1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Arctan integration question

  1. May 13, 2009 #1
    1. The problem statement, all variables and given/known data
    ∫xarctanx dx


    2. Relevant equations
    d/dx (arctanx) = 1/(1 + x^2)
    ∫1/(1 + x^2) = arctanx
    ∫u dv = uv - ∫v du

    3. The attempt at a solution
    Hi everyone,

    Here's what I've done so far:

    Use integration by parts:
    u = arctanx
    du = 1/(1 + x^2) dx

    dv = x dx
    v = (1/2)x^2

    ∫u dv = uv - ∫v du
    = arctanx(1/2)x^2 - (1/2)∫x^2/(1 + x^2) dx

    But how do you integrate this new integral without going back into arctanx, in which case you'll be left with zero?

    Thanks for any help
     
  2. jcsd
  3. May 13, 2009 #2

    benorin

    User Avatar
    Homework Helper

    Long division. [tex]\frac{x^2}{1+x^2}=1-\frac{1}{1+x^2}[/tex]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook