Optimal. Leaf size=10 \[ \frac {1}{6} (\log (x)+1)^6 \]
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Rubi [A] time = 0.02, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2302, 30} \[ \frac {1}{6} (\log (x)+1)^6 \]
Antiderivative was successfully verified.
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Rule 30
Rule 2302
Rubi steps
\begin {align*} \int \frac {(1+\log (x))^5}{x} \, dx &=\operatorname {Subst}\left (\int x^5 \, dx,x,1+\log (x)\right )\\ &=\frac {1}{6} (1+\log (x))^6\\ \end {align*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 1.00 \[ \frac {1}{6} (\log (x)+1)^6 \]
Antiderivative was successfully verified.
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fricas [B] time = 0.54, size = 31, normalized size = 3.10 \[ \frac {1}{6} \, \log \relax (x)^{6} + \log \relax (x)^{5} + \frac {5}{2} \, \log \relax (x)^{4} + \frac {10}{3} \, \log \relax (x)^{3} + \frac {5}{2} \, \log \relax (x)^{2} + \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.17, size = 31, normalized size = 3.10 \[ \frac {1}{6} \, \log \relax (x)^{6} + \log \relax (x)^{5} + \frac {5}{2} \, \log \relax (x)^{4} + \frac {10}{3} \, \log \relax (x)^{3} + \frac {5}{2} \, \log \relax (x)^{2} + \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 33, normalized size = 3.30 \[ \frac {\ln \relax (x )^{6}}{6}+\ln \relax (x )^{5}+\frac {5 \ln \relax (x )^{4}}{2}+\frac {10 \ln \relax (x )^{3}}{3}+\frac {5 \ln \relax (x )^{2}}{2}+\ln \relax (x )+\frac {1}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 8, normalized size = 0.80 \[ \frac {1}{6} \, {\left (\log \relax (x) + 1\right )}^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.39, size = 26, normalized size = 2.60 \[ \frac {\ln \relax (x)\,\left (\ln \relax (x)+2\right )\,\left ({\ln \relax (x)}^2+\ln \relax (x)+1\right )\,\left ({\ln \relax (x)}^2+3\,\ln \relax (x)+3\right )}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.14, size = 39, normalized size = 3.90 \[ \frac {\log {\relax (x )}^{6}}{6} + \log {\relax (x )}^{5} + \frac {5 \log {\relax (x )}^{4}}{2} + \frac {10 \log {\relax (x )}^{3}}{3} + \frac {5 \log {\relax (x )}^{2}}{2} + \log {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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