Optimal. Leaf size=5 \[ e^{e^x} \]
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Rubi [A]
time = 0.00, antiderivative size = 5, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {2320, 2225}
\begin {gather*} e^{e^x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rule 2320
Rubi steps
\begin {align*} \int e^{e^x+x} \, dx &=\text {Subst}\left (\int e^x \, dx,x,e^x\right )\\ &=e^{e^x}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 5, normalized size = 1.00 \begin {gather*} e^{e^x} \end {gather*}
Antiderivative was successfully verified.
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Mathics [C] Result contains higher order function than in optimal. Order 9 vs. order 3 in
optimal.
time = 1.83, size = 4, normalized size = 0.80 \begin {gather*} \text {ConditionalExpression}\left [E,\left \{\text {True}\right \}\right ] \end {gather*}
Warning: Unable to verify antiderivative.
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Maple [A]
time = 0.01, size = 4, normalized size = 0.80
method | result | size |
default | \({\mathrm e}^{{\mathrm e}^{x}}\) | \(4\) |
risch | \({\mathrm e}^{{\mathrm e}^{x}}\) | \(4\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 3, normalized size = 0.60 \begin {gather*} e^{\left (e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 3, normalized size = 0.60 \begin {gather*} e^{\left (e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.33, size = 3, normalized size = 0.60 \begin {gather*} e^{e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 3, normalized size = 0.60 \begin {gather*} \mathrm {e}^{\mathrm {e}^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 3, normalized size = 0.60 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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