I want to obtain the symbollic expression for this integral:
$\int^\infty_{-\infty} \, dx \, \left(\frac{y - x}{R^2 + (y-x)^2}\right)\, e^{-\frac{(x - \mu)^2}{4 s^2} - \frac{i k (y - x)^2}{2 R}}$,
where $i$ is the imaginary unit and all other variables are real. With symbolic, I just want to make clear that the answer should maintain the form of all the variables, but $x$ in the final form of the result.
Thanks!