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This comprehensive treatise provides a complete guide to the integral calculus, with detailed explanations and examples of the integration of explicit functions, as well as a thorough exploration of the theory of definite integrals and of elliptic functions. Written for students of mathematics and advanced practitioners alike, this book is an invaluable resource for anyone seeking a deeper understanding of this important branch of mathematics. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.