Why can calc101 integrate any function?
It is easy to type in simple-looking integrals that cannot be done by anyone, anywhere. Probably the random example x^2 tan[x+1/x] is like that. You are never charged for a tough integral that calc101.com can’t do. Over time mathematicians have figured out how to solve many classes of advanced integrals, but only by going far beyond the likes of trig or hyperbolic functions.