Optimal. Leaf size=14 \[ e^{e^{1+2 x}}-\log (3) \]
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Rubi [A] time = 0.01, antiderivative size = 9, normalized size of antiderivative = 0.64, number of steps used = 3, number of rules used = 3, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.188, Rules used = {12, 2282, 2194} \begin {gather*} e^{e^{2 x+1}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rule 2282
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 \int e^{1+e^{1+2 x}+2 x} \, dx\\ &=\operatorname {Subst}\left (\int e^{1+e x} \, dx,x,e^{2 x}\right )\\ &=e^{e^{1+2 x}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 9, normalized size = 0.64 \begin {gather*} e^{e^{1+2 x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 7, normalized size = 0.50 \begin {gather*} e^{\left (e^{\left (2 \, x + 1\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 7, normalized size = 0.50 \begin {gather*} e^{\left (e^{\left (2 \, x + 1\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 8, normalized size = 0.57
method | result | size |
derivativedivides | \({\mathrm e}^{{\mathrm e}^{2 x +1}}\) | \(8\) |
default | \({\mathrm e}^{{\mathrm e}^{2 x +1}}\) | \(8\) |
norman | \({\mathrm e}^{{\mathrm e}^{2 x +1}}\) | \(8\) |
risch | \({\mathrm e}^{{\mathrm e}^{2 x +1}}\) | \(8\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 7, normalized size = 0.50 \begin {gather*} e^{\left (e^{\left (2 \, x + 1\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.39, size = 7, normalized size = 0.50 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{2\,x+1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 7, normalized size = 0.50 \begin {gather*} e^{e^{2 x + 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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