A typical source of mistakes that frequently lead to a wrong or incomplete solution for the antiderivative of a given real function of one real variable is a misuse of the technique of change of variable. The increasing implementation of software in apparently mechanic tasks such as the calculation of antiderivatives has not improved the situation, yet those software packages issue generic warnings such as "the answer's is not guaranteed to be continuous" or "the solution might be only valid for parts of the function". The practical meaning of those vague machine messages is clearly envisaged in this book, which shows how to handle the technique of change of variable in order to provide correct solutions. This book is monographically focused on elementary antidifferentiation and reasonably self-contained, yet it is written in a "hand-book" style: it has plenty of examples and graphics in an increasing level of difficulty; the most standard changes of variable are studied and the hardest theoretic parts are included in a final Appendix. Each practical chapter has a list of exercises and solutions. This book is intended for instructors and university students of Mathematics of first and second year.

Antonio Martínez-Abejón, MD in Mathematics by the University of Zaragoza (Spain); PhD in Mathematics by the University of Cantabria (Spain); Martínez-Abejón has been a Teaching Assistant in the University of Zaragoza, a Visiting Researcher at the University of Texas at Austin (USA) and currently works as a Profesor Titular at the University of Oviedo (Spain) and member of the AMS. Active researcher in Functional Analysis, mainly in the isomorphic theory of Banach spaces, their local structure and their operators. He has coauthored with Manuel González the book Tauberian operators, published by Birkhäuser.