Integrand size = 127, antiderivative size = 28 \[ \int \frac {-900+300 x+\left (462 x-4 x^2\right ) \log (4)-6 x^2 \log ^2(4)+\left (\left (-462 x+154 x^2\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (-3+x)+\left (-6 x^2+2 x^3\right ) \log ^2(4) \log ^2(-3+x)+\left (-12+4 x+6 x \log (4)+\left (-6 x+2 x^2\right ) \log (4) \log (-3+x)\right ) \log \left (9 x^2\right )}{-1875 x+625 x^2} \, dx=\left (3+\frac {1}{25} \left (-\log (4) (x-x \log (-3+x))+\log \left (9 x^2\right )\right )\right )^2 \]
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Time = 0.28 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {1607, 6820, 12, 6818} \[ \int \frac {-900+300 x+\left (462 x-4 x^2\right ) \log (4)-6 x^2 \log ^2(4)+\left (\left (-462 x+154 x^2\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (-3+x)+\left (-6 x^2+2 x^3\right ) \log ^2(4) \log ^2(-3+x)+\left (-12+4 x+6 x \log (4)+\left (-6 x+2 x^2\right ) \log (4) \log (-3+x)\right ) \log \left (9 x^2\right )}{-1875 x+625 x^2} \, dx=\frac {1}{625} \left (\log \left (9 x^2\right )+x \log (4) \log (x-3)-x \log (4)+75\right )^2 \]
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Rule 12
Rule 1607
Rule 6818
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {-900+300 x+\left (462 x-4 x^2\right ) \log (4)-6 x^2 \log ^2(4)+\left (\left (-462 x+154 x^2\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (-3+x)+\left (-6 x^2+2 x^3\right ) \log ^2(4) \log ^2(-3+x)+\left (-12+4 x+6 x \log (4)+\left (-6 x+2 x^2\right ) \log (4) \log (-3+x)\right ) \log \left (9 x^2\right )}{x (-1875+625 x)} \, dx \\ & = \int \frac {2 (6-x (2+\log (64))-(-3+x) x \log (4) \log (-3+x)) \left (75-x \log (4)+x \log (4) \log (-3+x)+\log \left (9 x^2\right )\right )}{625 (3-x) x} \, dx \\ & = \frac {2}{625} \int \frac {(6-x (2+\log (64))-(-3+x) x \log (4) \log (-3+x)) \left (75-x \log (4)+x \log (4) \log (-3+x)+\log \left (9 x^2\right )\right )}{(3-x) x} \, dx \\ & = \frac {1}{625} \left (75-x \log (4)+x \log (4) \log (-3+x)+\log \left (9 x^2\right )\right )^2 \\ \end{align*}
Time = 0.05 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96 \[ \int \frac {-900+300 x+\left (462 x-4 x^2\right ) \log (4)-6 x^2 \log ^2(4)+\left (\left (-462 x+154 x^2\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (-3+x)+\left (-6 x^2+2 x^3\right ) \log ^2(4) \log ^2(-3+x)+\left (-12+4 x+6 x \log (4)+\left (-6 x+2 x^2\right ) \log (4) \log (-3+x)\right ) \log \left (9 x^2\right )}{-1875 x+625 x^2} \, dx=\frac {1}{625} \left (75-x \log (4)+x \log (4) \log (-3+x)+\log \left (9 x^2\right )\right )^2 \]
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Leaf count of result is larger than twice the leaf count of optimal. \(106\) vs. \(2(25)=50\).
Time = 1.44 (sec) , antiderivative size = 107, normalized size of antiderivative = 3.82
method | result | size |
parallelrisch | \(\frac {4 x^{2} \ln \left (2\right )^{2} \ln \left (-3+x \right )^{2}}{625}-\frac {8 \ln \left (2\right )^{2} \ln \left (-3+x \right ) x^{2}}{625}+\frac {4 x^{2} \ln \left (2\right )^{2}}{625}+\frac {4 \ln \left (2\right ) \ln \left (-3+x \right ) \ln \left (9 x^{2}\right ) x}{625}-\frac {4 \ln \left (2\right ) \ln \left (9 x^{2}\right ) x}{625}+\frac {12 \ln \left (2\right ) \ln \left (-3+x \right ) x}{25}-\frac {36 \ln \left (2\right )^{2}}{625}-\frac {12 x \ln \left (2\right )}{25}+\frac {\ln \left (9 x^{2}\right )^{2}}{625}-\frac {72 \ln \left (2\right )}{25}+\frac {6 \ln \left (9 x^{2}\right )}{25}\) | \(107\) |
default | \(\frac {4 x^{2} \ln \left (2\right )^{2} \ln \left (-3+x \right )^{2}}{625}-\frac {8 \ln \left (2\right )^{2} \ln \left (-3+x \right ) x^{2}}{625}+\frac {4 x^{2} \ln \left (2\right )^{2}}{625}-\frac {108 \ln \left (2\right )^{2}}{625}+\frac {\ln \left (2\right ) \left (924 \ln \left (-3+x \right )-300 x -4 x \ln \left (x^{2}\right )-8 \ln \left (-3+x \right ) x +4 \ln \left (-3+x \right ) \ln \left (x^{2}\right ) x +8 \ln \left (3\right ) \ln \left (-3+x \right ) x -8 x \ln \left (3\right )+24 \ln \left (3\right )+308 \left (-3+x \right ) \ln \left (-3+x \right )+924\right )}{625}+\frac {12 \ln \left (x \right )}{25}+\frac {8 \ln \left (3\right ) \ln \left (x \right )}{625}+\frac {\ln \left (x^{2}\right )^{2}}{625}\) | \(130\) |
parts | \(\frac {4 \ln \left (2\right ) \left (6 \ln \left (-3+x \right )+\ln \left (-3+x \right ) \ln \left (x^{2}\right ) x +4 x -x \ln \left (x^{2}\right )-2 \ln \left (-3+x \right ) x +2 \ln \left (3\right ) \ln \left (-3+x \right ) x -2 x \ln \left (3\right )+6 \ln \left (3\right )\right )}{625}+\frac {\ln \left (x^{2}\right )^{2}}{625}+\frac {8 \ln \left (3\right ) \ln \left (x \right )}{625}+\frac {8 \ln \left (2\right )^{2} \left (\frac {\left (-3+x \right )^{2} \ln \left (-3+x \right )^{2}}{2}-\frac {\ln \left (-3+x \right ) \left (-3+x \right )^{2}}{2}+\frac {\left (-3+x \right )^{2}}{4}+3 \left (-3+x \right ) \ln \left (-3+x \right )^{2}-6 \left (-3+x \right ) \ln \left (-3+x \right )-18+6 x \right )}{625}-\frac {24 x \ln \left (2\right )^{2}}{625}-\frac {8 x \ln \left (2\right )}{625}+\frac {12 \ln \left (x \right )}{25}-\frac {36 \ln \left (2\right ) \left (2 \ln \left (2\right )-25\right ) \ln \left (-3+x \right )}{625}-\frac {4 \ln \left (2\right ) \left (2 \ln \left (2\right ) \left (\frac {\ln \left (-3+x \right ) \left (-3+x \right )^{2}}{2}-\frac {\left (-3+x \right )^{2}}{4}\right )-9 \ln \left (-3+x \right )^{2} \ln \left (2\right )-77 \left (-3+x \right ) \ln \left (-3+x \right )-231+77 x \right )}{625}\) | \(215\) |
risch | \(\frac {4 x^{2} \ln \left (2\right )^{2} \ln \left (-3+x \right )^{2}}{625}+\left (\frac {8 x \ln \left (2\right ) \ln \left (x \right )}{625}-\frac {2 i \pi \ln \left (2\right ) x \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )}{625}+\frac {4 i \pi \ln \left (2\right ) x \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}}{625}-\frac {2 i \pi \ln \left (2\right ) x \operatorname {csgn}\left (i x^{2}\right )^{3}}{625}-\frac {8 x^{2} \ln \left (2\right )^{2}}{625}+\frac {8 x \ln \left (2\right ) \ln \left (3\right )}{625}+\frac {12 x \ln \left (2\right )}{25}\right ) \ln \left (-3+x \right )+\frac {4 \ln \left (x \right )^{2}}{625}-\frac {8 x \ln \left (2\right ) \ln \left (x \right )}{625}-\frac {4 i \pi \ln \left (2\right ) x \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}}{625}-\frac {2 i \ln \left (x \right ) \pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )}{625}+\frac {2 i \pi \ln \left (2\right ) x \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )}{625}-\frac {2 i \ln \left (x \right ) \pi \operatorname {csgn}\left (i x^{2}\right )^{3}}{625}+\frac {2 i \pi \ln \left (2\right ) x \operatorname {csgn}\left (i x^{2}\right )^{3}}{625}+\frac {4 i \ln \left (x \right ) \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}}{625}+\frac {4 x^{2} \ln \left (2\right )^{2}}{625}-\frac {8 x \ln \left (2\right ) \ln \left (3\right )}{625}-\frac {12 x \ln \left (2\right )}{25}+\frac {12 \ln \left (x \right )}{25}+\frac {8 \ln \left (3\right ) \ln \left (x \right )}{625}\) | \(266\) |
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Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (26) = 52\).
Time = 0.24 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.04 \[ \int \frac {-900+300 x+\left (462 x-4 x^2\right ) \log (4)-6 x^2 \log ^2(4)+\left (\left (-462 x+154 x^2\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (-3+x)+\left (-6 x^2+2 x^3\right ) \log ^2(4) \log ^2(-3+x)+\left (-12+4 x+6 x \log (4)+\left (-6 x+2 x^2\right ) \log (4) \log (-3+x)\right ) \log \left (9 x^2\right )}{-1875 x+625 x^2} \, dx=\frac {4}{625} \, x^{2} \log \left (2\right )^{2} \log \left (x - 3\right )^{2} + \frac {4}{625} \, x^{2} \log \left (2\right )^{2} - \frac {12}{25} \, x \log \left (2\right ) + \frac {2}{625} \, {\left (2 \, x \log \left (2\right ) \log \left (x - 3\right ) - 2 \, x \log \left (2\right ) + 75\right )} \log \left (9 \, x^{2}\right ) + \frac {1}{625} \, \log \left (9 \, x^{2}\right )^{2} - \frac {4}{625} \, {\left (2 \, x^{2} \log \left (2\right )^{2} - 75 \, x \log \left (2\right )\right )} \log \left (x - 3\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 109 vs. \(2 (29) = 58\).
Time = 0.37 (sec) , antiderivative size = 109, normalized size of antiderivative = 3.89 \[ \int \frac {-900+300 x+\left (462 x-4 x^2\right ) \log (4)-6 x^2 \log ^2(4)+\left (\left (-462 x+154 x^2\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (-3+x)+\left (-6 x^2+2 x^3\right ) \log ^2(4) \log ^2(-3+x)+\left (-12+4 x+6 x \log (4)+\left (-6 x+2 x^2\right ) \log (4) \log (-3+x)\right ) \log \left (9 x^2\right )}{-1875 x+625 x^2} \, dx=\frac {4 x^{2} \log {\left (2 \right )}^{2} \log {\left (x - 3 \right )}^{2}}{625} + \frac {4 x^{2} \log {\left (2 \right )}^{2}}{625} - \frac {12 x \log {\left (2 \right )}}{25} + \left (- \frac {8 x^{2} \log {\left (2 \right )}^{2}}{625} + \frac {12 x \log {\left (2 \right )}}{25}\right ) \log {\left (x - 3 \right )} + \left (\frac {4 x \log {\left (2 \right )} \log {\left (x - 3 \right )}}{625} - \frac {4 x \log {\left (2 \right )}}{625}\right ) \log {\left (9 x^{2} \right )} + \frac {12 \log {\left (x \right )}}{25} + \frac {\log {\left (9 x^{2} \right )}^{2}}{625} \]
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Leaf count of result is larger than twice the leaf count of optimal. 319 vs. \(2 (26) = 52\).
Time = 0.32 (sec) , antiderivative size = 319, normalized size of antiderivative = 11.39 \[ \int \frac {-900+300 x+\left (462 x-4 x^2\right ) \log (4)-6 x^2 \log ^2(4)+\left (\left (-462 x+154 x^2\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (-3+x)+\left (-6 x^2+2 x^3\right ) \log ^2(4) \log ^2(-3+x)+\left (-12+4 x+6 x \log (4)+\left (-6 x+2 x^2\right ) \log (4) \log (-3+x)\right ) \log \left (9 x^2\right )}{-1875 x+625 x^2} \, dx=-\frac {4}{625} \, {\left (x^{2} + 6 \, x + 18 \, \log \left (x - 3\right )\right )} \log \left (2\right )^{2} \log \left (x - 3\right ) + \frac {48}{625} \, {\left (x + 3 \, \log \left (x - 3\right )\right )} \log \left (2\right )^{2} \log \left (x - 3\right ) - \frac {8}{625} \, x {\left (\log \left (3\right ) - 2\right )} \log \left (2\right ) + \frac {2}{625} \, {\left ({\left (2 \, \log \left (x - 3\right )^{2} - 2 \, \log \left (x - 3\right ) + 1\right )} {\left (x - 3\right )}^{2} + 12 \, \log \left (x - 3\right )^{3} + 24 \, {\left (\log \left (x - 3\right )^{2} - 2 \, \log \left (x - 3\right ) + 2\right )} {\left (x - 3\right )}\right )} \log \left (2\right )^{2} - \frac {24}{625} \, {\left (\log \left (x - 3\right )^{3} + {\left (\log \left (x - 3\right )^{2} - 2 \, \log \left (x - 3\right ) + 2\right )} {\left (x - 3\right )}\right )} \log \left (2\right )^{2} + \frac {2}{625} \, {\left (x^{2} + 18 \, \log \left (x - 3\right )^{2} + 18 \, x + 54 \, \log \left (x - 3\right )\right )} \log \left (2\right )^{2} - \frac {24}{625} \, {\left (3 \, \log \left (x - 3\right )^{2} + 2 \, x + 6 \, \log \left (x - 3\right )\right )} \log \left (2\right )^{2} - \frac {24}{625} \, {\left (x + 3 \, \log \left (x - 3\right )\right )} \log \left (2\right )^{2} + \frac {308}{625} \, {\left (x + 3 \, \log \left (x - 3\right )\right )} \log \left (2\right ) \log \left (x - 3\right ) - \frac {462}{625} \, \log \left (2\right ) \log \left (x - 3\right )^{2} - \frac {154}{625} \, {\left (3 \, \log \left (x - 3\right )^{2} + 2 \, x + 6 \, \log \left (x - 3\right )\right )} \log \left (2\right ) - \frac {8}{625} \, {\left (x + 3 \, \log \left (x - 3\right )\right )} \log \left (2\right ) + \frac {8}{625} \, {\left (x {\left (\log \left (3\right ) - 1\right )} \log \left (2\right ) + x \log \left (2\right ) \log \left (x\right ) + 3 \, \log \left (2\right )\right )} \log \left (x - 3\right ) + \frac {924}{625} \, \log \left (2\right ) \log \left (x - 3\right ) - \frac {8}{625} \, {\left (x \log \left (2\right ) - \log \left (3\right )\right )} \log \left (x\right ) + \frac {4}{625} \, \log \left (x\right )^{2} + \frac {12}{25} \, \log \left (x\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (26) = 52\).
Time = 0.29 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.04 \[ \int \frac {-900+300 x+\left (462 x-4 x^2\right ) \log (4)-6 x^2 \log ^2(4)+\left (\left (-462 x+154 x^2\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (-3+x)+\left (-6 x^2+2 x^3\right ) \log ^2(4) \log ^2(-3+x)+\left (-12+4 x+6 x \log (4)+\left (-6 x+2 x^2\right ) \log (4) \log (-3+x)\right ) \log \left (9 x^2\right )}{-1875 x+625 x^2} \, dx=\frac {4}{625} \, x^{2} \log \left (2\right )^{2} \log \left (x - 3\right )^{2} + \frac {4}{625} \, x^{2} \log \left (2\right )^{2} - \frac {12}{25} \, x \log \left (2\right ) + \frac {4}{625} \, {\left (x \log \left (2\right ) \log \left (x - 3\right ) - x \log \left (2\right ) + \log \left (x\right )\right )} \log \left (9 \, x^{2}\right ) - \frac {4}{625} \, {\left (2 \, x^{2} \log \left (2\right )^{2} - 75 \, x \log \left (2\right )\right )} \log \left (x - 3\right ) - \frac {4}{625} \, \log \left (x\right )^{2} + \frac {12}{25} \, \log \left (x\right ) \]
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Time = 11.87 (sec) , antiderivative size = 88, normalized size of antiderivative = 3.14 \[ \int \frac {-900+300 x+\left (462 x-4 x^2\right ) \log (4)-6 x^2 \log ^2(4)+\left (\left (-462 x+154 x^2\right ) \log (4)+\left (12 x^2-2 x^3\right ) \log ^2(4)\right ) \log (-3+x)+\left (-6 x^2+2 x^3\right ) \log ^2(4) \log ^2(-3+x)+\left (-12+4 x+6 x \log (4)+\left (-6 x+2 x^2\right ) \log (4) \log (-3+x)\right ) \log \left (9 x^2\right )}{-1875 x+625 x^2} \, dx=\frac {12\,\ln \left (x\right )}{25}+\frac {4\,x^2\,{\ln \left (2\right )}^2}{625}+\frac {{\ln \left (9\,x^2\right )}^2}{625}-\ln \left (9\,x^2\right )\,\left (\frac {4\,x\,\ln \left (2\right )}{625}-\frac {4\,x\,\ln \left (x-3\right )\,\ln \left (2\right )}{625}\right )-\frac {12\,x\,\ln \left (2\right )}{25}-\ln \left (x-3\right )\,\left (\frac {8\,x^2\,{\ln \left (2\right )}^2}{625}-\frac {12\,x\,\ln \left (2\right )}{25}\right )+\frac {4\,x^2\,{\ln \left (x-3\right )}^2\,{\ln \left (2\right )}^2}{625} \]
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