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Homework Help: Integration with Sines and Cosines

  1. Feb 25, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex]\int[/tex]sinxcosx/sin^4x+cos^4x


    2. Relevant equations

    sin^2x=1/2-1/2cos(2x)

    cos^2x=1/2+1/2cos(2x)

    sinxcosx=1/2sin(2x)

    3. The attempt at a solution

    [tex]\int[/tex]1/2 sin(2x)/(1/2-1/2cos(2x))^2 + (1/2 + 1/2cos(2x))^2

    [tex]\int[/tex]1/2 sin(2x)/1/2 + 1/2cos^2(2x)

    ...?

    Am I on the right track?
     
  2. jcsd
  3. Feb 25, 2010 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Ayesh! :smile:

    (have an integral: ∫ and try using the X2 tag just above the Reply box :wink:)

    Yes, that's fine.

    (though it would have been quicker to notice that the original denominator is almost the square of cos2x + sin2x :wink:)

    And you should be able to integrate it immediately. :smile:
     
  4. Feb 26, 2010 #3
    Thank you!
     
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