Optimal. Leaf size=22 \[ -\frac {1}{5 x^5}-\log (x)+\frac {1}{5} \log \left (1+x^5\right ) \]
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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 = {272, 46}
\begin {gather*} -\frac {1}{5 x^5}+\frac {1}{5} \log \left (x^5+1\right )-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 46
Rule 272
Rubi steps
\begin {align*} \int \frac {1}{x^6 \left (1+x^5\right )} \, dx &=\frac {1}{5} \text {Subst}\left (\int \frac {1}{x^2 (1+x)} \, dx,x,x^5\right )\\ &=\frac {1}{5} \text {Subst}\left (\int \left (\frac {1}{x^2}-\frac {1}{x}+\frac {1}{1+x}\right ) \, dx,x,x^5\right )\\ &=-\frac {1}{5 x^5}-\log (x)+\frac {1}{5} \log \left (1+x^5\right )\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 22, normalized size = 1.00 \begin {gather*} -\frac {1}{5 x^5}-\log (x)+\frac {1}{5} \log \left (1+x^5\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.19, size = 36, normalized size = 1.64
method | result | size |
meijerg | \(-\frac {1}{5 x^{5}}-\ln \left (x \right )+\frac {\ln \left (x^{5}+1\right )}{5}\) | \(19\) |
risch | \(-\frac {1}{5 x^{5}}-\ln \left (x \right )+\frac {\ln \left (x^{5}+1\right )}{5}\) | \(19\) |
default | \(\frac {\ln \left (x +1\right )}{5}-\frac {1}{5 x^{5}}-\ln \left (x \right )+\frac {\ln \left (x^{4}-x^{3}+x^{2}-x +1\right )}{5}\) | \(36\) |
norman | \(\frac {\ln \left (x +1\right )}{5}-\frac {1}{5 x^{5}}-\ln \left (x \right )+\frac {\ln \left (x^{4}-x^{3}+x^{2}-x +1\right )}{5}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 20, normalized size = 0.91 \begin {gather*} -\frac {1}{5 \, x^{5}} + \frac {1}{5} \, \log \left (x^{5} + 1\right ) - \frac {1}{5} \, \log \left (x^{5}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 24, normalized size = 1.09 \begin {gather*} \frac {x^{5} \log \left (x^{5} + 1\right ) - 5 \, x^{5} \log \left (x\right ) - 1}{5 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 17, normalized size = 0.77 \begin {gather*} - \log {\left (x \right )} + \frac {\log {\left (x^{5} + 1 \right )}}{5} - \frac {1}{5 x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.30, size = 25, normalized size = 1.14 \begin {gather*} \frac {x^{5} - 1}{5 \, x^{5}} + \frac {1}{5} \, \log \left ({\left | x^{5} + 1 \right |}\right ) - \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 18, normalized size = 0.82 \begin {gather*} \frac {\ln \left (x^5+1\right )}{5}-\ln \left (x\right )-\frac {1}{5\,x^5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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