physics – How can I integrate a function containing divergence?

I want to calculate the embedding surface in the wormhole scenario. However, the integrand diverges at the throat ($r = r_0$) of this object. I will summarize the process. With the shape function $b(r)$, which is finite everywhere, for example:

$$b(r) = frac{a}{r^5} – frac{a}{r_0^5} + r_0,$$

note that this function obeys the condition $b(r_0) = r_0$. Then, the embedding results in

$$z(r) = pmint_{r_0}^r frac{dr’}{sqrt{frac{r’}{b(r’)} – 1}}.$$

In some cases, this integral is “simple” and we factorize this in elliptical integration, but in this case is not apply.

Any suggestions for how can I calculate this quantity in Wolfram?