The Picard-Vessiot antiderivative closure

F is a differential field of characteristic zero with algebraically closed field of constants C. A Picard-Vessiot antiderivative closure of F is a differential field extension E superset of F which is a union of Picard-Vessiot extensions of F, each obtained by iterated adjunction of antiderivatives, and such that every such Picard-Vessiot extension of F has an isomorphic copy in E. The group G of differential automorphisms of E over F is shown to be prounipotent. When C is the complex numbers and F = C(t) the rational functions in one variable, G is shown to be free prounipotent. (C) 2001 Academic Press.