Optimal. Leaf size=28 \[ -\frac{1}{5} (3-x)^5-\frac{4}{3} (3-x)^3+(x-3)^4 \]
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Rubi [A] time = 0.0106319, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {610, 43} \[ -\frac{1}{5} (3-x)^5-\frac{4}{3} (3-x)^3+(x-3)^4 \]
Antiderivative was successfully verified.
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Rule 610
Rule 43
Rubi steps
\begin{align*} \int \left (3-4 x+x^2\right )^2 \, dx &=\int (-3+x)^2 (-1+x)^2 \, dx\\ &=\int \left (4 (-3+x)^2+4 (-3+x)^3+(-3+x)^4\right ) \, dx\\ &=-\frac{4}{3} (3-x)^3-\frac{1}{5} (3-x)^5+(-3+x)^4\\ \end{align*}
Mathematica [A] time = 0.0006362, size = 28, normalized size = 1. \[ \frac{x^5}{5}-2 x^4+\frac{22 x^3}{3}-12 x^2+9 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.039, size = 25, normalized size = 0.9 \begin{align*}{\frac{{x}^{5}}{5}}-2\,{x}^{4}+{\frac{22\,{x}^{3}}{3}}-12\,{x}^{2}+9\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.978717, size = 32, normalized size = 1.14 \begin{align*} \frac{1}{5} \, x^{5} - 2 \, x^{4} + \frac{22}{3} \, x^{3} - 12 \, x^{2} + 9 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4252, size = 58, normalized size = 2.07 \begin{align*} \frac{1}{5} x^{5} - 2 x^{4} + \frac{22}{3} x^{3} - 12 x^{2} + 9 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058233, size = 24, normalized size = 0.86 \begin{align*} \frac{x^{5}}{5} - 2 x^{4} + \frac{22 x^{3}}{3} - 12 x^{2} + 9 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12871, size = 32, normalized size = 1.14 \begin{align*} \frac{1}{5} \, x^{5} - 2 \, x^{4} + \frac{22}{3} \, x^{3} - 12 \, x^{2} + 9 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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