Optimal. Leaf size=60 \[ \frac{100 x^9}{9}-\frac{45 x^8}{8}+\frac{111 x^7}{7}-\frac{37 x^6}{6}+\frac{148 x^5}{5}+\frac{65 x^4}{4}+\frac{107 x^3}{3}+\frac{33 x^2}{2}+18 x \]
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Rubi [A] time = 0.0362729, antiderivative size = 60, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 31, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.032, Rules used = {1657} \[ \frac{100 x^9}{9}-\frac{45 x^8}{8}+\frac{111 x^7}{7}-\frac{37 x^6}{6}+\frac{148 x^5}{5}+\frac{65 x^4}{4}+\frac{107 x^3}{3}+\frac{33 x^2}{2}+18 x \]
Antiderivative was successfully verified.
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Rule 1657
Rubi steps
\begin{align*} \int \left (3+2 x+5 x^2\right )^2 \left (2+x+3 x^2-5 x^3+4 x^4\right ) \, dx &=\int \left (18+33 x+107 x^2+65 x^3+148 x^4-37 x^5+111 x^6-45 x^7+100 x^8\right ) \, dx\\ &=18 x+\frac{33 x^2}{2}+\frac{107 x^3}{3}+\frac{65 x^4}{4}+\frac{148 x^5}{5}-\frac{37 x^6}{6}+\frac{111 x^7}{7}-\frac{45 x^8}{8}+\frac{100 x^9}{9}\\ \end{align*}
Mathematica [A] time = 0.0011501, size = 60, normalized size = 1. \[ \frac{100 x^9}{9}-\frac{45 x^8}{8}+\frac{111 x^7}{7}-\frac{37 x^6}{6}+\frac{148 x^5}{5}+\frac{65 x^4}{4}+\frac{107 x^3}{3}+\frac{33 x^2}{2}+18 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 45, normalized size = 0.8 \begin{align*} 18\,x+{\frac{33\,{x}^{2}}{2}}+{\frac{107\,{x}^{3}}{3}}+{\frac{65\,{x}^{4}}{4}}+{\frac{148\,{x}^{5}}{5}}-{\frac{37\,{x}^{6}}{6}}+{\frac{111\,{x}^{7}}{7}}-{\frac{45\,{x}^{8}}{8}}+{\frac{100\,{x}^{9}}{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.994845, size = 59, normalized size = 0.98 \begin{align*} \frac{100}{9} \, x^{9} - \frac{45}{8} \, x^{8} + \frac{111}{7} \, x^{7} - \frac{37}{6} \, x^{6} + \frac{148}{5} \, x^{5} + \frac{65}{4} \, x^{4} + \frac{107}{3} \, x^{3} + \frac{33}{2} \, x^{2} + 18 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.915561, size = 132, normalized size = 2.2 \begin{align*} \frac{100}{9} x^{9} - \frac{45}{8} x^{8} + \frac{111}{7} x^{7} - \frac{37}{6} x^{6} + \frac{148}{5} x^{5} + \frac{65}{4} x^{4} + \frac{107}{3} x^{3} + \frac{33}{2} x^{2} + 18 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.06944, size = 56, normalized size = 0.93 \begin{align*} \frac{100 x^{9}}{9} - \frac{45 x^{8}}{8} + \frac{111 x^{7}}{7} - \frac{37 x^{6}}{6} + \frac{148 x^{5}}{5} + \frac{65 x^{4}}{4} + \frac{107 x^{3}}{3} + \frac{33 x^{2}}{2} + 18 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15295, size = 59, normalized size = 0.98 \begin{align*} \frac{100}{9} \, x^{9} - \frac{45}{8} \, x^{8} + \frac{111}{7} \, x^{7} - \frac{37}{6} \, x^{6} + \frac{148}{5} \, x^{5} + \frac{65}{4} \, x^{4} + \frac{107}{3} \, x^{3} + \frac{33}{2} \, x^{2} + 18 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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