Any possible ideas that will help me solve this integral

Question

I have an integral $$I= \int_{-\infty}^\infty \frac{dz}{r^{m/2}}\frac{1}{\sqrt{a\cos^2\theta+b\cos\theta\cos\alpha+c\cos^2\alpha+d}},$$ where$$r^2=x^2+y^2+z^2= R^2+z^2$$ and $$\cos\theta=\hat{r}.\hat{z}$$ and $$\cos\alpha=\hat{\zeta}.\hat{z},$$ where $\zeta$ is a specified fixed direction. $a, b, c, d$ are constants and $m>1$ is a rational number. Any idea on any approximation method to solve this integral would be highly welcomed. Please share your ideas.