Integrand size = 22, antiderivative size = 51 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{2+3 x} \, dx=\frac {10013 x}{729}-\frac {8287 x^2}{486}-\frac {6427 x^3}{243}+\frac {2815 x^4}{54}+\frac {220 x^5}{9}-\frac {500 x^6}{9}-\frac {343 \log (2+3 x)}{2187} \]
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Time = 0.02 (sec) , antiderivative size = 51, 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} \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{2+3 x} \, dx=-\frac {500 x^6}{9}+\frac {220 x^5}{9}+\frac {2815 x^4}{54}-\frac {6427 x^3}{243}-\frac {8287 x^2}{486}+\frac {10013 x}{729}-\frac {343 \log (3 x+2)}{2187} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {10013}{729}-\frac {8287 x}{243}-\frac {6427 x^2}{81}+\frac {5630 x^3}{27}+\frac {1100 x^4}{9}-\frac {1000 x^5}{3}-\frac {343}{729 (2+3 x)}\right ) \, dx \\ & = \frac {10013 x}{729}-\frac {8287 x^2}{486}-\frac {6427 x^3}{243}+\frac {2815 x^4}{54}+\frac {220 x^5}{9}-\frac {500 x^6}{9}-\frac {343 \log (2+3 x)}{2187} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.82 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{2+3 x} \, dx=\frac {29296+60078 x-74583 x^2-115686 x^3+228015 x^4+106920 x^5-243000 x^6-686 \log (2+3 x)}{4374} \]
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Time = 2.43 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.71
method | result | size |
parallelrisch | \(-\frac {500 x^{6}}{9}+\frac {220 x^{5}}{9}+\frac {2815 x^{4}}{54}-\frac {6427 x^{3}}{243}-\frac {8287 x^{2}}{486}+\frac {10013 x}{729}-\frac {343 \ln \left (\frac {2}{3}+x \right )}{2187}\) | \(36\) |
default | \(\frac {10013 x}{729}-\frac {8287 x^{2}}{486}-\frac {6427 x^{3}}{243}+\frac {2815 x^{4}}{54}+\frac {220 x^{5}}{9}-\frac {500 x^{6}}{9}-\frac {343 \ln \left (2+3 x \right )}{2187}\) | \(38\) |
norman | \(\frac {10013 x}{729}-\frac {8287 x^{2}}{486}-\frac {6427 x^{3}}{243}+\frac {2815 x^{4}}{54}+\frac {220 x^{5}}{9}-\frac {500 x^{6}}{9}-\frac {343 \ln \left (2+3 x \right )}{2187}\) | \(38\) |
risch | \(\frac {10013 x}{729}-\frac {8287 x^{2}}{486}-\frac {6427 x^{3}}{243}+\frac {2815 x^{4}}{54}+\frac {220 x^{5}}{9}-\frac {500 x^{6}}{9}-\frac {343 \ln \left (2+3 x \right )}{2187}\) | \(38\) |
meijerg | \(-\frac {343 \ln \left (1+\frac {3 x}{2}\right )}{2187}-9 x +\frac {29 x \left (-\frac {9 x}{2}+6\right )}{3}+\frac {179 x \left (9 x^{2}-9 x +12\right )}{81}-\frac {116 x \left (-\frac {405}{8} x^{3}+45 x^{2}-45 x +60\right )}{81}-\frac {80 x \left (\frac {243}{4} x^{4}-\frac {405}{8} x^{3}+45 x^{2}-45 x +60\right )}{243}+\frac {1600 x \left (-\frac {8505}{16} x^{5}+\frac {1701}{4} x^{4}-\frac {2835}{8} x^{3}+315 x^{2}-315 x +420\right )}{15309}\) | \(103\) |
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Time = 0.23 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.73 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{2+3 x} \, dx=-\frac {500}{9} \, x^{6} + \frac {220}{9} \, x^{5} + \frac {2815}{54} \, x^{4} - \frac {6427}{243} \, x^{3} - \frac {8287}{486} \, x^{2} + \frac {10013}{729} \, x - \frac {343}{2187} \, \log \left (3 \, x + 2\right ) \]
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Time = 0.04 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.94 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{2+3 x} \, dx=- \frac {500 x^{6}}{9} + \frac {220 x^{5}}{9} + \frac {2815 x^{4}}{54} - \frac {6427 x^{3}}{243} - \frac {8287 x^{2}}{486} + \frac {10013 x}{729} - \frac {343 \log {\left (3 x + 2 \right )}}{2187} \]
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none
Time = 0.21 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.73 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{2+3 x} \, dx=-\frac {500}{9} \, x^{6} + \frac {220}{9} \, x^{5} + \frac {2815}{54} \, x^{4} - \frac {6427}{243} \, x^{3} - \frac {8287}{486} \, x^{2} + \frac {10013}{729} \, x - \frac {343}{2187} \, \log \left (3 \, x + 2\right ) \]
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Time = 0.29 (sec) , antiderivative size = 38, normalized size of antiderivative = 0.75 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{2+3 x} \, dx=-\frac {500}{9} \, x^{6} + \frac {220}{9} \, x^{5} + \frac {2815}{54} \, x^{4} - \frac {6427}{243} \, x^{3} - \frac {8287}{486} \, x^{2} + \frac {10013}{729} \, x - \frac {343}{2187} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 35, normalized size of antiderivative = 0.69 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{2+3 x} \, dx=\frac {10013\,x}{729}-\frac {343\,\ln \left (x+\frac {2}{3}\right )}{2187}-\frac {8287\,x^2}{486}-\frac {6427\,x^3}{243}+\frac {2815\,x^4}{54}+\frac {220\,x^5}{9}-\frac {500\,x^6}{9} \]
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