⌠

⌡ cot^2(x) dx

I approached this question by replacing cot^2 (x) w/ [cos^2(x)]/[sin^2(x)] => substituting sin^2(x) w/ u^2 => and ended up w/ -(1/3)cot(x) csc^2(x) + C

The answer key just gives -cot (x) - x + C

I have no idea of drawing any correlation so far except I didnt approach the trig sign from the correct position to begin with. Help with detailed algebraic work to this answer is what I ask please.