Primitive of Reciprocal of p plus q by Cosine of a x/Examples/5 + 3 cos x

Example of Use of Primitive of $\dfrac 1 {p + q \cos a x}$

 * $\ds \int \dfrac {\d x} {5 + 3 \cos x} = \dfrac 1 2 \map \arctan {\dfrac 1 2 \tan \dfrac x 2} + C$

Proof
From Primitive of $\dfrac 1 {p + q \cos a x}$:

The result follows on setting $a \gets 1$, $p \gets 5$ and $q \gets 3$, as follows.

We have that $5^2 > 3^2$, and so: