Yesterday I came across the sci.math.symbolic Usenet group and it seems to provide almost every bit of information about symbolic computations and computer algebra systems. This newsgroup dates back to 1986 so search it to find answers.
With this newsgroup I learned about lots of interesting stuff I wasn’t even aware of. Among it are Rubi (Rule-Based Integrator) and a poor’s man integrator. I really like the picture on the latter site. I’ve also found some good references to articles and books, for example a good introduction to expression simplification.
To sum up if you want to write your own CAS sci.math.symbolic is the point to start.