Integrand size = 20, antiderivative size = 49 \[ \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^4} \, dx=-\frac {250 x}{81}+\frac {7}{729 (2+3 x)^3}-\frac {107}{486 (2+3 x)^2}+\frac {185}{81 (2+3 x)}+\frac {1025}{243} \log (2+3 x) \]
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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} \[ \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^4} \, dx=-\frac {250 x}{81}+\frac {185}{81 (3 x+2)}-\frac {107}{486 (3 x+2)^2}+\frac {7}{729 (3 x+2)^3}+\frac {1025}{243} \log (3 x+2) \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {250}{81}-\frac {7}{81 (2+3 x)^4}+\frac {107}{81 (2+3 x)^3}-\frac {185}{27 (2+3 x)^2}+\frac {1025}{81 (2+3 x)}\right ) \, dx \\ & = -\frac {250 x}{81}+\frac {7}{729 (2+3 x)^3}-\frac {107}{486 (2+3 x)^2}+\frac {185}{81 (2+3 x)}+\frac {1025}{243} \log (2+3 x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.96 \[ \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^4} \, dx=\frac {\frac {14}{(2+3 x)^3}-\frac {321}{(2+3 x)^2}+\frac {3330}{2+3 x}-1500 (2+3 x)+6150 \log (2+3 x)}{1458} \]
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Time = 2.20 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.65
method | result | size |
risch | \(-\frac {250 x}{81}+\frac {\frac {185}{9} x^{2}+\frac {4333}{162} x +\frac {6346}{729}}{\left (2+3 x \right )^{3}}+\frac {1025 \ln \left (2+3 x \right )}{243}\) | \(32\) |
norman | \(\frac {-\frac {8063}{54} x^{2}-\frac {6013}{162} x -\frac {21173}{108} x^{3}-\frac {250}{3} x^{4}}{\left (2+3 x \right )^{3}}+\frac {1025 \ln \left (2+3 x \right )}{243}\) | \(37\) |
default | \(-\frac {250 x}{81}+\frac {7}{729 \left (2+3 x \right )^{3}}-\frac {107}{486 \left (2+3 x \right )^{2}}+\frac {185}{81 \left (2+3 x \right )}+\frac {1025 \ln \left (2+3 x \right )}{243}\) | \(40\) |
parallelrisch | \(\frac {221400 \ln \left (\frac {2}{3}+x \right ) x^{3}-162000 x^{4}+442800 \ln \left (\frac {2}{3}+x \right ) x^{2}-381114 x^{3}+295200 \ln \left (\frac {2}{3}+x \right ) x -290268 x^{2}+65600 \ln \left (\frac {2}{3}+x \right )-72156 x}{1944 \left (2+3 x \right )^{3}}\) | \(60\) |
meijerg | \(\frac {9 x \left (\frac {9}{4} x^{2}+\frac {9}{2} x +3\right )}{16 \left (1+\frac {3 x}{2}\right )^{3}}+\frac {27 x^{2} \left (3+\frac {3 x}{2}\right )}{32 \left (1+\frac {3 x}{2}\right )^{3}}-\frac {15 x^{3}}{16 \left (1+\frac {3 x}{2}\right )^{3}}+\frac {325 x \left (\frac {99}{2} x^{2}+45 x +12\right )}{648 \left (1+\frac {3 x}{2}\right )^{3}}+\frac {1025 \ln \left (1+\frac {3 x}{2}\right )}{243}-\frac {50 x \left (\frac {405}{8} x^{3}+\frac {495}{2} x^{2}+225 x +60\right )}{243 \left (1+\frac {3 x}{2}\right )^{3}}\) | \(104\) |
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Time = 0.21 (sec) , antiderivative size = 62, normalized size of antiderivative = 1.27 \[ \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^4} \, dx=-\frac {121500 \, x^{4} + 243000 \, x^{3} + 132030 \, x^{2} - 6150 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 2997 \, x - 12692}{1458 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]
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Time = 0.06 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.84 \[ \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^4} \, dx=- \frac {250 x}{81} - \frac {- 29970 x^{2} - 38997 x - 12692}{39366 x^{3} + 78732 x^{2} + 52488 x + 11664} + \frac {1025 \log {\left (3 x + 2 \right )}}{243} \]
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Time = 0.19 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.84 \[ \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^4} \, dx=-\frac {250}{81} \, x + \frac {29970 \, x^{2} + 38997 \, x + 12692}{1458 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac {1025}{243} \, \log \left (3 \, x + 2\right ) \]
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Time = 0.27 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.65 \[ \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^4} \, dx=-\frac {250}{81} \, x + \frac {29970 \, x^{2} + 38997 \, x + 12692}{1458 \, {\left (3 \, x + 2\right )}^{3}} + \frac {1025}{243} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.73 \[ \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^4} \, dx=\frac {1025\,\ln \left (x+\frac {2}{3}\right )}{243}-\frac {250\,x}{81}+\frac {\frac {185\,x^2}{243}+\frac {4333\,x}{4374}+\frac {6346}{19683}}{x^3+2\,x^2+\frac {4\,x}{3}+\frac {8}{27}} \]
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