Optimal. Leaf size=45 \[ \frac{20}{729} (3 x+2)^9-\frac{2}{9} (3 x+2)^8+\frac{13}{27} (3 x+2)^7-\frac{49}{486} (3 x+2)^6 \]
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Rubi [A] time = 0.0228015, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ \frac{20}{729} (3 x+2)^9-\frac{2}{9} (3 x+2)^8+\frac{13}{27} (3 x+2)^7-\frac{49}{486} (3 x+2)^6 \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^2 (2+3 x)^5 (3+5 x) \, dx &=\int \left (-\frac{49}{27} (2+3 x)^5+\frac{91}{9} (2+3 x)^6-\frac{16}{3} (2+3 x)^7+\frac{20}{27} (2+3 x)^8\right ) \, dx\\ &=-\frac{49}{486} (2+3 x)^6+\frac{13}{27} (2+3 x)^7-\frac{2}{9} (2+3 x)^8+\frac{20}{729} (2+3 x)^9\\ \end{align*}
Mathematica [A] time = 0.0022539, size = 48, normalized size = 1.07 \[ 540 x^9+1782 x^8+1917 x^7+\frac{273 x^6}{2}-1218 x^5-770 x^4+\frac{224 x^3}{3}+248 x^2+96 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 45, normalized size = 1. \begin{align*} 540\,{x}^{9}+1782\,{x}^{8}+1917\,{x}^{7}+{\frac{273\,{x}^{6}}{2}}-1218\,{x}^{5}-770\,{x}^{4}+{\frac{224\,{x}^{3}}{3}}+248\,{x}^{2}+96\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09928, size = 59, normalized size = 1.31 \begin{align*} 540 \, x^{9} + 1782 \, x^{8} + 1917 \, x^{7} + \frac{273}{2} \, x^{6} - 1218 \, x^{5} - 770 \, x^{4} + \frac{224}{3} \, x^{3} + 248 \, x^{2} + 96 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.35906, size = 126, normalized size = 2.8 \begin{align*} 540 x^{9} + 1782 x^{8} + 1917 x^{7} + \frac{273}{2} x^{6} - 1218 x^{5} - 770 x^{4} + \frac{224}{3} x^{3} + 248 x^{2} + 96 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.065173, size = 46, normalized size = 1.02 \begin{align*} 540 x^{9} + 1782 x^{8} + 1917 x^{7} + \frac{273 x^{6}}{2} - 1218 x^{5} - 770 x^{4} + \frac{224 x^{3}}{3} + 248 x^{2} + 96 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.94897, size = 59, normalized size = 1.31 \begin{align*} 540 \, x^{9} + 1782 \, x^{8} + 1917 \, x^{7} + \frac{273}{2} \, x^{6} - 1218 \, x^{5} - 770 \, x^{4} + \frac{224}{3} \, x^{3} + 248 \, x^{2} + 96 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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