Integration by Parts Problem (Natural Log)

[abel216]

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

 

[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?)