Integrand size = 22, antiderivative size = 64 \[ \int \frac {1}{(1-2 x)^2 (2+3 x) (3+5 x)^3} \, dx=\frac {8}{9317 (1-2 x)}-\frac {25}{242 (3+5 x)^2}+\frac {725}{1331 (3+5 x)}-\frac {1104 \log (1-2 x)}{717409}-\frac {81}{49} \log (2+3 x)+\frac {24225 \log (3+5 x)}{14641} \]
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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} \[ \int \frac {1}{(1-2 x)^2 (2+3 x) (3+5 x)^3} \, dx=\frac {8}{9317 (1-2 x)}+\frac {725}{1331 (5 x+3)}-\frac {25}{242 (5 x+3)^2}-\frac {1104 \log (1-2 x)}{717409}-\frac {81}{49} \log (3 x+2)+\frac {24225 \log (5 x+3)}{14641} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {16}{9317 (-1+2 x)^2}-\frac {2208}{717409 (-1+2 x)}-\frac {243}{49 (2+3 x)}+\frac {125}{121 (3+5 x)^3}-\frac {3625}{1331 (3+5 x)^2}+\frac {121125}{14641 (3+5 x)}\right ) \, dx \\ & = \frac {8}{9317 (1-2 x)}-\frac {25}{242 (3+5 x)^2}+\frac {725}{1331 (3+5 x)}-\frac {1104 \log (1-2 x)}{717409}-\frac {81}{49} \log (2+3 x)+\frac {24225 \log (3+5 x)}{14641} \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 60, normalized size of antiderivative = 0.94 \[ \int \frac {1}{(1-2 x)^2 (2+3 x) (3+5 x)^3} \, dx=\frac {3 \left (\frac {1232}{3-6 x}-\frac {148225}{3 (3+5 x)^2}+\frac {781550}{9+15 x}-736 \log (3-6 x)-790614 \log (2+3 x)+791350 \log (-3 (3+5 x))\right )}{1434818} \]
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Time = 0.89 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.81
method | result | size |
risch | \(\frac {\frac {50550}{9317} x^{2}+\frac {2910}{9317} x -\frac {28669}{18634}}{\left (-1+2 x \right ) \left (3+5 x \right )^{2}}-\frac {1104 \ln \left (-1+2 x \right )}{717409}-\frac {81 \ln \left (2+3 x \right )}{49}+\frac {24225 \ln \left (3+5 x \right )}{14641}\) | \(52\) |
default | \(-\frac {25}{242 \left (3+5 x \right )^{2}}+\frac {725}{1331 \left (3+5 x \right )}+\frac {24225 \ln \left (3+5 x \right )}{14641}-\frac {8}{9317 \left (-1+2 x \right )}-\frac {1104 \ln \left (-1+2 x \right )}{717409}-\frac {81 \ln \left (2+3 x \right )}{49}\) | \(53\) |
norman | \(\frac {-\frac {716725}{83853} x^{3}-\frac {93515}{167706} x^{2}+\frac {66068}{27951} x}{\left (-1+2 x \right ) \left (3+5 x \right )^{2}}-\frac {1104 \ln \left (-1+2 x \right )}{717409}-\frac {81 \ln \left (2+3 x \right )}{49}+\frac {24225 \ln \left (3+5 x \right )}{14641}\) | \(55\) |
parallelrisch | \(-\frac {1067328900 \ln \left (\frac {2}{3}+x \right ) x^{3}-1068322500 \ln \left (x +\frac {3}{5}\right ) x^{3}+993600 \ln \left (x -\frac {1}{2}\right ) x^{3}+747130230 \ln \left (\frac {2}{3}+x \right ) x^{2}-747825750 \ln \left (x +\frac {3}{5}\right ) x^{2}+695520 \ln \left (x -\frac {1}{2}\right ) x^{2}+110375650 x^{3}-256158936 \ln \left (\frac {2}{3}+x \right ) x +256397400 \ln \left (x +\frac {3}{5}\right ) x -238464 \ln \left (x -\frac {1}{2}\right ) x +7200655 x^{2}-192119202 \ln \left (\frac {2}{3}+x \right )+192298050 \ln \left (x +\frac {3}{5}\right )-178848 \ln \left (x -\frac {1}{2}\right )-30523416 x}{12913362 \left (-1+2 x \right ) \left (3+5 x \right )^{2}}\) | \(124\) |
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Time = 0.22 (sec) , antiderivative size = 98, normalized size of antiderivative = 1.53 \[ \int \frac {1}{(1-2 x)^2 (2+3 x) (3+5 x)^3} \, dx=\frac {7784700 \, x^{2} + 2374050 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) - 2371842 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (3 \, x + 2\right ) - 2208 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) + 448140 \, x - 2207513}{1434818 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]
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Time = 0.10 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.84 \[ \int \frac {1}{(1-2 x)^2 (2+3 x) (3+5 x)^3} \, dx=\frac {101100 x^{2} + 5820 x - 28669}{931700 x^{3} + 652190 x^{2} - 223608 x - 167706} - \frac {1104 \log {\left (x - \frac {1}{2} \right )}}{717409} + \frac {24225 \log {\left (x + \frac {3}{5} \right )}}{14641} - \frac {81 \log {\left (x + \frac {2}{3} \right )}}{49} \]
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Time = 0.20 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.84 \[ \int \frac {1}{(1-2 x)^2 (2+3 x) (3+5 x)^3} \, dx=\frac {101100 \, x^{2} + 5820 \, x - 28669}{18634 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac {24225}{14641} \, \log \left (5 \, x + 3\right ) - \frac {81}{49} \, \log \left (3 \, x + 2\right ) - \frac {1104}{717409} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.28 (sec) , antiderivative size = 66, normalized size of antiderivative = 1.03 \[ \int \frac {1}{(1-2 x)^2 (2+3 x) (3+5 x)^3} \, dx=-\frac {8}{9317 \, {\left (2 \, x - 1\right )}} - \frac {250 \, {\left (\frac {297}{2 \, x - 1} + 140\right )}}{14641 \, {\left (\frac {11}{2 \, x - 1} + 5\right )}^{2}} - \frac {81}{49} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) + \frac {24225}{14641} \, \log \left ({\left | -\frac {11}{2 \, x - 1} - 5 \right |}\right ) \]
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Time = 1.26 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.75 \[ \int \frac {1}{(1-2 x)^2 (2+3 x) (3+5 x)^3} \, dx=\frac {24225\,\ln \left (x+\frac {3}{5}\right )}{14641}-\frac {81\,\ln \left (x+\frac {2}{3}\right )}{49}-\frac {1104\,\ln \left (x-\frac {1}{2}\right )}{717409}-\frac {\frac {1011\,x^2}{9317}+\frac {291\,x}{46585}-\frac {28669}{931700}}{-x^3-\frac {7\,x^2}{10}+\frac {6\,x}{25}+\frac {9}{50}} \]
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