Integrand size = 20, antiderivative size = 56 \[ \int (1-2 x)^3 (2+3 x)^4 (3+5 x) \, dx=-\frac {343 (2+3 x)^5}{1215}+\frac {2009 (2+3 x)^6}{1458}-\frac {74}{81} (2+3 x)^7+\frac {107}{486} (2+3 x)^8-\frac {40 (2+3 x)^9}{2187} \]
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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} \[ \int (1-2 x)^3 (2+3 x)^4 (3+5 x) \, dx=-\frac {40 (3 x+2)^9}{2187}+\frac {107}{486} (3 x+2)^8-\frac {74}{81} (3 x+2)^7+\frac {2009 (3 x+2)^6}{1458}-\frac {343 (3 x+2)^5}{1215} \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {343}{81} (2+3 x)^4+\frac {2009}{81} (2+3 x)^5-\frac {518}{27} (2+3 x)^6+\frac {428}{81} (2+3 x)^7-\frac {40}{81} (2+3 x)^8\right ) \, dx \\ & = -\frac {343 (2+3 x)^5}{1215}+\frac {2009 (2+3 x)^6}{1458}-\frac {74}{81} (2+3 x)^7+\frac {107}{486} (2+3 x)^8-\frac {40 (2+3 x)^9}{2187} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 50, normalized size of antiderivative = 0.89 \[ \int (1-2 x)^3 (2+3 x)^4 (3+5 x) \, dx=48 x+40 x^2-168 x^3-252 x^4+\frac {1547 x^5}{5}+\frac {1393 x^6}{2}-54 x^7-\frac {1431 x^8}{2}-360 x^9 \]
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Time = 2.35 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.79
method | result | size |
gosper | \(-\frac {x \left (3600 x^{8}+7155 x^{7}+540 x^{6}-6965 x^{5}-3094 x^{4}+2520 x^{3}+1680 x^{2}-400 x -480\right )}{10}\) | \(44\) |
default | \(-360 x^{9}-\frac {1431}{2} x^{8}-54 x^{7}+\frac {1393}{2} x^{6}+\frac {1547}{5} x^{5}-252 x^{4}-168 x^{3}+40 x^{2}+48 x\) | \(45\) |
norman | \(-360 x^{9}-\frac {1431}{2} x^{8}-54 x^{7}+\frac {1393}{2} x^{6}+\frac {1547}{5} x^{5}-252 x^{4}-168 x^{3}+40 x^{2}+48 x\) | \(45\) |
risch | \(-360 x^{9}-\frac {1431}{2} x^{8}-54 x^{7}+\frac {1393}{2} x^{6}+\frac {1547}{5} x^{5}-252 x^{4}-168 x^{3}+40 x^{2}+48 x\) | \(45\) |
parallelrisch | \(-360 x^{9}-\frac {1431}{2} x^{8}-54 x^{7}+\frac {1393}{2} x^{6}+\frac {1547}{5} x^{5}-252 x^{4}-168 x^{3}+40 x^{2}+48 x\) | \(45\) |
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Time = 0.21 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.79 \[ \int (1-2 x)^3 (2+3 x)^4 (3+5 x) \, dx=-360 \, x^{9} - \frac {1431}{2} \, x^{8} - 54 \, x^{7} + \frac {1393}{2} \, x^{6} + \frac {1547}{5} \, x^{5} - 252 \, x^{4} - 168 \, x^{3} + 40 \, x^{2} + 48 \, x \]
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Time = 0.02 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.86 \[ \int (1-2 x)^3 (2+3 x)^4 (3+5 x) \, dx=- 360 x^{9} - \frac {1431 x^{8}}{2} - 54 x^{7} + \frac {1393 x^{6}}{2} + \frac {1547 x^{5}}{5} - 252 x^{4} - 168 x^{3} + 40 x^{2} + 48 x \]
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Time = 0.19 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.79 \[ \int (1-2 x)^3 (2+3 x)^4 (3+5 x) \, dx=-360 \, x^{9} - \frac {1431}{2} \, x^{8} - 54 \, x^{7} + \frac {1393}{2} \, x^{6} + \frac {1547}{5} \, x^{5} - 252 \, x^{4} - 168 \, x^{3} + 40 \, x^{2} + 48 \, x \]
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Time = 0.27 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.79 \[ \int (1-2 x)^3 (2+3 x)^4 (3+5 x) \, dx=-360 \, x^{9} - \frac {1431}{2} \, x^{8} - 54 \, x^{7} + \frac {1393}{2} \, x^{6} + \frac {1547}{5} \, x^{5} - 252 \, x^{4} - 168 \, x^{3} + 40 \, x^{2} + 48 \, x \]
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Time = 0.03 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.79 \[ \int (1-2 x)^3 (2+3 x)^4 (3+5 x) \, dx=-360\,x^9-\frac {1431\,x^8}{2}-54\,x^7+\frac {1393\,x^6}{2}+\frac {1547\,x^5}{5}-252\,x^4-168\,x^3+40\,x^2+48\,x \]
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