# Evaluating $\int \arccos\bigl(\frac{\cos(x)}{r}\bigr) \, \mathrm{d}x$

The title says it all, really - I am looking for

$$\int \arccos\left(\frac{\cos(x)}{r}\right) \, \mathrm{d}x$$

where $0<r<1$ and $x$ is in a domain where the integrand is real. It came up in a research problem involving billiard dynamics, but this is probably not relevant. I tried the usual techniques, Gradstein & Ryzhik and Mathematica without success. I am mostly seeking an exact answer, though it could involve obscure special functions.

Edit: Following Axoren, I am trying to expand the integrand in a series. Putting the following in mathematica