Integrand size = 22, antiderivative size = 53 \[ \int \frac {1}{(1-2 x) (2+3 x)^3 (3+5 x)} \, dx=\frac {3}{14 (2+3 x)^2}+\frac {111}{49 (2+3 x)}-\frac {8 \log (1-2 x)}{3773}-\frac {3897}{343} \log (2+3 x)+\frac {125}{11} \log (3+5 x) \]
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Time = 0.02 (sec) , antiderivative size = 53, 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} \[ \int \frac {1}{(1-2 x) (2+3 x)^3 (3+5 x)} \, dx=\frac {111}{49 (3 x+2)}+\frac {3}{14 (3 x+2)^2}-\frac {8 \log (1-2 x)}{3773}-\frac {3897}{343} \log (3 x+2)+\frac {125}{11} \log (5 x+3) \]
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Rule 84
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {16}{3773 (-1+2 x)}-\frac {9}{7 (2+3 x)^3}-\frac {333}{49 (2+3 x)^2}-\frac {11691}{343 (2+3 x)}+\frac {625}{11 (3+5 x)}\right ) \, dx \\ & = \frac {3}{14 (2+3 x)^2}+\frac {111}{49 (2+3 x)}-\frac {8 \log (1-2 x)}{3773}-\frac {3897}{343} \log (2+3 x)+\frac {125}{11} \log (3+5 x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.92 \[ \int \frac {1}{(1-2 x) (2+3 x)^3 (3+5 x)} \, dx=\frac {\frac {1617}{2 (2+3 x)^2}+\frac {8547}{2+3 x}-8 \log (1-2 x)-42867 \log (4+6 x)+42875 \log (6+10 x)}{3773} \]
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Time = 2.54 (sec) , antiderivative size = 40, normalized size of antiderivative = 0.75
method | result | size |
risch | \(\frac {\frac {333 x}{49}+\frac {465}{98}}{\left (2+3 x \right )^{2}}-\frac {8 \ln \left (-1+2 x \right )}{3773}-\frac {3897 \ln \left (2+3 x \right )}{343}+\frac {125 \ln \left (3+5 x \right )}{11}\) | \(40\) |
norman | \(\frac {-\frac {729}{98} x -\frac {4185}{392} x^{2}}{\left (2+3 x \right )^{2}}-\frac {8 \ln \left (-1+2 x \right )}{3773}-\frac {3897 \ln \left (2+3 x \right )}{343}+\frac {125 \ln \left (3+5 x \right )}{11}\) | \(43\) |
default | \(\frac {125 \ln \left (3+5 x \right )}{11}-\frac {8 \ln \left (-1+2 x \right )}{3773}+\frac {3}{14 \left (2+3 x \right )^{2}}+\frac {111}{49 \left (2+3 x \right )}-\frac {3897 \ln \left (2+3 x \right )}{343}\) | \(44\) |
parallelrisch | \(-\frac {3086424 \ln \left (\frac {2}{3}+x \right ) x^{2}-3087000 \ln \left (x +\frac {3}{5}\right ) x^{2}+576 \ln \left (x -\frac {1}{2}\right ) x^{2}+4115232 \ln \left (\frac {2}{3}+x \right ) x -4116000 \ln \left (x +\frac {3}{5}\right ) x +768 \ln \left (x -\frac {1}{2}\right ) x +322245 x^{2}+1371744 \ln \left (\frac {2}{3}+x \right )-1372000 \ln \left (x +\frac {3}{5}\right )+256 \ln \left (x -\frac {1}{2}\right )+224532 x}{30184 \left (2+3 x \right )^{2}}\) | \(85\) |
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Time = 0.22 (sec) , antiderivative size = 73, normalized size of antiderivative = 1.38 \[ \int \frac {1}{(1-2 x) (2+3 x)^3 (3+5 x)} \, dx=\frac {85750 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (5 \, x + 3\right ) - 85734 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 16 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (2 \, x - 1\right ) + 51282 \, x + 35805}{7546 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
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Time = 0.09 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.87 \[ \int \frac {1}{(1-2 x) (2+3 x)^3 (3+5 x)} \, dx=- \frac {- 666 x - 465}{882 x^{2} + 1176 x + 392} - \frac {8 \log {\left (x - \frac {1}{2} \right )}}{3773} + \frac {125 \log {\left (x + \frac {3}{5} \right )}}{11} - \frac {3897 \log {\left (x + \frac {2}{3} \right )}}{343} \]
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Time = 0.20 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.83 \[ \int \frac {1}{(1-2 x) (2+3 x)^3 (3+5 x)} \, dx=\frac {3 \, {\left (222 \, x + 155\right )}}{98 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac {125}{11} \, \log \left (5 \, x + 3\right ) - \frac {3897}{343} \, \log \left (3 \, x + 2\right ) - \frac {8}{3773} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.28 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.79 \[ \int \frac {1}{(1-2 x) (2+3 x)^3 (3+5 x)} \, dx=\frac {3 \, {\left (222 \, x + 155\right )}}{98 \, {\left (3 \, x + 2\right )}^{2}} + \frac {125}{11} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {3897}{343} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {8}{3773} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 35, normalized size of antiderivative = 0.66 \[ \int \frac {1}{(1-2 x) (2+3 x)^3 (3+5 x)} \, dx=\frac {125\,\ln \left (x+\frac {3}{5}\right )}{11}-\frac {3897\,\ln \left (x+\frac {2}{3}\right )}{343}-\frac {8\,\ln \left (x-\frac {1}{2}\right )}{3773}+\frac {\frac {37\,x}{49}+\frac {155}{294}}{x^2+\frac {4\,x}{3}+\frac {4}{9}} \]
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