where $ r_{min}$ is the root of the denominator. $ V(r)$ is a sum of $ ae^{br}$ terms, and the rest is constant.

I tried some naive solutions, but the problem is that the thing to integrate (let’s call it $ Y$ ) approaches infinity when $ r$ approaches $ r_{min}$ . So mathematically, this integral is supposed to converge (or is it?), but numerically it’s ill-posed.

In the naive approach, I find $ r_{min}$ numerically, but this gives a very high Y at the beginning of the integration (that should be $ \pm \infty$ if $ r_{min}$ was exact), and then I try to integrate with very small trapezoids, but it seems this approach is fundamentally flawed.

So… I should probably transform this integral, changing variables and stuff, but I don’t know where to begin…

Is there a known method to compute this ?