Hello! I wonder how hard is it to implement more or less general symbolic integration algorithm (number of lines in a certain language)? Maybe someone here did this or knows some good blog posts devoted to the subject.


And how hard is it to implement an algorithm to decide whether a given function could be integrated (in terms of elementary functions)?


I don't mean integrating only rational functions, something more general.


What's the easiest method to start (except integrating rational functions)?



The easiest symbolic integration method to try implementing.
Perhaps pmint, The Poor Man's Integrator, 


<http://www-sop.inria.fr/cafe/Manuel.Bronstein/pmint/index.html>


is of interest to you (<100 lines Maple).


The page contains also references to the literature and examples. 
Moreover, searching for Poor Man's Integrator turns up a couple of related and recent online discussions.


