# How to calculate this elliptic integral?

I need to calculate this integral $$\int \cos(t\theta)\sqrt{1-k^{2}cos(\theta)^{2}} \mathrm{d}\theta$$

But according to Wolfram|Alpha there is no result in terms of standart mathematical functions.

How do we calculate this integral?

Edit: t is integer.

• A definite version can be approximated by a Riemann sum, if that's what you mean. It's still unclear what you're asking. – Dzoooks Apr 29 at 21:16
• For each value of $t$ Mathematica can find the integral, but it gets complicated quickly. What do you need the integral for? – Somos Apr 30 at 2:02