Optimal. Leaf size=11 \[ -x+\frac {x^2}{2} \]
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Rubi [A]
time = 0.00, antiderivative size = 11, 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 = {1600}
\begin {gather*} \frac {x^2}{2}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 1600
Rubi steps
\begin {align*} \int \frac {-1+x^3}{1+x+x^2} \, dx &=\int (-1+x) \, dx\\ &=-x+\frac {x^2}{2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} -x+\frac {x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.32, size = 10, normalized size = 0.91
method | result | size |
gosper | \(\frac {x \left (x -2\right )}{2}\) | \(7\) |
default | \(-x +\frac {1}{2} x^{2}\) | \(10\) |
norman | \(-x +\frac {1}{2} x^{2}\) | \(10\) |
risch | \(-x +\frac {1}{2} x^{2}\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 9, normalized size = 0.82 \begin {gather*} \frac {1}{2} \, x^{2} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 9, normalized size = 0.82 \begin {gather*} \frac {1}{2} \, x^{2} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 5, normalized size = 0.45 \begin {gather*} \frac {x^{2}}{2} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 5.10, size = 9, normalized size = 0.82 \begin {gather*} \frac {1}{2} \, x^{2} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 6, normalized size = 0.55 \begin {gather*} \frac {x\,\left (x-2\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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