Why is this integral $\int_{2\pi}^0 {x^ae^{ia\theta}\over 1+\sqrt{2} x e^{i\theta}+x^2e^{2i\theta}}ixe^{i\theta}d\theta=O(x^{a+1})\to 0$ as $x\to 0$,where $|a|<1$?
I understand that limit value bit (!) but I don't see why the integrand should be of that order. I would have thought that the order should be $O(x^a)$.
Source : these notes.