It seems yes there is a reason if you need integrals. From TFA: "You can also try having Wolfram Alpha compute it, and it will time out. We will need to be more creative."
Mathematica/Maple/Sagemath don't have a freemium timeout mechanic and can solve a lot more. Truth be told I think that integration techniques are much less broadly crucial for everyone to learn than they used to be, although you need to have some clue of what's going on because you need to be able to guide yourself towards posing problems in such a way that the integrals that can be solved.
But there are integrals that you can easily solve by hand but both WolframAlpha and sage will (effectively) timeout on them. And I’m not even talking about something made deliberately hard for computers to symbolically analyze.
Sometimes you are looking for deeper insights in some equations that can only be achieved by finding symbolic solutions.
You would never figure out that black holes are a solution to the Einstein field equations of you just threw a numerical solver at it, for example. (Bad example because that's arguably the easiest solution to them but I hope you get my point.)
It's probably best to return a function that takes alpha as a parameter and numerically integrates for whichever finite set of alphas are required by the caller.