I have the following integral:
$\displaystyle\int\limits_{0}^\infty\frac{\arctan(\eta_2+x)}{(x+\eta_1)^2+\eta_3^2}\ d x$
where $\eta_1$, $\eta_2$ and $\eta_3$ are real numbers. If the integrand were even it could be evaluated through the residue theorem because limits of the integral could be changed to form $-\infty$ to $\infty$ and a semicircular contour in the upper (or lower) half plane could be used. But in this case I can't figure out how to close the region to use the residue theorem. I can't also find another method to evaluate the integral.
Can someone please offer a solution to the conclusion of this problem?