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Homework Help: 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?)
     
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