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 = 0.0355555, antiderivative size = 67, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0025085, 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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Maple [A] time = 0.001, size = 70, normalized size = 1. \begin{align*}{\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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.25272, size = 93, normalized size = 1.39 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49451, size = 289, normalized size = 4.31 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.077867, size = 82, normalized size = 1.22 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.51176, size = 93, normalized size = 1.39 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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