A student randomly asked me to compute
$\int\sqrt{\cos(2\theta)}\, \mathrm d\theta.$
I was unable to do so, as were several other instructors. I typed the integral into Wolfram and it says that it is an elliptic integral of type 2. I am not familiar with elliptic integrals and I don't have any idea why this student asked me to do this since we are not even doing derivatives yet. Is this integral important? Does it have a closed form answer?