I need to solve the equation
$I = \int_0^u\frac{dx}{(a + bx + i\epsilon)^2}$,
where $a$ and $b$ are real, and functions of $u$ ($u$ is another variable that I have to perform another integral after). I tried to use the Sokhotski–Plemelj theorem,
$\lim_{\epsilon\to 0}\int_{-\infty}^{+\infty}\frac{f(x)dx}{x-x_0+i\epsilon} = P\int_{-\infty}^{+\infty}\frac{f(x)dx}{x-x_0} + i\pi \delta(x - x_0)$
I don't know if I can directly use this theorem, once the integration limits in $I$ are different. If there is no problem, I have the Principal Value, $\frac{u}{a(a-bu)}$, but I am not sure about the argument of delta function. There is another way to proceed? Thanks in advance!