I want to solve the integral attached below by means of residue theorem. I tried the common integration ways and seeked references(e.g, Rjadov, et. al).
Finally, I decided to solve this integral by means of " Residue Theorem ". Can anyone help me ?
$$ \int_u^\infty \frac{Ei(-x)e^{-px}}{(x-\beta)}dx\,. $$
$$ p>0\ ,\ \beta>0\ \ ,\ u>0 \ , \ \ u < \beta $$