AUTHOR
Stenelund, Erik

DATE
1998-06-15

DEPARTMENT
Mathematics /

SUMMARY
In this paper we describe how the problems of computing indefinite integrals in closed form are now solved by computer algebra systems. After a review of some polynomal factorization algorithms like Yun's algorithm, we outline the major algorithm which is the Risch's algorithm. The Risch's algorithm always looks for an integral which is elementary, that is can be obtained from the rational functions in X by repeatedly adjoining a finite number of nested logarithms, exponentials, and algebraic numbers of functions. If the algorithm doesn't find such an integral then the answer is that the integral is not elementary. The integral of sin(x)/x is a wll-known example of an integral which is not an elementary function. In the appendix there are some detailed examples.

ISSN 1402-1781 / ISRN LTU-C/DUPP--98/02--SE / NR 1998:02