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How to Integrate It
A Practical Guide to Finding Elementary Integrals


  • Date Published: December 2017
  • availability: In stock
  • format: Paperback
  • isbn: 9781108408196

£ 22.99

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About the Authors
  • While differentiating elementary functions is merely a skill, finding their integrals is an art. This practical introduction to the art of integration gives readers the tools and confidence to tackle common and uncommon integrals. After a review of the basic properties of the Riemann integral, each chapter is devoted to a particular technique of elementary integration. Thorough explanations and plentiful worked examples prepare the reader for the extensive exercises at the end of each chapter. These exercises increase in difficulty from warm-up problems, through drill examples, to challenging extensions which illustrate such advanced topics as the irrationality of π and e, the solution of the Basel problem, Leibniz's series and Wallis's product. The author's accessible and engaging manner will appeal to a wide audience, including students, teachers and self-learners. The book can serve as a complete introduction to finding elementary integrals, or as a supplementary text for any beginning course in calculus.

    • A systematic introduction to integration, containing many fully worked examples to demonstrate how the techniques are applied in practice
    • Contains more than 500 exercises ranging in difficulty, from warm-ups to challenging extensions
    • Accessible and engaging, this book will be of interest to students, teachers and self-learners
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    Reviews & endorsements

    'Each chapter of this book starts with a quote, then a little motivating introduction or example, followed by a definition, a rule or some properties, then a wealth of practical examples and exercises which range in difficulty. … The chapters concerned with the integration techniques are finely written: they are short with minimal theoretical explanation, good practical rules, and a great number of examples and exercises. Students and teachers can find a lot of interesting things to learn or use. … This book is a very good introduction to the techniques of integration. It is not a theoretical book on integration; indeed, most of it can be well understood by pre-university students who are learning integral calculus.' Mathematical Association of America

    'This is a book for those who love to integrate, especially indefinite integrals … Plenty of exercises, both routine and challenging, are included.' M. Bona, Choice

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    Product details

    • Date Published: December 2017
    • format: Paperback
    • isbn: 9781108408196
    • length: 378 pages
    • dimensions: 227 x 151 x 21 mm
    • weight: 0.55kg
    • contains: 24 b/w illus. 20 tables 520 exercises
    • availability: In stock
  • Table of Contents

    1. The Riemann integral
    2. Basic properties of the definite integral – Part I
    3. Some basic standard forms
    4. Basic properties of the definite integral – Part II
    5. Standard forms
    6. Integration by substitution
    7. Integration by parts
    8. Trigonometric integrals
    9. Hyperbolic integrals
    10. Trigonometric and hyperbolic substitutions
    11. Integrating rational functions by partial fraction decomposition
    12. Six useful integrals
    13. Inverse hyperbolic functions and integrals leading to them
    14. Tangent half-angle substitution
    15. Further trigonometric integrals
    16. Further properties for definite integrals
    17. Integrating inverse functions
    18. Reduction formulae
    19. Some other special techniques and substitutions
    20. Improper integrals
    21. Two important improper integrals
    Appendix A. Partial fractions
    Appendix B. Answers to selected exercises

  • Author

    Seán M. Stewart, Omegadot Tuition, Sydney
    Seán M. Stewart is the co-founder and principal teaching fellow at Omegadot Tuition, Sydney. He has had over eighteen years of experience teaching mathematics and physics at both the secondary and tertiary levels. He is a member of numerous professional associations and societies in mathematics and physics. In 2004, he won the Petroleum Institute Outstanding Faculty Award for Teaching. He has written numerous research articles and co-authored the book Blackbody Radiation: A History of Thermal Radiation Computational Aids and Numerical Methods (2016).

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