Optimal. Leaf size=11 \[ \frac {2 e^{-x^2}}{5} \]
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Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 2209} \begin {gather*} \frac {2 e^{-x^2}}{5} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\frac {4}{5} \int e^{-x^2} x \, dx\right )\\ &=\frac {2 e^{-x^2}}{5}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} \frac {2 e^{-x^2}}{5} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 8, normalized size = 0.73 \begin {gather*} \frac {2}{5} \, e^{\left (-x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 8, normalized size = 0.73 \begin {gather*} \frac {2}{5} \, e^{\left (-x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 9, normalized size = 0.82
method | result | size |
gosper | \(\frac {2 \,{\mathrm e}^{-x^{2}}}{5}\) | \(9\) |
derivativedivides | \(\frac {2 \,{\mathrm e}^{-x^{2}}}{5}\) | \(9\) |
default | \(\frac {2 \,{\mathrm e}^{-x^{2}}}{5}\) | \(9\) |
norman | \(\frac {2 \,{\mathrm e}^{-x^{2}}}{5}\) | \(9\) |
risch | \(\frac {2 \,{\mathrm e}^{-x^{2}}}{5}\) | \(9\) |
meijerg | \(-\frac {2}{5}+\frac {2 \,{\mathrm e}^{-x^{2}}}{5}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 8, normalized size = 0.73 \begin {gather*} \frac {2}{5} \, e^{\left (-x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 8, normalized size = 0.73 \begin {gather*} \frac {2\,{\mathrm {e}}^{-x^2}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 7, normalized size = 0.64 \begin {gather*} \frac {2 e^{- x^{2}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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