This problem has already been worked for me but I am confused about a couple of things. First of all I don't really understand where the -1 + 1 comes from in the first step, and I'm also not really sure why the dx was moved to the numerator in Step 2. Can anyone explain to me what is going on in the first 2 steps? Thanks.
Problem: ∫ (x^2)/(x-1) dx
Step 1:∫ (x^2 -1 + 1)/(x-1) dx
Step 2: ∫ (X^2 -1)/(X-1) dx + (dx)/(x-1)
Step 3:∫ (x-1)(x+1)/(x-1) dx + ∫ (dx)/(x-1)
Step 4:∫ (x+1) dx + ∫ (dx)/(x-1)
Step 5:∫ x dx + ∫ dx + ∫ (dx)/(x-1)
Step 6: [(1/2x)^2] + x + ln [x-1] + C