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Integral using residues

  1. Oct 16, 2007 #1
    [SOLVED] Integral using residues

    1. The problem statement, all variables and given/known data
    Show integral of 1/(x^4+x^2+1) from 0 to infinity equals (pi*sqrt(3))/6 using method of residues



    2. Relevant equations



    3. The attempt at a solution
    Tried to solve x^4+x^2+1=0. Don't get very useful numbers for poles.
     
  2. jcsd
  3. Oct 17, 2007 #2

    cristo

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    Well what do you know about the method of residues? You've not really shown any work now, have you?
     
  4. Oct 17, 2007 #3
    don't worry i worked it out. I didn't solve the quartic properly to get the poles before. I got my 4 poles two of which Im parts are more than 0. I evaluated the residues at those two poles and got the value. Since it's even I can divide that number by two to get the integral from 0 to inf rather than -inf to inf. I didn't notice there was a much easier way to solve that quartic by letting y=x^2 and then using quadratic formula to find y then x would be just the sqrt of y.
     
  5. Oct 17, 2007 #4

    cristo

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    Well done!
     
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