Optimal. Leaf size=33 \[ -2-e^{2-e^x-x}-e^{3+\log ^2\left (\frac {4}{e^4}\right )}+2 x \]
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Rubi [A]
time = 0.03, antiderivative size = 18, normalized size of antiderivative = 0.55, number of steps
used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2320, 2228}
\begin {gather*} 2 x-e^{-x-e^x+2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2228
Rule 2320
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 x+\int e^{2-e^x-x} \left (1+e^x\right ) \, dx\\ &=2 x+\text {Subst}\left (\int \frac {e^{2-x} (1+x)}{x^2} \, dx,x,e^x\right )\\ &=-e^{2-e^x-x}+2 x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 18, normalized size = 0.55 \begin {gather*} -e^{2-e^x-x}+2 x \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.05, size = 32, normalized size = 0.97
method | result | size |
norman | \(2 x -{\mathrm e}^{-{\mathrm e}^{x}+2-x}\) | \(17\) |
risch | \(2 x -{\mathrm e}^{-{\mathrm e}^{x}+2-x}\) | \(17\) |
default | \(2 x -{\mathrm e}^{2} \expIntegral \left (1, {\mathrm e}^{x}\right )+{\mathrm e}^{2} \left (-{\mathrm e}^{-{\mathrm e}^{x}} {\mathrm e}^{-x}+\expIntegral \left (1, {\mathrm e}^{x}\right )\right )\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 16, normalized size = 0.48 \begin {gather*} 2 \, x - e^{\left (-x - e^{x} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 16, normalized size = 0.48 \begin {gather*} 2 \, x - e^{\left (-x - e^{x} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 10, normalized size = 0.30 \begin {gather*} 2 x - e^{- x - e^{x} + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 16, normalized size = 0.48 \begin {gather*} 2 \, x - e^{\left (-x - e^{x} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.07, size = 17, normalized size = 0.52 \begin {gather*} 2\,x-{\mathrm {e}}^{-x}\,{\mathrm {e}}^2\,{\mathrm {e}}^{-{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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