Optimal. Leaf size=15 \[ 2 e^{-e^{-\frac {2}{x^2}}+x} \]
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Rubi [A]
time = 0.31, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {6838}
\begin {gather*} 2 e^{x-e^{-\frac {2}{x^2}}} \end {gather*}
Antiderivative was successfully verified.
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Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 e^{-e^{-\frac {2}{x^2}}+x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 15, normalized size = 1.00 \begin {gather*} 2 e^{-e^{-\frac {2}{x^2}}+x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 14, normalized size = 0.93
method | result | size |
risch | \(2 \,{\mathrm e}^{-{\mathrm e}^{-\frac {2}{x^{2}}}+x}\) | \(14\) |
norman | \(2 \,{\mathrm e}^{-{\mathrm e}^{-\frac {2}{x^{2}}}+x}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 13, normalized size = 0.87 \begin {gather*} 2 \, e^{\left (x - e^{\left (-\frac {2}{x^{2}}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 12, normalized size = 0.80 \begin {gather*} 2 e^{x - e^{- \frac {2}{x^{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 13, normalized size = 0.87 \begin {gather*} 2 \, e^{\left (x - e^{\left (-\frac {2}{x^{2}}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.22, size = 13, normalized size = 0.87 \begin {gather*} 2\,{\mathrm {e}}^{-{\mathrm {e}}^{-\frac {2}{x^2}}}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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