Doubt about the integration of a particular function: how start to think on how to solve a non-standard integral?

Question

I have a poor knowledge on numerical integration, advanced techniques and wayouts to solve integrals. In particular I have this one here:

$$z(r) = \int dr\sqrt{\frac{-3e^R+q^2\lambda e^rr^2}{3e^{R}-e^r(3+q^2\lambda r^2)}} \tag{1}$$

Where $\lambda$,$q$ and $R$ are simply constants.

So, how can I solve the integral $(1)$?