Consider the following integral with $α,β,γ$ constant coefficients: \begin{equation}\int_{-\infty}^{\infty}\frac{e^{iαx}}{βx^2+iγx}dx\end{equation}
We can say that this is an inverse Fourier Transformation of a complex function.Can you please propose a way to solve this analytically or numerically. Is there any particular theory, books, papers?