Question Number 159935 by qaz last updated on 22/Nov/21
$$\mathrm{Prove}::\:\:\:\:\underset{\mathrm{x}\rightarrow+\infty} {\overline {\mathrm{lim}}xe}^{−\mathrm{x}} \int_{\mathrm{1}} ^{\mathrm{x}} \frac{\mathrm{e}^{\mathrm{t}} \mathrm{sin}\:\mathrm{t}}{\mathrm{t}}\mathrm{dt}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}} \\ $$