Integration in Mathematica: Past, Present, and Future
Wolfram Research, Inc.
Mathematica has the most powerful integration system. For
Integrate (in the upcoming version) can evaluate more than 95
percent of the indefinite integrals from the legendary handbook of I.S. Gradshteyn and
The lecture will be divided into three parts--indefinite integrals, definite integrals,
their relatives like integral transforms. The lecture will outline the most general
algorithms used to carry out indefinite and definite integrals. It will emphasize the
difference between a human doing an integral and a powerful software system doing
integration. A comparison of the integration capabilities in Version 2.2 with those
in Version 3
and the upcoming version will be made.
Parts of the extensive automatic, random, and table-comparing tests for integration, which
are run daily, will be shown. Some typical and some quite complicated examples of integrals
will also be shown.
Further, I will describe the directions in which we will develop the
Integrate function over the next years.