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 = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 34, normalized size = 1.00 \[ \frac {x^6}{6}-\frac {8 x^5}{5}+\frac {11 x^4}{2}-8 x^3+\frac {9 x^2}{2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 26, normalized size = 0.76 \[ \frac {1}{6} x^{6} - \frac {8}{5} x^{5} + \frac {11}{2} x^{4} - 8 x^{3} + \frac {9}{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 26, normalized size = 0.76 \[ \frac {1}{6} \, x^{6} - \frac {8}{5} \, x^{5} + \frac {11}{2} \, x^{4} - 8 \, x^{3} + \frac {9}{2} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 27, normalized size = 0.79 \[ \frac {1}{6} x^{6}-\frac {8}{5} x^{5}+\frac {11}{2} x^{4}-8 x^{3}+\frac {9}{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.02, size = 26, normalized size = 0.76 \[ \frac {1}{6} \, x^{6} - \frac {8}{5} \, x^{5} + \frac {11}{2} \, x^{4} - 8 \, x^{3} + \frac {9}{2} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 26, normalized size = 0.76 \[ \frac {x^6}{6}-\frac {8\,x^5}{5}+\frac {11\,x^4}{2}-8\,x^3+\frac {9\,x^2}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 29, normalized size = 0.85 \[ \frac {x^{6}}{6} - \frac {8 x^{5}}{5} + \frac {11 x^{4}}{2} - 8 x^{3} + \frac {9 x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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