Optimal. Leaf size=32 \[ \frac {x^9}{9}-x^8+\frac {22 x^7}{7}-4 x^6+\frac {9 x^5}{5} \]
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Rubi [A] time = 0.01, antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {698} \[ \frac {x^9}{9}-x^8+\frac {22 x^7}{7}-4 x^6+\frac {9 x^5}{5} \]
Antiderivative was successfully verified.
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Rule 698
Rubi steps
\begin {align*} \int x^4 \left (3-4 x+x^2\right )^2 \, dx &=\int \left (9 x^4-24 x^5+22 x^6-8 x^7+x^8\right ) \, dx\\ &=\frac {9 x^5}{5}-4 x^6+\frac {22 x^7}{7}-x^8+\frac {x^9}{9}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 32, normalized size = 1.00 \[ \frac {x^9}{9}-x^8+\frac {22 x^7}{7}-4 x^6+\frac {9 x^5}{5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 26, normalized size = 0.81 \[ \frac {1}{9} x^{9} - x^{8} + \frac {22}{7} x^{7} - 4 x^{6} + \frac {9}{5} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 26, normalized size = 0.81 \[ \frac {1}{9} \, x^{9} - x^{8} + \frac {22}{7} \, x^{7} - 4 \, x^{6} + \frac {9}{5} \, x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 27, normalized size = 0.84 \[ \frac {1}{9} x^{9}-x^{8}+\frac {22}{7} x^{7}-4 x^{6}+\frac {9}{5} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.08, size = 26, normalized size = 0.81 \[ \frac {1}{9} \, x^{9} - x^{8} + \frac {22}{7} \, x^{7} - 4 \, x^{6} + \frac {9}{5} \, x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 26, normalized size = 0.81 \[ \frac {x^9}{9}-x^8+\frac {22\,x^7}{7}-4\,x^6+\frac {9\,x^5}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 26, normalized size = 0.81 \[ \frac {x^{9}}{9} - x^{8} + \frac {22 x^{7}}{7} - 4 x^{6} + \frac {9 x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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