Integrand size = 20, antiderivative size = 56 \[ \int (1-2 x)^3 (2+3 x)^8 (3+5 x) \, dx=-\frac {343 (2+3 x)^9}{2187}+\frac {2009 (2+3 x)^{10}}{2430}-\frac {518}{891} (2+3 x)^{11}+\frac {107}{729} (2+3 x)^{12}-\frac {40 (2+3 x)^{13}}{3159} \]
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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} \[ \int (1-2 x)^3 (2+3 x)^8 (3+5 x) \, dx=-\frac {40 (3 x+2)^{13}}{3159}+\frac {107}{729} (3 x+2)^{12}-\frac {518}{891} (3 x+2)^{11}+\frac {2009 (3 x+2)^{10}}{2430}-\frac {343 (3 x+2)^9}{2187} \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {343}{81} (2+3 x)^8+\frac {2009}{81} (2+3 x)^9-\frac {518}{27} (2+3 x)^{10}+\frac {428}{81} (2+3 x)^{11}-\frac {40}{81} (2+3 x)^{12}\right ) \, dx \\ & = -\frac {343 (2+3 x)^9}{2187}+\frac {2009 (2+3 x)^{10}}{2430}-\frac {518}{891} (2+3 x)^{11}+\frac {107}{729} (2+3 x)^{12}-\frac {40 (2+3 x)^{13}}{3159} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 72, normalized size of antiderivative = 1.29 \[ \int (1-2 x)^3 (2+3 x)^8 (3+5 x) \, dx=768 x+2944 x^2+3328 x^3-9216 x^4-\frac {159712 x^5}{5}-17456 x^6+67248 x^7+128412 x^8+38331 x^9-\frac {1290573 x^{10}}{10}-\frac {1966842 x^{11}}{11}-96957 x^{12}-\frac {262440 x^{13}}{13} \]
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Time = 2.32 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.14
method | result | size |
gosper | \(-\frac {x \left (28868400 x^{12}+138648510 x^{11}+255689460 x^{10}+184551939 x^{9}-54813330 x^{8}-183629160 x^{7}-96164640 x^{6}+24962080 x^{5}+45677632 x^{4}+13178880 x^{3}-4759040 x^{2}-4209920 x -1098240\right )}{1430}\) | \(64\) |
default | \(-\frac {262440}{13} x^{13}-96957 x^{12}-\frac {1966842}{11} x^{11}-\frac {1290573}{10} x^{10}+38331 x^{9}+128412 x^{8}+67248 x^{7}-17456 x^{6}-\frac {159712}{5} x^{5}-9216 x^{4}+3328 x^{3}+2944 x^{2}+768 x\) | \(65\) |
norman | \(-\frac {262440}{13} x^{13}-96957 x^{12}-\frac {1966842}{11} x^{11}-\frac {1290573}{10} x^{10}+38331 x^{9}+128412 x^{8}+67248 x^{7}-17456 x^{6}-\frac {159712}{5} x^{5}-9216 x^{4}+3328 x^{3}+2944 x^{2}+768 x\) | \(65\) |
risch | \(-\frac {262440}{13} x^{13}-96957 x^{12}-\frac {1966842}{11} x^{11}-\frac {1290573}{10} x^{10}+38331 x^{9}+128412 x^{8}+67248 x^{7}-17456 x^{6}-\frac {159712}{5} x^{5}-9216 x^{4}+3328 x^{3}+2944 x^{2}+768 x\) | \(65\) |
parallelrisch | \(-\frac {262440}{13} x^{13}-96957 x^{12}-\frac {1966842}{11} x^{11}-\frac {1290573}{10} x^{10}+38331 x^{9}+128412 x^{8}+67248 x^{7}-17456 x^{6}-\frac {159712}{5} x^{5}-9216 x^{4}+3328 x^{3}+2944 x^{2}+768 x\) | \(65\) |
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Time = 0.22 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.14 \[ \int (1-2 x)^3 (2+3 x)^8 (3+5 x) \, dx=-\frac {262440}{13} \, x^{13} - 96957 \, x^{12} - \frac {1966842}{11} \, x^{11} - \frac {1290573}{10} \, x^{10} + 38331 \, x^{9} + 128412 \, x^{8} + 67248 \, x^{7} - 17456 \, x^{6} - \frac {159712}{5} \, x^{5} - 9216 \, x^{4} + 3328 \, x^{3} + 2944 \, x^{2} + 768 \, x \]
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Time = 0.03 (sec) , antiderivative size = 70, normalized size of antiderivative = 1.25 \[ \int (1-2 x)^3 (2+3 x)^8 (3+5 x) \, dx=- \frac {262440 x^{13}}{13} - 96957 x^{12} - \frac {1966842 x^{11}}{11} - \frac {1290573 x^{10}}{10} + 38331 x^{9} + 128412 x^{8} + 67248 x^{7} - 17456 x^{6} - \frac {159712 x^{5}}{5} - 9216 x^{4} + 3328 x^{3} + 2944 x^{2} + 768 x \]
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Time = 0.21 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.14 \[ \int (1-2 x)^3 (2+3 x)^8 (3+5 x) \, dx=-\frac {262440}{13} \, x^{13} - 96957 \, x^{12} - \frac {1966842}{11} \, x^{11} - \frac {1290573}{10} \, x^{10} + 38331 \, x^{9} + 128412 \, x^{8} + 67248 \, x^{7} - 17456 \, x^{6} - \frac {159712}{5} \, x^{5} - 9216 \, x^{4} + 3328 \, x^{3} + 2944 \, x^{2} + 768 \, x \]
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Time = 0.28 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.14 \[ \int (1-2 x)^3 (2+3 x)^8 (3+5 x) \, dx=-\frac {262440}{13} \, x^{13} - 96957 \, x^{12} - \frac {1966842}{11} \, x^{11} - \frac {1290573}{10} \, x^{10} + 38331 \, x^{9} + 128412 \, x^{8} + 67248 \, x^{7} - 17456 \, x^{6} - \frac {159712}{5} \, x^{5} - 9216 \, x^{4} + 3328 \, x^{3} + 2944 \, x^{2} + 768 \, x \]
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Time = 0.08 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.14 \[ \int (1-2 x)^3 (2+3 x)^8 (3+5 x) \, dx=-\frac {262440\,x^{13}}{13}-96957\,x^{12}-\frac {1966842\,x^{11}}{11}-\frac {1290573\,x^{10}}{10}+38331\,x^9+128412\,x^8+67248\,x^7-17456\,x^6-\frac {159712\,x^5}{5}-9216\,x^4+3328\,x^3+2944\,x^2+768\,x \]
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