Primitive of Reciprocal of 1 minus Cosine of x

Theorem

 * $\ds \int \frac {\d x} {1 - \cos x} = -\cot \frac x 2 + C$

Proof
From Primitive of $\dfrac 1 {1 - \cos a x}$:
 * $\ds \int \frac {\d x} {1 - \cos a x} = \frac {-1} a \cot \frac {a x} 2 + C$

The result follows by setting $a = 1$.

Also see

 * Primitive of $\dfrac 1 {1 + \cos x}$