Famed for his achievements in number theory and mathematical analysis, G. H. Hardy ranks among the twentieth century's great mathematicians and educators. In this classic treatise, Hardy explores the integration of functions of a single variable with his characteristic clarity and precision. Following an Introduction, Hardy discusses elementary functions, their classification and integration, and he presents a summary of results. After a survey of the integration of rational functions, he proceeds to the integration of algebraical functions and concludes with an examination of the integration of transcendental functions. A pair of Appendixes contain a bibliography and an Abelian proof. 1916.