Integration in Mathematica: Past, Present, and Future

Oleg Marichev
Wolfram Research, Inc.

Mathematica has the most powerful integration system. For example, Integrate (in the upcoming version) can evaluate more than 95 percent of the indefinite integrals from the legendary handbook of I.S. Gradshteyn and I.M. Ryzhik.

The lecture will be divided into three parts--indefinite integrals, definite integrals, and 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.