An extension of Liouville's theorem on integration in finite terms

In this paper we give an extension of the Liouville theorem [RISC69, p. 169] and give a number of examples which show that integration with special functions involves some phenomena that do not occur in integration with the elementary functions alone. Our main result generalizes Liouville's theorem by allowing, in addition to the elementary functions, special functions such as the error function, Fresnel integrals and the logarithmic integral to appear in the integral of an elementary function. The basic conclusion is that these functions, if they appear, appear linearly.