Integrand size = 22, antiderivative size = 65 \[ \int \frac {(2+3 x)^2}{(1-2 x)^3 (3+5 x)^3} \, dx=\frac {49}{2662 (1-2 x)^2}+\frac {273}{14641 (1-2 x)}-\frac {1}{2662 (3+5 x)^2}-\frac {72}{14641 (3+5 x)}-\frac {1509 \log (1-2 x)}{161051}+\frac {1509 \log (3+5 x)}{161051} \]
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Time = 0.02 (sec) , antiderivative size = 65, 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} \[ \int \frac {(2+3 x)^2}{(1-2 x)^3 (3+5 x)^3} \, dx=\frac {273}{14641 (1-2 x)}-\frac {72}{14641 (5 x+3)}+\frac {49}{2662 (1-2 x)^2}-\frac {1}{2662 (5 x+3)^2}-\frac {1509 \log (1-2 x)}{161051}+\frac {1509 \log (5 x+3)}{161051} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {98}{1331 (-1+2 x)^3}+\frac {546}{14641 (-1+2 x)^2}-\frac {3018}{161051 (-1+2 x)}+\frac {5}{1331 (3+5 x)^3}+\frac {360}{14641 (3+5 x)^2}+\frac {7545}{161051 (3+5 x)}\right ) \, dx \\ & = \frac {49}{2662 (1-2 x)^2}+\frac {273}{14641 (1-2 x)}-\frac {1}{2662 (3+5 x)^2}-\frac {72}{14641 (3+5 x)}-\frac {1509 \log (1-2 x)}{161051}+\frac {1509 \log (3+5 x)}{161051} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.74 \[ \int \frac {(2+3 x)^2}{(1-2 x)^3 (3+5 x)^3} \, dx=\frac {-\frac {11 \left (-9322-23774 x+4527 x^2+30180 x^3\right )}{\left (-3+x+10 x^2\right )^2}+3018 \log (-3-5 x)-3018 \log (1-2 x)}{322102} \]
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Time = 0.90 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.74
method | result | size |
norman | \(\frac {-\frac {15090}{14641} x^{3}-\frac {4527}{29282} x^{2}+\frac {11887}{14641} x +\frac {4661}{14641}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {1509 \ln \left (-1+2 x \right )}{161051}+\frac {1509 \ln \left (3+5 x \right )}{161051}\) | \(48\) |
risch | \(\frac {-\frac {15090}{14641} x^{3}-\frac {4527}{29282} x^{2}+\frac {11887}{14641} x +\frac {4661}{14641}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {1509 \ln \left (-1+2 x \right )}{161051}+\frac {1509 \ln \left (3+5 x \right )}{161051}\) | \(49\) |
default | \(-\frac {1}{2662 \left (3+5 x \right )^{2}}-\frac {72}{14641 \left (3+5 x \right )}+\frac {1509 \ln \left (3+5 x \right )}{161051}+\frac {49}{2662 \left (-1+2 x \right )^{2}}-\frac {273}{14641 \left (-1+2 x \right )}-\frac {1509 \ln \left (-1+2 x \right )}{161051}\) | \(54\) |
parallelrisch | \(\frac {905400 \ln \left (x +\frac {3}{5}\right ) x^{4}-905400 \ln \left (x -\frac {1}{2}\right ) x^{4}+1484439+181080 \ln \left (x +\frac {3}{5}\right ) x^{3}-181080 \ln \left (x -\frac {1}{2}\right ) x^{3}+13075700 x^{4}-534186 \ln \left (x +\frac {3}{5}\right ) x^{2}+534186 \ln \left (x -\frac {1}{2}\right ) x^{2}+1619200 x^{3}-54324 \ln \left (x +\frac {3}{5}\right ) x +54324 \ln \left (x -\frac {1}{2}\right ) x -7864054 x^{2}+81486 \ln \left (x +\frac {3}{5}\right )-81486 \ln \left (x -\frac {1}{2}\right )}{966306 \left (-1+2 x \right )^{2} \left (3+5 x \right )^{2}}\) | \(114\) |
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Time = 0.22 (sec) , antiderivative size = 95, normalized size of antiderivative = 1.46 \[ \int \frac {(2+3 x)^2}{(1-2 x)^3 (3+5 x)^3} \, dx=-\frac {331980 \, x^{3} + 49797 \, x^{2} - 3018 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 3018 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) - 261514 \, x - 102542}{322102 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \]
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Time = 0.08 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.83 \[ \int \frac {(2+3 x)^2}{(1-2 x)^3 (3+5 x)^3} \, dx=- \frac {30180 x^{3} + 4527 x^{2} - 23774 x - 9322}{2928200 x^{4} + 585640 x^{3} - 1727638 x^{2} - 175692 x + 263538} - \frac {1509 \log {\left (x - \frac {1}{2} \right )}}{161051} + \frac {1509 \log {\left (x + \frac {3}{5} \right )}}{161051} \]
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Time = 0.19 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.86 \[ \int \frac {(2+3 x)^2}{(1-2 x)^3 (3+5 x)^3} \, dx=-\frac {30180 \, x^{3} + 4527 \, x^{2} - 23774 \, x - 9322}{29282 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac {1509}{161051} \, \log \left (5 \, x + 3\right ) - \frac {1509}{161051} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.29 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.71 \[ \int \frac {(2+3 x)^2}{(1-2 x)^3 (3+5 x)^3} \, dx=-\frac {30180 \, x^{3} + 4527 \, x^{2} - 23774 \, x - 9322}{29282 \, {\left (10 \, x^{2} + x - 3\right )}^{2}} + \frac {1509}{161051} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {1509}{161051} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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Time = 0.05 (sec) , antiderivative size = 45, normalized size of antiderivative = 0.69 \[ \int \frac {(2+3 x)^2}{(1-2 x)^3 (3+5 x)^3} \, dx=\frac {3018\,\mathrm {atanh}\left (\frac {20\,x}{11}+\frac {1}{11}\right )}{161051}+\frac {-\frac {1509\,x^3}{146410}-\frac {4527\,x^2}{2928200}+\frac {11887\,x}{1464100}+\frac {4661}{1464100}}{x^4+\frac {x^3}{5}-\frac {59\,x^2}{100}-\frac {3\,x}{50}+\frac {9}{100}} \]
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