Integrand size = 22, antiderivative size = 67 \[ \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {7}{729} (2+3 x)^7+\frac {763 (2+3 x)^8}{5832}-\frac {4099 (2+3 x)^9}{6561}+\frac {1657 (2+3 x)^{10}}{1458}-\frac {3800 (2+3 x)^{11}}{8019}+\frac {125 (2+3 x)^{12}}{2187} \]
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Time = 0.02 (sec) , antiderivative size = 67, 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} \[ \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^3 \, dx=\frac {125 (3 x+2)^{12}}{2187}-\frac {3800 (3 x+2)^{11}}{8019}+\frac {1657 (3 x+2)^{10}}{1458}-\frac {4099 (3 x+2)^9}{6561}+\frac {763 (3 x+2)^8}{5832}-\frac {7}{729} (3 x+2)^7 \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {49}{243} (2+3 x)^6+\frac {763}{243} (2+3 x)^7-\frac {4099}{243} (2+3 x)^8+\frac {8285}{243} (2+3 x)^9-\frac {3800}{243} (2+3 x)^{10}+\frac {500}{243} (2+3 x)^{11}\right ) \, dx \\ & = -\frac {7}{729} (2+3 x)^7+\frac {763 (2+3 x)^8}{5832}-\frac {4099 (2+3 x)^9}{6561}+\frac {1657 (2+3 x)^{10}}{1458}-\frac {3800 (2+3 x)^{11}}{8019}+\frac {125 (2+3 x)^{12}}{2187} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 67, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^3 \, dx=1728 x+8640 x^2+20208 x^3+10172 x^4-61804 x^5-\frac {464744 x^6}{3}-110115 x^7+\frac {1081971 x^8}{8}+363093 x^9+\frac {685017 x^{10}}{2}+\frac {1749600 x^{11}}{11}+30375 x^{12} \]
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Time = 2.29 (sec) , antiderivative size = 59, normalized size of antiderivative = 0.88
method | result | size |
gosper | \(\frac {x \left (8019000 x^{11}+41990400 x^{10}+90422244 x^{9}+95856552 x^{8}+35705043 x^{7}-29070360 x^{6}-40897472 x^{5}-16316256 x^{4}+2685408 x^{3}+5334912 x^{2}+2280960 x +456192\right )}{264}\) | \(59\) |
default | \(30375 x^{12}+\frac {1749600}{11} x^{11}+\frac {685017}{2} x^{10}+363093 x^{9}+\frac {1081971}{8} x^{8}-110115 x^{7}-\frac {464744}{3} x^{6}-61804 x^{5}+10172 x^{4}+20208 x^{3}+8640 x^{2}+1728 x\) | \(60\) |
norman | \(30375 x^{12}+\frac {1749600}{11} x^{11}+\frac {685017}{2} x^{10}+363093 x^{9}+\frac {1081971}{8} x^{8}-110115 x^{7}-\frac {464744}{3} x^{6}-61804 x^{5}+10172 x^{4}+20208 x^{3}+8640 x^{2}+1728 x\) | \(60\) |
risch | \(30375 x^{12}+\frac {1749600}{11} x^{11}+\frac {685017}{2} x^{10}+363093 x^{9}+\frac {1081971}{8} x^{8}-110115 x^{7}-\frac {464744}{3} x^{6}-61804 x^{5}+10172 x^{4}+20208 x^{3}+8640 x^{2}+1728 x\) | \(60\) |
parallelrisch | \(30375 x^{12}+\frac {1749600}{11} x^{11}+\frac {685017}{2} x^{10}+363093 x^{9}+\frac {1081971}{8} x^{8}-110115 x^{7}-\frac {464744}{3} x^{6}-61804 x^{5}+10172 x^{4}+20208 x^{3}+8640 x^{2}+1728 x\) | \(60\) |
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Time = 0.21 (sec) , antiderivative size = 59, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^3 \, dx=30375 \, x^{12} + \frac {1749600}{11} \, x^{11} + \frac {685017}{2} \, x^{10} + 363093 \, x^{9} + \frac {1081971}{8} \, x^{8} - 110115 \, x^{7} - \frac {464744}{3} \, x^{6} - 61804 \, x^{5} + 10172 \, x^{4} + 20208 \, x^{3} + 8640 \, x^{2} + 1728 \, x \]
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Time = 0.03 (sec) , antiderivative size = 65, normalized size of antiderivative = 0.97 \[ \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^3 \, dx=30375 x^{12} + \frac {1749600 x^{11}}{11} + \frac {685017 x^{10}}{2} + 363093 x^{9} + \frac {1081971 x^{8}}{8} - 110115 x^{7} - \frac {464744 x^{6}}{3} - 61804 x^{5} + 10172 x^{4} + 20208 x^{3} + 8640 x^{2} + 1728 x \]
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Time = 0.20 (sec) , antiderivative size = 59, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^3 \, dx=30375 \, x^{12} + \frac {1749600}{11} \, x^{11} + \frac {685017}{2} \, x^{10} + 363093 \, x^{9} + \frac {1081971}{8} \, x^{8} - 110115 \, x^{7} - \frac {464744}{3} \, x^{6} - 61804 \, x^{5} + 10172 \, x^{4} + 20208 \, x^{3} + 8640 \, x^{2} + 1728 \, x \]
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Time = 0.28 (sec) , antiderivative size = 59, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^3 \, dx=30375 \, x^{12} + \frac {1749600}{11} \, x^{11} + \frac {685017}{2} \, x^{10} + 363093 \, x^{9} + \frac {1081971}{8} \, x^{8} - 110115 \, x^{7} - \frac {464744}{3} \, x^{6} - 61804 \, x^{5} + 10172 \, x^{4} + 20208 \, x^{3} + 8640 \, x^{2} + 1728 \, x \]
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Time = 0.06 (sec) , antiderivative size = 59, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^3 \, dx=30375\,x^{12}+\frac {1749600\,x^{11}}{11}+\frac {685017\,x^{10}}{2}+363093\,x^9+\frac {1081971\,x^8}{8}-110115\,x^7-\frac {464744\,x^6}{3}-61804\,x^5+10172\,x^4+20208\,x^3+8640\,x^2+1728\,x \]
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