I'm all about open-source materials, as a rule. But the fact remains that the best damn table of integrals is Mathematica, that fruit of the cellular automaton that implements Stephen Wolfram's mind. I should probably work out what else it does, while I have a their evilly cheap student-license edition chugging away doing quadrature.
- Magickal calculus engine. Beautiful like the Fae, and as possessed of glamour. It gives you integrals, but at great cost.
- Lack of any decent published work explicitly using Mathematica or libraries for it in the years approximately 2001-2009, when the newness had worn off and before they had added functions anyone cared about. (c.f. the explosion of R or scipy in that time)
Here are some links that I am finding useful to explore it with.