 
Summary: Definite Integration of Parametric Rational
Functions: Applying a DITLU
A. A. Adams£
School of Computer Science,
University of St Andrews
aaa@cs.stand.ac.uk
November 2, 2003
Abstract. In [2] we presented a Definite Integral Table Lookup (the DITLU) for
parametric functions, including a minimal prototype implementation demonstrat
ing its capabilities. In this paper we present a possible application of a DITLU,
which would extend its utility for a modest investment of effort. The naive algo
rithm for indefinite integration of rational functions (see e.g. [12, Ü2.10]) can be
implemented for parametric rational functions. This involves splitting the ratio
nal function integrand using partial fractions. The resulting integrands all fall
within a limited class which may be covered in a DITLU by a very small number
of table entries. Extensions of this idea to less naive integration algorithms, and
the number of table entries required to implement them, are also considered.
1 Introduction
Definite integration is acknowledged [15] to be a tricky problem for Computer
Algebra Systems [CAS] when a symbolic answer is required or when the original
