Optimal. Leaf size=11 \[ -2 x+\frac {x^2}{2} \]
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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 = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {641}
\begin {gather*} \frac {x^2}{2}-2 x \end {gather*}
Antiderivative was successfully verified.
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Rule 641
Rubi steps
\begin {align*} \int \frac {-4+x^2}{2+x} \, dx &=\int (-2+x) \, dx\\ &=-2 x+\frac {x^2}{2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} -2 x+\frac {x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.20, size = 10, normalized size = 0.91
method | result | size |
gosper | \(\frac {x \left (x -4\right )}{2}\) | \(7\) |
meijerg | \(-\frac {x \left (-\frac {3 x}{2}+6\right )}{3}\) | \(9\) |
default | \(-2 x +\frac {1}{2} x^{2}\) | \(10\) |
norman | \(-2 x +\frac {1}{2} x^{2}\) | \(10\) |
risch | \(-2 x +\frac {1}{2} x^{2}\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 9, normalized size = 0.82 \begin {gather*} \frac {1}{2} \, x^{2} - 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} - 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 7, normalized size = 0.64 \begin {gather*} \frac {x^{2}}{2} - 2 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 4.30, size = 9, normalized size = 0.82 \begin {gather*} \frac {1}{2} \, x^{2} - 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-4\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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