Optimal. Leaf size=67 \[ \frac{125 (3 x+2)^{12}}{2187}-\frac{3800 (3 x+2)^{11}}{8019}+\frac{1657 (3 x+2)^{10}}{1458}-\frac{4099 (3 x+2)^9}{6561}+\frac{763 (3 x+2)^8}{5832}-\frac{7}{729} (3 x+2)^7 \]
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Rubi [A] time = 0.0311978, 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} \[ \frac{125 (3 x+2)^{12}}{2187}-\frac{3800 (3 x+2)^{11}}{8019}+\frac{1657 (3 x+2)^{10}}{1458}-\frac{4099 (3 x+2)^9}{6561}+\frac{763 (3 x+2)^8}{5832}-\frac{7}{729} (3 x+2)^7 \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^3 \, dx &=\int \left (-\frac{49}{243} (2+3 x)^6+\frac{763}{243} (2+3 x)^7-\frac{4099}{243} (2+3 x)^8+\frac{8285}{243} (2+3 x)^9-\frac{3800}{243} (2+3 x)^{10}+\frac{500}{243} (2+3 x)^{11}\right ) \, dx\\ &=-\frac{7}{729} (2+3 x)^7+\frac{763 (2+3 x)^8}{5832}-\frac{4099 (2+3 x)^9}{6561}+\frac{1657 (2+3 x)^{10}}{1458}-\frac{3800 (2+3 x)^{11}}{8019}+\frac{125 (2+3 x)^{12}}{2187}\\ \end{align*}
Mathematica [A] time = 0.0024754, size = 67, normalized size = 1. \[ 30375 x^{12}+\frac{1749600 x^{11}}{11}+\frac{685017 x^{10}}{2}+363093 x^9+\frac{1081971 x^8}{8}-110115 x^7-\frac{464744 x^6}{3}-61804 x^5+10172 x^4+20208 x^3+8640 x^2+1728 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 60, normalized size = 0.9 \begin{align*} 30375\,{x}^{12}+{\frac{1749600\,{x}^{11}}{11}}+{\frac{685017\,{x}^{10}}{2}}+363093\,{x}^{9}+{\frac{1081971\,{x}^{8}}{8}}-110115\,{x}^{7}-{\frac{464744\,{x}^{6}}{3}}-61804\,{x}^{5}+10172\,{x}^{4}+20208\,{x}^{3}+8640\,{x}^{2}+1728\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03213, size = 80, normalized size = 1.19 \begin{align*} 30375 \, x^{12} + \frac{1749600}{11} \, x^{11} + \frac{685017}{2} \, x^{10} + 363093 \, x^{9} + \frac{1081971}{8} \, x^{8} - 110115 \, x^{7} - \frac{464744}{3} \, x^{6} - 61804 \, x^{5} + 10172 \, x^{4} + 20208 \, x^{3} + 8640 \, x^{2} + 1728 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.5488, size = 215, normalized size = 3.21 \begin{align*} 30375 x^{12} + \frac{1749600}{11} x^{11} + \frac{685017}{2} x^{10} + 363093 x^{9} + \frac{1081971}{8} x^{8} - 110115 x^{7} - \frac{464744}{3} x^{6} - 61804 x^{5} + 10172 x^{4} + 20208 x^{3} + 8640 x^{2} + 1728 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.073613, size = 65, normalized size = 0.97 \begin{align*} 30375 x^{12} + \frac{1749600 x^{11}}{11} + \frac{685017 x^{10}}{2} + 363093 x^{9} + \frac{1081971 x^{8}}{8} - 110115 x^{7} - \frac{464744 x^{6}}{3} - 61804 x^{5} + 10172 x^{4} + 20208 x^{3} + 8640 x^{2} + 1728 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.3954, size = 80, normalized size = 1.19 \begin{align*} 30375 \, x^{12} + \frac{1749600}{11} \, x^{11} + \frac{685017}{2} \, x^{10} + 363093 \, x^{9} + \frac{1081971}{8} \, x^{8} - 110115 \, x^{7} - \frac{464744}{3} \, x^{6} - 61804 \, x^{5} + 10172 \, x^{4} + 20208 \, x^{3} + 8640 \, x^{2} + 1728 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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