Integrand size = 22, antiderivative size = 75 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)} \, dx=\frac {4}{3773 (1-2 x)^2}+\frac {1072}{290521 (1-2 x)}+\frac {27}{686 (2+3 x)^2}+\frac {1107}{2401 (2+3 x)}-\frac {89792 \log (1-2 x)}{22370117}-\frac {39393 \log (2+3 x)}{16807}+\frac {3125 \log (3+5 x)}{1331} \]
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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} \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)} \, dx=\frac {1072}{290521 (1-2 x)}+\frac {1107}{2401 (3 x+2)}+\frac {4}{3773 (1-2 x)^2}+\frac {27}{686 (3 x+2)^2}-\frac {89792 \log (1-2 x)}{22370117}-\frac {39393 \log (3 x+2)}{16807}+\frac {3125 \log (5 x+3)}{1331} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {16}{3773 (-1+2 x)^3}+\frac {2144}{290521 (-1+2 x)^2}-\frac {179584}{22370117 (-1+2 x)}-\frac {81}{343 (2+3 x)^3}-\frac {3321}{2401 (2+3 x)^2}-\frac {118179}{16807 (2+3 x)}+\frac {15625}{1331 (3+5 x)}\right ) \, dx \\ & = \frac {4}{3773 (1-2 x)^2}+\frac {1072}{290521 (1-2 x)}+\frac {27}{686 (2+3 x)^2}+\frac {1107}{2401 (2+3 x)}-\frac {89792 \log (1-2 x)}{22370117}-\frac {39393 \log (2+3 x)}{16807}+\frac {3125 \log (3+5 x)}{1331} \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 58, normalized size of antiderivative = 0.77 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)} \, dx=\frac {\frac {77 \left (569697-1414978 x-1006716 x^2+3176136 x^3\right )}{\left (-2+x+6 x^2\right )^2}-179584 \log (5-10 x)-104864166 \log (5 (2+3 x))+105043750 \log (3+5 x)}{44740234} \]
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Time = 0.90 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.75
method | result | size |
norman | \(\frac {-\frac {707489}{290521} x -\frac {503358}{290521} x^{2}+\frac {1588068}{290521} x^{3}+\frac {569697}{581042}}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{2}}-\frac {89792 \ln \left (-1+2 x \right )}{22370117}-\frac {39393 \ln \left (2+3 x \right )}{16807}+\frac {3125 \ln \left (3+5 x \right )}{1331}\) | \(56\) |
risch | \(\frac {-\frac {707489}{290521} x -\frac {503358}{290521} x^{2}+\frac {1588068}{290521} x^{3}+\frac {569697}{581042}}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{2}}-\frac {89792 \ln \left (-1+2 x \right )}{22370117}-\frac {39393 \ln \left (2+3 x \right )}{16807}+\frac {3125 \ln \left (3+5 x \right )}{1331}\) | \(57\) |
default | \(\frac {3125 \ln \left (3+5 x \right )}{1331}+\frac {4}{3773 \left (-1+2 x \right )^{2}}-\frac {1072}{290521 \left (-1+2 x \right )}-\frac {89792 \ln \left (-1+2 x \right )}{22370117}+\frac {27}{686 \left (2+3 x \right )^{2}}+\frac {1107}{2401 \left (2+3 x \right )}-\frac {39393 \ln \left (2+3 x \right )}{16807}\) | \(62\) |
parallelrisch | \(-\frac {7550219952 \ln \left (\frac {2}{3}+x \right ) x^{4}-7563150000 \ln \left (x +\frac {3}{5}\right ) x^{4}+12930048 \ln \left (x -\frac {1}{2}\right ) x^{4}+130173274+2516739984 \ln \left (\frac {2}{3}+x \right ) x^{3}-2521050000 \ln \left (x +\frac {3}{5}\right ) x^{3}+4310016 \ln \left (x -\frac {1}{2}\right ) x^{3}+1961159508 x^{4}-4823751636 \ln \left (\frac {2}{3}+x \right ) x^{2}+4832012500 \ln \left (x +\frac {3}{5}\right ) x^{2}-8260864 \ln \left (x -\frac {1}{2}\right ) x^{2}+164594892 x^{3}-838913328 \ln \left (\frac {2}{3}+x \right ) x +840350000 \ln \left (x +\frac {3}{5}\right ) x -1436672 \ln \left (x -\frac {1}{2}\right ) x -1097928755 x^{2}+838913328 \ln \left (\frac {2}{3}+x \right )-840350000 \ln \left (x +\frac {3}{5}\right )+1436672 \ln \left (x -\frac {1}{2}\right )}{89480468 \left (-1+2 x \right )^{2} \left (2+3 x \right )^{2}}\) | \(154\) |
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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 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)} \, dx=\frac {244562472 \, x^{3} - 77517132 \, x^{2} + 105043750 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (5 \, x + 3\right ) - 104864166 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 179584 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )} \log \left (2 \, x - 1\right ) - 108953306 \, x + 43866669}{44740234 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )}} \]
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Time = 0.11 (sec) , antiderivative size = 65, normalized size of antiderivative = 0.87 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)} \, dx=- \frac {- 3176136 x^{3} + 1006716 x^{2} + 1414978 x - 569697}{20917512 x^{4} + 6972504 x^{3} - 13363966 x^{2} - 2324168 x + 2324168} - \frac {89792 \log {\left (x - \frac {1}{2} \right )}}{22370117} + \frac {3125 \log {\left (x + \frac {3}{5} \right )}}{1331} - \frac {39393 \log {\left (x + \frac {2}{3} \right )}}{16807} \]
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Time = 0.20 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.85 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)} \, dx=\frac {3176136 \, x^{3} - 1006716 \, x^{2} - 1414978 \, x + 569697}{581042 \, {\left (36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right )}} + \frac {3125}{1331} \, \log \left (5 \, x + 3\right ) - \frac {39393}{16807} \, \log \left (3 \, x + 2\right ) - \frac {89792}{22370117} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.27 (sec) , antiderivative size = 59, normalized size of antiderivative = 0.79 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)} \, dx=\frac {3176136 \, x^{3} - 1006716 \, x^{2} - 1414978 \, x + 569697}{581042 \, {\left (3 \, x + 2\right )}^{2} {\left (2 \, x - 1\right )}^{2}} + \frac {3125}{1331} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {39393}{16807} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {89792}{22370117} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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Time = 0.05 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.75 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)} \, dx=\frac {3125\,\ln \left (x+\frac {3}{5}\right )}{1331}-\frac {39393\,\ln \left (x+\frac {2}{3}\right )}{16807}-\frac {89792\,\ln \left (x-\frac {1}{2}\right )}{22370117}-\frac {-\frac {44113\,x^3}{290521}+\frac {83893\,x^2}{1743126}+\frac {707489\,x}{10458756}-\frac {189899}{6972504}}{x^4+\frac {x^3}{3}-\frac {23\,x^2}{36}-\frac {x}{9}+\frac {1}{9}} \]
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