Optimal. Leaf size=54 \[ \frac{100 x^9}{9}+\frac{5 x^8}{2}+\frac{321 x^7}{7}+\frac{86 x^6}{3}+78 x^5+59 x^4+\frac{241 x^3}{3}+42 x^2+36 x \]
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Rubi [A] time = 0.042492, antiderivative size = 54, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.04, Rules used = {1657} \[ \frac{100 x^9}{9}+\frac{5 x^8}{2}+\frac{321 x^7}{7}+\frac{86 x^6}{3}+78 x^5+59 x^4+\frac{241 x^3}{3}+42 x^2+36 x \]
Antiderivative was successfully verified.
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Rule 1657
Rubi steps
\begin{align*} \int \left (3-x+2 x^2\right )^2 \left (2+3 x+5 x^2\right )^2 \, dx &=\int \left (36+84 x+241 x^2+236 x^3+390 x^4+172 x^5+321 x^6+20 x^7+100 x^8\right ) \, dx\\ &=36 x+42 x^2+\frac{241 x^3}{3}+59 x^4+78 x^5+\frac{86 x^6}{3}+\frac{321 x^7}{7}+\frac{5 x^8}{2}+\frac{100 x^9}{9}\\ \end{align*}
Mathematica [A] time = 0.0017383, size = 54, normalized size = 1. \[ \frac{100 x^9}{9}+\frac{5 x^8}{2}+\frac{321 x^7}{7}+\frac{86 x^6}{3}+78 x^5+59 x^4+\frac{241 x^3}{3}+42 x^2+36 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.044, size = 45, normalized size = 0.8 \begin{align*} 36\,x+42\,{x}^{2}+{\frac{241\,{x}^{3}}{3}}+59\,{x}^{4}+78\,{x}^{5}+{\frac{86\,{x}^{6}}{3}}+{\frac{321\,{x}^{7}}{7}}+{\frac{5\,{x}^{8}}{2}}+{\frac{100\,{x}^{9}}{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.967055, size = 59, normalized size = 1.09 \begin{align*} \frac{100}{9} \, x^{9} + \frac{5}{2} \, x^{8} + \frac{321}{7} \, x^{7} + \frac{86}{3} \, x^{6} + 78 \, x^{5} + 59 \, x^{4} + \frac{241}{3} \, x^{3} + 42 \, x^{2} + 36 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.904191, size = 122, normalized size = 2.26 \begin{align*} \frac{100}{9} x^{9} + \frac{5}{2} x^{8} + \frac{321}{7} x^{7} + \frac{86}{3} x^{6} + 78 x^{5} + 59 x^{4} + \frac{241}{3} x^{3} + 42 x^{2} + 36 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.108465, size = 51, normalized size = 0.94 \begin{align*} \frac{100 x^{9}}{9} + \frac{5 x^{8}}{2} + \frac{321 x^{7}}{7} + \frac{86 x^{6}}{3} + 78 x^{5} + 59 x^{4} + \frac{241 x^{3}}{3} + 42 x^{2} + 36 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19494, size = 59, normalized size = 1.09 \begin{align*} \frac{100}{9} \, x^{9} + \frac{5}{2} \, x^{8} + \frac{321}{7} \, x^{7} + \frac{86}{3} \, x^{6} + 78 \, x^{5} + 59 \, x^{4} + \frac{241}{3} \, x^{3} + 42 \, x^{2} + 36 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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