Hey guys,

I was thinking about making a program, which integrates a function symbolically, this sounds stupid and very hard, but is it really so difficult? Which algorithms are used by software like Mathematica?
I think it'd be possible, because one genius in my school made a program, which calculated the derivative of a function without using Symbolic! Well, i know calculating derivatives is a lot easier than calculating integrals, but it should be possible with Asm or so? Such a program would be so cool.

~ Anima

The problem is that there's a systematic way to find a derivative of a program, but much of integration is inductive—and not all functions even have integrals that can be expressed normally, remember.

Well, I wouldn't really care, if the program can't calculate an integral, because most of the integrals we have in school are solvable.
Now... is there any useful algorithm for symbolic Integration? What algorithms are used by the TI calculators with CAS?