Primitive of Reciprocal of p plus q by Sine of a x/Examples/3 + 2 sin x

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

 * $\ds \int \dfrac {\d x} {3 + 2 \sin x} = \frac 2 {\sqrt 5} \map \arctan {\frac {3 \tan \dfrac x 2 + 2} {\sqrt 5} } + C$

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

The result follows on setting $a = 1$, $p \gets 3$ and $q \gets 2$, as follows.

We have that $2^2 - 3^2 < 0$, and so: