Originally Posted by
FernandoRevilla Always there is someone. You have correctly found $\displaystyle CPV=\lim_{R\to +\infty}\int_{-R}^Rf(x)\;dx$ (Cauchy Principal Value). As the given integral is convergent then, $\displaystyle \int_{-\infty}^{+\infty}f(x)\;dx=CPV=\pi/\sqrt{2}$