Integral de cos(x) / sin(x)

Strategy: Make in terms of sin's and cos's; Use Subtitution.

⌠ ⌡ cot x dx =

⌠cos x ⌡sin x

dx

set
u = sin x.
then we find
du = cos x dx

substitute du=cos x, u=sin x

⌠cos x ⌡sin x

dx =

⌠du ⌡u

solve integral

= ln |u| + C

substitute back u=sin x

= ln |sin x| + C