Integrand size = 20, antiderivative size = 49 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^4} \, dx=-\frac {40 x}{81}+\frac {343}{729 (2+3 x)^3}-\frac {2009}{486 (2+3 x)^2}+\frac {518}{81 (2+3 x)}+\frac {428}{243} \log (2+3 x) \]
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Time = 0.01 (sec) , antiderivative size = 49, 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} \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^4} \, dx=-\frac {40 x}{81}+\frac {518}{81 (3 x+2)}-\frac {2009}{486 (3 x+2)^2}+\frac {343}{729 (3 x+2)^3}+\frac {428}{243} \log (3 x+2) \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {40}{81}-\frac {343}{81 (2+3 x)^4}+\frac {2009}{81 (2+3 x)^3}-\frac {518}{27 (2+3 x)^2}+\frac {428}{81 (2+3 x)}\right ) \, dx \\ & = -\frac {40 x}{81}+\frac {343}{729 (2+3 x)^3}-\frac {2009}{486 (2+3 x)^2}+\frac {518}{81 (2+3 x)}+\frac {428}{243} \log (2+3 x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.94 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^4} \, dx=\frac {22088+70767 x+32076 x^2-51840 x^3-19440 x^4+2568 (2+3 x)^3 \log (2+3 x)}{1458 (2+3 x)^3} \]
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Time = 2.38 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.65
method | result | size |
risch | \(-\frac {40 x}{81}+\frac {\frac {518}{9} x^{2}+\frac {10423}{162} x +\frac {12964}{729}}{\left (2+3 x \right )^{3}}+\frac {428 \ln \left (2+3 x \right )}{243}\) | \(32\) |
norman | \(\frac {-\frac {3181}{162} x -\frac {2167}{27} x^{2}-\frac {4681}{54} x^{3}-\frac {40}{3} x^{4}}{\left (2+3 x \right )^{3}}+\frac {428 \ln \left (2+3 x \right )}{243}\) | \(37\) |
default | \(-\frac {40 x}{81}+\frac {343}{729 \left (2+3 x \right )^{3}}-\frac {2009}{486 \left (2+3 x \right )^{2}}+\frac {518}{81 \left (2+3 x \right )}+\frac {428 \ln \left (2+3 x \right )}{243}\) | \(40\) |
parallelrisch | \(\frac {92448 \ln \left (\frac {2}{3}+x \right ) x^{3}-25920 x^{4}+184896 \ln \left (\frac {2}{3}+x \right ) x^{2}-168516 x^{3}+123264 \ln \left (\frac {2}{3}+x \right ) x -156024 x^{2}+27392 \ln \left (\frac {2}{3}+x \right )-38172 x}{1944 \left (2+3 x \right )^{3}}\) | \(60\) |
meijerg | \(\frac {x \left (\frac {9}{4} x^{2}+\frac {9}{2} x +3\right )}{16 \left (1+\frac {3 x}{2}\right )^{3}}-\frac {13 x^{2} \left (3+\frac {3 x}{2}\right )}{96 \left (1+\frac {3 x}{2}\right )^{3}}+\frac {x^{3}}{8 \left (1+\frac {3 x}{2}\right )^{3}}-\frac {x \left (\frac {99}{2} x^{2}+45 x +12\right )}{18 \left (1+\frac {3 x}{2}\right )^{3}}+\frac {428 \ln \left (1+\frac {3 x}{2}\right )}{243}-\frac {8 x \left (\frac {405}{8} x^{3}+\frac {495}{2} x^{2}+225 x +60\right )}{243 \left (1+\frac {3 x}{2}\right )^{3}}\) | \(104\) |
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Time = 0.23 (sec) , antiderivative size = 62, normalized size of antiderivative = 1.27 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^4} \, dx=-\frac {19440 \, x^{4} + 38880 \, x^{3} - 57996 \, x^{2} - 2568 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 88047 \, x - 25928}{1458 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]
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Time = 0.06 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.84 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^4} \, dx=- \frac {40 x}{81} - \frac {- 83916 x^{2} - 93807 x - 25928}{39366 x^{3} + 78732 x^{2} + 52488 x + 11664} + \frac {428 \log {\left (3 x + 2 \right )}}{243} \]
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Time = 0.21 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.84 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^4} \, dx=-\frac {40}{81} \, x + \frac {7 \, {\left (11988 \, x^{2} + 13401 \, x + 3704\right )}}{1458 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac {428}{243} \, \log \left (3 \, x + 2\right ) \]
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Time = 0.28 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.65 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^4} \, dx=-\frac {40}{81} \, x + \frac {7 \, {\left (11988 \, x^{2} + 13401 \, x + 3704\right )}}{1458 \, {\left (3 \, x + 2\right )}^{3}} + \frac {428}{243} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.73 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^4} \, dx=\frac {428\,\ln \left (x+\frac {2}{3}\right )}{243}-\frac {40\,x}{81}+\frac {\frac {518\,x^2}{243}+\frac {10423\,x}{4374}+\frac {12964}{19683}}{x^3+2\,x^2+\frac {4\,x}{3}+\frac {8}{27}} \]
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