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Improper integral with arctan

  1. Aug 11, 2011 #1
    1. The problem statement, all variables and given/known data
    find the integral from 1 to infinity of (arctanx/x^2)dx


    2. Relevant equations



    3. The attempt at a solution
    i used integration by parts:
    u=arctanx
    du=1/(1+x^2)dx
    dv=x^-2dx
    u=(-1/x)

    -arctanx/x + [(1/(x)(1+x^2))dx]from 1 to infinity
    i have a partial solution in my book, and here it suggests that i change the integrand to
    (1/x)-(x/(1+x^2)) which if i work backward, i can see is equal to the original integrand, but i don't see how to get from (1/(x)(1+x^2)) to (1/x)-(x/(1+x^2))
    help?
     
  2. jcsd
  3. Aug 11, 2011 #2
    It's done with partial fractions; have you covered partial fractions before?
     
  4. Aug 11, 2011 #3
    yes! thankyou :)
     
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