Optimal. Leaf size=67 \[ -\frac{50 (3 x+2)^{12}}{2187}+\frac{2180 (3 x+2)^{11}}{8019}-\frac{4099 (3 x+2)^{10}}{3645}+\frac{11599 (3 x+2)^9}{6561}-\frac{931 (3 x+2)^8}{1458}+\frac{49}{729} (3 x+2)^7 \]
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Rubi [A] time = 0.0294662, 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} \[ -\frac{50 (3 x+2)^{12}}{2187}+\frac{2180 (3 x+2)^{11}}{8019}-\frac{4099 (3 x+2)^{10}}{3645}+\frac{11599 (3 x+2)^9}{6561}-\frac{931 (3 x+2)^8}{1458}+\frac{49}{729} (3 x+2)^7 \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^2 \, dx &=\int \left (\frac{343}{243} (2+3 x)^6-\frac{3724}{243} (2+3 x)^7+\frac{11599}{243} (2+3 x)^8-\frac{8198}{243} (2+3 x)^9+\frac{2180}{243} (2+3 x)^{10}-\frac{200}{243} (2+3 x)^{11}\right ) \, dx\\ &=\frac{49}{729} (2+3 x)^7-\frac{931 (2+3 x)^8}{1458}+\frac{11599 (2+3 x)^9}{6561}-\frac{4099 (2+3 x)^{10}}{3645}+\frac{2180 (2+3 x)^{11}}{8019}-\frac{50 (2+3 x)^{12}}{2187}\\ \end{align*}
Mathematica [A] time = 0.0023537, size = 71, normalized size = 1.06 \[ -12150 x^{12}-\frac{539460 x^{11}}{11}-\frac{348219 x^{10}}{5}-22695 x^9+\frac{85833 x^8}{2}+45531 x^7+\frac{13202 x^6}{3}-\frac{78132 x^5}{5}-7800 x^4+\frac{2608 x^3}{3}+1824 x^2+576 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 60, normalized size = 0.9 \begin{align*} -12150\,{x}^{12}-{\frac{539460\,{x}^{11}}{11}}-{\frac{348219\,{x}^{10}}{5}}-22695\,{x}^{9}+{\frac{85833\,{x}^{8}}{2}}+45531\,{x}^{7}+{\frac{13202\,{x}^{6}}{3}}-{\frac{78132\,{x}^{5}}{5}}-7800\,{x}^{4}+{\frac{2608\,{x}^{3}}{3}}+1824\,{x}^{2}+576\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03016, size = 80, normalized size = 1.19 \begin{align*} -12150 \, x^{12} - \frac{539460}{11} \, x^{11} - \frac{348219}{5} \, x^{10} - 22695 \, x^{9} + \frac{85833}{2} \, x^{8} + 45531 \, x^{7} + \frac{13202}{3} \, x^{6} - \frac{78132}{5} \, x^{5} - 7800 \, x^{4} + \frac{2608}{3} \, x^{3} + 1824 \, x^{2} + 576 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.1108, size = 209, normalized size = 3.12 \begin{align*} -12150 x^{12} - \frac{539460}{11} x^{11} - \frac{348219}{5} x^{10} - 22695 x^{9} + \frac{85833}{2} x^{8} + 45531 x^{7} + \frac{13202}{3} x^{6} - \frac{78132}{5} x^{5} - 7800 x^{4} + \frac{2608}{3} x^{3} + 1824 x^{2} + 576 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.072343, size = 68, normalized size = 1.01 \begin{align*} - 12150 x^{12} - \frac{539460 x^{11}}{11} - \frac{348219 x^{10}}{5} - 22695 x^{9} + \frac{85833 x^{8}}{2} + 45531 x^{7} + \frac{13202 x^{6}}{3} - \frac{78132 x^{5}}{5} - 7800 x^{4} + \frac{2608 x^{3}}{3} + 1824 x^{2} + 576 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.24727, size = 80, normalized size = 1.19 \begin{align*} -12150 \, x^{12} - \frac{539460}{11} \, x^{11} - \frac{348219}{5} \, x^{10} - 22695 \, x^{9} + \frac{85833}{2} \, x^{8} + 45531 \, x^{7} + \frac{13202}{3} \, x^{6} - \frac{78132}{5} \, x^{5} - 7800 \, x^{4} + \frac{2608}{3} \, x^{3} + 1824 \, x^{2} + 576 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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