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Complex Integral I just can't figure out

  1. Apr 6, 2010 #1
    hi, this is really frustrating because I've been working on this one integral for the last 2 1/2 horus and i cant figure out what I did wrong...

    it's the Integral sin^2(x)/(3-2cos(x)) dx from x=0 to x=2pi


    I tried the substitution z=e^(itheta) plugging in sin and cos as functions of z and I

    ultimately get:

    i * integral (z^4+2z^2+1)/(z^2-3z+1)dz over |z|=1

    Then the poles inside the unit circle are @ z=0 and (3-sqrt(5))/2

    so I find the residue @ z=0 to be 3 and @ (3-sqrt5)/2 something like

    (looking in my mess of notes) 4(15-6sqrt(5))^2/((3-sqrt(5)^2(-sqrt(5))

    then I plug in 2pi X Sum residues X i

    but it doesn't agree with the answer I get on my calculator which is around 1.19

    any help is really appreciated thanks!
     
  2. jcsd
  3. Apr 7, 2010 #2
    sorry to anyone who was trying to figure it out...i solved it

    turns out i substitutes 1/2(z+1/z) for sine instead of 1/(2i)(z-1/z)

    I make the stupidest mistakes ever and it costs me. anyone know how i can

    avoid these =(
     
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