Integrand size = 20, antiderivative size = 56 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x) \, dx=-\frac {49}{243} (2+3 x)^7+\frac {2009 (2+3 x)^8}{1944}-\frac {518}{729} (2+3 x)^9+\frac {214 (2+3 x)^{10}}{1215}-\frac {40 (2+3 x)^{11}}{2673} \]
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Time = 0.02 (sec) , antiderivative size = 56, 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} \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x) \, dx=-\frac {40 (3 x+2)^{11}}{2673}+\frac {214 (3 x+2)^{10}}{1215}-\frac {518}{729} (3 x+2)^9+\frac {2009 (3 x+2)^8}{1944}-\frac {49}{243} (3 x+2)^7 \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {343}{81} (2+3 x)^6+\frac {2009}{81} (2+3 x)^7-\frac {518}{27} (2+3 x)^8+\frac {428}{81} (2+3 x)^9-\frac {40}{81} (2+3 x)^{10}\right ) \, dx \\ & = -\frac {49}{243} (2+3 x)^7+\frac {2009 (2+3 x)^8}{1944}-\frac {518}{729} (2+3 x)^9+\frac {214 (2+3 x)^{10}}{1215}-\frac {40 (2+3 x)^{11}}{2673} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 62, normalized size of antiderivative = 1.11 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x) \, dx=192 x+448 x^2-208 x^3-2340 x^4-\frac {10444 x^5}{5}+4368 x^6+8937 x^7+\frac {10179 x^8}{8}-9450 x^9-\frac {45198 x^{10}}{5}-\frac {29160 x^{11}}{11} \]
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Time = 2.36 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.96
method | result | size |
gosper | \(-\frac {x \left (1166400 x^{10}+3977424 x^{9}+4158000 x^{8}-559845 x^{7}-3932280 x^{6}-1921920 x^{5}+919072 x^{4}+1029600 x^{3}+91520 x^{2}-197120 x -84480\right )}{440}\) | \(54\) |
default | \(-\frac {29160}{11} x^{11}-\frac {45198}{5} x^{10}-9450 x^{9}+\frac {10179}{8} x^{8}+8937 x^{7}+4368 x^{6}-\frac {10444}{5} x^{5}-2340 x^{4}-208 x^{3}+448 x^{2}+192 x\) | \(55\) |
norman | \(-\frac {29160}{11} x^{11}-\frac {45198}{5} x^{10}-9450 x^{9}+\frac {10179}{8} x^{8}+8937 x^{7}+4368 x^{6}-\frac {10444}{5} x^{5}-2340 x^{4}-208 x^{3}+448 x^{2}+192 x\) | \(55\) |
risch | \(-\frac {29160}{11} x^{11}-\frac {45198}{5} x^{10}-9450 x^{9}+\frac {10179}{8} x^{8}+8937 x^{7}+4368 x^{6}-\frac {10444}{5} x^{5}-2340 x^{4}-208 x^{3}+448 x^{2}+192 x\) | \(55\) |
parallelrisch | \(-\frac {29160}{11} x^{11}-\frac {45198}{5} x^{10}-9450 x^{9}+\frac {10179}{8} x^{8}+8937 x^{7}+4368 x^{6}-\frac {10444}{5} x^{5}-2340 x^{4}-208 x^{3}+448 x^{2}+192 x\) | \(55\) |
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Time = 0.22 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x) \, dx=-\frac {29160}{11} \, x^{11} - \frac {45198}{5} \, x^{10} - 9450 \, x^{9} + \frac {10179}{8} \, x^{8} + 8937 \, x^{7} + 4368 \, x^{6} - \frac {10444}{5} \, x^{5} - 2340 \, x^{4} - 208 \, x^{3} + 448 \, x^{2} + 192 \, x \]
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Time = 0.03 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.07 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x) \, dx=- \frac {29160 x^{11}}{11} - \frac {45198 x^{10}}{5} - 9450 x^{9} + \frac {10179 x^{8}}{8} + 8937 x^{7} + 4368 x^{6} - \frac {10444 x^{5}}{5} - 2340 x^{4} - 208 x^{3} + 448 x^{2} + 192 x \]
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Time = 0.22 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x) \, dx=-\frac {29160}{11} \, x^{11} - \frac {45198}{5} \, x^{10} - 9450 \, x^{9} + \frac {10179}{8} \, x^{8} + 8937 \, x^{7} + 4368 \, x^{6} - \frac {10444}{5} \, x^{5} - 2340 \, x^{4} - 208 \, x^{3} + 448 \, x^{2} + 192 \, x \]
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Time = 0.28 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x) \, dx=-\frac {29160}{11} \, x^{11} - \frac {45198}{5} \, x^{10} - 9450 \, x^{9} + \frac {10179}{8} \, x^{8} + 8937 \, x^{7} + 4368 \, x^{6} - \frac {10444}{5} \, x^{5} - 2340 \, x^{4} - 208 \, x^{3} + 448 \, x^{2} + 192 \, x \]
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Time = 0.05 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x) \, dx=-\frac {29160\,x^{11}}{11}-\frac {45198\,x^{10}}{5}-9450\,x^9+\frac {10179\,x^8}{8}+8937\,x^7+4368\,x^6-\frac {10444\,x^5}{5}-2340\,x^4-208\,x^3+448\,x^2+192\,x \]
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