先看兩篇中文文章，或許有助於理解接下來的英文內容。
以下內容的PDF文件下載地址：https://ksda.ccny.cuny.edu/PostedPapers/liouv06.pdf
This talk should be regarded as an elementary introduction to differential algebra. It culminates in a purely algebraic proof, due to M. Rosenlicht, of an 1835 theorem of Liouville on the existence of “elementary” integrals of “elementary” functions. The precise meaning of elementary will be specified. As an application of that theorem we prove that the indefinite integral ∫e^(x^2)dx cannot be expressed in terms of elementary functions.
這次演講應該被看作是對微分代數的初步介紹。由M.Rosenlicht 於1835年提出的關於“初等”函數的“初等”積分的存在性的劉維爾定理，其結果是一個純粹的代數證明。“基本”的精確意義將被指定。作爲該定理的一個應用，我們證明了不定積分∫e^(x^2)dx不能用初等函數表示。
