I want to integrate -ln|cos(x)|+k, I and I should end with tan(x).

However, I'm stuck. I don't know what I need to do after $\displaystyle -x^{-1}*|cos(x)|-ln(x)*sin(x)$

This is how far I've gotten so far:

http://img504.imageshack.us/img504/6739/tanjf9.gif