Integrand size = 22, antiderivative size = 52 \[ \int \frac {(1-2 x)^2 (2+3 x)^3}{(3+5 x)^3} \, dx=-\frac {153 x}{3125}-\frac {216 x^2}{625}+\frac {36 x^3}{125}-\frac {121}{31250 (3+5 x)^2}-\frac {209}{3125 (3+5 x)}+\frac {23}{125} \log (3+5 x) \]
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Time = 0.02 (sec) , antiderivative size = 52, 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} \[ \int \frac {(1-2 x)^2 (2+3 x)^3}{(3+5 x)^3} \, dx=\frac {36 x^3}{125}-\frac {216 x^2}{625}-\frac {153 x}{3125}-\frac {209}{3125 (5 x+3)}-\frac {121}{31250 (5 x+3)^2}+\frac {23}{125} \log (5 x+3) \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {153}{3125}-\frac {432 x}{625}+\frac {108 x^2}{125}+\frac {121}{3125 (3+5 x)^3}+\frac {209}{625 (3+5 x)^2}+\frac {23}{25 (3+5 x)}\right ) \, dx \\ & = -\frac {153 x}{3125}-\frac {216 x^2}{625}+\frac {36 x^3}{125}-\frac {121}{31250 (3+5 x)^2}-\frac {209}{3125 (3+5 x)}+\frac {23}{125} \log (3+5 x) \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.92 \[ \int \frac {(1-2 x)^2 (2+3 x)^3}{(3+5 x)^3} \, dx=\frac {7567+24640 x-4050 x^2-56250 x^3+45000 x^5+1150 (3+5 x)^2 \log (6 (3+5 x))}{6250 (3+5 x)^2} \]
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Time = 2.36 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.71
method | result | size |
norman | \(\frac {-\frac {7}{75} x -\frac {361}{90} x^{2}-9 x^{3}+\frac {36}{5} x^{5}}{\left (3+5 x \right )^{2}}+\frac {23 \ln \left (3+5 x \right )}{125}\) | \(37\) |
risch | \(\frac {36 x^{3}}{125}-\frac {216 x^{2}}{625}-\frac {153 x}{3125}+\frac {-\frac {209 x}{625}-\frac {6391}{31250}}{\left (3+5 x \right )^{2}}+\frac {23 \ln \left (3+5 x \right )}{125}\) | \(37\) |
default | \(-\frac {153 x}{3125}-\frac {216 x^{2}}{625}+\frac {36 x^{3}}{125}-\frac {121}{31250 \left (3+5 x \right )^{2}}-\frac {209}{3125 \left (3+5 x \right )}+\frac {23 \ln \left (3+5 x \right )}{125}\) | \(41\) |
parallelrisch | \(\frac {16200 x^{5}+10350 \ln \left (x +\frac {3}{5}\right ) x^{2}-20250 x^{3}+12420 \ln \left (x +\frac {3}{5}\right ) x -9025 x^{2}+3726 \ln \left (x +\frac {3}{5}\right )-210 x}{2250 \left (3+5 x \right )^{2}}\) | \(51\) |
meijerg | \(\frac {4 x \left (\frac {5 x}{3}+2\right )}{27 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {2 x^{2}}{27 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {29 x \left (15 x +6\right )}{225 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {23 \ln \left (1+\frac {5 x}{3}\right )}{125}-\frac {9 x \left (\frac {100}{9} x^{2}+30 x +12\right )}{100 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {162 x \left (-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {162 x \left (\frac {1250}{81} x^{4}-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )^{2}}\) | \(127\) |
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Time = 0.22 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.00 \[ \int \frac {(1-2 x)^2 (2+3 x)^3}{(3+5 x)^3} \, dx=\frac {225000 \, x^{5} - 281250 \, x^{3} - 143100 \, x^{2} + 5750 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 24220 \, x - 6391}{31250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
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Time = 0.06 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.85 \[ \int \frac {(1-2 x)^2 (2+3 x)^3}{(3+5 x)^3} \, dx=\frac {36 x^{3}}{125} - \frac {216 x^{2}}{625} - \frac {153 x}{3125} + \frac {- 10450 x - 6391}{781250 x^{2} + 937500 x + 281250} + \frac {23 \log {\left (5 x + 3 \right )}}{125} \]
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Time = 0.20 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.79 \[ \int \frac {(1-2 x)^2 (2+3 x)^3}{(3+5 x)^3} \, dx=\frac {36}{125} \, x^{3} - \frac {216}{625} \, x^{2} - \frac {153}{3125} \, x - \frac {11 \, {\left (950 \, x + 581\right )}}{31250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {23}{125} \, \log \left (5 \, x + 3\right ) \]
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Time = 0.28 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^2 (2+3 x)^3}{(3+5 x)^3} \, dx=\frac {36}{125} \, x^{3} - \frac {216}{625} \, x^{2} - \frac {153}{3125} \, x - \frac {11 \, {\left (950 \, x + 581\right )}}{31250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {23}{125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
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Time = 0.03 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^2 (2+3 x)^3}{(3+5 x)^3} \, dx=\frac {23\,\ln \left (x+\frac {3}{5}\right )}{125}-\frac {153\,x}{3125}-\frac {\frac {209\,x}{15625}+\frac {6391}{781250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}-\frac {216\,x^2}{625}+\frac {36\,x^3}{125} \]
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