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Help with Integration

  1. Sep 29, 2009 #1
    1. The problem statement, all variables and given/known data
    Integrate
    1/sqrt(cos[2x]) from theta prime to pi/4


    2. Relevant 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.

    3. 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...
     
    Last edited: Sep 29, 2009
  2. jcsd
  3. Sep 29, 2009 #2
    [tex]\int\frac{1}{\sqrt{\cos2x}}dx[/tex]

    This doesn't have an elementary antiderivative...
     
  4. Sep 29, 2009 #3
    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...
     
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