Optimal. Leaf size=12 \[ \frac {\log (4) (2+\log (-3+x))}{x} \]
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Rubi [A] time = 0.36, antiderivative size = 18, normalized size of antiderivative = 1.50, number of steps used = 12, number of rules used = 10, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.303, Rules used = {1593, 6741, 12, 6688, 6742, 77, 2395, 36, 31, 29} \begin {gather*} \frac {\log (4) \log (x-3)}{x}+\frac {2 \log (4)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 29
Rule 31
Rule 36
Rule 77
Rule 1593
Rule 2395
Rule 6688
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {(6-x) \log (4)+(3-x) \log (4) \log (-3+x)}{(-3+x) x^2} \, dx\\ &=\int \frac {\log (4) (-6+x-3 \log (-3+x)+x \log (-3+x))}{(3-x) x^2} \, dx\\ &=\log (4) \int \frac {-6+x-3 \log (-3+x)+x \log (-3+x)}{(3-x) x^2} \, dx\\ &=\log (4) \int \frac {-6+x+(-3+x) \log (-3+x)}{(3-x) x^2} \, dx\\ &=\log (4) \int \left (\frac {6-x}{(-3+x) x^2}-\frac {\log (-3+x)}{x^2}\right ) \, dx\\ &=\log (4) \int \frac {6-x}{(-3+x) x^2} \, dx-\log (4) \int \frac {\log (-3+x)}{x^2} \, dx\\ &=\frac {\log (4) \log (-3+x)}{x}+\log (4) \int \left (\frac {1}{3 (-3+x)}-\frac {2}{x^2}-\frac {1}{3 x}\right ) \, dx-\log (4) \int \frac {1}{(-3+x) x} \, dx\\ &=\frac {2 \log (4)}{x}+\frac {1}{3} \log (4) \log (3-x)+\frac {\log (4) \log (-3+x)}{x}-\frac {1}{3} \log (4) \log (x)-\frac {1}{3} \log (4) \int \frac {1}{-3+x} \, dx+\frac {1}{3} \log (4) \int \frac {1}{x} \, dx\\ &=\frac {2 \log (4)}{x}+\frac {\log (4) \log (-3+x)}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 15, normalized size = 1.25 \begin {gather*} -\frac {\log (4) (-2-\log (-3+x))}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 17, normalized size = 1.42 \begin {gather*} \frac {2 \, {\left (\log \relax (2) \log \left (x - 3\right ) + 2 \, \log \relax (2)\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 19, normalized size = 1.58 \begin {gather*} \frac {2 \, \log \relax (2) \log \left (x - 3\right )}{x} + \frac {4 \, \log \relax (2)}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 18, normalized size = 1.50
method | result | size |
norman | \(\frac {2 \ln \relax (2) \ln \left (x -3\right )+4 \ln \relax (2)}{x}\) | \(18\) |
risch | \(\frac {2 \ln \relax (2) \ln \left (x -3\right )}{x}+\frac {4 \ln \relax (2)}{x}\) | \(20\) |
derivativedivides | \(2 \ln \relax (2) \left (-\frac {\ln \left (x -3\right ) \left (x -3\right )}{3 x}+\frac {2}{x}+\frac {\ln \left (x -3\right )}{3}\right )\) | \(29\) |
default | \(2 \ln \relax (2) \left (-\frac {\ln \left (x -3\right ) \left (x -3\right )}{3 x}+\frac {2}{x}+\frac {\ln \left (x -3\right )}{3}\right )\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.51, size = 44, normalized size = 3.67 \begin {gather*} \frac {4}{3} \, {\left (\frac {3}{x} + \log \left (x - 3\right ) - \log \relax (x)\right )} \log \relax (2) + \frac {4}{3} \, \log \relax (2) \log \relax (x) - \frac {2 \, {\left (2 \, x \log \relax (2) - 3 \, \log \relax (2)\right )} \log \left (x - 3\right )}{3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.15, size = 54, normalized size = 4.50 \begin {gather*} \frac {36\,\ln \relax (2)+18\,\ln \left (x-3\right )\,\ln \relax (2)-x\,\left (24\,\ln \relax (2)+12\,\ln \left (x-3\right )\,\ln \relax (2)\right )+x^2\,\left (4\,\ln \relax (2)+\ln \left (x-3\right )\,\ln \relax (4)\right )}{x\,{\left (x-3\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 17, normalized size = 1.42 \begin {gather*} \frac {2 \log {\relax (2 )} \log {\left (x - 3 \right )}}{x} + \frac {4 \log {\relax (2 )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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