Optimal. Leaf size=56 \[ \frac{25}{729} (3 x+2)^{12}-\frac{740 (3 x+2)^{11}}{2673}+\frac{503}{810} (3 x+2)^{10}-\frac{518 (3 x+2)^9}{2187}+\frac{49 (3 x+2)^8}{1944} \]
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Rubi [A] time = 0.0295273, antiderivative size = 56, 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} \[ \frac{25}{729} (3 x+2)^{12}-\frac{740 (3 x+2)^{11}}{2673}+\frac{503}{810} (3 x+2)^{10}-\frac{518 (3 x+2)^9}{2187}+\frac{49 (3 x+2)^8}{1944} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^2 \, dx &=\int \left (\frac{49}{81} (2+3 x)^7-\frac{518}{81} (2+3 x)^8+\frac{503}{27} (2+3 x)^9-\frac{740}{81} (2+3 x)^{10}+\frac{100}{81} (2+3 x)^{11}\right ) \, dx\\ &=\frac{49 (2+3 x)^8}{1944}-\frac{518 (2+3 x)^9}{2187}+\frac{503}{810} (2+3 x)^{10}-\frac{740 (2+3 x)^{11}}{2673}+\frac{25}{729} (2+3 x)^{12}\\ \end{align*}
Mathematica [A] time = 0.0023, size = 69, normalized size = 1.23 \[ 18225 x^{12}+\frac{1064340 x^{11}}{11}+\frac{2116287 x^{10}}{10}+228996 x^9+\frac{719739 x^8}{8}-65934 x^7-98182 x^6-\frac{203752 x^5}{5}+5764 x^4+\frac{38816 x^3}{3}+5664 x^2+1152 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 60, normalized size = 1.1 \begin{align*} 18225\,{x}^{12}+{\frac{1064340\,{x}^{11}}{11}}+{\frac{2116287\,{x}^{10}}{10}}+228996\,{x}^{9}+{\frac{719739\,{x}^{8}}{8}}-65934\,{x}^{7}-98182\,{x}^{6}-{\frac{203752\,{x}^{5}}{5}}+5764\,{x}^{4}+{\frac{38816\,{x}^{3}}{3}}+5664\,{x}^{2}+1152\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.16154, size = 80, normalized size = 1.43 \begin{align*} 18225 \, x^{12} + \frac{1064340}{11} \, x^{11} + \frac{2116287}{10} \, x^{10} + 228996 \, x^{9} + \frac{719739}{8} \, x^{8} - 65934 \, x^{7} - 98182 \, x^{6} - \frac{203752}{5} \, x^{5} + 5764 \, x^{4} + \frac{38816}{3} \, x^{3} + 5664 \, x^{2} + 1152 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42947, size = 216, normalized size = 3.86 \begin{align*} 18225 x^{12} + \frac{1064340}{11} x^{11} + \frac{2116287}{10} x^{10} + 228996 x^{9} + \frac{719739}{8} x^{8} - 65934 x^{7} - 98182 x^{6} - \frac{203752}{5} x^{5} + 5764 x^{4} + \frac{38816}{3} x^{3} + 5664 x^{2} + 1152 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.074762, size = 66, normalized size = 1.18 \begin{align*} 18225 x^{12} + \frac{1064340 x^{11}}{11} + \frac{2116287 x^{10}}{10} + 228996 x^{9} + \frac{719739 x^{8}}{8} - 65934 x^{7} - 98182 x^{6} - \frac{203752 x^{5}}{5} + 5764 x^{4} + \frac{38816 x^{3}}{3} + 5664 x^{2} + 1152 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.43703, size = 80, normalized size = 1.43 \begin{align*} 18225 \, x^{12} + \frac{1064340}{11} \, x^{11} + \frac{2116287}{10} \, x^{10} + 228996 \, x^{9} + \frac{719739}{8} \, x^{8} - 65934 \, x^{7} - 98182 \, x^{6} - \frac{203752}{5} \, x^{5} + 5764 \, x^{4} + \frac{38816}{3} \, x^{3} + 5664 \, x^{2} + 1152 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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