This book intends to be an essential text on the one-variable integration of rational and irrational functions.The book presents the principal results of the integration of all cases of rational functions and all instances of irrational functions that, by a change of variable, can be transformed into rational functions. It also presents the methods necessary to achieve that. The book presents problems with several types of simple integrals and reduction formulas. It also includes integration applications, namely, calculating the volume of solids of revolution and areas of solids of revolution. It also contains applications such as calculating the geometric centre of a region and the area of finite and infinite regions, among others. The final chapter contains proposed problems and their solutions.
