Integrand size = 20, antiderivative size = 38 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^3} \, dx=\frac {20 x}{27}+\frac {49}{162 (2+3 x)^2}-\frac {91}{27 (2+3 x)}-\frac {16}{9} \log (2+3 x) \]
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Time = 0.01 (sec) , antiderivative size = 38, 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} \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^3} \, dx=\frac {20 x}{27}-\frac {91}{27 (3 x+2)}+\frac {49}{162 (3 x+2)^2}-\frac {16}{9} \log (3 x+2) \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {20}{27}-\frac {49}{27 (2+3 x)^3}+\frac {91}{9 (2+3 x)^2}-\frac {16}{3 (2+3 x)}\right ) \, dx \\ & = \frac {20 x}{27}+\frac {49}{162 (2+3 x)^2}-\frac {91}{27 (2+3 x)}-\frac {16}{9} \log (2+3 x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.08 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^3} \, dx=\frac {-1283-1878 x+900 x^2+1080 x^3-288 (2+3 x)^2 \log (4+6 x)}{162 (2+3 x)^2} \]
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Time = 2.22 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.71
method | result | size |
risch | \(\frac {20 x}{27}+\frac {-\frac {91 x}{9}-\frac {1043}{162}}{\left (2+3 x \right )^{2}}-\frac {16 \ln \left (2+3 x \right )}{9}\) | \(27\) |
default | \(\frac {20 x}{27}+\frac {49}{162 \left (2+3 x \right )^{2}}-\frac {91}{27 \left (2+3 x \right )}-\frac {16 \ln \left (2+3 x \right )}{9}\) | \(31\) |
norman | \(\frac {\frac {73}{6} x +\frac {187}{8} x^{2}+\frac {20}{3} x^{3}}{\left (2+3 x \right )^{2}}-\frac {16 \ln \left (2+3 x \right )}{9}\) | \(32\) |
parallelrisch | \(-\frac {1152 \ln \left (\frac {2}{3}+x \right ) x^{2}-480 x^{3}+1536 \ln \left (\frac {2}{3}+x \right ) x -1683 x^{2}+512 \ln \left (\frac {2}{3}+x \right )-876 x}{72 \left (2+3 x \right )^{2}}\) | \(46\) |
meijerg | \(\frac {3 x \left (\frac {3 x}{2}+2\right )}{16 \left (1+\frac {3 x}{2}\right )^{2}}-\frac {7 x^{2}}{16 \left (1+\frac {3 x}{2}\right )^{2}}+\frac {2 x \left (\frac {27 x}{2}+6\right )}{27 \left (1+\frac {3 x}{2}\right )^{2}}-\frac {16 \ln \left (1+\frac {3 x}{2}\right )}{9}+\frac {5 x \left (9 x^{2}+27 x +12\right )}{27 \left (1+\frac {3 x}{2}\right )^{2}}\) | \(72\) |
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Time = 0.22 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.24 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^3} \, dx=\frac {1080 \, x^{3} + 1440 \, x^{2} - 288 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 1158 \, x - 1043}{162 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
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Time = 0.05 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.82 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^3} \, dx=\frac {20 x}{27} + \frac {- 1638 x - 1043}{1458 x^{2} + 1944 x + 648} - \frac {16 \log {\left (3 x + 2 \right )}}{9} \]
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Time = 0.21 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.82 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^3} \, dx=\frac {20}{27} \, x - \frac {7 \, {\left (234 \, x + 149\right )}}{162 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac {16}{9} \, \log \left (3 \, x + 2\right ) \]
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Time = 0.28 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^3} \, dx=\frac {20}{27} \, x - \frac {7 \, {\left (234 \, x + 149\right )}}{162 \, {\left (3 \, x + 2\right )}^{2}} - \frac {16}{9} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 1.17 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^3} \, dx=\frac {20\,x}{27}-\frac {16\,\ln \left (x+\frac {2}{3}\right )}{9}-\frac {\frac {91\,x}{81}+\frac {1043}{1458}}{x^2+\frac {4\,x}{3}+\frac {4}{9}} \]
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