When you antiderive 1/x, loge|X| has a modulus sign because :

loge(x) = y

e^y = x

theres no way that x can be negative because a positive constant (e) to the power of anything will never equal a negative.

eg. x^(1/50) = 50Rtx ... x^50... no matter which way you go it doesnt hit 0 or lower

not sure how to express what im trying to say.

e^x=y... as x --> 0, y --> 1.... and as x --> infinity, y also does

At least, thats why i thought we put a modulus in... why we only do it after antideriving im not sure, it could be something to do with the gradient of the graph going in a certain direction.

(edit: I just read what coblin wrote, lol ... i think ive just dumbed down what he said)