Optimal. Leaf size=22 \[ -\frac {1}{8 x^8}-\frac {1}{8} \log \left (1-x^8\right )+\log (x) \]
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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 = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {266, 44} \[ -\frac {1}{8 x^8}-\frac {1}{8} \log \left (1-x^8\right )+\log (x) \]
Antiderivative was successfully verified.
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Rule 44
Rule 266
Rubi steps
\begin {align*} \int \frac {1}{x^9 \left (1-x^8\right )} \, dx &=\frac {1}{8} \operatorname {Subst}\left (\int \frac {1}{(1-x) x^2} \, dx,x,x^8\right )\\ &=\frac {1}{8} \operatorname {Subst}\left (\int \left (\frac {1}{1-x}+\frac {1}{x^2}+\frac {1}{x}\right ) \, dx,x,x^8\right )\\ &=-\frac {1}{8 x^8}+\log (x)-\frac {1}{8} \log \left (1-x^8\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 22, normalized size = 1.00 \[ -\frac {1}{8 x^8}-\frac {1}{8} \log \left (1-x^8\right )+\log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 24, normalized size = 1.09 \[ -\frac {x^{8} \log \left (x^{8} - 1\right ) - 8 \, x^{8} \log \relax (x) + 1}{8 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 26, normalized size = 1.18 \[ -\frac {x^{8} + 1}{8 \, x^{8}} + \frac {1}{8} \, \log \left (x^{8}\right ) - \frac {1}{8} \, \log \left ({\left | x^{8} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 37, normalized size = 1.68 \[ \ln \relax (x )-\frac {\ln \left (x -1\right )}{8}-\frac {\ln \left (x +1\right )}{8}-\frac {\ln \left (x^{2}+1\right )}{8}-\frac {\ln \left (x^{4}+1\right )}{8}-\frac {1}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.07, size = 20, normalized size = 0.91 \[ -\frac {1}{8 \, x^{8}} - \frac {1}{8} \, \log \left (x^{8} - 1\right ) + \frac {1}{8} \, \log \left (x^{8}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 16, normalized size = 0.73 \[ \ln \relax (x)-\frac {\ln \left (x^8-1\right )}{8}-\frac {1}{8\,x^8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 17, normalized size = 0.77 \[ \log {\relax (x )} - \frac {\log {\left (x^{8} - 1 \right )}}{8} - \frac {1}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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