Optimal. Leaf size=14 \[ \left (\frac {20}{9}+x\right ) (4-\log (x)) \log (x) \]
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Rubi [A] time = 0.05, antiderivative size = 27, normalized size of antiderivative = 1.93, number of steps used = 10, number of rules used = 7, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.259, Rules used = {12, 14, 43, 2346, 2301, 2295, 2296} \begin {gather*} -x \log ^2(x)-\frac {20 \log ^2(x)}{9}+4 x \log (x)+\frac {80 \log (x)}{9} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 43
Rule 2295
Rule 2296
Rule 2301
Rule 2346
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{9} \int \frac {80+36 x+(-40+18 x) \log (x)-9 x \log ^2(x)}{x} \, dx\\ &=\frac {1}{9} \int \left (\frac {4 (20+9 x)}{x}+\frac {2 (-20+9 x) \log (x)}{x}-9 \log ^2(x)\right ) \, dx\\ &=\frac {2}{9} \int \frac {(-20+9 x) \log (x)}{x} \, dx+\frac {4}{9} \int \frac {20+9 x}{x} \, dx-\int \log ^2(x) \, dx\\ &=-x \log ^2(x)+\frac {4}{9} \int \left (9+\frac {20}{x}\right ) \, dx+2 (2 \int \log (x) \, dx)-\frac {40}{9} \int \frac {\log (x)}{x} \, dx\\ &=4 x+\frac {80 \log (x)}{9}-\frac {20 \log ^2(x)}{9}-x \log ^2(x)+2 (-2 x+2 x \log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 27, normalized size = 1.93 \begin {gather*} \frac {80 \log (x)}{9}+4 x \log (x)-\frac {20 \log ^2(x)}{9}-x \log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 21, normalized size = 1.50 \begin {gather*} -\frac {1}{9} \, {\left (9 \, x + 20\right )} \log \relax (x)^{2} + \frac {4}{9} \, {\left (9 \, x + 20\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 21, normalized size = 1.50 \begin {gather*} -\frac {1}{9} \, {\left (9 \, x + 20\right )} \log \relax (x)^{2} + 4 \, x \log \relax (x) + \frac {80}{9} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 22, normalized size = 1.57
method | result | size |
risch | \(\frac {\left (-9 x -20\right ) \ln \relax (x )^{2}}{9}+4 x \ln \relax (x )+\frac {80 \ln \relax (x )}{9}\) | \(22\) |
default | \(-x \ln \relax (x )^{2}+4 x \ln \relax (x )-\frac {20 \ln \relax (x )^{2}}{9}+\frac {80 \ln \relax (x )}{9}\) | \(24\) |
norman | \(-x \ln \relax (x )^{2}+4 x \ln \relax (x )-\frac {20 \ln \relax (x )^{2}}{9}+\frac {80 \ln \relax (x )}{9}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.44, size = 32, normalized size = 2.29 \begin {gather*} -{\left (\log \relax (x)^{2} - 2 \, \log \relax (x) + 2\right )} x + 2 \, x \log \relax (x) - \frac {20}{9} \, \log \relax (x)^{2} + 2 \, x + \frac {80}{9} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.30, size = 13, normalized size = 0.93 \begin {gather*} -\frac {\ln \relax (x)\,\left (9\,x+20\right )\,\left (\ln \relax (x)-4\right )}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 24, normalized size = 1.71 \begin {gather*} 4 x \log {\relax (x )} + \left (- x - \frac {20}{9}\right ) \log {\relax (x )}^{2} + \frac {80 \log {\relax (x )}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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