Sokhotski–Plemelj Theorem

Here is the formula,

$\lim_{\varepsilon\rightarrow 0^+} \int_a^b \frac{f(x)}{x\pm i \varepsilon}\,dx = \mp i \pi f(0) + \mathcal{P}\int_a^b \frac{f(x)}{x}\, dx,$ where the second term is the principal value integral.

Don’t ask my why.

Sokhotski–Plemelj theorem