Integrand size = 20, antiderivative size = 55 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^5} \, dx=\frac {343}{972 (2+3 x)^4}-\frac {2009}{729 (2+3 x)^3}+\frac {259}{81 (2+3 x)^2}-\frac {428}{243 (2+3 x)}-\frac {40}{243} \log (2+3 x) \]
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Time = 0.02 (sec) , antiderivative size = 55, 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} \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^5} \, dx=-\frac {428}{243 (3 x+2)}+\frac {259}{81 (3 x+2)^2}-\frac {2009}{729 (3 x+2)^3}+\frac {343}{972 (3 x+2)^4}-\frac {40}{243} \log (3 x+2) \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {343}{81 (2+3 x)^5}+\frac {2009}{81 (2+3 x)^4}-\frac {518}{27 (2+3 x)^3}+\frac {428}{81 (2+3 x)^2}-\frac {40}{81 (2+3 x)}\right ) \, dx \\ & = \frac {343}{972 (2+3 x)^4}-\frac {2009}{729 (2+3 x)^3}+\frac {259}{81 (2+3 x)^2}-\frac {428}{243 (2+3 x)}-\frac {40}{243} \log (2+3 x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.75 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^5} \, dx=-\frac {18835+97116 x+193428 x^2+138672 x^3+480 (2+3 x)^4 \log (4+6 x)}{2916 (2+3 x)^4} \]
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Time = 2.39 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.62
method | result | size |
risch | \(\frac {-\frac {428}{9} x^{3}-\frac {199}{3} x^{2}-\frac {8093}{243} x -\frac {18835}{2916}}{\left (2+3 x \right )^{4}}-\frac {40 \ln \left (2+3 x \right )}{243}\) | \(34\) |
norman | \(\frac {\frac {4507}{216} x^{2}+\frac {8563}{216} x^{3}+\frac {883}{162} x +\frac {18835}{576} x^{4}}{\left (2+3 x \right )^{4}}-\frac {40 \ln \left (2+3 x \right )}{243}\) | \(37\) |
default | \(\frac {343}{972 \left (2+3 x \right )^{4}}-\frac {2009}{729 \left (2+3 x \right )^{3}}+\frac {259}{81 \left (2+3 x \right )^{2}}-\frac {428}{243 \left (2+3 x \right )}-\frac {40 \ln \left (2+3 x \right )}{243}\) | \(46\) |
parallelrisch | \(-\frac {207360 \ln \left (\frac {2}{3}+x \right ) x^{4}+552960 \ln \left (\frac {2}{3}+x \right ) x^{3}-508545 x^{4}+552960 \ln \left (\frac {2}{3}+x \right ) x^{2}-616536 x^{3}+245760 \ln \left (\frac {2}{3}+x \right ) x -324504 x^{2}+40960 \ln \left (\frac {2}{3}+x \right )-84768 x}{15552 \left (2+3 x \right )^{4}}\) | \(69\) |
meijerg | \(\frac {3 x \left (\frac {27}{8} x^{3}+9 x^{2}+9 x +4\right )}{128 \left (1+\frac {3 x}{2}\right )^{4}}-\frac {13 x^{2} \left (\frac {9}{4} x^{2}+6 x +6\right )}{384 \left (1+\frac {3 x}{2}\right )^{4}}+\frac {x^{3} \left (\frac {3 x}{2}+4\right )}{64 \left (1+\frac {3 x}{2}\right )^{4}}+\frac {9 x^{4}}{32 \left (1+\frac {3 x}{2}\right )^{4}}+\frac {x \left (\frac {3375}{8} x^{3}+585 x^{2}+315 x +60\right )}{243 \left (1+\frac {3 x}{2}\right )^{4}}-\frac {40 \ln \left (1+\frac {3 x}{2}\right )}{243}\) | \(111\) |
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Time = 0.22 (sec) , antiderivative size = 67, normalized size of antiderivative = 1.22 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^5} \, dx=-\frac {138672 \, x^{3} + 193428 \, x^{2} + 480 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 97116 \, x + 18835}{2916 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
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Time = 0.07 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.84 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^5} \, dx=- \frac {138672 x^{3} + 193428 x^{2} + 97116 x + 18835}{236196 x^{4} + 629856 x^{3} + 629856 x^{2} + 279936 x + 46656} - \frac {40 \log {\left (3 x + 2 \right )}}{243} \]
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Time = 0.20 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.87 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^5} \, dx=-\frac {138672 \, x^{3} + 193428 \, x^{2} + 97116 \, x + 18835}{2916 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} - \frac {40}{243} \, \log \left (3 \, x + 2\right ) \]
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Time = 0.29 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.00 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^5} \, dx=-\frac {428}{243 \, {\left (3 \, x + 2\right )}} + \frac {259}{81 \, {\left (3 \, x + 2\right )}^{2}} - \frac {2009}{729 \, {\left (3 \, x + 2\right )}^{3}} + \frac {343}{972 \, {\left (3 \, x + 2\right )}^{4}} + \frac {40}{243} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) \]
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Time = 1.35 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.80 \[ \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^5} \, dx=-\frac {40\,\ln \left (x+\frac {2}{3}\right )}{243}-\frac {\frac {428\,x^3}{729}+\frac {199\,x^2}{243}+\frac {8093\,x}{19683}+\frac {18835}{236196}}{x^4+\frac {8\,x^3}{3}+\frac {8\,x^2}{3}+\frac {32\,x}{27}+\frac {16}{81}} \]
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