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.

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

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