Optimal. Leaf size=21 \[ \frac {5}{3} (\log (x)+3)^3-\frac {1}{4} (\log (x)+3)^4 \]
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Rubi [A] time = 0.04, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2365, 43} \[ \frac {5}{3} (\log (x)+3)^3-\frac {1}{4} (\log (x)+3)^4 \]
Antiderivative was successfully verified.
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Rule 43
Rule 2365
Rubi steps
\begin {align*} \int \frac {(2-\log (x)) (3+\log (x))^2}{x} \, dx &=\operatorname {Subst}\left (\int (2-x) (3+x)^2 \, dx,x,\log (x)\right )\\ &=\operatorname {Subst}\left (\int \left (5 (3+x)^2-(3+x)^3\right ) \, dx,x,\log (x)\right )\\ &=\frac {5}{3} (3+\log (x))^3-\frac {1}{4} (3+\log (x))^4\\ \end {align*}
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Mathematica [A] time = 0.02, size = 29, normalized size = 1.38 \[ -\frac {1}{4} \log ^4(x)-\frac {4 \log ^3(x)}{3}+\frac {3 \log ^2(x)}{2}+18 \log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 23, normalized size = 1.10 \[ -\frac {1}{4} \, \log \relax (x)^{4} - \frac {4}{3} \, \log \relax (x)^{3} + \frac {3}{2} \, \log \relax (x)^{2} + 18 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 23, normalized size = 1.10 \[ -\frac {1}{4} \, \log \relax (x)^{4} - \frac {4}{3} \, \log \relax (x)^{3} + \frac {3}{2} \, \log \relax (x)^{2} + 18 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 24, normalized size = 1.14 \[ -\frac {\ln \relax (x )^{4}}{4}-\frac {4 \ln \relax (x )^{3}}{3}+\frac {3 \ln \relax (x )^{2}}{2}+18 \ln \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 23, normalized size = 1.10 \[ -\frac {1}{4} \, \log \relax (x)^{4} - \frac {4}{3} \, \log \relax (x)^{3} + \frac {3}{2} \, \log \relax (x)^{2} + 18 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.37, size = 22, normalized size = 1.05 \[ \frac {\ln \relax (x)\,\left (-3\,{\ln \relax (x)}^3-16\,{\ln \relax (x)}^2+18\,\ln \relax (x)+216\right )}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 27, normalized size = 1.29 \[ - \frac {\log {\relax (x )}^{4}}{4} - \frac {4 \log {\relax (x )}^{3}}{3} + \frac {3 \log {\relax (x )}^{2}}{2} + 18 \log {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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