Optimal. Leaf size=13 \[ -\frac {1}{2} e^{2-x^2} \]
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Rubi [A]
time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2240}
\begin {gather*} -\frac {1}{2} e^{2-x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2240
Rubi steps
\begin {align*} \int e^{2-x^2} x \, dx &=-\frac {1}{2} e^{2-x^2}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} -\frac {1}{2} e^{2-x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 11, normalized size = 0.85
method | result | size |
gosper | \(-\frac {{\mathrm e}^{-x^{2}+2}}{2}\) | \(11\) |
derivativedivides | \(-\frac {{\mathrm e}^{-x^{2}+2}}{2}\) | \(11\) |
default | \(-\frac {{\mathrm e}^{-x^{2}+2}}{2}\) | \(11\) |
norman | \(-\frac {{\mathrm e}^{-x^{2}+2}}{2}\) | \(11\) |
risch | \(-\frac {{\mathrm e}^{-x^{2}+2}}{2}\) | \(11\) |
meijerg | \(\frac {{\mathrm e}^{2} \left (1-{\mathrm e}^{-x^{2}}\right )}{2}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 10, normalized size = 0.77 \begin {gather*} -\frac {1}{2} \, e^{\left (-x^{2} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 10, normalized size = 0.77 \begin {gather*} -\frac {1}{2} \, e^{\left (-x^{2} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 8, normalized size = 0.62 \begin {gather*} - \frac {e^{2 - x^{2}}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.71, size = 10, normalized size = 0.77 \begin {gather*} -\frac {1}{2} \, e^{\left (-x^{2} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 10, normalized size = 0.77 \begin {gather*} -\frac {{\mathrm {e}}^2\,{\mathrm {e}}^{-x^2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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