How do you integrate this:

$\displaystyle \int \frac {1}{1+sinx}dx$

I tried expanding the '1' as $\displaystyle sin^2 x+cos^2 x$

And then i tried multiplying numerator and denominator by $\displaystyle cos x$.. But it was of no use..

What do you do generally, when you have a trigonometric equation in the denominator??