Integrand size = 22, antiderivative size = 64 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)^2} \, dx=\frac {8}{5929 (1-2 x)}-\frac {27}{49 (2+3 x)}-\frac {125}{121 (3+5 x)}-\frac {1088 \log (1-2 x)}{456533}+\frac {1998}{343} \log (2+3 x)-\frac {7750 \log (3+5 x)}{1331} \]
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Time = 0.02 (sec) , antiderivative size = 64, 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} \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)^2} \, dx=\frac {8}{5929 (1-2 x)}-\frac {27}{49 (3 x+2)}-\frac {125}{121 (5 x+3)}-\frac {1088 \log (1-2 x)}{456533}+\frac {1998}{343} \log (3 x+2)-\frac {7750 \log (5 x+3)}{1331} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {16}{5929 (-1+2 x)^2}-\frac {2176}{456533 (-1+2 x)}+\frac {81}{49 (2+3 x)^2}+\frac {5994}{343 (2+3 x)}+\frac {625}{121 (3+5 x)^2}-\frac {38750}{1331 (3+5 x)}\right ) \, dx \\ & = \frac {8}{5929 (1-2 x)}-\frac {27}{49 (2+3 x)}-\frac {125}{121 (3+5 x)}-\frac {1088 \log (1-2 x)}{456533}+\frac {1998}{343} \log (2+3 x)-\frac {7750 \log (3+5 x)}{1331} \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 59, normalized size of antiderivative = 0.92 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)^2} \, dx=\frac {2 \left (-544 \log (1-2 x)+1329669 \log (4+6 x)+7 \left (\frac {44}{1-2 x}-\frac {35937}{4+6 x}-\frac {67375}{6+10 x}-189875 \log (6+10 x)\right )\right )}{456533} \]
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Time = 2.71 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.83
method | result | size |
default | \(-\frac {125}{121 \left (3+5 x \right )}-\frac {7750 \ln \left (3+5 x \right )}{1331}-\frac {8}{5929 \left (-1+2 x \right )}-\frac {1088 \ln \left (-1+2 x \right )}{456533}-\frac {27}{49 \left (2+3 x \right )}+\frac {1998 \ln \left (2+3 x \right )}{343}\) | \(53\) |
risch | \(\frac {-\frac {69540}{5929} x^{2}-\frac {9544}{5929} x +\frac {22003}{5929}}{\left (3+5 x \right ) \left (2+3 x \right ) \left (-1+2 x \right )}-\frac {1088 \ln \left (-1+2 x \right )}{456533}+\frac {1998 \ln \left (2+3 x \right )}{343}-\frac {7750 \ln \left (3+5 x \right )}{1331}\) | \(59\) |
norman | \(\frac {\frac {110015}{5929} x^{3}+\frac {88829}{35574} x^{2}-\frac {211285}{35574} x}{\left (3+5 x \right ) \left (2+3 x \right ) \left (-1+2 x \right )}-\frac {1088 \ln \left (-1+2 x \right )}{456533}+\frac {1998 \ln \left (2+3 x \right )}{343}-\frac {7750 \ln \left (3+5 x \right )}{1331}\) | \(62\) |
parallelrisch | \(\frac {478680840 \ln \left (\frac {2}{3}+x \right ) x^{3}-478485000 \ln \left (x +\frac {3}{5}\right ) x^{3}-195840 \ln \left (x -\frac {1}{2}\right ) x^{3}+366988644 \ln \left (\frac {2}{3}+x \right ) x^{2}-366838500 \ln \left (x +\frac {3}{5}\right ) x^{2}-150144 \ln \left (x -\frac {1}{2}\right ) x^{2}+50826930 x^{3}-111692196 \ln \left (\frac {2}{3}+x \right ) x +111646500 \ln \left (x +\frac {3}{5}\right ) x +45696 \ln \left (x -\frac {1}{2}\right ) x +6839833 x^{2}-95736168 \ln \left (\frac {2}{3}+x \right )+95697000 \ln \left (x +\frac {3}{5}\right )+39168 \ln \left (x -\frac {1}{2}\right )-16268945 x}{2739198 \left (3+5 x \right ) \left (2+3 x \right ) \left (-1+2 x \right )}\) | \(131\) |
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Time = 0.22 (sec) , antiderivative size = 98, normalized size of antiderivative = 1.53 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)^2} \, dx=-\frac {5354580 \, x^{2} + 2658250 \, {\left (30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right )} \log \left (5 \, x + 3\right ) - 2659338 \, {\left (30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right )} \log \left (3 \, x + 2\right ) + 1088 \, {\left (30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right )} \log \left (2 \, x - 1\right ) + 734888 \, x - 1694231}{456533 \, {\left (30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right )}} \]
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Time = 0.09 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.84 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)^2} \, dx=\frac {- 69540 x^{2} - 9544 x + 22003}{177870 x^{3} + 136367 x^{2} - 41503 x - 35574} - \frac {1088 \log {\left (x - \frac {1}{2} \right )}}{456533} - \frac {7750 \log {\left (x + \frac {3}{5} \right )}}{1331} + \frac {1998 \log {\left (x + \frac {2}{3} \right )}}{343} \]
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Time = 0.21 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.84 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)^2} \, dx=-\frac {69540 \, x^{2} + 9544 \, x - 22003}{5929 \, {\left (30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right )}} - \frac {7750}{1331} \, \log \left (5 \, x + 3\right ) + \frac {1998}{343} \, \log \left (3 \, x + 2\right ) - \frac {1088}{456533} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.27 (sec) , antiderivative size = 77, normalized size of antiderivative = 1.20 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)^2} \, dx=-\frac {125}{121 \, {\left (5 \, x + 3\right )}} + \frac {5 \, {\left (\frac {1185937}{5 \, x + 3} - 215574\right )}}{65219 \, {\left (\frac {11}{5 \, x + 3} - 2\right )} {\left (\frac {1}{5 \, x + 3} + 3\right )}} + \frac {1998}{343} \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) - \frac {1088}{456533} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.73 \[ \int \frac {1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)^2} \, dx=\frac {1998\,\ln \left (x+\frac {2}{3}\right )}{343}-\frac {1088\,\ln \left (x-\frac {1}{2}\right )}{456533}-\frac {7750\,\ln \left (x+\frac {3}{5}\right )}{1331}+\frac {\frac {2318\,x^2}{5929}+\frac {4772\,x}{88935}-\frac {22003}{177870}}{-x^3-\frac {23\,x^2}{30}+\frac {7\,x}{30}+\frac {1}{5}} \]
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