I'm trying to solve the following integral:
$$ \int_{-\infty}^{+\infty} \frac{e^{iax}}{1+x^4}dx $$
From what I understand, since we have the complex exponential we consider the poles not only in the upper half plane but in the whole plane but then is the contour a circle englobing all poles or 2 semi-circles, one in the upper half plane, one in the lower half plane, each containing 2 poles? Or is it something else?
Many thanks!