Optimal. Leaf size=36 \[ \frac {x^8}{8}-\frac {8 x^7}{7}+\frac {11 x^6}{3}-\frac {24 x^5}{5}+\frac {9 x^4}{4} \]
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Rubi [A] time = 0.01, antiderivative size = 36, 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} \begin {gather*} \frac {x^8}{8}-\frac {8 x^7}{7}+\frac {11 x^6}{3}-\frac {24 x^5}{5}+\frac {9 x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Rule 698
Rubi steps
\begin {align*} \int x^3 \left (3-4 x+x^2\right )^2 \, dx &=\int \left (9 x^3-24 x^4+22 x^5-8 x^6+x^7\right ) \, dx\\ &=\frac {9 x^4}{4}-\frac {24 x^5}{5}+\frac {11 x^6}{3}-\frac {8 x^7}{7}+\frac {x^8}{8}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 36, normalized size = 1.00 \begin {gather*} \frac {x^8}{8}-\frac {8 x^7}{7}+\frac {11 x^6}{3}-\frac {24 x^5}{5}+\frac {9 x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^3 \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 = 0.36, size = 26, normalized size = 0.72 \begin {gather*} \frac {1}{8} x^{8} - \frac {8}{7} x^{7} + \frac {11}{3} x^{6} - \frac {24}{5} x^{5} + \frac {9}{4} x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 26, normalized size = 0.72 \begin {gather*} \frac {1}{8} \, x^{8} - \frac {8}{7} \, x^{7} + \frac {11}{3} \, x^{6} - \frac {24}{5} \, x^{5} + \frac {9}{4} \, x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 27, normalized size = 0.75 \begin {gather*} \frac {1}{8} x^{8}-\frac {8}{7} x^{7}+\frac {11}{3} x^{6}-\frac {24}{5} x^{5}+\frac {9}{4} x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.08, size = 26, normalized size = 0.72 \begin {gather*} \frac {1}{8} \, x^{8} - \frac {8}{7} \, x^{7} + \frac {11}{3} \, x^{6} - \frac {24}{5} \, x^{5} + \frac {9}{4} \, x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 26, normalized size = 0.72 \begin {gather*} \frac {x^8}{8}-\frac {8\,x^7}{7}+\frac {11\,x^6}{3}-\frac {24\,x^5}{5}+\frac {9\,x^4}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 31, normalized size = 0.86 \begin {gather*} \frac {x^{8}}{8} - \frac {8 x^{7}}{7} + \frac {11 x^{6}}{3} - \frac {24 x^{5}}{5} + \frac {9 x^{4}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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