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How do I find this integral?

  1. Dec 24, 2017 #1
    1. The problem statement, all variables and given/known data
    Find the integral of 1/(1+cosx) dx from -pi/2 to pi/2.

    2. Relevant equations
    None.

    3. The attempt at a solution
    Here's my work:
    1/(1+cosx)=(1-cosx)/((1+cosx)(1-cosx))=(1-cosx)/(1-cos^2 x)=(1-cosx)/sin^2 x
    This is what I've got so far. But this doesn't seem to simplify the integrand.
     
  2. jcsd
  3. Dec 24, 2017 #2

    PeroK

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    That looks good so far. What about splitting up the integral into two now?
     
  4. Dec 24, 2017 #3
    Never mind. I got it. You gave me the big hint already, splitting it up.
     
  5. Dec 24, 2017 #4
    Thank you so much! Merry Christmas!
     
  6. Dec 24, 2017 #5

    PeroK

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    There was a quicker way. Hint: ##x = 2(x/2)##.
     
  7. Dec 24, 2017 #6
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