Risch algorithm for symbolic integration

by Chetna for SymPy

The Risch algorithm is a complete algorithm to integrate any elementary function. Given an elementary function, it will either produce an antiderivative, or prove that none exists.The project is to continue where Aaron Meurer left off in his 2010 GSoC project, implementing the algorithm from Manuel Bronstein's book, Symbolic Integration I: Transcendental Functions. A successful implementation of this would not only provide concrete algorithms for transcendental functions but would also form the basis for very similar Karr Algorithm, decision procedure for symbolic summation, yet to be implemented in Sympy. This could also prove a quick start for further extension to build Risch Algorithms for Algebraic functions and hence needs to be taken immediately to complete the integral module in sympy.