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Trigonometric Intergrals

  1. Oct 22, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the integral of cos4 xdx


    2. Relevant equations

    cos2x = 2cos2x-1
    cos2x = (cos2x+1)/2


    3. The attempt at a solution

    I tried using cos4x = cos2x * cos2x and i simplified it to
    cos4x = ((cos2x)2 + 2cos2x + 1)/4

    I'm not sure if this is right. How do i go about getting the integral of this expression if it is correct. Thanks
     
  2. jcsd
  3. Oct 22, 2009 #2

    Mark44

    Staff: Mentor

    So far, so good. You just need to take it one step farther, by replacing (cos2x)2 with (cos4x + 1)/2. At that point you'll have an integral with four terms, and you can split this up into four integrals, each of which is pretty easy.
     
  4. Oct 22, 2009 #3
    Hey i got the answer (sin4x)/32 + (sin2x)/4 + (3x)/8 + C which seems to be right. Thanks for your help :)
     
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