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

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

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?