Integrand size = 22, antiderivative size = 42 \[ \int \frac {1}{(1-2 x) (2+3 x)^2 (3+5 x)} \, dx=\frac {3}{7 (2+3 x)}-\frac {4}{539} \log (1-2 x)-\frac {111}{49} \log (2+3 x)+\frac {25}{11} \log (3+5 x) \]
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Time = 0.01 (sec) , antiderivative size = 42, 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 = {84} \[ \int \frac {1}{(1-2 x) (2+3 x)^2 (3+5 x)} \, dx=\frac {3}{7 (3 x+2)}-\frac {4}{539} \log (1-2 x)-\frac {111}{49} \log (3 x+2)+\frac {25}{11} \log (5 x+3) \]
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Rule 84
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {8}{539 (-1+2 x)}-\frac {9}{7 (2+3 x)^2}-\frac {333}{49 (2+3 x)}+\frac {125}{11 (3+5 x)}\right ) \, dx \\ & = \frac {3}{7 (2+3 x)}-\frac {4}{539} \log (1-2 x)-\frac {111}{49} \log (2+3 x)+\frac {25}{11} \log (3+5 x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 38, normalized size of antiderivative = 0.90 \[ \int \frac {1}{(1-2 x) (2+3 x)^2 (3+5 x)} \, dx=\frac {1}{539} \left (\frac {231}{2+3 x}-4 \log (1-2 x)-1221 \log (4+6 x)+1225 \log (6+10 x)\right ) \]
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Time = 2.56 (sec) , antiderivative size = 33, normalized size of antiderivative = 0.79
method | result | size |
risch | \(\frac {1}{\frac {14}{3}+7 x}-\frac {4 \ln \left (-1+2 x \right )}{539}-\frac {111 \ln \left (2+3 x \right )}{49}+\frac {25 \ln \left (3+5 x \right )}{11}\) | \(33\) |
default | \(\frac {25 \ln \left (3+5 x \right )}{11}-\frac {4 \ln \left (-1+2 x \right )}{539}+\frac {3}{7 \left (2+3 x \right )}-\frac {111 \ln \left (2+3 x \right )}{49}\) | \(35\) |
norman | \(-\frac {9 x}{14 \left (2+3 x \right )}-\frac {4 \ln \left (-1+2 x \right )}{539}-\frac {111 \ln \left (2+3 x \right )}{49}+\frac {25 \ln \left (3+5 x \right )}{11}\) | \(36\) |
parallelrisch | \(-\frac {7326 \ln \left (\frac {2}{3}+x \right ) x -7350 \ln \left (x +\frac {3}{5}\right ) x +24 \ln \left (x -\frac {1}{2}\right ) x +4884 \ln \left (\frac {2}{3}+x \right )-4900 \ln \left (x +\frac {3}{5}\right )+16 \ln \left (x -\frac {1}{2}\right )+693 x}{1078 \left (2+3 x \right )}\) | \(53\) |
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none
Time = 0.22 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.19 \[ \int \frac {1}{(1-2 x) (2+3 x)^2 (3+5 x)} \, dx=\frac {1225 \, {\left (3 \, x + 2\right )} \log \left (5 \, x + 3\right ) - 1221 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 4 \, {\left (3 \, x + 2\right )} \log \left (2 \, x - 1\right ) + 231}{539 \, {\left (3 \, x + 2\right )}} \]
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Time = 0.08 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.86 \[ \int \frac {1}{(1-2 x) (2+3 x)^2 (3+5 x)} \, dx=- \frac {4 \log {\left (x - \frac {1}{2} \right )}}{539} + \frac {25 \log {\left (x + \frac {3}{5} \right )}}{11} - \frac {111 \log {\left (x + \frac {2}{3} \right )}}{49} + \frac {3}{21 x + 14} \]
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none
Time = 0.20 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.81 \[ \int \frac {1}{(1-2 x) (2+3 x)^2 (3+5 x)} \, dx=\frac {3}{7 \, {\left (3 \, x + 2\right )}} + \frac {25}{11} \, \log \left (5 \, x + 3\right ) - \frac {111}{49} \, \log \left (3 \, x + 2\right ) - \frac {4}{539} \, \log \left (2 \, x - 1\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 40, normalized size of antiderivative = 0.95 \[ \int \frac {1}{(1-2 x) (2+3 x)^2 (3+5 x)} \, dx=\frac {3}{7 \, {\left (3 \, x + 2\right )}} + \frac {25}{11} \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) - \frac {4}{539} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) \]
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Time = 1.39 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.62 \[ \int \frac {1}{(1-2 x) (2+3 x)^2 (3+5 x)} \, dx=\frac {25\,\ln \left (x+\frac {3}{5}\right )}{11}-\frac {111\,\ln \left (x+\frac {2}{3}\right )}{49}-\frac {4\,\ln \left (x-\frac {1}{2}\right )}{539}+\frac {1}{7\,\left (x+\frac {2}{3}\right )} \]
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