calculus - Integral of trig fraction using substitution?

I'm chewing on an integral problem and don't have a clue where to begin. If someone could assist by suggesting a good starting point, I'd really appreciate it! Not asking for anyone to solve the integral, just looking for a hint or two:

$$\int{\frac{1}{1+\sin{x}+\cos{x}}\,\,dx}$$

I'm completely stuck - tried substituting for $\tan^2{x}=\sec^2{x}-1$ and so forth, but haven't found it to be terribly useful yet. Maybe I'm missing something. I also suspect this is a prime candidate for u- or t-substitution.

Thanks!