Whyyy? Lol ....I'm so screwed for exams ><;

dy/dx = 1/x, find y: for R\{0}

Since 1/x is defined for all values except 0, the antiderivative (and the derivative) should also exist for those values.

Notice that ln(x) is only defined for x>0. To correct for this, we place: ln|x| so that it is defined for R\{0}. That's a floppy argument, and what I'm about to suggest is still floppy, but if you look at ln|x| for x is less than zero, you'll notice that it is decreasing. Look at 1/x, it is the derivative of ln|x| and for values less than zero, it has negative numbers! It makes sense.