I use it for computing integrals / solving ODEs when I don't have access to one of the CAS's I know how to use. It's nice to get a quick answer and not have to remember syntax, since I only have this problem about once every six months or so.
are you sure you are not referring to Mathematica or taking derivatives? ODEs and integrals are hard to solve for even simple cases, I cannot imagine wolfram alpha being able to solve anything even remotely complicated without throwing an error.