Optimal. Leaf size=33 \[ x-\log ^2(\log (4))+\log ^2(2) \log ^2\left (\frac {1}{5} (9-\log (2 (2-x)))\right ) \]
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Rubi [A] time = 0.32, antiderivative size = 24, normalized size of antiderivative = 0.73, number of steps used = 4, number of rules used = 7, integrand size = 54, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.130, Rules used = {6741, 6742, 2390, 12, 2302, 29, 6686} \begin {gather*} x+\log ^2(2) \log ^2\left (\frac {1}{5} (9-\log (4-2 x))\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 29
Rule 2302
Rule 2390
Rule 6686
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {18-9 x+(-2+x) \log (4-2 x)+2 \log ^2(2) \log \left (\frac {1}{5} (9-\log (4-2 x))\right )}{(2-x) (9-\log (4-2 x))} \, dx\\ &=\int \left (1+\frac {2 \log ^2(2) \log \left (\frac {1}{5} (9-\log (4-2 x))\right )}{(-2+x) (-9+\log (4-2 x))}\right ) \, dx\\ &=x+\left (2 \log ^2(2)\right ) \int \frac {\log \left (\frac {1}{5} (9-\log (4-2 x))\right )}{(-2+x) (-9+\log (4-2 x))} \, dx\\ &=x+\log ^2(2) \log ^2\left (\frac {1}{5} (9-\log (4-2 x))\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 24, normalized size = 0.73 \begin {gather*} x+\log ^2(2) \log ^2\left (\frac {1}{5} (9-\log (4-2 x))\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 20, normalized size = 0.61 \begin {gather*} \log \relax (2)^{2} \log \left (-\frac {1}{5} \, \log \left (-2 \, x + 4\right ) + \frac {9}{5}\right )^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.14, size = 68, normalized size = 2.06 \begin {gather*} -2 \, \log \relax (5) \log \relax (2)^{2} \log \left (\log \relax (2) + \log \left (-x + 2\right ) - 9\right ) - \log \relax (2)^{2} \log \left (\log \relax (2) + \log \left (-x + 2\right ) - 9\right )^{2} + 2 \, \log \relax (2)^{2} \log \left (\log \relax (2) + \log \left (-x + 2\right ) - 9\right ) \log \left (-\log \left (-2 \, x + 4\right ) + 9\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 21, normalized size = 0.64
method | result | size |
norman | \(x +\ln \relax (2)^{2} \ln \left (-\frac {\ln \left (4-2 x \right )}{5}+\frac {9}{5}\right )^{2}\) | \(21\) |
risch | \(x +\ln \relax (2)^{2} \ln \left (-\frac {\ln \left (4-2 x \right )}{5}+\frac {9}{5}\right )^{2}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.47, size = 162, normalized size = 4.91 \begin {gather*} 2 \, \log \relax (2)^{2} \log \left (i \, \pi + \log \relax (2) + \log \left (x - 2\right ) - 9\right ) \log \left (-\frac {1}{5} \, \log \left (-2 \, x + 4\right ) + \frac {9}{5}\right ) - {\left (2 \, \log \relax (5) \log \left (-i \, \pi - \log \relax (2) - \log \left (x - 2\right ) + 9\right ) - \log \left (-i \, \pi - \log \relax (2) - \log \left (x - 2\right ) + 9\right )^{2} + 2 \, \log \left (i \, \pi + \log \relax (2) + \log \left (x - 2\right ) - 9\right ) \log \left (-\frac {1}{5} \, \log \left (-2 \, x + 4\right ) + \frac {9}{5}\right )\right )} \log \relax (2)^{2} + 2 \, {\left (i \, \pi + \log \relax (2) + \log \left (x - 2\right ) - 9\right )} \log \left (i \, \pi + \log \relax (2) + \log \left (x - 2\right ) - 9\right ) - 2 \, \log \left (i \, \pi + \log \relax (2) + \log \left (x - 2\right ) - 9\right ) \log \left (-2 \, x + 4\right ) + x + 18 \, \log \left (i \, \pi + \log \relax (2) + \log \left (x - 2\right ) - 9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.62, size = 20, normalized size = 0.61 \begin {gather*} {\ln \relax (2)}^2\,{\ln \left (\frac {9}{5}-\frac {\ln \left (4-2\,x\right )}{5}\right )}^2+x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.33, size = 20, normalized size = 0.61 \begin {gather*} x + \log {\relax (2 )}^{2} \log {\left (\frac {9}{5} - \frac {\log {\left (4 - 2 x \right )}}{5} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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