Optimal. Leaf size=16 \[ \log \left (5 e^{\frac {\log ^2(3 x)}{x^2}} x\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 13, normalized size of antiderivative = 0.81, number of steps used = 5, number of rules used = 3, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {14, 2304, 2305} \begin {gather*} \frac {\log ^2(3 x)}{x^2}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2304
Rule 2305
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {1}{x}+\frac {2 \log (3 x)}{x^3}-\frac {2 \log ^2(3 x)}{x^3}\right ) \, dx\\ &=\log (x)+2 \int \frac {\log (3 x)}{x^3} \, dx-2 \int \frac {\log ^2(3 x)}{x^3} \, dx\\ &=-\frac {1}{2 x^2}+\log (x)-\frac {\log (3 x)}{x^2}+\frac {\log ^2(3 x)}{x^2}-2 \int \frac {\log (3 x)}{x^3} \, dx\\ &=\log (x)+\frac {\log ^2(3 x)}{x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 0.81 \begin {gather*} \log (x)+\frac {\log ^2(3 x)}{x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 19, normalized size = 1.19 \begin {gather*} \frac {x^{2} \log \left (3 \, x\right ) + \log \left (3 \, x\right )^{2}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.30, size = 13, normalized size = 0.81 \begin {gather*} \frac {\log \left (3 \, x\right )^{2}}{x^{2}} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 14, normalized size = 0.88
method | result | size |
risch | \(\frac {\ln \left (3 x \right )^{2}}{x^{2}}+\ln \relax (x )\) | \(14\) |
derivativedivides | \(\frac {\ln \left (3 x \right )^{2}}{x^{2}}+\ln \left (3 x \right )\) | \(16\) |
default | \(\frac {\ln \left (3 x \right )^{2}}{x^{2}}+\ln \left (3 x \right )\) | \(16\) |
norman | \(\frac {\ln \left (3 x \right )^{2}+x^{2} \ln \left (3 x \right )}{x^{2}}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.62, size = 38, normalized size = 2.38 \begin {gather*} \frac {2 \, \log \left (3 \, x\right )^{2} + 2 \, \log \left (3 \, x\right ) + 1}{2 \, x^{2}} - \frac {\log \left (3 \, x\right )}{x^{2}} - \frac {1}{2 \, x^{2}} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.44, size = 13, normalized size = 0.81 \begin {gather*} \ln \relax (x)+\frac {{\ln \left (3\,x\right )}^2}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 12, normalized size = 0.75 \begin {gather*} \log {\relax (x )} + \frac {\log {\left (3 x \right )}^{2}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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