Optimal. Leaf size=67 \[ \frac {250 (3 x+2)^{14}}{5103}-\frac {3800 (3 x+2)^{13}}{9477}+\frac {8285 (3 x+2)^{12}}{8748}-\frac {4099 (3 x+2)^{11}}{8019}+\frac {763 (3 x+2)^{10}}{7290}-\frac {49 (3 x+2)^9}{6561} \]
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Rubi [A] time = 0.04, antiderivative size = 67, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \[ \frac {250 (3 x+2)^{14}}{5103}-\frac {3800 (3 x+2)^{13}}{9477}+\frac {8285 (3 x+2)^{12}}{8748}-\frac {4099 (3 x+2)^{11}}{8019}+\frac {763 (3 x+2)^{10}}{7290}-\frac {49 (3 x+2)^9}{6561} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^3 \, dx &=\int \left (-\frac {49}{243} (2+3 x)^8+\frac {763}{243} (2+3 x)^9-\frac {4099}{243} (2+3 x)^{10}+\frac {8285}{243} (2+3 x)^{11}-\frac {3800}{243} (2+3 x)^{12}+\frac {500}{243} (2+3 x)^{13}\right ) \, dx\\ &=-\frac {49 (2+3 x)^9}{6561}+\frac {763 (2+3 x)^{10}}{7290}-\frac {4099 (2+3 x)^{11}}{8019}+\frac {8285 (2+3 x)^{12}}{8748}-\frac {3800 (2+3 x)^{13}}{9477}+\frac {250 (2+3 x)^{14}}{5103}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 85, normalized size = 1.27 \[ \frac {1640250 x^{14}}{7}+\frac {20120400 x^{13}}{13}+\frac {17759655 x^{12}}{4}+\frac {77509953 x^{11}}{11}+\frac {62652123 x^{10}}{10}+2124195 x^9-1660896 x^8-\frac {17018256 x^7}{7}-\frac {3530000 x^6}{3}-\frac {202208 x^5}{5}+261440 x^4+155136 x^3+44928 x^2+6912 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 69, normalized size = 1.03 \[ \frac {1640250}{7} x^{14} + \frac {20120400}{13} x^{13} + \frac {17759655}{4} x^{12} + \frac {77509953}{11} x^{11} + \frac {62652123}{10} x^{10} + 2124195 x^{9} - 1660896 x^{8} - \frac {17018256}{7} x^{7} - \frac {3530000}{3} x^{6} - \frac {202208}{5} x^{5} + 261440 x^{4} + 155136 x^{3} + 44928 x^{2} + 6912 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.91, size = 69, normalized size = 1.03 \[ \frac {1640250}{7} \, x^{14} + \frac {20120400}{13} \, x^{13} + \frac {17759655}{4} \, x^{12} + \frac {77509953}{11} \, x^{11} + \frac {62652123}{10} \, x^{10} + 2124195 \, x^{9} - 1660896 \, x^{8} - \frac {17018256}{7} \, x^{7} - \frac {3530000}{3} \, x^{6} - \frac {202208}{5} \, x^{5} + 261440 \, x^{4} + 155136 \, x^{3} + 44928 \, x^{2} + 6912 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 70, normalized size = 1.04 \[ \frac {1640250}{7} x^{14}+\frac {20120400}{13} x^{13}+\frac {17759655}{4} x^{12}+\frac {77509953}{11} x^{11}+\frac {62652123}{10} x^{10}+2124195 x^{9}-1660896 x^{8}-\frac {17018256}{7} x^{7}-\frac {3530000}{3} x^{6}-\frac {202208}{5} x^{5}+261440 x^{4}+155136 x^{3}+44928 x^{2}+6912 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 69, normalized size = 1.03 \[ \frac {1640250}{7} \, x^{14} + \frac {20120400}{13} \, x^{13} + \frac {17759655}{4} \, x^{12} + \frac {77509953}{11} \, x^{11} + \frac {62652123}{10} \, x^{10} + 2124195 \, x^{9} - 1660896 \, x^{8} - \frac {17018256}{7} \, x^{7} - \frac {3530000}{3} \, x^{6} - \frac {202208}{5} \, x^{5} + 261440 \, x^{4} + 155136 \, x^{3} + 44928 \, x^{2} + 6912 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 69, normalized size = 1.03 \[ \frac {1640250\,x^{14}}{7}+\frac {20120400\,x^{13}}{13}+\frac {17759655\,x^{12}}{4}+\frac {77509953\,x^{11}}{11}+\frac {62652123\,x^{10}}{10}+2124195\,x^9-1660896\,x^8-\frac {17018256\,x^7}{7}-\frac {3530000\,x^6}{3}-\frac {202208\,x^5}{5}+261440\,x^4+155136\,x^3+44928\,x^2+6912\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 82, normalized size = 1.22 \[ \frac {1640250 x^{14}}{7} + \frac {20120400 x^{13}}{13} + \frac {17759655 x^{12}}{4} + \frac {77509953 x^{11}}{11} + \frac {62652123 x^{10}}{10} + 2124195 x^{9} - 1660896 x^{8} - \frac {17018256 x^{7}}{7} - \frac {3530000 x^{6}}{3} - \frac {202208 x^{5}}{5} + 261440 x^{4} + 155136 x^{3} + 44928 x^{2} + 6912 x \]
Verification of antiderivative is not currently implemented for this CAS.
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