Question

How do you integrate `sqrt(1+(4cos^2))dx`?

Answer 1

Normally, you might expect that the `1` be a `4` so you can just do trig substitution. Unfortunately we can't do that.

If you are not in a very advanced Calculus course, where you might work with elliptic integrals, you don't have to know how to do this analytically. At best you can do a numeric integral.

So, you can evaluate `int_a^b sqrt(1+4cos^2x)dx` on your calculator or on Wolfram Alpha, but it's not something I believe you have been taught to do by hand.

http://www.wolframalpha.com/input/?i=integral+of+sqrt%281%2B4cos^2%28x%29%29