Optimal. Leaf size=21 \[ \frac {5}{3} (3+\log (x))^3-\frac {1}{4} (3+\log (x))^4 \]
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Rubi [A]
time = 0.02, 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 = {2412, 45}
\begin {gather*} \frac {5}{3} (\log (x)+3)^3-\frac {1}{4} (\log (x)+3)^4 \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 2412
Rubi steps
\begin {align*} \int \frac {(2-\log (x)) (3+\log (x))^2}{x} \, dx &=\text {Subst}\left (\int (2-x) (3+x)^2 \, dx,x,\log (x)\right )\\ &=\text {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 = 0.01, size = 29, normalized size = 1.38 \begin {gather*} 18 \log (x)+\frac {3 \log ^2(x)}{2}-\frac {4 \log ^3(x)}{3}-\frac {\log ^4(x)}{4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 24, normalized size = 1.14
method | result | size |
derivativedivides | \(-\frac {\ln \left (x \right )^{4}}{4}-\frac {4 \ln \left (x \right )^{3}}{3}+\frac {3 \ln \left (x \right )^{2}}{2}+18 \ln \left (x \right )\) | \(24\) |
default | \(-\frac {\ln \left (x \right )^{4}}{4}-\frac {4 \ln \left (x \right )^{3}}{3}+\frac {3 \ln \left (x \right )^{2}}{2}+18 \ln \left (x \right )\) | \(24\) |
norman | \(-\frac {\ln \left (x \right )^{4}}{4}-\frac {4 \ln \left (x \right )^{3}}{3}+\frac {3 \ln \left (x \right )^{2}}{2}+18 \ln \left (x \right )\) | \(24\) |
risch | \(-\frac {\ln \left (x \right )^{4}}{4}-\frac {4 \ln \left (x \right )^{3}}{3}+\frac {3 \ln \left (x \right )^{2}}{2}+18 \ln \left (x \right )\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 23, normalized size = 1.10 \begin {gather*} -\frac {1}{4} \, \log \left (x\right )^{4} - \frac {4}{3} \, \log \left (x\right )^{3} + \frac {3}{2} \, \log \left (x\right )^{2} + 18 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 23, normalized size = 1.10 \begin {gather*} -\frac {1}{4} \, \log \left (x\right )^{4} - \frac {4}{3} \, \log \left (x\right )^{3} + \frac {3}{2} \, \log \left (x\right )^{2} + 18 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 27, normalized size = 1.29 \begin {gather*} - \frac {\log {\left (x \right )}^{4}}{4} - \frac {4 \log {\left (x \right )}^{3}}{3} + \frac {3 \log {\left (x \right )}^{2}}{2} + 18 \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 6.12, size = 23, normalized size = 1.10 \begin {gather*} -\frac {1}{4} \, \log \left (x\right )^{4} - \frac {4}{3} \, \log \left (x\right )^{3} + \frac {3}{2} \, \log \left (x\right )^{2} + 18 \, \log \left (x\right ) \end {gather*}
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 \begin {gather*} \frac {\ln \left (x\right )\,\left (-3\,{\ln \left (x\right )}^3-16\,{\ln \left (x\right )}^2+18\,\ln \left (x\right )+216\right )}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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