Elementary indefinite integration theory for the computer

摘要

In this paper various algebraic properties of the indefinite Riemann integral that are appropriate for its use on the computer are examined. From this analysis it is seen that the operation of the integral on certain simply described families of functions, called invariant algebras, indicates how it must also act on more complex families of maps. Several examples of the theory are presented, illustrating among other things the relationship existing between integrals of certain types of hypergeometric functions and the integrals of the exponential and trigonometric functions.