Integrand size = 22, antiderivative size = 78 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^3 \, dx=-\frac {343 (2+3 x)^8}{17496}+\frac {1813 (2+3 x)^9}{6561}-\frac {10073 (2+3 x)^{10}}{7290}+\frac {66193 (2+3 x)^{11}}{24057}-\frac {7195 (2+3 x)^{12}}{4374}+\frac {3700 (2+3 x)^{13}}{9477}-\frac {500 (2+3 x)^{14}}{15309} \]
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Time = 0.02 (sec) , antiderivative size = 78, 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} \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^3 \, dx=-\frac {500 (3 x+2)^{14}}{15309}+\frac {3700 (3 x+2)^{13}}{9477}-\frac {7195 (3 x+2)^{12}}{4374}+\frac {66193 (3 x+2)^{11}}{24057}-\frac {10073 (3 x+2)^{10}}{7290}+\frac {1813 (3 x+2)^9}{6561}-\frac {343 (3 x+2)^8}{17496} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {343}{729} (2+3 x)^7+\frac {1813}{243} (2+3 x)^8-\frac {10073}{243} (2+3 x)^9+\frac {66193}{729} (2+3 x)^{10}-\frac {14390}{243} (2+3 x)^{11}+\frac {3700}{243} (2+3 x)^{12}-\frac {1000}{729} (2+3 x)^{13}\right ) \, dx \\ & = -\frac {343 (2+3 x)^8}{17496}+\frac {1813 (2+3 x)^9}{6561}-\frac {10073 (2+3 x)^{10}}{7290}+\frac {66193 (2+3 x)^{11}}{24057}-\frac {7195 (2+3 x)^{12}}{4374}+\frac {3700 (2+3 x)^{13}}{9477}-\frac {500 (2+3 x)^{14}}{15309} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 85, normalized size of antiderivative = 1.09 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^3 \, dx=3456 x+16416 x^2+31200 x^3-20732 x^4-\frac {1022472 x^5}{5}-299014 x^6+\frac {1241998 x^7}{7}+\frac {8511675 x^8}{8}+1119837 x^9-\frac {2909493 x^{10}}{10}-\frac {19532907 x^{11}}{11}-\frac {3595185 x^{12}}{2}-\frac {10862100 x^{13}}{13}-\frac {1093500 x^{14}}{7} \]
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Time = 2.40 (sec) , antiderivative size = 69, normalized size of antiderivative = 0.88
method | result | size |
gosper | \(-\frac {x \left (6254820000 x^{13}+33455268000 x^{12}+71975603700 x^{11}+71099781480 x^{10}+11649609972 x^{9}-44838273480 x^{8}-42600933375 x^{7}-7104228560 x^{6}+11972520560 x^{5}+8187955776 x^{4}+830109280 x^{3}-1249248000 x^{2}-657296640 x -138378240\right )}{40040}\) | \(69\) |
default | \(-\frac {1093500}{7} x^{14}-\frac {10862100}{13} x^{13}-\frac {3595185}{2} x^{12}-\frac {19532907}{11} x^{11}-\frac {2909493}{10} x^{10}+1119837 x^{9}+\frac {8511675}{8} x^{8}+\frac {1241998}{7} x^{7}-299014 x^{6}-\frac {1022472}{5} x^{5}-20732 x^{4}+31200 x^{3}+16416 x^{2}+3456 x\) | \(70\) |
norman | \(-\frac {1093500}{7} x^{14}-\frac {10862100}{13} x^{13}-\frac {3595185}{2} x^{12}-\frac {19532907}{11} x^{11}-\frac {2909493}{10} x^{10}+1119837 x^{9}+\frac {8511675}{8} x^{8}+\frac {1241998}{7} x^{7}-299014 x^{6}-\frac {1022472}{5} x^{5}-20732 x^{4}+31200 x^{3}+16416 x^{2}+3456 x\) | \(70\) |
risch | \(-\frac {1093500}{7} x^{14}-\frac {10862100}{13} x^{13}-\frac {3595185}{2} x^{12}-\frac {19532907}{11} x^{11}-\frac {2909493}{10} x^{10}+1119837 x^{9}+\frac {8511675}{8} x^{8}+\frac {1241998}{7} x^{7}-299014 x^{6}-\frac {1022472}{5} x^{5}-20732 x^{4}+31200 x^{3}+16416 x^{2}+3456 x\) | \(70\) |
parallelrisch | \(-\frac {1093500}{7} x^{14}-\frac {10862100}{13} x^{13}-\frac {3595185}{2} x^{12}-\frac {19532907}{11} x^{11}-\frac {2909493}{10} x^{10}+1119837 x^{9}+\frac {8511675}{8} x^{8}+\frac {1241998}{7} x^{7}-299014 x^{6}-\frac {1022472}{5} x^{5}-20732 x^{4}+31200 x^{3}+16416 x^{2}+3456 x\) | \(70\) |
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Time = 0.22 (sec) , antiderivative size = 69, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^3 \, dx=-\frac {1093500}{7} \, x^{14} - \frac {10862100}{13} \, x^{13} - \frac {3595185}{2} \, x^{12} - \frac {19532907}{11} \, x^{11} - \frac {2909493}{10} \, x^{10} + 1119837 \, x^{9} + \frac {8511675}{8} \, x^{8} + \frac {1241998}{7} \, x^{7} - 299014 \, x^{6} - \frac {1022472}{5} \, x^{5} - 20732 \, x^{4} + 31200 \, x^{3} + 16416 \, x^{2} + 3456 \, x \]
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Time = 0.03 (sec) , antiderivative size = 82, normalized size of antiderivative = 1.05 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^3 \, dx=- \frac {1093500 x^{14}}{7} - \frac {10862100 x^{13}}{13} - \frac {3595185 x^{12}}{2} - \frac {19532907 x^{11}}{11} - \frac {2909493 x^{10}}{10} + 1119837 x^{9} + \frac {8511675 x^{8}}{8} + \frac {1241998 x^{7}}{7} - 299014 x^{6} - \frac {1022472 x^{5}}{5} - 20732 x^{4} + 31200 x^{3} + 16416 x^{2} + 3456 x \]
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Time = 0.20 (sec) , antiderivative size = 69, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^3 \, dx=-\frac {1093500}{7} \, x^{14} - \frac {10862100}{13} \, x^{13} - \frac {3595185}{2} \, x^{12} - \frac {19532907}{11} \, x^{11} - \frac {2909493}{10} \, x^{10} + 1119837 \, x^{9} + \frac {8511675}{8} \, x^{8} + \frac {1241998}{7} \, x^{7} - 299014 \, x^{6} - \frac {1022472}{5} \, x^{5} - 20732 \, x^{4} + 31200 \, x^{3} + 16416 \, x^{2} + 3456 \, x \]
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Time = 0.29 (sec) , antiderivative size = 69, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^3 \, dx=-\frac {1093500}{7} \, x^{14} - \frac {10862100}{13} \, x^{13} - \frac {3595185}{2} \, x^{12} - \frac {19532907}{11} \, x^{11} - \frac {2909493}{10} \, x^{10} + 1119837 \, x^{9} + \frac {8511675}{8} \, x^{8} + \frac {1241998}{7} \, x^{7} - 299014 \, x^{6} - \frac {1022472}{5} \, x^{5} - 20732 \, x^{4} + 31200 \, x^{3} + 16416 \, x^{2} + 3456 \, x \]
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Time = 0.17 (sec) , antiderivative size = 69, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^3 \, dx=-\frac {1093500\,x^{14}}{7}-\frac {10862100\,x^{13}}{13}-\frac {3595185\,x^{12}}{2}-\frac {19532907\,x^{11}}{11}-\frac {2909493\,x^{10}}{10}+1119837\,x^9+\frac {8511675\,x^8}{8}+\frac {1241998\,x^7}{7}-299014\,x^6-\frac {1022472\,x^5}{5}-20732\,x^4+31200\,x^3+16416\,x^2+3456\,x \]
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