$\displaystyle \int \frac {\sqrt{4-x^2}}{x}dx$

I was thinking along the lines of $\displaystyle x = \cos u$ because $\displaystyle \sin^2x = 1 - \cos^2 x$, but I don't know where to take it.

Also, a partial fractions problem:

$\displaystyle \int \frac {1}{x(x+1)}dx$

These things always turn out to be much simpler than they look.