Integrand size = 22, antiderivative size = 56 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^2 \, dx=\frac {49 (2+3 x)^8}{1944}-\frac {518 (2+3 x)^9}{2187}+\frac {503}{810} (2+3 x)^{10}-\frac {740 (2+3 x)^{11}}{2673}+\frac {25}{729} (2+3 x)^{12} \]
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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, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^2 \, dx=\frac {25}{729} (3 x+2)^{12}-\frac {740 (3 x+2)^{11}}{2673}+\frac {503}{810} (3 x+2)^{10}-\frac {518 (3 x+2)^9}{2187}+\frac {49 (3 x+2)^8}{1944} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {49}{81} (2+3 x)^7-\frac {518}{81} (2+3 x)^8+\frac {503}{27} (2+3 x)^9-\frac {740}{81} (2+3 x)^{10}+\frac {100}{81} (2+3 x)^{11}\right ) \, dx \\ & = \frac {49 (2+3 x)^8}{1944}-\frac {518 (2+3 x)^9}{2187}+\frac {503}{810} (2+3 x)^{10}-\frac {740 (2+3 x)^{11}}{2673}+\frac {25}{729} (2+3 x)^{12} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.23 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^2 \, dx=1152 x+5664 x^2+\frac {38816 x^3}{3}+5764 x^4-\frac {203752 x^5}{5}-98182 x^6-65934 x^7+\frac {719739 x^8}{8}+228996 x^9+\frac {2116287 x^{10}}{10}+\frac {1064340 x^{11}}{11}+18225 x^{12} \]
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Time = 2.27 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.05
method | result | size |
gosper | \(\frac {x \left (24057000 x^{11}+127720800 x^{10}+279349884 x^{9}+302274720 x^{8}+118756935 x^{7}-87032880 x^{6}-129600240 x^{5}-53790528 x^{4}+7608480 x^{3}+17079040 x^{2}+7476480 x +1520640\right )}{1320}\) | \(59\) |
default | \(18225 x^{12}+\frac {1064340}{11} x^{11}+\frac {2116287}{10} x^{10}+228996 x^{9}+\frac {719739}{8} x^{8}-65934 x^{7}-98182 x^{6}-\frac {203752}{5} x^{5}+5764 x^{4}+\frac {38816}{3} x^{3}+5664 x^{2}+1152 x\) | \(60\) |
norman | \(18225 x^{12}+\frac {1064340}{11} x^{11}+\frac {2116287}{10} x^{10}+228996 x^{9}+\frac {719739}{8} x^{8}-65934 x^{7}-98182 x^{6}-\frac {203752}{5} x^{5}+5764 x^{4}+\frac {38816}{3} x^{3}+5664 x^{2}+1152 x\) | \(60\) |
risch | \(18225 x^{12}+\frac {1064340}{11} x^{11}+\frac {2116287}{10} x^{10}+228996 x^{9}+\frac {719739}{8} x^{8}-65934 x^{7}-98182 x^{6}-\frac {203752}{5} x^{5}+5764 x^{4}+\frac {38816}{3} x^{3}+5664 x^{2}+1152 x\) | \(60\) |
parallelrisch | \(18225 x^{12}+\frac {1064340}{11} x^{11}+\frac {2116287}{10} x^{10}+228996 x^{9}+\frac {719739}{8} x^{8}-65934 x^{7}-98182 x^{6}-\frac {203752}{5} x^{5}+5764 x^{4}+\frac {38816}{3} x^{3}+5664 x^{2}+1152 x\) | \(60\) |
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Time = 0.22 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.05 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^2 \, dx=18225 \, x^{12} + \frac {1064340}{11} \, x^{11} + \frac {2116287}{10} \, x^{10} + 228996 \, x^{9} + \frac {719739}{8} \, x^{8} - 65934 \, x^{7} - 98182 \, x^{6} - \frac {203752}{5} \, x^{5} + 5764 \, x^{4} + \frac {38816}{3} \, x^{3} + 5664 \, x^{2} + 1152 \, x \]
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Time = 0.03 (sec) , antiderivative size = 66, normalized size of antiderivative = 1.18 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^2 \, dx=18225 x^{12} + \frac {1064340 x^{11}}{11} + \frac {2116287 x^{10}}{10} + 228996 x^{9} + \frac {719739 x^{8}}{8} - 65934 x^{7} - 98182 x^{6} - \frac {203752 x^{5}}{5} + 5764 x^{4} + \frac {38816 x^{3}}{3} + 5664 x^{2} + 1152 x \]
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Time = 0.20 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.05 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^2 \, dx=18225 \, x^{12} + \frac {1064340}{11} \, x^{11} + \frac {2116287}{10} \, x^{10} + 228996 \, x^{9} + \frac {719739}{8} \, x^{8} - 65934 \, x^{7} - 98182 \, x^{6} - \frac {203752}{5} \, x^{5} + 5764 \, x^{4} + \frac {38816}{3} \, x^{3} + 5664 \, x^{2} + 1152 \, x \]
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Time = 0.27 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.05 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^2 \, dx=18225 \, x^{12} + \frac {1064340}{11} \, x^{11} + \frac {2116287}{10} \, x^{10} + 228996 \, x^{9} + \frac {719739}{8} \, x^{8} - 65934 \, x^{7} - 98182 \, x^{6} - \frac {203752}{5} \, x^{5} + 5764 \, x^{4} + \frac {38816}{3} \, x^{3} + 5664 \, x^{2} + 1152 \, x \]
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Time = 0.06 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.05 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^2 \, dx=18225\,x^{12}+\frac {1064340\,x^{11}}{11}+\frac {2116287\,x^{10}}{10}+228996\,x^9+\frac {719739\,x^8}{8}-65934\,x^7-98182\,x^6-\frac {203752\,x^5}{5}+5764\,x^4+\frac {38816\,x^3}{3}+5664\,x^2+1152\,x \]
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