I need to integrate this expression:
$$\int^{\pi}_0\frac{\gamma^{10} \theta^2 \sin\theta}{(\gamma^2 \theta^2 + 1)^5} d\theta.$$
I can use the fact that gamma is very large, which I think means I should rearrange the bottom line to allow an expansion, i.e. $$\int^{\pi}_0\frac{\theta^2 \sin\theta}{(\theta^2 + \dfrac{1}{\gamma^2})^5}d\theta ,$$
but I'm still not sure how to continue from here. Any hints would be great, thanks.