Definite Integration

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 accomplished 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.