Let $R > r > 0$ be constants. I'm trying to work out the following integral:
$$ \int_{R-r}^R\arccos\bigg(\frac{\cosh(y)\cosh(r)-\cosh(R)}{\sinh(y)\sinh(r)}\bigg)\sinh(y)dy.$$
So far, I substituted $u = \cosh(y)$ to get
$$ \int_{\cosh(R-r)}^{\cosh(R)}\arccos\bigg(\frac{\cosh(r)u-\cosh(R)}{\sinh(r)\sqrt{u^2-1}}\bigg)dy,$$
but at this point I am stuck. I would be grateful for any hints or solutions!