The Art of Integration

“The Art of Integration” takes the readers on a journey from first principles of mathematical integrals to advanced techniques useful in competitions. It focuses on building intuition. This book aims to bridge the gap between routine school methods and deeper mathematical understanding. Whether you are encountering integration for the first time or looking to strengthen your mastery, this book helps you to see integration as an art.

Chapters covered:

• Foundational Integration (Basic Rules)
• Basic Techniques - Integration by Substitution/Parts, Even/Odd Integrals, King's Property
• Trigonometric Integration - Trigonometric Substitution, Weierstrass Substitution, Hyperbolic Integrals and Substitution.
• Improper Integrals - Comparison Tests, P-Test, Dirichlet's Test for Convergence
• Advanced Integration (I/II) - Binomial Differentials, Gamma/Beta Function, Frullani's Integral, Guassian Identities, Euler Substitution, Series Expansion, Feynman's Trick/Differentiating under the integral sign (Recap on partial derivatives), Glasser's Integral and Special Function (Riemann Zeta Function, Dirichlet Eta/Beta Function)
• List of Integration Formulae and Known Integrals/Constants

Created by Aarav Gandewar

Published in Singapore
Printed in the United States of America

Note: A pdf version of the entire book will be provided.

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Visit the GitHub repository to view the specimen copy of the first 30 pages this document