» On the existence of antiderivatives of some real functions

An antiderivative of a real function $f(x)$ defined on an interval $I\subset \mathbb{R}$ is a function $F(x)$ whose derivative is equal to $f(x)$ , that is, $F'(x)=f(x)$ , for all $x\in I$ . Antidifferentiation is the process of finding the set of all antiderivatives of a given function. If $f$ and $g$ are defined on the same interval $I$ , then the set of antiderivatives of the sum of $f$ and $g$ equals the sum of the general antiderivatives of $f$ and $g$ . In general, the antiderivatives of the product of two functions $f$ and $g$ do not coincide to the product of the antiderivatives of $f$ and $g$ . Moreover, the fact that $f$ and $g$ have antiderivatives does not imply that the product $f\cdot g$ has antiderivatives. Our aim in this paper is to present some conditions which ensure that the product $f\cdot g$ and the composition $f \circ g$ of two functions $f$ and $g$ has antiderivatives.