Optimal. Leaf size=25 \[ e^{x \left (20+\log \left (\frac {1}{x}-\log \left (\frac {e^{-x} \log (2)}{x}\right )\right )\right )} \]
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Rubi [A] time = 1.63, antiderivative size = 29, normalized size of antiderivative = 1.16, number of steps used = 1, number of rules used = 1, integrand size = 113, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.009, Rules used = {6706} \begin {gather*} e^{20 x} \left (\frac {1-x \log \left (\frac {e^{-x} \log (2)}{x}\right )}{x}\right )^x \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{20 x} \left (\frac {1-x \log \left (\frac {e^{-x} \log (2)}{x}\right )}{x}\right )^x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 26, normalized size = 1.04 \begin {gather*} e^{20 x} \left (\frac {1}{x}-\log \left (\frac {e^{-x} \log (2)}{x}\right )\right )^x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 28, normalized size = 1.12 \begin {gather*} e^{\left (x \log \left (-\frac {x \log \left (\frac {e^{\left (-x\right )} \log \relax (2)}{x}\right ) - 1}{x}\right ) + 20 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.64, size = 25, normalized size = 1.00 \begin {gather*} e^{\left (x \log \left (\frac {1}{x} - \log \left (\frac {e^{\left (-x\right )} \log \relax (2)}{x}\right )\right ) + 20 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.22, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (x \ln \left (\frac {\ln \relax (2) {\mathrm e}^{-x}}{x}\right )-1\right ) \ln \left (\frac {-x \ln \left (\frac {\ln \relax (2) {\mathrm e}^{-x}}{x}\right )+1}{x}\right )+20 x \ln \left (\frac {\ln \relax (2) {\mathrm e}^{-x}}{x}\right )-x^{2}-x -19\right ) {\mathrm e}^{x \ln \left (\frac {-x \ln \left (\frac {\ln \relax (2) {\mathrm e}^{-x}}{x}\right )+1}{x}\right )+20 x}}{x \ln \left (\frac {\ln \relax (2) {\mathrm e}^{-x}}{x}\right )-1}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 28, normalized size = 1.12 \begin {gather*} e^{\left (x \log \left (x^{2} + x \log \relax (x) - x \log \left (\log \relax (2)\right ) + 1\right ) - x \log \relax (x) + 20 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.90, size = 21, normalized size = 0.84 \begin {gather*} {\mathrm {e}}^{20\,x}\,{\left (x-\ln \left (\frac {\ln \relax (2)}{x}\right )+\frac {1}{x}\right )}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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