I think I figured out why this stuff is all taught with substitution and we weren't - college encompasses all levels of students from all levels of schools, so they have to stick to stuff that people can fall back to every time. However, Godwin was in the upper level of schools, so we were taught to just look at problems and know what to do.
I /think/ I got full credit for the quiz today, but I'm not sure of this one. It went a lot better once I realized I had to divide (3w-1)/(w-2) before taking the integral. >.> I was beginning to freak a bit.