Closed and exact differential form with respect to parameters

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With respect to parameters $a$ and $b$ decide, whether the 1-differential form is closed or exact.If so, find the primitive function $f(xy),\omega=df$

$ \omega = (y- \frac{a}{2}x^{2a-1}\sin(2by))dx + bx^{2a}\sin^2(by)dy=\omega_1dx+\omega_2 dy $

I dont really know how to get into this. I am really thankful for any hint on how to solve this.