Integrand size = 22, antiderivative size = 50 \[ \int \frac {(1-2 x)^3}{(2+3 x)^2 (3+5 x)^3} \, dx=\frac {343}{3 (2+3 x)}-\frac {1331}{50 (3+5 x)^2}+\frac {8712}{25 (3+5 x)}-1617 \log (2+3 x)+1617 \log (3+5 x) \]
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Time = 0.02 (sec) , antiderivative size = 50, 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} \[ \int \frac {(1-2 x)^3}{(2+3 x)^2 (3+5 x)^3} \, dx=\frac {343}{3 (3 x+2)}+\frac {8712}{25 (5 x+3)}-\frac {1331}{50 (5 x+3)^2}-1617 \log (3 x+2)+1617 \log (5 x+3) \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {343}{(2+3 x)^2}-\frac {4851}{2+3 x}+\frac {1331}{5 (3+5 x)^3}-\frac {8712}{5 (3+5 x)^2}+\frac {8085}{3+5 x}\right ) \, dx \\ & = \frac {343}{3 (2+3 x)}-\frac {1331}{50 (3+5 x)^2}+\frac {8712}{25 (3+5 x)}-1617 \log (2+3 x)+1617 \log (3+5 x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.96 \[ \int \frac {(1-2 x)^3}{(2+3 x)^2 (3+5 x)^3} \, dx=-\frac {1331}{50 (3+5 x)^2}+\frac {343}{6+9 x}+\frac {8712}{75+125 x}-1617 \log (5 (2+3 x))+1617 \log (3+5 x) \]
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Time = 2.48 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.88
method | result | size |
risch | \(\frac {\frac {121283}{15} x^{2}+\frac {498563}{50} x +\frac {76666}{25}}{\left (2+3 x \right ) \left (3+5 x \right )^{2}}-1617 \ln \left (2+3 x \right )+1617 \ln \left (3+5 x \right )\) | \(44\) |
default | \(\frac {343}{3 \left (2+3 x \right )}-\frac {1331}{50 \left (3+5 x \right )^{2}}+\frac {8712}{25 \left (3+5 x \right )}-1617 \ln \left (2+3 x \right )+1617 \ln \left (3+5 x \right )\) | \(45\) |
norman | \(\frac {-\frac {141895}{9} x^{2}-\frac {38333}{3} x^{3}-\frac {29105}{6} x}{\left (2+3 x \right ) \left (3+5 x \right )^{2}}-1617 \ln \left (2+3 x \right )+1617 \ln \left (3+5 x \right )\) | \(47\) |
parallelrisch | \(-\frac {2182950 \ln \left (\frac {2}{3}+x \right ) x^{3}-2182950 \ln \left (x +\frac {3}{5}\right ) x^{3}+4074840 \ln \left (\frac {2}{3}+x \right ) x^{2}-4074840 \ln \left (x +\frac {3}{5}\right ) x^{2}+229998 x^{3}+2532222 \ln \left (\frac {2}{3}+x \right ) x -2532222 \ln \left (x +\frac {3}{5}\right ) x +283790 x^{2}+523908 \ln \left (\frac {2}{3}+x \right )-523908 \ln \left (x +\frac {3}{5}\right )+87315 x}{18 \left (2+3 x \right ) \left (3+5 x \right )^{2}}\) | \(93\) |
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none
Time = 0.23 (sec) , antiderivative size = 75, normalized size of antiderivative = 1.50 \[ \int \frac {(1-2 x)^3}{(2+3 x)^2 (3+5 x)^3} \, dx=\frac {1212830 \, x^{2} + 242550 \, {\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (5 \, x + 3\right ) - 242550 \, {\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (3 \, x + 2\right ) + 1495689 \, x + 459996}{150 \, {\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} \]
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Time = 0.07 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.84 \[ \int \frac {(1-2 x)^3}{(2+3 x)^2 (3+5 x)^3} \, dx=- \frac {- 1212830 x^{2} - 1495689 x - 459996}{11250 x^{3} + 21000 x^{2} + 13050 x + 2700} + 1617 \log {\left (x + \frac {3}{5} \right )} - 1617 \log {\left (x + \frac {2}{3} \right )} \]
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none
Time = 0.21 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.92 \[ \int \frac {(1-2 x)^3}{(2+3 x)^2 (3+5 x)^3} \, dx=\frac {1212830 \, x^{2} + 1495689 \, x + 459996}{150 \, {\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} + 1617 \, \log \left (5 \, x + 3\right ) - 1617 \, \log \left (3 \, x + 2\right ) \]
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none
Time = 0.55 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.98 \[ \int \frac {(1-2 x)^3}{(2+3 x)^2 (3+5 x)^3} \, dx=\frac {343}{3 \, {\left (3 \, x + 2\right )}} - \frac {1089 \, {\left (\frac {14}{3 \, x + 2} - 59\right )}}{2 \, {\left (\frac {1}{3 \, x + 2} - 5\right )}^{2}} + 1617 \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) \]
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Time = 0.05 (sec) , antiderivative size = 35, normalized size of antiderivative = 0.70 \[ \int \frac {(1-2 x)^3}{(2+3 x)^2 (3+5 x)^3} \, dx=\frac {\frac {121283\,x^2}{1125}+\frac {498563\,x}{3750}+\frac {76666}{1875}}{x^3+\frac {28\,x^2}{15}+\frac {29\,x}{25}+\frac {6}{25}}-3234\,\mathrm {atanh}\left (30\,x+19\right ) \]
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