Optimal. Leaf size=46 \[ \frac{20 x^7}{7}-\frac{4 x^6}{3}+\frac{61 x^5}{5}+\frac{x^4}{4}+\frac{53 x^3}{3}+\frac{15 x^2}{2}+18 x \]
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Rubi [A] time = 0.0296107, antiderivative size = 46, 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} \[ \frac{20 x^7}{7}-\frac{4 x^6}{3}+\frac{61 x^5}{5}+\frac{x^4}{4}+\frac{53 x^3}{3}+\frac{15 x^2}{2}+18 x \]
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 ) \, dx &=\int \left (18+15 x+53 x^2+x^3+61 x^4-8 x^5+20 x^6\right ) \, dx\\ &=18 x+\frac{15 x^2}{2}+\frac{53 x^3}{3}+\frac{x^4}{4}+\frac{61 x^5}{5}-\frac{4 x^6}{3}+\frac{20 x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.000904, size = 46, normalized size = 1. \[ \frac{20 x^7}{7}-\frac{4 x^6}{3}+\frac{61 x^5}{5}+\frac{x^4}{4}+\frac{53 x^3}{3}+\frac{15 x^2}{2}+18 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.045, size = 35, normalized size = 0.8 \begin{align*} 18\,x+{\frac{15\,{x}^{2}}{2}}+{\frac{53\,{x}^{3}}{3}}+{\frac{{x}^{4}}{4}}+{\frac{61\,{x}^{5}}{5}}-{\frac{4\,{x}^{6}}{3}}+{\frac{20\,{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.964242, size = 46, normalized size = 1. \begin{align*} \frac{20}{7} \, x^{7} - \frac{4}{3} \, x^{6} + \frac{61}{5} \, x^{5} + \frac{1}{4} \, x^{4} + \frac{53}{3} \, x^{3} + \frac{15}{2} \, x^{2} + 18 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.82888, size = 95, normalized size = 2.07 \begin{align*} \frac{20}{7} x^{7} - \frac{4}{3} x^{6} + \frac{61}{5} x^{5} + \frac{1}{4} x^{4} + \frac{53}{3} x^{3} + \frac{15}{2} x^{2} + 18 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.097347, size = 41, normalized size = 0.89 \begin{align*} \frac{20 x^{7}}{7} - \frac{4 x^{6}}{3} + \frac{61 x^{5}}{5} + \frac{x^{4}}{4} + \frac{53 x^{3}}{3} + \frac{15 x^{2}}{2} + 18 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17085, size = 46, normalized size = 1. \begin{align*} \frac{20}{7} \, x^{7} - \frac{4}{3} \, x^{6} + \frac{61}{5} \, x^{5} + \frac{1}{4} \, x^{4} + \frac{53}{3} \, x^{3} + \frac{15}{2} \, x^{2} + 18 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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