Check whether the differential form is correct

Question

I have the following differential form $$ \omega = \left( 2x \sin(y) + \alpha \frac{y+1}{\left(x-1\right)^2 +\left(y+1\right)^2}\right)dx + \left( \beta x^2 \cos(y) - \alpha \frac{x-1}{\left(x-1\right)^2 +\left(y+1\right)^2}\right)dx $$ defined in $\mathbb{R}-\left\lbrace \left( 1,-1 \right) \right\rbrace $ and I have to check for which values of $\alpha$ and $\beta$ it's closed and exact. In order to verify closure I check equality with cross partial derivatives and it holds if $\beta = 1$ and $\forall \alpha \in \mathbb{R}$. My problem is to find the value for which it's exact. I set $$ U(x,y)= \int \omega_1 dx $$ but I am not able to solve the integral. There is a easy way?