6} + 1\right ) - \frac{1}{6} \, \log \left (x^{6}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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