MathNet 2019-part-04 — 184 problems (EN–VI) Question 52

Let $I_{n}=n \int_{0}^{1} \frac{\cos x}{1+e^{n x}} d x$, where $n \in \mathbb{N}^{*}$. Compute $\lim _{n \rightarrow \infty} I_{n}$.