Hi I'm doing a question regarding averaging a radial perterbation about an orbit.

I've reduced the problem to needing to show that

$\displaystyle \int_0^{2\pi} \frac{\sin f}{(1+e\cos f)^{\gamma +2}} df = 0$

Where we have that $\displaystyle 0<e<1$ could I have a hint from anyone as to how to proceed with this?