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Integration by Parts Problem (Natural Log)

  • Thread starter abel216
  • Start date
  • #1
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Homework Statement


[Intgrl]ln(x^(2)+4)dx


Homework Equations


[Intgrl]udv=uv-[Intgrl]vdu


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
 

Answers and Replies

  • #2
139
12
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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