Who's up to the challenge?16

Calculus Level 5

$\displaystyle\int _{ 0 }^{ \infty }{ { e }^{ -x }{ 2 }^{ x }\ln x\, dx=\dfrac { A\gamma +\ln(B-\ln(C)) }{ \ln(D)-F } } \\ \\ A,B,C,D,F\quad \in \mathrm{N}$

find $$A+B+C+D+F$$.

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