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

  • #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
 

Answers and Replies

  • #2


Try subbing x=tan(u), dx=1/cos^2(u)
 
  • #4
1,851
7


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.).
 
  • #5


ah thank you that works
 

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