How do you integrate the square root of cos³(x)?

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Player_13 said:
X-43D, I don't think that's correct. I plugged a value for each in my calculator, and the answers were different.

How much did you get?
 
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Yeah I've been playing with it, can't really get anywhere. I was tryin to figure out a way with trig identities to simplify it, but I can't get rid of the square root.
 
So I walk into class and my teacher begins to explain the problem... And all she has on the overhead is how to set up the problem, then tells us that she pluged it into the calculator. I guess there is no simple way of solving this, sorry for "wasting" your time with this.
 
It's quite likely that it is impossible to find this antiderivative (the EllipticF function most likely can't be expressed in terms of simple functions, although I'm not entirely certain about that)~