On the existence of antiderivatives of some real functions

Taşcu, Ioana



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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.

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Tașcu, Ioana