Integrand size = 20, antiderivative size = 45 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x) \, dx=-\frac {49}{486} (2+3 x)^6+\frac {13}{27} (2+3 x)^7-\frac {2}{9} (2+3 x)^8+\frac {20}{729} (2+3 x)^9 \]
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Time = 0.01 (sec) , antiderivative size = 45, 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} \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x) \, dx=\frac {20}{729} (3 x+2)^9-\frac {2}{9} (3 x+2)^8+\frac {13}{27} (3 x+2)^7-\frac {49}{486} (3 x+2)^6 \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {49}{27} (2+3 x)^5+\frac {91}{9} (2+3 x)^6-\frac {16}{3} (2+3 x)^7+\frac {20}{27} (2+3 x)^8\right ) \, dx \\ & = -\frac {49}{486} (2+3 x)^6+\frac {13}{27} (2+3 x)^7-\frac {2}{9} (2+3 x)^8+\frac {20}{729} (2+3 x)^9 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.07 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x) \, dx=96 x+248 x^2+\frac {224 x^3}{3}-770 x^4-1218 x^5+\frac {273 x^6}{2}+1917 x^7+1782 x^8+540 x^9 \]
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Time = 2.22 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.98
method | result | size |
gosper | \(\frac {x \left (3240 x^{8}+10692 x^{7}+11502 x^{6}+819 x^{5}-7308 x^{4}-4620 x^{3}+448 x^{2}+1488 x +576\right )}{6}\) | \(44\) |
default | \(540 x^{9}+1782 x^{8}+1917 x^{7}+\frac {273}{2} x^{6}-1218 x^{5}-770 x^{4}+\frac {224}{3} x^{3}+248 x^{2}+96 x\) | \(45\) |
norman | \(540 x^{9}+1782 x^{8}+1917 x^{7}+\frac {273}{2} x^{6}-1218 x^{5}-770 x^{4}+\frac {224}{3} x^{3}+248 x^{2}+96 x\) | \(45\) |
risch | \(540 x^{9}+1782 x^{8}+1917 x^{7}+\frac {273}{2} x^{6}-1218 x^{5}-770 x^{4}+\frac {224}{3} x^{3}+248 x^{2}+96 x\) | \(45\) |
parallelrisch | \(540 x^{9}+1782 x^{8}+1917 x^{7}+\frac {273}{2} x^{6}-1218 x^{5}-770 x^{4}+\frac {224}{3} x^{3}+248 x^{2}+96 x\) | \(45\) |
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Time = 0.21 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.98 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x) \, dx=540 \, x^{9} + 1782 \, x^{8} + 1917 \, x^{7} + \frac {273}{2} \, x^{6} - 1218 \, x^{5} - 770 \, x^{4} + \frac {224}{3} \, x^{3} + 248 \, x^{2} + 96 \, x \]
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Time = 0.02 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.02 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x) \, dx=540 x^{9} + 1782 x^{8} + 1917 x^{7} + \frac {273 x^{6}}{2} - 1218 x^{5} - 770 x^{4} + \frac {224 x^{3}}{3} + 248 x^{2} + 96 x \]
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Time = 0.19 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.98 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x) \, dx=540 \, x^{9} + 1782 \, x^{8} + 1917 \, x^{7} + \frac {273}{2} \, x^{6} - 1218 \, x^{5} - 770 \, x^{4} + \frac {224}{3} \, x^{3} + 248 \, x^{2} + 96 \, x \]
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Time = 0.27 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.98 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x) \, dx=540 \, x^{9} + 1782 \, x^{8} + 1917 \, x^{7} + \frac {273}{2} \, x^{6} - 1218 \, x^{5} - 770 \, x^{4} + \frac {224}{3} \, x^{3} + 248 \, x^{2} + 96 \, x \]
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Time = 0.04 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.98 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x) \, dx=540\,x^9+1782\,x^8+1917\,x^7+\frac {273\,x^6}{2}-1218\,x^5-770\,x^4+\frac {224\,x^3}{3}+248\,x^2+96\,x \]
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