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Around Symbolic Integration

Manuel Bronstein

This tutorial is an introduction to algorithms for computing symbolic antiderivatives. Our goal is to describe the main lines of the Risch algorithm with recent enhancements to real integrands. Topics covered: integration of rational functions, differential fields and Liouville's Theorem, integration of transcendental elementary functions (log, exp, tan and arctan cases), the Risch differential equation, integration of algebraic functions. The algorithmic aspects will be stressed, while the mathematical background will be kept to a minimum.