MathNet 2023-part-03 — 191 problems (EN–VI) Question 154

Consider the function $I:(0 ;+\infty) \rightarrow \mathbb{R}$, $I(a)=\int_{-a}^{a} \frac{d x}{\left(e^{x}+1\right)(|x|+a)}$. Show that $I$ is a constant function.