Integrand size = 22, antiderivative size = 75 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^2 (3+5 x)^2} \, dx=\frac {4}{5929 (1-2 x)^2}+\frac {1088}{456533 (1-2 x)}-\frac {81}{343 (2+3 x)}-\frac {625}{1331 (3+5 x)}-\frac {92496 \log (1-2 x)}{35153041}+\frac {6156 \log (2+3 x)}{2401}-\frac {37500 \log (3+5 x)}{14641} \]
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Time = 0.03 (sec) , antiderivative size = 75, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^2 (3+5 x)^2} \, dx=\frac {1088}{456533 (1-2 x)}-\frac {81}{343 (3 x+2)}-\frac {625}{1331 (5 x+3)}+\frac {4}{5929 (1-2 x)^2}-\frac {92496 \log (1-2 x)}{35153041}+\frac {6156 \log (3 x+2)}{2401}-\frac {37500 \log (5 x+3)}{14641} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {16}{5929 (-1+2 x)^3}+\frac {2176}{456533 (-1+2 x)^2}-\frac {184992}{35153041 (-1+2 x)}+\frac {243}{343 (2+3 x)^2}+\frac {18468}{2401 (2+3 x)}+\frac {3125}{1331 (3+5 x)^2}-\frac {187500}{14641 (3+5 x)}\right ) \, dx \\ & = \frac {4}{5929 (1-2 x)^2}+\frac {1088}{456533 (1-2 x)}-\frac {81}{343 (2+3 x)}-\frac {625}{1331 (3+5 x)}-\frac {92496 \log (1-2 x)}{35153041}+\frac {6156 \log (2+3 x)}{2401}-\frac {37500 \log (3+5 x)}{14641} \\ \end{align*}
Time = 0.07 (sec) , antiderivative size = 68, normalized size of antiderivative = 0.91 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^2 (3+5 x)^2} \, dx=\frac {2 \left (77 \left (\frac {154}{(1-2 x)^2}+\frac {544}{1-2 x}-\frac {107811}{4+6 x}-\frac {214375}{6+10 x}\right )-46248 \log (1-2 x)+45064998 \log (4+6 x)-45018750 \log (6+10 x)\right )}{35153041} \]
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Time = 0.90 (sec) , antiderivative size = 62, normalized size of antiderivative = 0.83
method | result | size |
default | \(-\frac {625}{1331 \left (3+5 x \right )}-\frac {37500 \ln \left (3+5 x \right )}{14641}+\frac {4}{5929 \left (-1+2 x \right )^{2}}-\frac {1088}{456533 \left (-1+2 x \right )}-\frac {92496 \ln \left (-1+2 x \right )}{35153041}-\frac {81}{343 \left (2+3 x \right )}+\frac {6156 \ln \left (2+3 x \right )}{2401}\) | \(62\) |
risch | \(\frac {-\frac {4761360}{456533} x^{3}+\frac {1699584}{456533} x^{2}+\frac {262860}{65219} x -\frac {743807}{456533}}{\left (-1+2 x \right )^{2} \left (2+3 x \right ) \left (3+5 x \right )}-\frac {92496 \ln \left (-1+2 x \right )}{35153041}+\frac {6156 \ln \left (2+3 x \right )}{2401}-\frac {37500 \ln \left (3+5 x \right )}{14641}\) | \(64\) |
norman | \(\frac {\frac {3154320}{65219} x^{4}+\frac {1126704}{456533} x^{3}-\frac {98484}{3773} x^{2}+\frac {1464217}{456533}}{\left (-1+2 x \right )^{2} \left (2+3 x \right ) \left (3+5 x \right )}-\frac {92496 \ln \left (-1+2 x \right )}{35153041}+\frac {6156 \ln \left (2+3 x \right )}{2401}-\frac {37500 \ln \left (3+5 x \right )}{14641}\) | \(65\) |
parallelrisch | \(\frac {27038998800 \ln \left (\frac {2}{3}+x \right ) x^{4}-27011250000 \ln \left (x +\frac {3}{5}\right ) x^{4}-27748800 \ln \left (x -\frac {1}{2}\right ) x^{4}+563723545+7210399680 \ln \left (\frac {2}{3}+x \right ) x^{3}-7203000000 \ln \left (x +\frac {3}{5}\right ) x^{3}-7399680 \ln \left (x -\frac {1}{2}\right ) x^{3}+8500892400 x^{4}-16674049260 \ln \left (\frac {2}{3}+x \right ) x^{2}+16656937500 \ln \left (x +\frac {3}{5}\right ) x^{2}+17111760 \ln \left (x -\frac {1}{2}\right ) x^{2}+433781040 x^{3}-2253249900 \ln \left (\frac {2}{3}+x \right ) x +2250937500 \ln \left (x +\frac {3}{5}\right ) x +2312400 \ln \left (x -\frac {1}{2}\right ) x -4587877140 x^{2}+2703899880 \ln \left (\frac {2}{3}+x \right )-2701125000 \ln \left (x +\frac {3}{5}\right )-2774880 \ln \left (x -\frac {1}{2}\right )}{175765205 \left (-1+2 x \right )^{2} \left (2+3 x \right ) \left (3+5 x \right )}\) | \(161\) |
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Leaf count of result is larger than twice the leaf count of optimal. 123 vs. \(2 (61) = 122\).
Time = 0.23 (sec) , antiderivative size = 123, normalized size of antiderivative = 1.64 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^2 (3+5 x)^2} \, dx=-\frac {366624720 \, x^{3} - 130867968 \, x^{2} + 90037500 \, {\left (60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right )} \log \left (5 \, x + 3\right ) - 90129996 \, {\left (60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right )} \log \left (3 \, x + 2\right ) + 92496 \, {\left (60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right )} \log \left (2 \, x - 1\right ) - 141681540 \, x + 57273139}{35153041 \, {\left (60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right )}} \]
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Time = 0.11 (sec) , antiderivative size = 65, normalized size of antiderivative = 0.87 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^2 (3+5 x)^2} \, dx=- \frac {4761360 x^{3} - 1699584 x^{2} - 1840020 x + 743807}{27391980 x^{4} + 7304528 x^{3} - 16891721 x^{2} - 2282665 x + 2739198} - \frac {92496 \log {\left (x - \frac {1}{2} \right )}}{35153041} - \frac {37500 \log {\left (x + \frac {3}{5} \right )}}{14641} + \frac {6156 \log {\left (x + \frac {2}{3} \right )}}{2401} \]
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Time = 0.18 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.85 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^2 (3+5 x)^2} \, dx=-\frac {4761360 \, x^{3} - 1699584 \, x^{2} - 1840020 \, x + 743807}{456533 \, {\left (60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right )}} - \frac {37500}{14641} \, \log \left (5 \, x + 3\right ) + \frac {6156}{2401} \, \log \left (3 \, x + 2\right ) - \frac {92496}{35153041} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.27 (sec) , antiderivative size = 86, normalized size of antiderivative = 1.15 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^2 (3+5 x)^2} \, dx=-\frac {625}{1331 \, {\left (5 \, x + 3\right )}} - \frac {5 \, {\left (\frac {156456196}{5 \, x + 3} - \frac {430519419}{{\left (5 \, x + 3\right )}^{2}} - 14216316\right )}}{5021863 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}^{2} {\left (\frac {1}{5 \, x + 3} + 3\right )}} + \frac {6156}{2401} \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) - \frac {92496}{35153041} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \]
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Time = 0.05 (sec) , antiderivative size = 55, normalized size of antiderivative = 0.73 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^2 (3+5 x)^2} \, dx=\frac {6156\,\ln \left (x+\frac {2}{3}\right )}{2401}-\frac {92496\,\ln \left (x-\frac {1}{2}\right )}{35153041}-\frac {37500\,\ln \left (x+\frac {3}{5}\right )}{14641}+\frac {-\frac {79356\,x^3}{456533}+\frac {141632\,x^2}{2282665}+\frac {4381\,x}{65219}-\frac {743807}{27391980}}{x^4+\frac {4\,x^3}{15}-\frac {37\,x^2}{60}-\frac {x}{12}+\frac {1}{10}} \]
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