So, we are trying to find the integral using a u du substitution. You chose the right u and du. so I will just walk through this...
dx is called the differential it tells us what we are taking the integral with respect to x.
So for the u du substitution we used
So what we did here was we chose a u such that when we take it's derivative with respect to x (du/dx) we will be able to simplify our integral a bit using u and du.
if we simplify the du to we can replace the
substituting our u and du into the original integral we get
I pulled the 1\4 out in front of the integral because we can do that with constants.
which is a much simpler integral.
Taking this intergal we get
and we get