What is the right first step to take when integrating $1/(2+ \sin x + \cos x)$? I want a hint on this following integral. I don't know the first step, do I do $u$-sub. or do I use trig. sub or something?
$$\int \frac{1}{2+ \sin x + \cos x} ~\mathrm{d}x$$

Hint: let $u = \tan (x/2)$. Then find $\sin x$, and $\cos x$ in terms of $u$. Also solve for $dx$ in terms of $du$.
