Optimal. Leaf size=45 \[ -\frac{50}{891} (3 x+2)^{11}+\frac{13}{54} (3 x+2)^{10}-\frac{8}{81} (3 x+2)^9+\frac{7}{648} (3 x+2)^8 \]
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Rubi [A] time = 0.0284157, 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} \[ -\frac{50}{891} (3 x+2)^{11}+\frac{13}{54} (3 x+2)^{10}-\frac{8}{81} (3 x+2)^9+\frac{7}{648} (3 x+2)^8 \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x) (2+3 x)^7 (3+5 x)^2 \, dx &=\int \left (\frac{7}{27} (2+3 x)^7-\frac{8}{3} (2+3 x)^8+\frac{65}{9} (2+3 x)^9-\frac{50}{27} (2+3 x)^{10}\right ) \, dx\\ &=\frac{7}{648} (2+3 x)^8-\frac{8}{81} (2+3 x)^9+\frac{13}{54} (2+3 x)^{10}-\frac{50}{891} (2+3 x)^{11}\\ \end{align*}
Mathematica [A] time = 0.0022983, size = 62, normalized size = 1.38 \[ -\frac{109350 x^{11}}{11}-\frac{117369 x^{10}}{2}-150174 x^9-\frac{1706265 x^8}{8}-173286 x^7-62622 x^6+21336 x^5+38804 x^4+\frac{66080 x^3}{3}+6816 x^2+1152 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 55, normalized size = 1.2 \begin{align*} -{\frac{109350\,{x}^{11}}{11}}-{\frac{117369\,{x}^{10}}{2}}-150174\,{x}^{9}-{\frac{1706265\,{x}^{8}}{8}}-173286\,{x}^{7}-62622\,{x}^{6}+21336\,{x}^{5}+38804\,{x}^{4}+{\frac{66080\,{x}^{3}}{3}}+6816\,{x}^{2}+1152\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.25851, size = 73, normalized size = 1.62 \begin{align*} -\frac{109350}{11} \, x^{11} - \frac{117369}{2} \, x^{10} - 150174 \, x^{9} - \frac{1706265}{8} \, x^{8} - 173286 \, x^{7} - 62622 \, x^{6} + 21336 \, x^{5} + 38804 \, x^{4} + \frac{66080}{3} \, x^{3} + 6816 \, x^{2} + 1152 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.292, size = 196, normalized size = 4.36 \begin{align*} -\frac{109350}{11} x^{11} - \frac{117369}{2} x^{10} - 150174 x^{9} - \frac{1706265}{8} x^{8} - 173286 x^{7} - 62622 x^{6} + 21336 x^{5} + 38804 x^{4} + \frac{66080}{3} x^{3} + 6816 x^{2} + 1152 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.06802, size = 60, normalized size = 1.33 \begin{align*} - \frac{109350 x^{11}}{11} - \frac{117369 x^{10}}{2} - 150174 x^{9} - \frac{1706265 x^{8}}{8} - 173286 x^{7} - 62622 x^{6} + 21336 x^{5} + 38804 x^{4} + \frac{66080 x^{3}}{3} + 6816 x^{2} + 1152 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.45369, size = 73, normalized size = 1.62 \begin{align*} -\frac{109350}{11} \, x^{11} - \frac{117369}{2} \, x^{10} - 150174 \, x^{9} - \frac{1706265}{8} \, x^{8} - 173286 \, x^{7} - 62622 \, x^{6} + 21336 \, x^{5} + 38804 \, x^{4} + \frac{66080}{3} \, x^{3} + 6816 \, x^{2} + 1152 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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