Question Number 212616 by im13 last updated on 19/Oct/24
$$ \\ $$$$ \\ $$$${if}\:\:\mathrm{f}\left(\mathrm{x}\right)=\:^{{a}} {x}={x}^{{x}^{{x}^{\iddots^{{x}} } } } \left({there}\:{are}\:{a}\:{x}'{s};{a}\in\mathbb{N}\:{and}\:{a}\neq\mathrm{0}\right) \\ $$$$\int{f}\left({x}\right){dx}=? \\ $$
Commented by Frix last updated on 20/Oct/24
$$\mathrm{There}'\mathrm{s}\:\mathrm{not}\:\mathrm{even}\:\mathrm{a}\:\mathrm{closed}\:\mathrm{form}\:\mathrm{for}\:\int{x}^{{x}} {dx} \\ $$