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 = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {610, 43} \begin {gather*} -\frac {1}{5} (3-x)^5-\frac {4}{3} (3-x)^3+(x-3)^4 \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 610
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*}
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Mathematica [A] time = 0.00, size = 28, normalized size = 1.00 \begin {gather*} \frac {x^5}{5}-2 x^4+\frac {22 x^3}{3}-12 x^2+9 x \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (3-4 x+x^2\right )^2 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.33, size = 24, normalized size = 0.86 \begin {gather*} \frac {1}{5} x^{5} - 2 x^{4} + \frac {22}{3} x^{3} - 12 x^{2} + 9 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 24, normalized size = 0.86 \begin {gather*} \frac {1}{5} \, x^{5} - 2 \, x^{4} + \frac {22}{3} \, x^{3} - 12 \, x^{2} + 9 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 25, normalized size = 0.89 \begin {gather*} \frac {1}{5} x^{5}-2 x^{4}+\frac {22}{3} x^{3}-12 x^{2}+9 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.06, size = 24, normalized size = 0.86 \begin {gather*} \frac {1}{5} \, x^{5} - 2 \, x^{4} + \frac {22}{3} \, x^{3} - 12 \, x^{2} + 9 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 24, normalized size = 0.86 \begin {gather*} \frac {x^5}{5}-2\,x^4+\frac {22\,x^3}{3}-12\,x^2+9\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 24, normalized size = 0.86 \begin {gather*} \frac {x^{5}}{5} - 2 x^{4} + \frac {22 x^{3}}{3} - 12 x^{2} + 9 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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