This happened a couple of times today. While working on some problems, you find unexpected relationship between objects, which are not obvious to find directly. For example today I found out that
$$\large\int_0^1 \frac{(1-x^2)^{k-1} \left(\frac{1-x}{1+x}\right)^{-k} \left(\left(\frac{1-x}{1+x}\right)^{2k}-1\right)}{k \log\left(\frac{1-x}{1+x}\right)} \ dx = 1 $$
(I did not double check it so it may be wrong. But that's just an example. Another one is here)
I don't really know what to do in this situations.. I mean I could just forget about it, but maybe it would lead into interesting generalizations? On the other hand these "generalizations" are tough to see because the result pops up almost "by chance" while doing unrelated calculations.
What do you do when something like this happens?