It looks like you need the trigonometric identity sin(2x) = 2sin(x)cos(x).
After some simplification, you can integrate using partial fractions.
I am having a hard time doing this.
Use substitution and the results you established to evaluate the integral:
the integral is sin(2x) / (2 + cos(x))
The results I established are :
cos(x) = (1 - t^2) / (1 + t^2)
sin (x) = 2t / (1 + t^2)
dx = (2 / (1+ t^2)) dt