Integrand size = 20, antiderivative size = 37 \[ \int \frac {(1-2 x)^3 (2+3 x)}{3+5 x} \, dx=-\frac {27 x}{625}-\frac {183 x^2}{125}+\frac {172 x^3}{75}-\frac {6 x^4}{5}+\frac {1331 \log (3+5 x)}{3125} \]
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Time = 0.01 (sec) , antiderivative size = 37, 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} \[ \int \frac {(1-2 x)^3 (2+3 x)}{3+5 x} \, dx=-\frac {6 x^4}{5}+\frac {172 x^3}{75}-\frac {183 x^2}{125}-\frac {27 x}{625}+\frac {1331 \log (5 x+3)}{3125} \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {27}{625}-\frac {366 x}{125}+\frac {172 x^2}{25}-\frac {24 x^3}{5}+\frac {1331}{625 (3+5 x)}\right ) \, dx \\ & = -\frac {27 x}{625}-\frac {183 x^2}{125}+\frac {172 x^3}{75}-\frac {6 x^4}{5}+\frac {1331 \log (3+5 x)}{3125} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 35, normalized size of antiderivative = 0.95 \[ \int \frac {(1-2 x)^3 (2+3 x)}{3+5 x} \, dx=\frac {-5 \left (-2160+81 x+2745 x^2-4300 x^3+2250 x^4\right )+3993 \log (3+5 x)}{9375} \]
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Time = 2.43 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.70
method | result | size |
parallelrisch | \(-\frac {6 x^{4}}{5}+\frac {172 x^{3}}{75}-\frac {183 x^{2}}{125}-\frac {27 x}{625}+\frac {1331 \ln \left (x +\frac {3}{5}\right )}{3125}\) | \(26\) |
default | \(-\frac {27 x}{625}-\frac {183 x^{2}}{125}+\frac {172 x^{3}}{75}-\frac {6 x^{4}}{5}+\frac {1331 \ln \left (3+5 x \right )}{3125}\) | \(28\) |
norman | \(-\frac {27 x}{625}-\frac {183 x^{2}}{125}+\frac {172 x^{3}}{75}-\frac {6 x^{4}}{5}+\frac {1331 \ln \left (3+5 x \right )}{3125}\) | \(28\) |
risch | \(-\frac {27 x}{625}-\frac {183 x^{2}}{125}+\frac {172 x^{3}}{75}-\frac {6 x^{4}}{5}+\frac {1331 \ln \left (3+5 x \right )}{3125}\) | \(28\) |
meijerg | \(\frac {1331 \ln \left (1+\frac {5 x}{3}\right )}{3125}-\frac {9 x}{5}-\frac {3 x \left (-5 x +6\right )}{25}+\frac {3 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{25}+\frac {54 x \left (-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{3125}\) | \(52\) |
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Time = 0.22 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.73 \[ \int \frac {(1-2 x)^3 (2+3 x)}{3+5 x} \, dx=-\frac {6}{5} \, x^{4} + \frac {172}{75} \, x^{3} - \frac {183}{125} \, x^{2} - \frac {27}{625} \, x + \frac {1331}{3125} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.05 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.92 \[ \int \frac {(1-2 x)^3 (2+3 x)}{3+5 x} \, dx=- \frac {6 x^{4}}{5} + \frac {172 x^{3}}{75} - \frac {183 x^{2}}{125} - \frac {27 x}{625} + \frac {1331 \log {\left (5 x + 3 \right )}}{3125} \]
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Time = 0.20 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.73 \[ \int \frac {(1-2 x)^3 (2+3 x)}{3+5 x} \, dx=-\frac {6}{5} \, x^{4} + \frac {172}{75} \, x^{3} - \frac {183}{125} \, x^{2} - \frac {27}{625} \, x + \frac {1331}{3125} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.28 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.76 \[ \int \frac {(1-2 x)^3 (2+3 x)}{3+5 x} \, dx=-\frac {6}{5} \, x^{4} + \frac {172}{75} \, x^{3} - \frac {183}{125} \, x^{2} - \frac {27}{625} \, x + \frac {1331}{3125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
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Time = 0.03 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.68 \[ \int \frac {(1-2 x)^3 (2+3 x)}{3+5 x} \, dx=\frac {1331\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {27\,x}{625}-\frac {183\,x^2}{125}+\frac {172\,x^3}{75}-\frac {6\,x^4}{5} \]
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