Optimal. Leaf size=45 \[ -\frac{50}{729} (3 x+2)^9+\frac{65}{216} (3 x+2)^8-\frac{8}{63} (3 x+2)^7+\frac{7}{486} (3 x+2)^6 \]
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Rubi [A] time = 0.0217211, 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} \[ -\frac{50}{729} (3 x+2)^9+\frac{65}{216} (3 x+2)^8-\frac{8}{63} (3 x+2)^7+\frac{7}{486} (3 x+2)^6 \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x) (2+3 x)^5 (3+5 x)^2 \, dx &=\int \left (\frac{7}{27} (2+3 x)^5-\frac{8}{3} (2+3 x)^6+\frac{65}{9} (2+3 x)^7-\frac{50}{27} (2+3 x)^8\right ) \, dx\\ &=\frac{7}{486} (2+3 x)^6-\frac{8}{63} (2+3 x)^7+\frac{65}{216} (2+3 x)^8-\frac{50}{729} (2+3 x)^9\\ \end{align*}
Mathematica [A] time = 0.0020228, size = 52, normalized size = 1.16 \[ -1350 x^9-\frac{49005 x^8}{8}-\frac{79434 x^7}{7}-\frac{20631 x^6}{2}-3390 x^5+2090 x^4+\frac{8240 x^3}{3}+1272 x^2+288 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 45, normalized size = 1. \begin{align*} -1350\,{x}^{9}-{\frac{49005\,{x}^{8}}{8}}-{\frac{79434\,{x}^{7}}{7}}-{\frac{20631\,{x}^{6}}{2}}-3390\,{x}^{5}+2090\,{x}^{4}+{\frac{8240\,{x}^{3}}{3}}+1272\,{x}^{2}+288\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.14581, size = 59, normalized size = 1.31 \begin{align*} -1350 \, x^{9} - \frac{49005}{8} \, x^{8} - \frac{79434}{7} \, x^{7} - \frac{20631}{2} \, x^{6} - 3390 \, x^{5} + 2090 \, x^{4} + \frac{8240}{3} \, x^{3} + 1272 \, x^{2} + 288 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.29791, size = 144, normalized size = 3.2 \begin{align*} -1350 x^{9} - \frac{49005}{8} x^{8} - \frac{79434}{7} x^{7} - \frac{20631}{2} x^{6} - 3390 x^{5} + 2090 x^{4} + \frac{8240}{3} x^{3} + 1272 x^{2} + 288 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.065484, size = 49, normalized size = 1.09 \begin{align*} - 1350 x^{9} - \frac{49005 x^{8}}{8} - \frac{79434 x^{7}}{7} - \frac{20631 x^{6}}{2} - 3390 x^{5} + 2090 x^{4} + \frac{8240 x^{3}}{3} + 1272 x^{2} + 288 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.79763, size = 59, normalized size = 1.31 \begin{align*} -1350 \, x^{9} - \frac{49005}{8} \, x^{8} - \frac{79434}{7} \, x^{7} - \frac{20631}{2} \, x^{6} - 3390 \, x^{5} + 2090 \, x^{4} + \frac{8240}{3} \, x^{3} + 1272 \, x^{2} + 288 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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