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Homework Help: How to integrate 1/(x^2 +1)^2, does partial fractions work?

  1. Dec 10, 2009 #1
    how do you integrate 1/(x2 + 1)2 ?


    i have tried integration by partial fractions but when you set 1 equal to (Ax +B)(x2+1) + (Cx + D) this leads to A=B=C=0 and D=1 which just gives you the original equation
     
  2. jcsd
  3. Dec 10, 2009 #2
    Re: integration

    Try subbing x=tan(u), dx=1/cos^2(u)
     
  4. Dec 10, 2009 #3
  5. Dec 10, 2009 #4
    Re: integration

    Partial fraction in terms of the complex linear fractions 1/(x±i) and 1/(x±i)^2 will also work. You can then take together terms with their complex conjugate and then rewrite everything in a manifestly real form (you need to use the relation between the logarithm and arctan etc.).
     
  6. Dec 10, 2009 #5
    Re: integration

    ah thank you that works
     
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