How to calculate the principal part of this improper integral via contour integration?
\begin{equation} P\int_{0}^{+\infty}\frac{dx}{x^2+x-2} \end{equation}
I have seen some examples where you integrate along a semicircle and then take the limit $R\to\infty$, where $R$ is the radius. But here the integrand is not a even function and in addition there are poles on the real line (that's why is divergent)... Any help is appreciated.