Question Number 151838 by talminator2856791 last updated on 23/Aug/21
$$\: \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\frac{\left({x}^{\mathrm{log}\left(\lfloor\left(\lfloor{x}\rfloor!\right)^{\left(\mathrm{log}\left(\lfloor{x}−\mathrm{1}\rfloor!\right)\right)^{−\mathrm{1}} } \rfloor\right)+\mathrm{1}} +\mathrm{1}\right)^{{x}} }{\lfloor{x}^{\mathrm{log}\left({x}^{{x}} \right)+\mathrm{1}} \rfloor!+\mathrm{1}}\:{dx} \\ $$$$\: \\ $$