I am currently trying to find the indefinite integral
$$\int \sqrt{1 -\frac{1-\cos (x)}{z(x-\sin(x))}}{dx} $$ where $z$ is a constant. I have not been able to make any progress, and have tried checking tables of integrals and other relevant resources, but none of these appear to provide me with an answer. How would any of you go about solving this integral?