Optimal. Leaf size=14 \[ e^{2 e^{-x} \left (12+e^{256}\right )} \]
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Rubi [A] time = 0.10, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 2282, 2194} \begin {gather*} e^{2 \left (12+e^{256}\right ) e^{-x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rule 2282
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (2 \left (12+e^{256}\right )\right ) \int e^{e^{-x} \left (24+2 e^{256}\right )-x} \, dx\right )\\ &=\left (2 \left (12+e^{256}\right )\right ) \operatorname {Subst}\left (\int e^{2 \left (12+e^{256}\right ) x} \, dx,x,e^{-x}\right )\\ &=e^{2 e^{-x} \left (12+e^{256}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 14, normalized size = 1.00 \begin {gather*} e^{2 e^{-x} \left (12+e^{256}\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 11, normalized size = 0.79 \begin {gather*} e^{\left (2 \, {\left (e^{256} + 12\right )} e^{\left (-x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -2 \, {\left (e^{256} + 12\right )} e^{\left (2 \, {\left (e^{256} + 12\right )} e^{\left (-x\right )} - x\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 13, normalized size = 0.93
method | result | size |
norman | \({\mathrm e}^{\left (2 \,{\mathrm e}^{256}+24\right ) {\mathrm e}^{-x}}\) | \(13\) |
derivativedivides | \(-\frac {\left (-2 \,{\mathrm e}^{256}-24\right ) {\mathrm e}^{\left (2 \,{\mathrm e}^{256}+24\right ) {\mathrm e}^{-x}}}{2 \,{\mathrm e}^{256}+24}\) | \(29\) |
default | \(-\frac {\left (-2 \,{\mathrm e}^{256}-24\right ) {\mathrm e}^{\left (2 \,{\mathrm e}^{256}+24\right ) {\mathrm e}^{-x}}}{2 \,{\mathrm e}^{256}+24}\) | \(29\) |
risch | \(\frac {{\mathrm e}^{2 \left ({\mathrm e}^{256}+12\right ) {\mathrm e}^{-x}} {\mathrm e}^{256}}{{\mathrm e}^{256}+12}+\frac {12 \,{\mathrm e}^{2 \left ({\mathrm e}^{256}+12\right ) {\mathrm e}^{-x}}}{{\mathrm e}^{256}+12}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 16, normalized size = 1.14 \begin {gather*} e^{\left (24 \, e^{\left (-x\right )} + 2 \, e^{\left (-x + 256\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.13, size = 16, normalized size = 1.14 \begin {gather*} {\mathrm {e}}^{24\,{\mathrm {e}}^{-x}+2\,{\mathrm {e}}^{256-x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 10, normalized size = 0.71 \begin {gather*} e^{\left (24 + 2 e^{256}\right ) e^{- x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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