To get the asymptotes, test its end behaviors by taking both limits as and as . Both of which are 0, therefore there is only one asymptote which is .

To answer your second question, the reason it turns into is because when you are integrating using the reverse power rule which says

however this only works if , because then denominator becomes 0. In your case, we have , so so it doesn't work. So we use . Make sure that it's absolute value of x and not just regular x. If you don't put the absolute value signs, you'll get it wrong.

Cheers!