An antiderivative of a real function defined on an interval is a function whose derivative is equal to , that is, , for all . Antidifferentiation is the process of finding the set of all antiderivatives of a given function. If and are defined on the same interval , then the set of antiderivatives of the sum of and equals the sum of the general antiderivatives of and . In general, the antiderivatives of the product of two functions and do not coincide to the product of the antiderivatives of and . Moreover, the fact that and have antiderivatives does not imply that the product has antiderivatives. Our aim in this paper is to present some conditions which ensure that the product and the composition of two functions and has antiderivatives.