Optimal. Leaf size=24 \[ (-10+5 \log (3)) \left (2+\log \left (\frac {1}{3} e^5 \left (e^{e^x}+x\right )\right )\right ) \]
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Rubi [A] time = 0.06, antiderivative size = 16, normalized size of antiderivative = 0.67, number of steps used = 1, number of rules used = 1, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {6684} \begin {gather*} -5 (2-\log (3)) \log \left (x+e^{e^x}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-5 (2-\log (3)) \log \left (e^{e^x}+x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 14, normalized size = 0.58 \begin {gather*} 5 (-2+\log (3)) \log \left (e^{e^x}+x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 26, normalized size = 1.08 \begin {gather*} -5 \, x \log \relax (3) + 5 \, {\left (\log \relax (3) - 2\right )} \log \left (x e^{x} + e^{\left (x + e^{x}\right )}\right ) + 10 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.22, size = 37, normalized size = 1.54 \begin {gather*} -5 \, x \log \relax (3) + 5 \, \log \relax (3) \log \left (x e^{x} + e^{\left (x + e^{x}\right )}\right ) + 10 \, x - 10 \, \log \left (x e^{x} + e^{\left (x + e^{x}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 14, normalized size = 0.58
method | result | size |
norman | \(\left (5 \ln \relax (3)-10\right ) \ln \left (x +{\mathrm e}^{{\mathrm e}^{x}}\right )\) | \(14\) |
risch | \(5 \ln \left (x +{\mathrm e}^{{\mathrm e}^{x}}\right ) \ln \relax (3)-10 \ln \left (x +{\mathrm e}^{{\mathrm e}^{x}}\right )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 12, normalized size = 0.50 \begin {gather*} 5 \, {\left (\log \relax (3) - 2\right )} \log \left (x + e^{\left (e^{x}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.16, size = 13, normalized size = 0.54 \begin {gather*} \ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^x}\right )\,\left (5\,\ln \relax (3)-10\right ) \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 = 0.58 \begin {gather*} 5 \left (-2 + \log {\relax (3 )}\right ) \log {\left (x + e^{e^{x}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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