Integrating 1/sqrt(cos[2x]): Homework Help and Solution Explanation

[hungryhippo]

Homework Statement

Integrate
1/sqrt(cos[2x]) from theta prime to pi/4

Homework Equations

Your basic trig identities:
cos[2x]= 2cos^2[x]-1 = 1- 2sin^2[x] = cos^2[x]-sin^2[x]
sin^2[x]+cos^2[x] = 1
sin[2x] = 2sin[x]cos[x]

Apparently, you're supose to manipulate so that you can do a substitution to eliminate all trigonometric terms, i.e. cosx, sinx, and whatever may come up. Then, since a substitution occurred, you can then change the bounds of integration.

It should be similar to integrating 1/cosx by manipulation and substitution.

The Attempt at a Solution

Well, the first thing for me was trying to get rid of the square root in the denominator, multiplying top and bottom by cos[2x] everything i seem to have done thus far, ends up going in circles...

 

[Bohrok]

$$\int\frac{1}{\sqrt{\cos2x}}dx$$

This doesn't have an elementary antiderivative...

 

[hungryhippo]

$$\int\frac{1}{\sqrt{\cos2x}}dx$$

This doesn't have an elementary antiderivative...

I'm not sure about this question, but from what I was told, you have to use identities and manipulation in order to get it into a form that substitution is possible...