Optimal. Leaf size=17 \[ \frac {(36+\log (x)) \left (4-\frac {6 x}{5}+\log (x)\right )}{x} \]
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Rubi [A]
time = 0.05, antiderivative size = 27, normalized size of antiderivative = 1.59, number of steps
used = 8, number of rules used = 5, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.227, Rules used = {12, 14, 45,
2341, 2342} \begin {gather*} \frac {144}{x}+\frac {\log ^2(x)}{x}+\frac {40 \log (x)}{x}-\frac {6 \log (x)}{5} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 45
Rule 2341
Rule 2342
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {-520-6 x-190 \log (x)-5 \log ^2(x)}{x^2} \, dx\\ &=\frac {1}{5} \int \left (-\frac {2 (260+3 x)}{x^2}-\frac {190 \log (x)}{x^2}-\frac {5 \log ^2(x)}{x^2}\right ) \, dx\\ &=-\left (\frac {2}{5} \int \frac {260+3 x}{x^2} \, dx\right )-38 \int \frac {\log (x)}{x^2} \, dx-\int \frac {\log ^2(x)}{x^2} \, dx\\ &=\frac {38}{x}+\frac {38 \log (x)}{x}+\frac {\log ^2(x)}{x}-\frac {2}{5} \int \left (\frac {260}{x^2}+\frac {3}{x}\right ) \, dx-2 \int \frac {\log (x)}{x^2} \, dx\\ &=\frac {144}{x}-\frac {6 \log (x)}{5}+\frac {40 \log (x)}{x}+\frac {\log ^2(x)}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 27, normalized size = 1.59 \begin {gather*} \frac {144}{x}-\frac {6 \log (x)}{5}+\frac {40 \log (x)}{x}+\frac {\log ^2(x)}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 26, normalized size = 1.53
method | result | size |
norman | \(\frac {144+\ln \left (x \right )^{2}-\frac {6 x \ln \left (x \right )}{5}+40 \ln \left (x \right )}{x}\) | \(20\) |
default | \(\frac {\ln \left (x \right )^{2}}{x}+\frac {40 \ln \left (x \right )}{x}+\frac {144}{x}-\frac {6 \ln \left (x \right )}{5}\) | \(26\) |
risch | \(\frac {\ln \left (x \right )^{2}}{x}+\frac {40 \ln \left (x \right )}{x}-\frac {6 \left (x \ln \left (x \right )-120\right )}{5 x}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 31, normalized size = 1.82 \begin {gather*} \frac {\log \left (x\right )^{2} + 2 \, \log \left (x\right ) + 2}{x} + \frac {38 \, \log \left (x\right )}{x} + \frac {142}{x} - \frac {6}{5} \, \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 = 22, normalized size = 1.29 \begin {gather*} -\frac {2 \, {\left (3 \, x - 100\right )} \log \left (x\right ) - 5 \, \log \left (x\right )^{2} - 720}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 22, normalized size = 1.29 \begin {gather*} - \frac {6 \log {\left (x \right )}}{5} + \frac {\log {\left (x \right )}^{2}}{x} + \frac {40 \log {\left (x \right )}}{x} + \frac {144}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 25, normalized size = 1.47 \begin {gather*} \frac {\log \left (x\right )^{2}}{x} + \frac {40 \, \log \left (x\right )}{x} + \frac {144}{x} - \frac {6}{5} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.35, size = 19, normalized size = 1.12 \begin {gather*} \frac {{\ln \left (x\right )}^2+40\,\ln \left (x\right )+144}{x}-\frac {6\,\ln \left (x\right )}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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