Optimal. Leaf size=12 \[ e^{-1+e^{\frac {1}{x}}-x} \]
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Rubi [A] time = 0.20, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {6706} \begin {gather*} e^{-x+e^{\frac {1}{x}}-1} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{-1+e^{\frac {1}{x}}-x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 12, normalized size = 1.00 \begin {gather*} e^{-1+e^{\frac {1}{x}}-x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 18, normalized size = 1.50 \begin {gather*} \frac {e^{\left (-x + e^{\frac {1}{x}} + \log \left (x^{2}\right ) - 1\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 10, normalized size = 0.83 \begin {gather*} e^{\left (-x + e^{\frac {1}{x}} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 1.28, size = 60, normalized size = 5.00
method | result | size |
risch | \({\mathrm e}^{-1-\frac {i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}}{2}+i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-\frac {i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )}{2}+{\mathrm e}^{\frac {1}{x}}-x}\) | \(60\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 10, normalized size = 0.83 \begin {gather*} e^{\left (-x + e^{\frac {1}{x}} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.32, size = 12, normalized size = 1.00 \begin {gather*} {\mathrm {e}}^{-x}\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{{\mathrm {e}}^{1/x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.30, size = 8, normalized size = 0.67 \begin {gather*} e^{- x + e^{\frac {1}{x}} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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