Often times when integrating functions I end up with something like $\displaystyle (2n)log|x|$ (or some kind of expression for the argument of log(x) that doesn't allow me to immediately remove the absolute value signs).

I'm always tempted to use properties of logarithms however, to bring the even numerical coefficient (or even something like 1/2) into the argument as an exponent and then remove the absolute value bars. I think this is most likely wrong, but wanted to confirm it.