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Definite Integration Victor Adamchik

Summary: Definite Integration
Victor Adamchik
Mathematica's capability for definite integration gained substantial power in Version 3.0. Comprehensiveness
and accuracy were two major trends that were given strong consideration and have been successfully accom-
plished in the new development. Definite integration procedures were tested against all major handbooks of
integrals. Mathematica now is able to calculate about half of the definite and almost all indefinite integrals
from the well-known collection of integrals compiled by Gradshteyn and Ryzhik. Moreover, Version 3.0 makes
it possible to calculate thousands of new integrals not included in any published handbooks. Other essential
features of Integrate are convergence tests, principal-value integrals, and the assumptions mechanism. In
the next sections, we will discuss each of these features.
New Classes of Integrals
Integrate was significantly extended to handle new classes of integrals. Here are some of them:
integrals of rational functions

2 x3
+ 1

x7 + x3 + 1


Source: Adamchik, Victor - School of Computer Science, Carnegie Mellon University


Collections: Computer Technologies and Information Sciences