Optimal. Leaf size=22 \[ 3+e^{e^4-2 x}+3 x \log (5)+(2+x) \log (5) \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.68, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {2194} \begin {gather*} e^{e^4-2 x}+4 x \log (5) \end {gather*}
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 x \log (5)-2 \int e^{e^4-2 x} \, dx\\ &=e^{e^4-2 x}+4 x \log (5)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 0.64 \begin {gather*} e^{e^4-2 x}+x \log (625) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 13, normalized size = 0.59 \begin {gather*} 4 \, x \log \relax (5) + e^{\left (-2 \, x + e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.27, size = 13, normalized size = 0.59 \begin {gather*} 4 \, x \log \relax (5) + e^{\left (-2 \, x + e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 14, normalized size = 0.64
method | result | size |
default | \({\mathrm e}^{{\mathrm e}^{4}-2 x}+4 x \ln \relax (5)\) | \(14\) |
norman | \({\mathrm e}^{{\mathrm e}^{4}-2 x}+4 x \ln \relax (5)\) | \(14\) |
risch | \({\mathrm e}^{{\mathrm e}^{4}-2 x}+4 x \ln \relax (5)\) | \(14\) |
derivativedivides | \({\mathrm e}^{{\mathrm e}^{4}-2 x}-2 \ln \relax (5) \ln \left ({\mathrm e}^{{\mathrm e}^{4}-2 x}\right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 13, normalized size = 0.59 \begin {gather*} 4 \, x \log \relax (5) + e^{\left (-2 \, x + e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 14, normalized size = 0.64 \begin {gather*} 4\,x\,\ln \relax (5)+{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{{\mathrm {e}}^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 14, normalized size = 0.64 \begin {gather*} 4 x \log {\relax (5 )} + e^{- 2 x + e^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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