 
Summary: Definite Integration
Victor Adamchik
Introduction
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 wellknown 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, principalvalue 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:
Å integrals of rational functions
Å
1
2 x3
+ 1
þþþþþþþþþþþþþþþþþþþþþþþþþþþþþþþþþþþ
x7 + x3 + 1
