An Integral of a Polynomial with Multiple Roots

A full integral of a polynomial is defined as its integral with the property that any multiple root of the polynomial is a root of this integral. The paper investigates relationships between the existence of a full integral and the form of a polynomial. In particular, it is proved that a full integral exists if the polynomial has no more than one multiple root. On the other hand, if the number of multiple roots of a polynomial strictly exceeds the number of its simple roots increased by one, then the polynomial has no full integral. Bibliography: 7 titles.