What would be the easiest way to evaluate $\oint\limits_{K}(1-\frac{y^2}{x^2}\cos(\frac{y}{x}))\,\mathrm{dx} +(\sin(\frac{y}{x})+\frac{y}{x}\cos(\frac{y}{x}))\mathrm{dy}$ where $K$ is counter-clockwise oriented closed arc of ellipse $(\frac{x-20}{2})^2+y^2=1$?
I've tried using polar coordinates by substituing $x=2\cos(\phi)+20$ and $y=\sin(\phi)$ but in the end I'm left with a very unpleasent integral. Any help is appreciated! :)