let then so
You can change your x-limits of integration to u-limits if you would like, or you could keep them in terms of x. I prefer to keep them in terms of x but if you were to change them to u-limits, you would plug 0 =x and 4=x into the u equals equation.
Can you finish from here? Integrate, put u back in terms of x, then evaluate from zero to four.
PS: This is exactly what you did. U-sub can be intimidating at first, but after a couple of weeks it will seem a lot easier. Trust yourself enough to make mistakes. You were on the right track EXACTLY! I bet if you had kept going you would have definitely gotten it..because I didn't do anything different from what you did in your first posting.