Integrand size = 22, antiderivative size = 86 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)^2} \, dx=\frac {8}{41503 (1-2 x)^2}+\frac {2704}{3195731 (1-2 x)}-\frac {81}{686 (2+3 x)^2}-\frac {6156}{2401 (2+3 x)}-\frac {3125}{1331 (3+5 x)}-\frac {274224 \log (1-2 x)}{246071287}+\frac {333639 \log (2+3 x)}{16807}-\frac {290625 \log (3+5 x)}{14641} \]
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Time = 0.03 (sec) , antiderivative size = 86, 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} \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)^2} \, dx=\frac {2704}{3195731 (1-2 x)}-\frac {6156}{2401 (3 x+2)}-\frac {3125}{1331 (5 x+3)}+\frac {8}{41503 (1-2 x)^2}-\frac {81}{686 (3 x+2)^2}-\frac {274224 \log (1-2 x)}{246071287}+\frac {333639 \log (3 x+2)}{16807}-\frac {290625 \log (5 x+3)}{14641} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {32}{41503 (-1+2 x)^3}+\frac {5408}{3195731 (-1+2 x)^2}-\frac {548448}{246071287 (-1+2 x)}+\frac {243}{343 (2+3 x)^3}+\frac {18468}{2401 (2+3 x)^2}+\frac {1000917}{16807 (2+3 x)}+\frac {15625}{1331 (3+5 x)^2}-\frac {1453125}{14641 (3+5 x)}\right ) \, dx \\ & = \frac {8}{41503 (1-2 x)^2}+\frac {2704}{3195731 (1-2 x)}-\frac {81}{686 (2+3 x)^2}-\frac {6156}{2401 (2+3 x)}-\frac {3125}{1331 (3+5 x)}-\frac {274224 \log (1-2 x)}{246071287}+\frac {333639 \log (2+3 x)}{16807}-\frac {290625 \log (3+5 x)}{14641} \\ \end{align*}
Time = 0.10 (sec) , antiderivative size = 74, normalized size of antiderivative = 0.86 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)^2} \, dx=\frac {-\frac {1155481250}{3+5 x}+\frac {41503 (-3251+6558 x)}{\left (-2+x+6 x^2\right )^2}-\frac {154 (-7937593+16395384 x)}{-2+x+6 x^2}-548448 \log (5-10 x)+9769617198 \log (5 (2+3 x))-9769068750 \log (3+5 x)}{492142574} \]
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Time = 2.80 (sec) , antiderivative size = 68, normalized size of antiderivative = 0.79
method | result | size |
norman | \(\frac {-\frac {761974020}{3195731} x^{4}-\frac {229003542}{3195731} x^{3}+\frac {147486147}{6391462} x +\frac {478741107}{3195731} x^{2}-\frac {160532983}{6391462}}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{2} \left (3+5 x \right )}-\frac {274224 \ln \left (-1+2 x \right )}{246071287}+\frac {333639 \ln \left (2+3 x \right )}{16807}-\frac {290625 \ln \left (3+5 x \right )}{14641}\) | \(68\) |
risch | \(\frac {-\frac {761974020}{3195731} x^{4}-\frac {229003542}{3195731} x^{3}+\frac {147486147}{6391462} x +\frac {478741107}{3195731} x^{2}-\frac {160532983}{6391462}}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{2} \left (3+5 x \right )}-\frac {274224 \ln \left (-1+2 x \right )}{246071287}+\frac {333639 \ln \left (2+3 x \right )}{16807}-\frac {290625 \ln \left (3+5 x \right )}{14641}\) | \(69\) |
default | \(-\frac {3125}{1331 \left (3+5 x \right )}-\frac {290625 \ln \left (3+5 x \right )}{14641}+\frac {8}{41503 \left (-1+2 x \right )^{2}}-\frac {2704}{3195731 \left (-1+2 x \right )}-\frac {274224 \ln \left (-1+2 x \right )}{246071287}-\frac {81}{686 \left (2+3 x \right )^{2}}-\frac {6156}{2401 \left (2+3 x \right )}+\frac {333639 \ln \left (2+3 x \right )}{16807}\) | \(71\) |
parallelrisch | \(\frac {-235165517356+6955576950000 \ln \left (x +\frac {3}{5}\right ) x^{2}-6174398069136 \ln \left (\frac {2}{3}+x \right ) x^{3}-625220400000 \ln \left (x +\frac {3}{5}\right ) x -6955967444976 \ln \left (\frac {2}{3}+x \right ) x^{2}+625255500672 \ln \left (\frac {2}{3}+x \right ) x -2044157997420 x^{5}+615025868457 x^{3}-2846632790232 x^{4}+1600531609215 x^{2}-737114112 \ln \left (x -\frac {1}{2}\right ) x^{4}+13130365514112 \ln \left (\frac {2}{3}+x \right ) x^{4}+937883251008 \ln \left (\frac {2}{3}+x \right )+346619136 \ln \left (x -\frac {1}{2}\right ) x^{3}+390494976 \ln \left (x -\frac {1}{2}\right ) x^{2}-35100672 \ln \left (x -\frac {1}{2}\right ) x -937830600000 \ln \left (x +\frac {3}{5}\right )+14068248765120 \ln \left (\frac {2}{3}+x \right ) x^{5}+6174051450000 \ln \left (x +\frac {3}{5}\right ) x^{3}-14067459000000 \ln \left (x +\frac {3}{5}\right ) x^{5}-13129628400000 \ln \left (x +\frac {3}{5}\right ) x^{4}-52651008 \ln \left (x -\frac {1}{2}\right )-789765120 \ln \left (x -\frac {1}{2}\right ) x^{5}}{3937140592 \left (-1+2 x \right )^{2} \left (2+3 x \right )^{2} \left (3+5 x \right )}\) | \(193\) |
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Leaf count of result is larger than twice the leaf count of optimal. 148 vs. \(2 (70) = 140\).
Time = 0.23 (sec) , antiderivative size = 148, normalized size of antiderivative = 1.72 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)^2} \, dx=-\frac {117343999080 \, x^{4} + 35266545468 \, x^{3} - 73726130478 \, x^{2} + 9769068750 \, {\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )} \log \left (5 \, x + 3\right ) - 9769617198 \, {\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )} \log \left (3 \, x + 2\right ) + 548448 \, {\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )} \log \left (2 \, x - 1\right ) - 11356433319 \, x + 12361039691}{492142574 \, {\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )}} \]
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Time = 0.12 (sec) , antiderivative size = 75, normalized size of antiderivative = 0.87 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)^2} \, dx=- \frac {1523948040 x^{4} + 458007084 x^{3} - 957482214 x^{2} - 147486147 x + 160532983}{1150463160 x^{5} + 1073765616 x^{4} - 504925498 x^{3} - 568840118 x^{2} + 51131696 x + 76697544} - \frac {274224 \log {\left (x - \frac {1}{2} \right )}}{246071287} - \frac {290625 \log {\left (x + \frac {3}{5} \right )}}{14641} + \frac {333639 \log {\left (x + \frac {2}{3} \right )}}{16807} \]
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Time = 0.21 (sec) , antiderivative size = 74, normalized size of antiderivative = 0.86 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)^2} \, dx=-\frac {1523948040 \, x^{4} + 458007084 \, x^{3} - 957482214 \, x^{2} - 147486147 \, x + 160532983}{6391462 \, {\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )}} - \frac {290625}{14641} \, \log \left (5 \, x + 3\right ) + \frac {333639}{16807} \, \log \left (3 \, x + 2\right ) - \frac {274224}{246071287} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.28 (sec) , antiderivative size = 95, normalized size of antiderivative = 1.10 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)^2} \, dx=-\frac {3125}{1331 \, {\left (5 \, x + 3\right )}} - \frac {5 \, {\left (\frac {84659379036}{5 \, x + 3} - \frac {206753119043}{{\left (5 \, x + 3\right )}^{2}} - \frac {95568773322}{{\left (5 \, x + 3\right )}^{3}} - 7983405324\right )}}{70306082 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}^{2} {\left (\frac {1}{5 \, x + 3} + 3\right )}^{2}} + \frac {333639}{16807} \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) - \frac {274224}{246071287} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \]
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Time = 1.37 (sec) , antiderivative size = 66, normalized size of antiderivative = 0.77 \[ \int \frac {1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)^2} \, dx=\frac {333639\,\ln \left (x+\frac {2}{3}\right )}{16807}-\frac {274224\,\ln \left (x-\frac {1}{2}\right )}{246071287}-\frac {290625\,\ln \left (x+\frac {3}{5}\right )}{14641}-\frac {\frac {4233189\,x^4}{3195731}+\frac {12722419\,x^3}{31957310}-\frac {159580369\,x^2}{191743860}-\frac {49162049\,x}{383487720}+\frac {160532983}{1150463160}}{x^5+\frac {14\,x^4}{15}-\frac {79\,x^3}{180}-\frac {89\,x^2}{180}+\frac {2\,x}{45}+\frac {1}{15}} \]
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