Evaluate ∫ (√x - x + xcot^2 x) / x dx

I tried to solve this and after a few steps I keep getting stuck at finding ∫ cot^2x/x or maybe I just did the first few steps wrong:/

can you please solve this and show me?

(√x - x + xcot^2 x) / x = x^(-1/2) - 1 + cot^2 x

you should be able to do that,

note
cot^2 = cos^2 / sin^2 = (1 - sin^2) / sin^2 = csc^2 - 1

for csc^2, find the derivative of cot to see that it is -csc^2 I think