Optimal. Leaf size=56 \[ \frac{10}{243} (3 x+2)^{10}-\frac{740 (3 x+2)^9}{2187}+\frac{503}{648} (3 x+2)^8-\frac{74}{243} (3 x+2)^7+\frac{49 (3 x+2)^6}{1458} \]
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Rubi [A] time = 0.0249215, 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} \[ \frac{10}{243} (3 x+2)^{10}-\frac{740 (3 x+2)^9}{2187}+\frac{503}{648} (3 x+2)^8-\frac{74}{243} (3 x+2)^7+\frac{49 (3 x+2)^6}{1458} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^2 \, dx &=\int \left (\frac{49}{81} (2+3 x)^5-\frac{518}{81} (2+3 x)^6+\frac{503}{27} (2+3 x)^7-\frac{740}{81} (2+3 x)^8+\frac{100}{81} (2+3 x)^9\right ) \, dx\\ &=\frac{49 (2+3 x)^6}{1458}-\frac{74}{243} (2+3 x)^7+\frac{503}{648} (2+3 x)^8-\frac{740 (2+3 x)^9}{2187}+\frac{10}{243} (2+3 x)^{10}\\ \end{align*}
Mathematica [A] time = 0.0019774, size = 55, normalized size = 0.98 \[ 2430 x^{10}+9540 x^9+\frac{109863 x^8}{8}+6336 x^7-\frac{9331 x^6}{2}-6734 x^5-2030 x^4+\frac{3152 x^3}{3}+984 x^2+288 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 50, normalized size = 0.9 \begin{align*} 2430\,{x}^{10}+9540\,{x}^{9}+{\frac{109863\,{x}^{8}}{8}}+6336\,{x}^{7}-{\frac{9331\,{x}^{6}}{2}}-6734\,{x}^{5}-2030\,{x}^{4}+{\frac{3152\,{x}^{3}}{3}}+984\,{x}^{2}+288\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.36112, size = 66, normalized size = 1.18 \begin{align*} 2430 \, x^{10} + 9540 \, x^{9} + \frac{109863}{8} \, x^{8} + 6336 \, x^{7} - \frac{9331}{2} \, x^{6} - 6734 \, x^{5} - 2030 \, x^{4} + \frac{3152}{3} \, x^{3} + 984 \, x^{2} + 288 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.23825, size = 154, normalized size = 2.75 \begin{align*} 2430 x^{10} + 9540 x^{9} + \frac{109863}{8} x^{8} + 6336 x^{7} - \frac{9331}{2} x^{6} - 6734 x^{5} - 2030 x^{4} + \frac{3152}{3} x^{3} + 984 x^{2} + 288 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.068971, size = 53, normalized size = 0.95 \begin{align*} 2430 x^{10} + 9540 x^{9} + \frac{109863 x^{8}}{8} + 6336 x^{7} - \frac{9331 x^{6}}{2} - 6734 x^{5} - 2030 x^{4} + \frac{3152 x^{3}}{3} + 984 x^{2} + 288 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.81899, size = 66, normalized size = 1.18 \begin{align*} 2430 \, x^{10} + 9540 \, x^{9} + \frac{109863}{8} \, x^{8} + 6336 \, x^{7} - \frac{9331}{2} \, x^{6} - 6734 \, x^{5} - 2030 \, x^{4} + \frac{3152}{3} \, x^{3} + 984 \, x^{2} + 288 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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