Optimal. Leaf size=13 \[ e^{e-2 e^{11-3 x}} \]
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Rubi [A] time = 0.02, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {12, 2282, 2194} \begin {gather*} e^{e-2 e^{11-3 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} &=6 \int e^{11+e-2 e^{11-3 x}-3 x} \, dx\\ &=-\left (2 \operatorname {Subst}\left (\int e^{11+e-2 e^{11} x} \, dx,x,e^{-3 x}\right )\right )\\ &=e^{e-2 e^{11-3 x}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 13, normalized size = 1.00 \begin {gather*} e^{e-2 e^{11-3 x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 16, normalized size = 1.23 \begin {gather*} e^{\left (e - \frac {1}{2} \, e^{\left (-3 \, x + 2 \, \log \relax (2) + 11\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 12, normalized size = 0.92 \begin {gather*} e^{\left (e - 2 \, e^{\left (-3 \, x + 11\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 13, normalized size = 1.00
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}-2 \,{\mathrm e}^{11-3 x}}\) | \(13\) |
derivativedivides | \({\mathrm e}^{{\mathrm e}} {\mathrm e}^{-2 \,{\mathrm e}^{11-3 x}}\) | \(20\) |
default | \({\mathrm e}^{{\mathrm e}} {\mathrm e}^{-2 \,{\mathrm e}^{11-3 x}}\) | \(20\) |
norman | \({\mathrm e}^{{\mathrm e}} {\mathrm e}^{-2 \,{\mathrm e}^{11-3 x}}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 12, normalized size = 0.92 \begin {gather*} e^{\left (e - 2 \, e^{\left (-3 \, x + 11\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 13, normalized size = 1.00 \begin {gather*} {\mathrm {e}}^{-2\,{\mathrm {e}}^{-3\,x}\,{\mathrm {e}}^{11}}\,{\mathrm {e}}^{\mathrm {e}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 14, normalized size = 1.08 \begin {gather*} e^{e} e^{- 2 e^{11 - 3 x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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