# Integration by Parts Problem (Natural Log)

1. May 17, 2009

### 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

2. May 17, 2009

### VKint

You're almost done. Just write
$$\int \frac{2x^2}{x^2 + 4} dx = 2 \int \left( 1 - \frac{1}{1 + \left(\frac{x}{2}\right)^2} \right) dx$$
and substitute $$t = \frac{x}{2}$$. (You do know how to integrate $$\frac{1}{1 + x^2}$$, right?)