Question Number 32635 by mondodotto@gmail.com last updated on 29/Mar/18
Commented by Joel578 last updated on 30/Mar/18
$$\mathrm{Use}\:\mathrm{substitution} \\ $$$${u}\:=\:{e}^{{e}^{\iddots^{{x}} } } \:\:\left(\mathrm{8}\:{e}\:\mathrm{as}\:\mathrm{powers}\right) \\ $$$$\mathrm{and}\:\mathrm{gives}\:\mathrm{you} \\ $$$${I}\:=\:\int\:{e}^{{u}} \:{du} \\ $$