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Integration Problem

  1. Feb 26, 2007 #1
    1. The problem statement, all variables and given/known data

    [tex] \int {\frac{sin^{2}x}{1+sin^{2}x}dx}[/tex]

    2. Relevant equations

    Let t = tan x/2, then dx = 2/(1+t^2) and sin x = 2t / (1+t^2)

    3. The attempt at a solution

    I got up to the point where [tex] \int {\frac{8t^{2}}{(1+6t^{2}+t^{4})(1+t^{2})} dt}[/tex]. Not sure if I'm on the right track and if I am, do I use partial fractions after this?

    The final answer is attached. Can't really make out the handwriting :/

    Attached Files:

    Last edited: Feb 26, 2007
  2. jcsd
  3. Feb 26, 2007 #2
    Yes, it looks like partial fractions is the way to go after your substitution.
  4. Feb 26, 2007 #3
    Hmm after I do partial fractions, I get
    [tex] \int {\frac{2}{1+t^{2}} + {\frac{-2t^{2}-2}{(1+6t^{2}+t^{4})} dt}[/tex]

    After this, I do not know what's the next step. Kindly advise. Thanks.
  5. Feb 26, 2007 #4
    you are summing 2 functions of t , one of these two look very much like a derivative of a certain function..
  6. Feb 26, 2007 #5
    If you mean 2tan^-1 t, I can get this part. But what about the 2nd function?
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