Optimal. Leaf size=56 \[ \frac{40 x^9}{9}-\frac{9 x^8}{2}+\frac{190 x^7}{7}-\frac{83 x^6}{6}+\frac{288 x^5}{5}-5 x^4+60 x^3+\frac{27 x^2}{2}+54 x \]
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Rubi [A] time = 0.0318655, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.043, Rules used = {1657} \[ \frac{40 x^9}{9}-\frac{9 x^8}{2}+\frac{190 x^7}{7}-\frac{83 x^6}{6}+\frac{288 x^5}{5}-5 x^4+60 x^3+\frac{27 x^2}{2}+54 x \]
Antiderivative was successfully verified.
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Rule 1657
Rubi steps
\begin{align*} \int \left (3-x+2 x^2\right )^3 \left (2+3 x+5 x^2\right ) \, dx &=\int \left (54+27 x+180 x^2-20 x^3+288 x^4-83 x^5+190 x^6-36 x^7+40 x^8\right ) \, dx\\ &=54 x+\frac{27 x^2}{2}+60 x^3-5 x^4+\frac{288 x^5}{5}-\frac{83 x^6}{6}+\frac{190 x^7}{7}-\frac{9 x^8}{2}+\frac{40 x^9}{9}\\ \end{align*}
Mathematica [A] time = 0.0012394, size = 56, normalized size = 1. \[ \frac{40 x^9}{9}-\frac{9 x^8}{2}+\frac{190 x^7}{7}-\frac{83 x^6}{6}+\frac{288 x^5}{5}-5 x^4+60 x^3+\frac{27 x^2}{2}+54 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 45, normalized size = 0.8 \begin{align*} 54\,x+{\frac{27\,{x}^{2}}{2}}+60\,{x}^{3}-5\,{x}^{4}+{\frac{288\,{x}^{5}}{5}}-{\frac{83\,{x}^{6}}{6}}+{\frac{190\,{x}^{7}}{7}}-{\frac{9\,{x}^{8}}{2}}+{\frac{40\,{x}^{9}}{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.967082, size = 59, normalized size = 1.05 \begin{align*} \frac{40}{9} \, x^{9} - \frac{9}{2} \, x^{8} + \frac{190}{7} \, x^{7} - \frac{83}{6} \, x^{6} + \frac{288}{5} \, x^{5} - 5 \, x^{4} + 60 \, x^{3} + \frac{27}{2} \, x^{2} + 54 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.882358, size = 122, normalized size = 2.18 \begin{align*} \frac{40}{9} x^{9} - \frac{9}{2} x^{8} + \frac{190}{7} x^{7} - \frac{83}{6} x^{6} + \frac{288}{5} x^{5} - 5 x^{4} + 60 x^{3} + \frac{27}{2} x^{2} + 54 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.107796, size = 53, normalized size = 0.95 \begin{align*} \frac{40 x^{9}}{9} - \frac{9 x^{8}}{2} + \frac{190 x^{7}}{7} - \frac{83 x^{6}}{6} + \frac{288 x^{5}}{5} - 5 x^{4} + 60 x^{3} + \frac{27 x^{2}}{2} + 54 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20353, size = 59, normalized size = 1.05 \begin{align*} \frac{40}{9} \, x^{9} - \frac{9}{2} \, x^{8} + \frac{190}{7} \, x^{7} - \frac{83}{6} \, x^{6} + \frac{288}{5} \, x^{5} - 5 \, x^{4} + 60 \, x^{3} + \frac{27}{2} \, x^{2} + 54 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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