Question Number 162859 by HongKing last updated on 01/Jan/22
$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\int}}\:\frac{\mathrm{e}^{\boldsymbol{\mathrm{cos}}\:\mathrm{2}\boldsymbol{\mathrm{x}}} \:\centerdot\:\mathrm{sin}\left(\mathrm{x}\:+\:\mathrm{sin}\:\mathrm{2x}\right)}{\mathrm{sin}\:\mathrm{x}}\:\mathrm{dx}\:=\:\frac{\pi{e}}{\mathrm{2}} \\ $$