Integrand size = 22, antiderivative size = 45 \[ \int \frac {(1-2 x)^2 (2+3 x)^2}{(3+5 x)^3} \, dx=-\frac {264 x}{625}+\frac {18 x^2}{125}-\frac {121}{6250 (3+5 x)^2}-\frac {682}{3125 (3+5 x)}+\frac {829 \log (3+5 x)}{3125} \]
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Time = 0.02 (sec) , antiderivative size = 45, 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} \[ \int \frac {(1-2 x)^2 (2+3 x)^2}{(3+5 x)^3} \, dx=\frac {18 x^2}{125}-\frac {264 x}{625}-\frac {682}{3125 (5 x+3)}-\frac {121}{6250 (5 x+3)^2}+\frac {829 \log (5 x+3)}{3125} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {264}{625}+\frac {36 x}{125}+\frac {121}{625 (3+5 x)^3}+\frac {682}{625 (3+5 x)^2}+\frac {829}{625 (3+5 x)}\right ) \, dx \\ & = -\frac {264 x}{625}+\frac {18 x^2}{125}-\frac {121}{6250 (3+5 x)^2}-\frac {682}{3125 (3+5 x)}+\frac {829 \log (3+5 x)}{3125} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.93 \[ \int \frac {(1-2 x)^2 (2+3 x)^2}{(3+5 x)^3} \, dx=\frac {\frac {5 \left (-4277-17564 x-23760 x^2-7800 x^3+4500 x^4\right )}{(3+5 x)^2}+1658 \log (3+5 x)}{6250} \]
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Time = 2.37 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.71
method | result | size |
risch | \(\frac {18 x^{2}}{125}-\frac {264 x}{625}+\frac {-\frac {682 x}{625}-\frac {4213}{6250}}{\left (3+5 x \right )^{2}}+\frac {829 \ln \left (3+5 x \right )}{3125}\) | \(32\) |
default | \(-\frac {264 x}{625}+\frac {18 x^{2}}{125}-\frac {121}{6250 \left (3+5 x \right )^{2}}-\frac {682}{3125 \left (3+5 x \right )}+\frac {829 \ln \left (3+5 x \right )}{3125}\) | \(36\) |
norman | \(\frac {-\frac {4961}{1875} x -\frac {21383}{2250} x^{2}-\frac {156}{25} x^{3}+\frac {18}{5} x^{4}}{\left (3+5 x \right )^{2}}+\frac {829 \ln \left (3+5 x \right )}{3125}\) | \(37\) |
parallelrisch | \(\frac {202500 x^{4}+373050 \ln \left (x +\frac {3}{5}\right ) x^{2}-351000 x^{3}+447660 \ln \left (x +\frac {3}{5}\right ) x -534575 x^{2}+134298 \ln \left (x +\frac {3}{5}\right )-148830 x}{56250 \left (3+5 x \right )^{2}}\) | \(51\) |
meijerg | \(\frac {2 x \left (\frac {5 x}{3}+2\right )}{27 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {2 x^{2}}{27 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {23 x \left (15 x +6\right )}{450 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {829 \ln \left (1+\frac {5 x}{3}\right )}{3125}+\frac {3 x \left (\frac {100}{9} x^{2}+30 x +12\right )}{125 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {54 x \left (-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )^{2}}\) | \(97\) |
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Time = 0.22 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.16 \[ \int \frac {(1-2 x)^2 (2+3 x)^2}{(3+5 x)^3} \, dx=\frac {22500 \, x^{4} - 39000 \, x^{3} - 71100 \, x^{2} + 1658 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 30580 \, x - 4213}{6250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
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Time = 0.06 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.82 \[ \int \frac {(1-2 x)^2 (2+3 x)^2}{(3+5 x)^3} \, dx=\frac {18 x^{2}}{125} - \frac {264 x}{625} + \frac {- 6820 x - 4213}{156250 x^{2} + 187500 x + 56250} + \frac {829 \log {\left (5 x + 3 \right )}}{3125} \]
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Time = 0.20 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.80 \[ \int \frac {(1-2 x)^2 (2+3 x)^2}{(3+5 x)^3} \, dx=\frac {18}{125} \, x^{2} - \frac {264}{625} \, x - \frac {11 \, {\left (620 \, x + 383\right )}}{6250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {829}{3125} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.30 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^2 (2+3 x)^2}{(3+5 x)^3} \, dx=\frac {18}{125} \, x^{2} - \frac {264}{625} \, x - \frac {11 \, {\left (620 \, x + 383\right )}}{6250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {829}{3125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^2 (2+3 x)^2}{(3+5 x)^3} \, dx=\frac {829\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {264\,x}{625}-\frac {\frac {682\,x}{15625}+\frac {4213}{156250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}+\frac {18\,x^2}{125} \]
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