Optimal. Leaf size=34 \[ \frac{x^6}{6}-\frac{8 x^5}{5}+\frac{11 x^4}{2}-8 x^3+\frac{9 x^2}{2} \]
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Rubi [A] time = 0.0107675, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083, Rules used = {631} \[ \frac{x^6}{6}-\frac{8 x^5}{5}+\frac{11 x^4}{2}-8 x^3+\frac{9 x^2}{2} \]
Antiderivative was successfully verified.
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Rule 631
Rubi steps
\begin{align*} \int x \left (3-4 x+x^2\right )^2 \, dx &=\int \left (9 x-24 x^2+22 x^3-8 x^4+x^5\right ) \, dx\\ &=\frac{9 x^2}{2}-8 x^3+\frac{11 x^4}{2}-\frac{8 x^5}{5}+\frac{x^6}{6}\\ \end{align*}
Mathematica [A] time = 0.0010482, size = 34, normalized size = 1. \[ \frac{x^6}{6}-\frac{8 x^5}{5}+\frac{11 x^4}{2}-8 x^3+\frac{9 x^2}{2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.04, size = 27, normalized size = 0.8 \begin{align*}{\frac{9\,{x}^{2}}{2}}-8\,{x}^{3}+{\frac{11\,{x}^{4}}{2}}-{\frac{8\,{x}^{5}}{5}}+{\frac{{x}^{6}}{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0305, size = 35, normalized size = 1.03 \begin{align*} \frac{1}{6} \, x^{6} - \frac{8}{5} \, x^{5} + \frac{11}{2} \, x^{4} - 8 \, x^{3} + \frac{9}{2} \, x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.60726, size = 65, normalized size = 1.91 \begin{align*} \frac{1}{6} x^{6} - \frac{8}{5} x^{5} + \frac{11}{2} x^{4} - 8 x^{3} + \frac{9}{2} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.059149, size = 29, normalized size = 0.85 \begin{align*} \frac{x^{6}}{6} - \frac{8 x^{5}}{5} + \frac{11 x^{4}}{2} - 8 x^{3} + \frac{9 x^{2}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10512, size = 35, normalized size = 1.03 \begin{align*} \frac{1}{6} \, x^{6} - \frac{8}{5} \, x^{5} + \frac{11}{2} \, x^{4} - 8 \, x^{3} + \frac{9}{2} \, x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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