Optimal. Leaf size=23 \[ -1-3 \left (-3+\left (\frac {1}{3}-x\right )^2\right ) x+(-6-x) x \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 0.61, 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 = {12} \begin {gather*} -3 x^3+x^2+\frac {8 x}{3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \left (8+6 x-27 x^2\right ) \, dx\\ &=\frac {8 x}{3}+x^2-3 x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 0.61 \begin {gather*} \frac {8 x}{3}+x^2-3 x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 12, normalized size = 0.52 \begin {gather*} -3 \, x^{3} + x^{2} + \frac {8}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 12, normalized size = 0.52 \begin {gather*} -3 \, x^{3} + x^{2} + \frac {8}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 13, normalized size = 0.57
method | result | size |
default | \(-3 x^{3}+x^{2}+\frac {8}{3} x\) | \(13\) |
norman | \(-3 x^{3}+x^{2}+\frac {8}{3} x\) | \(13\) |
risch | \(-3 x^{3}+x^{2}+\frac {8}{3} x\) | \(13\) |
gosper | \(-\frac {x \left (9 x^{2}-3 x -8\right )}{3}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 12, normalized size = 0.52 \begin {gather*} -3 \, x^{3} + x^{2} + \frac {8}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 13, normalized size = 0.57 \begin {gather*} \frac {x\,\left (-9\,x^2+3\,x+8\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 12, normalized size = 0.52 \begin {gather*} - 3 x^{3} + x^{2} + \frac {8 x}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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