Optimal. Leaf size=30 \[ 2 x^5+\frac{x^4}{4}+\frac{16 x^3}{3}+\frac{7 x^2}{2}+6 x \]
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Rubi [A] time = 0.0161242, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048, Rules used = {1657} \[ 2 x^5+\frac{x^4}{4}+\frac{16 x^3}{3}+\frac{7 x^2}{2}+6 x \]
Antiderivative was successfully verified.
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Rule 1657
Rubi steps
\begin{align*} \int \left (3-x+2 x^2\right ) \left (2+3 x+5 x^2\right ) \, dx &=\int \left (6+7 x+16 x^2+x^3+10 x^4\right ) \, dx\\ &=6 x+\frac{7 x^2}{2}+\frac{16 x^3}{3}+\frac{x^4}{4}+2 x^5\\ \end{align*}
Mathematica [A] time = 0.0009675, size = 30, normalized size = 1. \[ 2 x^5+\frac{x^4}{4}+\frac{16 x^3}{3}+\frac{7 x^2}{2}+6 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 25, normalized size = 0.8 \begin{align*} 6\,x+{\frac{7\,{x}^{2}}{2}}+{\frac{16\,{x}^{3}}{3}}+{\frac{{x}^{4}}{4}}+2\,{x}^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.99311, size = 32, normalized size = 1.07 \begin{align*} 2 \, x^{5} + \frac{1}{4} \, x^{4} + \frac{16}{3} \, x^{3} + \frac{7}{2} \, x^{2} + 6 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.71146, size = 59, normalized size = 1.97 \begin{align*} 2 x^{5} + \frac{1}{4} x^{4} + \frac{16}{3} x^{3} + \frac{7}{2} x^{2} + 6 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.062864, size = 26, normalized size = 0.87 \begin{align*} 2 x^{5} + \frac{x^{4}}{4} + \frac{16 x^{3}}{3} + \frac{7 x^{2}}{2} + 6 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17373, size = 32, normalized size = 1.07 \begin{align*} 2 \, x^{5} + \frac{1}{4} \, x^{4} + \frac{16}{3} \, x^{3} + \frac{7}{2} \, x^{2} + 6 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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