Optimal. Leaf size=22 \[ \frac {x^8}{8}-\frac {2 x^5}{5}+\frac {x^2}{2} \]
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Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {270} \begin {gather*} \frac {x^8}{8}-\frac {2 x^5}{5}+\frac {x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int x \left (1-x^3\right )^2 \, dx &=\int \left (x-2 x^4+x^7\right ) \, dx\\ &=\frac {x^2}{2}-\frac {2 x^5}{5}+\frac {x^8}{8}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 22, normalized size = 1.00 \begin {gather*} \frac {x^8}{8}-\frac {2 x^5}{5}+\frac {x^2}{2} \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 \left (1-x^3\right )^2 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.12, size = 16, normalized size = 0.73 \begin {gather*} \frac {1}{8} x^{8} - \frac {2}{5} x^{5} + \frac {1}{2} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 16, normalized size = 0.73 \begin {gather*} \frac {1}{8} \, x^{8} - \frac {2}{5} \, x^{5} + \frac {1}{2} \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 0.77 \begin {gather*} \frac {1}{8} x^{8}-\frac {2}{5} x^{5}+\frac {1}{2} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 16, normalized size = 0.73 \begin {gather*} \frac {1}{8} \, x^{8} - \frac {2}{5} \, x^{5} + \frac {1}{2} \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 17, normalized size = 0.77 \begin {gather*} \frac {x^2\,\left (5\,x^6-16\,x^3+20\right )}{40} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 15, normalized size = 0.68 \begin {gather*} \frac {x^{8}}{8} - \frac {2 x^{5}}{5} + \frac {x^{2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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