VonNemo19’s first reply to the OP is rude and totally uncalled for. Look at the context in which the problem is being solved. If this problem is part of a larger and more important question, and you need an answer to it quickly, then by all means use a calculator. I agree that in such a case, toying with analytic methods would be a waste of time. However, if you are investigating a problem for its own sake, when you are interested not so much in the answer as in why the answer is what it is, then you don’t use a calculator. A calculator can only give you the answer, not insights into the anatomy of the problem. It is my belief that the latter is what is intended by the OP.

Also, I don’t think I can agree with Plato that investigating 18th-century problems is a waste of time. Some antiquated problems may be outdated in this day and age, but that does not mean that are no longer interesting, or even important. Why do you think schools still teach students how to prove that is irrational, or that there are infinitely many primes? These problems have been “solved” for over two thousands years, but why do we still bother with them? There are good reasons for this – it’s useful for sharpening the mathematical minds of young students, it’s interesting to see mathematics from the point of view of the ancient Greeks, and so on – and the same good reasons apply to the 18th century as to antiquity. Such problems are therefore far from being a waste of time.