Dave's Math Tables: Integral cot(x)

(Math | Calculus | Integrals | Table Of | cot x)

Discussion of cot x = ln|sin x| + C.

1. Proof

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
Q.E.D.