Optimal. Leaf size=14 \[ e^{1-e^{5+e^4+x}} \]
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Rubi [A]
time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2320, 2225}
\begin {gather*} e^{1-e^{x+e^4+5}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rule 2320
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\text {Subst}\left (\int e^{6+e^4-e^{5+e^4} x} \, dx,x,e^x\right )\\ &=e^{1-e^{5+e^4+x}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 14, normalized size = 1.00 \begin {gather*} e^{1-e^{5+e^4+x}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 14, normalized size = 1.00
method | result | size |
risch | \({\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{4}+x +5}+1}\) | \(12\) |
derivativedivides | \({\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{4}+x +5}+1}\) | \(14\) |
default | \({\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{4}+x +5}+1}\) | \(14\) |
norman | \({\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{4}+x +5}+1}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 11, normalized size = 0.79 \begin {gather*} e^{\left (-e^{\left (x + e^{4} + 5\right )} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 11, normalized size = 0.79 \begin {gather*} e^{\left (-e^{\left (x + e^{4} + 5\right )} + 1\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 = 0.71 \begin {gather*} e^{1 - e^{x + 5 + e^{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 11, normalized size = 0.79 \begin {gather*} e^{\left (-e^{\left (x + e^{4} + 5\right )} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.30, size = 12, normalized size = 0.86 \begin {gather*} \mathrm {e}\,{\mathrm {e}}^{-{\mathrm {e}}^{x+{\mathrm {e}}^4+5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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