Integrand size = 20, antiderivative size = 45 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^3} \, dx=\frac {116 x}{27}-\frac {20 x^2}{27}+\frac {343}{486 (2+3 x)^2}-\frac {2009}{243 (2+3 x)}-\frac {518}{81} \log (2+3 x) \]
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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, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^3} \, dx=-\frac {20 x^2}{27}+\frac {116 x}{27}-\frac {2009}{243 (3 x+2)}+\frac {343}{486 (3 x+2)^2}-\frac {518}{81} \log (3 x+2) \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {116}{27}-\frac {40 x}{27}-\frac {343}{81 (2+3 x)^3}+\frac {2009}{81 (2+3 x)^2}-\frac {518}{27 (2+3 x)}\right ) \, dx \\ & = \frac {116 x}{27}-\frac {20 x^2}{27}+\frac {343}{486 (2+3 x)^2}-\frac {2009}{243 (2+3 x)}-\frac {518}{81} \log (2+3 x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.02 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^3} \, dx=-\frac {11509+15150 x-15030 x^2-14472 x^3+3240 x^4+3108 (2+3 x)^2 \log (4+6 x)}{486 (2+3 x)^2} \]
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Time = 2.38 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.71
method | result | size |
risch | \(-\frac {20 x^{2}}{27}+\frac {116 x}{27}+\frac {-\frac {2009 x}{81}-\frac {7693}{486}}{\left (2+3 x \right )^{2}}-\frac {518 \ln \left (2+3 x \right )}{81}\) | \(32\) |
default | \(\frac {116 x}{27}-\frac {20 x^{2}}{27}+\frac {343}{486 \left (2+3 x \right )^{2}}-\frac {2009}{243 \left (2+3 x \right )}-\frac {518 \ln \left (2+3 x \right )}{81}\) | \(36\) |
norman | \(\frac {\frac {2153}{54} x +\frac {2021}{24} x^{2}+\frac {268}{9} x^{3}-\frac {20}{3} x^{4}}{\left (2+3 x \right )^{2}}-\frac {518 \ln \left (2+3 x \right )}{81}\) | \(37\) |
parallelrisch | \(-\frac {4320 x^{4}+37296 \ln \left (\frac {2}{3}+x \right ) x^{2}-19296 x^{3}+49728 \ln \left (\frac {2}{3}+x \right ) x -54567 x^{2}+16576 \ln \left (\frac {2}{3}+x \right )-25836 x}{648 \left (2+3 x \right )^{2}}\) | \(51\) |
meijerg | \(\frac {3 x \left (\frac {3 x}{2}+2\right )}{16 \left (1+\frac {3 x}{2}\right )^{2}}-\frac {13 x^{2}}{16 \left (1+\frac {3 x}{2}\right )^{2}}-\frac {x \left (\frac {27 x}{2}+6\right )}{18 \left (1+\frac {3 x}{2}\right )^{2}}-\frac {518 \ln \left (1+\frac {3 x}{2}\right )}{81}+\frac {x \left (9 x^{2}+27 x +12\right )}{3 \left (1+\frac {3 x}{2}\right )^{2}}+\frac {8 x \left (-\frac {135}{8} x^{3}+45 x^{2}+135 x +60\right )}{81 \left (1+\frac {3 x}{2}\right )^{2}}\) | \(97\) |
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Time = 0.22 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.16 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^3} \, dx=-\frac {3240 \, x^{4} - 14472 \, x^{3} - 23616 \, x^{2} + 3108 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 3702 \, x + 7693}{486 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
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Time = 0.06 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.80 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^3} \, dx=- \frac {20 x^{2}}{27} + \frac {116 x}{27} - \frac {12054 x + 7693}{4374 x^{2} + 5832 x + 1944} - \frac {518 \log {\left (3 x + 2 \right )}}{81} \]
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Time = 0.20 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.80 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^3} \, dx=-\frac {20}{27} \, x^{2} + \frac {116}{27} \, x - \frac {49 \, {\left (246 \, x + 157\right )}}{486 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac {518}{81} \, \log \left (3 \, x + 2\right ) \]
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Time = 0.28 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^3} \, dx=-\frac {20}{27} \, x^{2} + \frac {116}{27} \, x - \frac {49 \, {\left (246 \, x + 157\right )}}{486 \, {\left (3 \, x + 2\right )}^{2}} - \frac {518}{81} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^3} \, dx=\frac {116\,x}{27}-\frac {518\,\ln \left (x+\frac {2}{3}\right )}{81}-\frac {\frac {2009\,x}{729}+\frac {7693}{4374}}{x^2+\frac {4\,x}{3}+\frac {4}{9}}-\frac {20\,x^2}{27} \]
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