Optimal. Leaf size=67 \[ \frac{50}{729} (3 x+2)^{10}-\frac{3800 (3 x+2)^9}{6561}+\frac{8285 (3 x+2)^8}{5832}-\frac{4099 (3 x+2)^7}{5103}+\frac{763 (3 x+2)^6}{4374}-\frac{49 (3 x+2)^5}{3645} \]
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Rubi [A] time = 0.0274436, 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} \[ \frac{50}{729} (3 x+2)^{10}-\frac{3800 (3 x+2)^9}{6561}+\frac{8285 (3 x+2)^8}{5832}-\frac{4099 (3 x+2)^7}{5103}+\frac{763 (3 x+2)^6}{4374}-\frac{49 (3 x+2)^5}{3645} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^3 \, dx &=\int \left (-\frac{49}{243} (2+3 x)^4+\frac{763}{243} (2+3 x)^5-\frac{4099}{243} (2+3 x)^6+\frac{8285}{243} (2+3 x)^7-\frac{3800}{243} (2+3 x)^8+\frac{500}{243} (2+3 x)^9\right ) \, dx\\ &=-\frac{49 (2+3 x)^5}{3645}+\frac{763 (2+3 x)^6}{4374}-\frac{4099 (2+3 x)^7}{5103}+\frac{8285 (2+3 x)^8}{5832}-\frac{3800 (2+3 x)^9}{6561}+\frac{50}{729} (2+3 x)^{10}\\ \end{align*}
Mathematica [A] time = 0.002391, size = 57, normalized size = 0.85 \[ 4050 x^{10}+15600 x^9+\frac{175365 x^8}{8}+\frac{66873 x^7}{7}-\frac{46885 x^6}{6}-\frac{52853 x^5}{5}-2992 x^4+1704 x^3+1512 x^2+432 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 50, normalized size = 0.8 \begin{align*} 4050\,{x}^{10}+15600\,{x}^{9}+{\frac{175365\,{x}^{8}}{8}}+{\frac{66873\,{x}^{7}}{7}}-{\frac{46885\,{x}^{6}}{6}}-{\frac{52853\,{x}^{5}}{5}}-2992\,{x}^{4}+1704\,{x}^{3}+1512\,{x}^{2}+432\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.83487, size = 66, normalized size = 0.99 \begin{align*} 4050 \, x^{10} + 15600 \, x^{9} + \frac{175365}{8} \, x^{8} + \frac{66873}{7} \, x^{7} - \frac{46885}{6} \, x^{6} - \frac{52853}{5} \, x^{5} - 2992 \, x^{4} + 1704 \, x^{3} + 1512 \, x^{2} + 432 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.51789, size = 163, normalized size = 2.43 \begin{align*} 4050 x^{10} + 15600 x^{9} + \frac{175365}{8} x^{8} + \frac{66873}{7} x^{7} - \frac{46885}{6} x^{6} - \frac{52853}{5} x^{5} - 2992 x^{4} + 1704 x^{3} + 1512 x^{2} + 432 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.06788, size = 54, normalized size = 0.81 \begin{align*} 4050 x^{10} + 15600 x^{9} + \frac{175365 x^{8}}{8} + \frac{66873 x^{7}}{7} - \frac{46885 x^{6}}{6} - \frac{52853 x^{5}}{5} - 2992 x^{4} + 1704 x^{3} + 1512 x^{2} + 432 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 4.24283, size = 66, normalized size = 0.99 \begin{align*} 4050 \, x^{10} + 15600 \, x^{9} + \frac{175365}{8} \, x^{8} + \frac{66873}{7} \, x^{7} - \frac{46885}{6} \, x^{6} - \frac{52853}{5} \, x^{5} - 2992 \, x^{4} + 1704 \, x^{3} + 1512 \, x^{2} + 432 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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