Question Number 149675 by mathdanisur last updated on 06/Aug/21
$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\sqrt[{\boldsymbol{\mathrm{n}}}]{\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)^{\boldsymbol{\mathrm{n}}+\mathrm{1}} }}\:=\:? \\ $$