Integrand size = 20, antiderivative size = 45 \[ \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^3} \, dx=\frac {175 x}{27}-\frac {125 x^2}{27}+\frac {7}{486 (2+3 x)^2}-\frac {107}{243 (2+3 x)}-\frac {185}{81} \log (2+3 x) \]
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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} \[ \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^3} \, dx=-\frac {125 x^2}{27}+\frac {175 x}{27}-\frac {107}{243 (3 x+2)}+\frac {7}{486 (3 x+2)^2}-\frac {185}{81} \log (3 x+2) \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {175}{27}-\frac {250 x}{27}-\frac {7}{81 (2+3 x)^3}+\frac {107}{81 (2+3 x)^2}-\frac {185}{27 (2+3 x)}\right ) \, dx \\ & = \frac {175 x}{27}-\frac {125 x^2}{27}+\frac {7}{486 (2+3 x)^2}-\frac {107}{243 (2+3 x)}-\frac {185}{81} \log (2+3 x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.02 \[ \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^3} \, dx=\frac {3993+16386 x+18900 x^2+450 x^3-6750 x^4-370 (2+3 x)^2 \log (2+3 x)}{162 (2+3 x)^2} \]
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Time = 2.20 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.71
method | result | size |
risch | \(-\frac {125 x^{2}}{27}+\frac {175 x}{27}+\frac {-\frac {107 x}{81}-\frac {421}{486}}{\left (2+3 x \right )^{2}}-\frac {185 \ln \left (2+3 x \right )}{81}\) | \(32\) |
default | \(\frac {175 x}{27}-\frac {125 x^{2}}{27}+\frac {7}{486 \left (2+3 x \right )^{2}}-\frac {107}{243 \left (2+3 x \right )}-\frac {185 \ln \left (2+3 x \right )}{81}\) | \(36\) |
norman | \(\frac {\frac {1469}{54} x +\frac {1469}{24} x^{2}+\frac {25}{9} x^{3}-\frac {125}{3} x^{4}}{\left (2+3 x \right )^{2}}-\frac {185 \ln \left (2+3 x \right )}{81}\) | \(37\) |
parallelrisch | \(-\frac {27000 x^{4}+13320 \ln \left (\frac {2}{3}+x \right ) x^{2}-1800 x^{3}+17760 \ln \left (\frac {2}{3}+x \right ) x -39663 x^{2}+5920 \ln \left (\frac {2}{3}+x \right )-17628 x}{648 \left (2+3 x \right )^{2}}\) | \(51\) |
meijerg | \(\frac {27 x \left (\frac {3 x}{2}+2\right )}{16 \left (1+\frac {3 x}{2}\right )^{2}}+\frac {81 x^{2}}{16 \left (1+\frac {3 x}{2}\right )^{2}}+\frac {5 x \left (\frac {27 x}{2}+6\right )}{12 \left (1+\frac {3 x}{2}\right )^{2}}-\frac {185 \ln \left (1+\frac {3 x}{2}\right )}{81}-\frac {325 x \left (9 x^{2}+27 x +12\right )}{108 \left (1+\frac {3 x}{2}\right )^{2}}+\frac {50 x \left (-\frac {135}{8} x^{3}+45 x^{2}+135 x +60\right )}{81 \left (1+\frac {3 x}{2}\right )^{2}}\) | \(97\) |
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Time = 0.22 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.16 \[ \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^3} \, dx=-\frac {20250 \, x^{4} - 1350 \, x^{3} - 28800 \, x^{2} + 1110 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 11958 \, x + 421}{486 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
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Time = 0.05 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.80 \[ \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^3} \, dx=- \frac {125 x^{2}}{27} + \frac {175 x}{27} - \frac {642 x + 421}{4374 x^{2} + 5832 x + 1944} - \frac {185 \log {\left (3 x + 2 \right )}}{81} \]
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Time = 0.21 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.80 \[ \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^3} \, dx=-\frac {125}{27} \, x^{2} + \frac {175}{27} \, x - \frac {642 \, x + 421}{486 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac {185}{81} \, \log \left (3 \, x + 2\right ) \]
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Time = 0.27 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^3} \, dx=-\frac {125}{27} \, x^{2} + \frac {175}{27} \, x - \frac {642 \, x + 421}{486 \, {\left (3 \, x + 2\right )}^{2}} - \frac {185}{81} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^3} \, dx=\frac {175\,x}{27}-\frac {185\,\ln \left (x+\frac {2}{3}\right )}{81}-\frac {\frac {107\,x}{729}+\frac {421}{4374}}{x^2+\frac {4\,x}{3}+\frac {4}{9}}-\frac {125\,x^2}{27} \]
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