1. Not finding help here? Sign up for a free 30min 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!

Power series

  1. Feb 5, 2005 #1
    Evaluate the indefinite integral as a power series and find radius of convergence. (i don't know how to type the integral and summations signs, sorry)


    (integral sign) (x-tan^-1x)/x^3 dx. ( if you write this out it makes more sense)

    i was able to find the power series of tan^-1x = x^(2n+1) (-1)^n/(2n+1).
    i don't know how to continue on with this. all we have learned is to use the power series of the geometric series 1/(1-x), and some integration/differentiation methods.

    i am rather confused on the whole topic, so if anyone has any ideas, the simplest explanations would be greatly appreciated. thanks
     
  2. jcsd
  3. Feb 5, 2005 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    So your integral is
    [tex] \int \frac{x-\arctan x}{x^{3}} dx [/tex]

    ??Okay,for term by term integration of it,separate it into 2 integrals...Though it's not really helpful for the convergence part...

    Daniel.
     
  4. Feb 5, 2005 #3
    that is the integral, thanks, but i am not sure what to do after pulling it apart into two integrals. quite honestly, i am puzzled by this whole topic. any advice?
     
  5. Feb 5, 2005 #4

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    1.Pull apart into integrals.
    2.Integrate the first.It's elementary.
    3.Write the series expansion of "artan" and devide its terms by x^{3}.
    4.Integrate by parts eery term of the new series...
    5.Think of a way to get the convergence radius.

    Daniel.

    P.S.It can be done exactly (find the antiderivative).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Power series
  1. Power series (Replies: 5)

  2. Power Series (Replies: 5)

  3. Power series (Replies: 2)

  4. Power Series (Replies: 15)

  5. Power series (Replies: 8)

Loading...