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Homework Help: Integral using partial fraction

  1. Dec 31, 2009 #1
    The problem statement, all variables and given/known data

    integral using partial fraction

    Hi everyone ,,

    got the following question :


    The attempt at a solution

    I reached the following ,,

    integral ( 4/(X^2+x+1) + (-4x-1)/(X^2+x+1)^2) )

    and now I don't know how to integrate .. -_-

    help please
     
  2. jcsd
  3. Dec 31, 2009 #2
    here is a hint:

    x^2+x+1=(x+1/2)^2+3/4, use subst: (sqrt(3)/2)*t=x+1/2, do you see why?

    the second one: for the numerator: -(4x+1)=-(4x+2-1)=-2(2x+1)+1 then separate the fractions, for the first fraction use subst. u=x^2+x+1, do u see why? for the second fracction, proceed using the first hint i gave initially.

    come back if you have more questions.
     
  4. Dec 31, 2009 #3
    thx m8 ,, I'll check the hints ,, and I'll come back If i have more questions :)
     
  5. Jan 2, 2010 #4
    thanks very much sutupidmath ,, I've answered it thanks to your hint ,, thanks again :)
     
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