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!

Integrate x^2/(1+4•x^2)? Partial fractions

  1. Oct 2, 2012 #1
    One last question


    to Integrate x^2/(1+4•x^2). I would assume you would do long division but 4x^2 is bigger than x^2. so would you either pull out a 1/4 and it would be 1/4 ∫ x^2/(1/4+•x^2) dx or would the first term when doing long division be 1/4? or am I just totally wrong and you wouldn't do long division because the top is smaller than the bottom?
     
  2. jcsd
  3. Oct 2, 2012 #2
    Yes, you do a long division and you get 1/4 + remainder. What is the remainder?
     
  4. Oct 2, 2012 #3
    Ok, finished it but it was ugly. And I think I messed up my algebra somewhere.
    your remainder ends up being -1/4 so you get∫ 1/4 +( -1/4/ (1+4x^2))so I decided to pull out the 4 to get the form x^2+a^2 so you get 1/4x + ∫-1/4 / (4((1/4)+x^2)) --> -1/16∫ 1/((1/4)+x^2) -->-1/16(1/(1/2)) times arctan(x/(1/2)) + C
    So my final answer is

    1/4 X - 1/8 arctan(2x) + C

    If someone could check my math, I would be so thankful!
     
  5. Oct 2, 2012 #4
    Your result is correct.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook