Integrand size = 22, antiderivative size = 37 \[ \int \frac {(1-2 x)^2 (3+5 x)^2}{2+3 x} \, dx=\frac {340 x}{81}-\frac {251 x^2}{54}-\frac {140 x^3}{27}+\frac {25 x^4}{3}+\frac {49}{243} \log (2+3 x) \]
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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, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int \frac {(1-2 x)^2 (3+5 x)^2}{2+3 x} \, dx=\frac {25 x^4}{3}-\frac {140 x^3}{27}-\frac {251 x^2}{54}+\frac {340 x}{81}+\frac {49}{243} \log (3 x+2) \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {340}{81}-\frac {251 x}{27}-\frac {140 x^2}{9}+\frac {100 x^3}{3}+\frac {49}{81 (2+3 x)}\right ) \, dx \\ & = \frac {340 x}{81}-\frac {251 x^2}{54}-\frac {140 x^3}{27}+\frac {25 x^4}{3}+\frac {49}{243} \log (2+3 x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.86 \[ \int \frac {(1-2 x)^2 (3+5 x)^2}{2+3 x} \, dx=\frac {2452+6120 x-6777 x^2-7560 x^3+12150 x^4+294 \log (2+3 x)}{1458} \]
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Time = 1.86 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.70
method | result | size |
parallelrisch | \(\frac {25 x^{4}}{3}-\frac {140 x^{3}}{27}-\frac {251 x^{2}}{54}+\frac {340 x}{81}+\frac {49 \ln \left (\frac {2}{3}+x \right )}{243}\) | \(26\) |
default | \(\frac {340 x}{81}-\frac {251 x^{2}}{54}-\frac {140 x^{3}}{27}+\frac {25 x^{4}}{3}+\frac {49 \ln \left (2+3 x \right )}{243}\) | \(28\) |
norman | \(\frac {340 x}{81}-\frac {251 x^{2}}{54}-\frac {140 x^{3}}{27}+\frac {25 x^{4}}{3}+\frac {49 \ln \left (2+3 x \right )}{243}\) | \(28\) |
risch | \(\frac {340 x}{81}-\frac {251 x^{2}}{54}-\frac {140 x^{3}}{27}+\frac {25 x^{4}}{3}+\frac {49 \ln \left (2+3 x \right )}{243}\) | \(28\) |
meijerg | \(\frac {49 \ln \left (1+\frac {3 x}{2}\right )}{243}-2 x +\frac {59 x \left (-\frac {9 x}{2}+6\right )}{27}+\frac {20 x \left (9 x^{2}-9 x +12\right )}{81}-\frac {40 x \left (-\frac {405}{8} x^{3}+45 x^{2}-45 x +60\right )}{243}\) | \(52\) |
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none
Time = 0.23 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.73 \[ \int \frac {(1-2 x)^2 (3+5 x)^2}{2+3 x} \, dx=\frac {25}{3} \, x^{4} - \frac {140}{27} \, x^{3} - \frac {251}{54} \, x^{2} + \frac {340}{81} \, x + \frac {49}{243} \, \log \left (3 \, x + 2\right ) \]
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Time = 0.04 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.92 \[ \int \frac {(1-2 x)^2 (3+5 x)^2}{2+3 x} \, dx=\frac {25 x^{4}}{3} - \frac {140 x^{3}}{27} - \frac {251 x^{2}}{54} + \frac {340 x}{81} + \frac {49 \log {\left (3 x + 2 \right )}}{243} \]
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none
Time = 0.19 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.73 \[ \int \frac {(1-2 x)^2 (3+5 x)^2}{2+3 x} \, dx=\frac {25}{3} \, x^{4} - \frac {140}{27} \, x^{3} - \frac {251}{54} \, x^{2} + \frac {340}{81} \, x + \frac {49}{243} \, \log \left (3 \, x + 2\right ) \]
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Time = 0.28 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.76 \[ \int \frac {(1-2 x)^2 (3+5 x)^2}{2+3 x} \, dx=\frac {25}{3} \, x^{4} - \frac {140}{27} \, x^{3} - \frac {251}{54} \, x^{2} + \frac {340}{81} \, x + \frac {49}{243} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.68 \[ \int \frac {(1-2 x)^2 (3+5 x)^2}{2+3 x} \, dx=\frac {340\,x}{81}+\frac {49\,\ln \left (x+\frac {2}{3}\right )}{243}-\frac {251\,x^2}{54}-\frac {140\,x^3}{27}+\frac {25\,x^4}{3} \]
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