Introduction to Elementary Functions I'm looking for an introductory text on algebraic treatment of elementary functions. Really short and easy-going. Video lectures are even better.
I want to learn basic ideas (i.e. definitions) behind integration and differentiation of elementary functions.
I'm also interested in how computer algebra systems like REDUCE or AXIOM treat them as rational functions with some "kernels" (exponents and logarithm's and so on).
Though ideally I'd be happy to start with just polynomials and exponents (sin, cos). So to write symbolic integration and differentiation for a simpler class of functions (no logarithms, division and roots).

The answers are provided in the comments. It is a good idea to stick first with books about computer algebra in general, not just about one specific topic.
There are two books to start with


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*"Algorithms for Computer Algebra" by Geddes, Czapor, Labahn.

*"Computer algebra: systems and algorithms for algebraic computation" by Davenport, Siret, Tournier
As you see, the second one is free. For symbolic integration it turns out there is a plenty of literature.
MSE question Is there CAS design wisdom regarding categorizing expressions? may help a bit too.
