1. May 17, 2009 #1

   abel216

   

   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

    

   abel216, May 17, 2009
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3. May 17, 2009 #2

   VKint

   

   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?)

    

   VKint, May 17, 2009

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