Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integral using series

  1. Sep 20, 2006 #1


    User Avatar
    Homework Helper
    Gold Member

    [tex]\int \frac{x-\tan^{-1} x}{x^3}[/tex]

    I know the series form of tan-1 x = [tex] \sum_{n=0}^{\infty} \frac{x^{2n+1}}{2n+1} [/tex]

    I know I need to subtract the x from that series and divide the x cubed form that series but i can't seem to be able to right the resulting series in a general form, any hints?

    I thought it would be: [tex] -1/3x + \sum_{n=2}^{\infty} -x^{2n+2}/(2n+1)(2n+2)[/tex]. But this isnt it. Any Help?
  2. jcsd
  3. Sep 20, 2006 #2
    I don't see how you arrived at that series. What you may want to consider doing also, for simplicity's sake, is to separate the integral into one that can be easily evaluated and one that should be done by series. Redo your solution paying particular attention to integrating -arctan(x)/x^3
  4. Sep 21, 2006 #3


    User Avatar
    Homework Helper

    Dividing by x^3 just reduces the power of x by 3, ie, x^n/x^3=x^(n-3). Your answer is close.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook