Integrand size = 20, antiderivative size = 51 \[ \int \frac {(1-2 x) (2+3 x)^5}{3+5 x} \, dx=\frac {166663 x}{15625}+\frac {127779 x^2}{6250}+\frac {2469 x^3}{625}-\frac {17469 x^4}{500}-\frac {5427 x^5}{125}-\frac {81 x^6}{5}+\frac {11 \log (3+5 x)}{78125} \]
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Time = 0.01 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int \frac {(1-2 x) (2+3 x)^5}{3+5 x} \, dx=-\frac {81 x^6}{5}-\frac {5427 x^5}{125}-\frac {17469 x^4}{500}+\frac {2469 x^3}{625}+\frac {127779 x^2}{6250}+\frac {166663 x}{15625}+\frac {11 \log (5 x+3)}{78125} \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {166663}{15625}+\frac {127779 x}{3125}+\frac {7407 x^2}{625}-\frac {17469 x^3}{125}-\frac {5427 x^4}{25}-\frac {486 x^5}{5}+\frac {11}{15625 (3+5 x)}\right ) \, dx \\ & = \frac {166663 x}{15625}+\frac {127779 x^2}{6250}+\frac {2469 x^3}{625}-\frac {17469 x^4}{500}-\frac {5427 x^5}{125}-\frac {81 x^6}{5}+\frac {11 \log (3+5 x)}{78125} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.82 \[ \int \frac {(1-2 x) (2+3 x)^5}{3+5 x} \, dx=\frac {2813811+16666300 x+31944750 x^2+6172500 x^3-54590625 x^4-67837500 x^5-25312500 x^6+220 \log (3+5 x)}{1562500} \]
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Time = 0.73 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.71
method | result | size |
parallelrisch | \(-\frac {81 x^{6}}{5}-\frac {5427 x^{5}}{125}-\frac {17469 x^{4}}{500}+\frac {2469 x^{3}}{625}+\frac {127779 x^{2}}{6250}+\frac {166663 x}{15625}+\frac {11 \ln \left (x +\frac {3}{5}\right )}{78125}\) | \(36\) |
default | \(\frac {166663 x}{15625}+\frac {127779 x^{2}}{6250}+\frac {2469 x^{3}}{625}-\frac {17469 x^{4}}{500}-\frac {5427 x^{5}}{125}-\frac {81 x^{6}}{5}+\frac {11 \ln \left (3+5 x \right )}{78125}\) | \(38\) |
norman | \(\frac {166663 x}{15625}+\frac {127779 x^{2}}{6250}+\frac {2469 x^{3}}{625}-\frac {17469 x^{4}}{500}-\frac {5427 x^{5}}{125}-\frac {81 x^{6}}{5}+\frac {11 \ln \left (3+5 x \right )}{78125}\) | \(38\) |
risch | \(\frac {166663 x}{15625}+\frac {127779 x^{2}}{6250}+\frac {2469 x^{3}}{625}-\frac {17469 x^{4}}{500}-\frac {5427 x^{5}}{125}-\frac {81 x^{6}}{5}+\frac {11 \ln \left (3+5 x \right )}{78125}\) | \(38\) |
meijerg | \(\frac {11 \ln \left (1+\frac {5 x}{3}\right )}{78125}+\frac {176 x}{5}-\frac {24 x \left (-5 x +6\right )}{5}-\frac {54 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{25}+\frac {243 x \left (-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{250}-\frac {37179 x \left (\frac {2500}{27} x^{4}-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{62500}+\frac {19683 x \left (-\frac {218750}{243} x^{5}+\frac {17500}{27} x^{4}-\frac {4375}{9} x^{3}+\frac {3500}{9} x^{2}-350 x +420\right )}{1093750}\) | \(103\) |
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Time = 0.21 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.73 \[ \int \frac {(1-2 x) (2+3 x)^5}{3+5 x} \, dx=-\frac {81}{5} \, x^{6} - \frac {5427}{125} \, x^{5} - \frac {17469}{500} \, x^{4} + \frac {2469}{625} \, x^{3} + \frac {127779}{6250} \, x^{2} + \frac {166663}{15625} \, x + \frac {11}{78125} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.04 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.94 \[ \int \frac {(1-2 x) (2+3 x)^5}{3+5 x} \, dx=- \frac {81 x^{6}}{5} - \frac {5427 x^{5}}{125} - \frac {17469 x^{4}}{500} + \frac {2469 x^{3}}{625} + \frac {127779 x^{2}}{6250} + \frac {166663 x}{15625} + \frac {11 \log {\left (5 x + 3 \right )}}{78125} \]
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Time = 0.20 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.73 \[ \int \frac {(1-2 x) (2+3 x)^5}{3+5 x} \, dx=-\frac {81}{5} \, x^{6} - \frac {5427}{125} \, x^{5} - \frac {17469}{500} \, x^{4} + \frac {2469}{625} \, x^{3} + \frac {127779}{6250} \, x^{2} + \frac {166663}{15625} \, x + \frac {11}{78125} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.27 (sec) , antiderivative size = 38, normalized size of antiderivative = 0.75 \[ \int \frac {(1-2 x) (2+3 x)^5}{3+5 x} \, dx=-\frac {81}{5} \, x^{6} - \frac {5427}{125} \, x^{5} - \frac {17469}{500} \, x^{4} + \frac {2469}{625} \, x^{3} + \frac {127779}{6250} \, x^{2} + \frac {166663}{15625} \, x + \frac {11}{78125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 35, normalized size of antiderivative = 0.69 \[ \int \frac {(1-2 x) (2+3 x)^5}{3+5 x} \, dx=\frac {166663\,x}{15625}+\frac {11\,\ln \left (x+\frac {3}{5}\right )}{78125}+\frac {127779\,x^2}{6250}+\frac {2469\,x^3}{625}-\frac {17469\,x^4}{500}-\frac {5427\,x^5}{125}-\frac {81\,x^6}{5} \]
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