Calculus

You are given one positive integer $N$. Calculate $$\int_{0}^{\infty} \frac{e^{2 \pi x} - 1}{e^{2 \pi x} + 1} \left(\frac{1}{x} - \frac{x}{N^2 + x^2}\right) \,\mathrm{d}x \,.$$ It is possible to prove that its value can be written as a fraction $\frac{a}{b}$, where $a$ and $b$ are positive integers and $b$ is coprime with $998,244,353$. You need to find $a \cdot b^{-1}$ modulo $998,244,353$, w