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!

Integration by Parts Problem (Natural Log)

  1. May 17, 2009 #1
    1. The problem statement, all variables and given/known data
    [Intgrl]ln(x^(2)+4)dx


    2. Relevant equations
    [Intgrl]udv=uv-[Intgrl]vdu


    3. The attempt at a solution
    [Intgrl]ln(x^(2)+4)dx, u=ln(x^(2)+4), du=(2x/x^(2)+4), dv=dx, v=x
    xln(x^(2)+4)-[Intgrl](2x^(2)/(x^(2)+4))dx
     
  2. jcsd
  3. May 17, 2009 #2
    You're almost done. Just write
    [tex] \int \frac{2x^2}{x^2 + 4} dx = 2 \int \left( 1 - \frac{1}{1 + \left(\frac{x}{2}\right)^2} \right) dx [/tex]
    and substitute [tex] t = \frac{x}{2} [/tex]. (You do know how to integrate [tex] \frac{1}{1 + x^2} [/tex], right?)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook