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?