Primitive of Reciprocal of 1 plus Cosine of x

Theorem

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

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

The result follows by setting $a = 1$.

Also see

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