Nonelementary Integrals: Indefinite Nonintegrable Functions

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Nonelementary Integrals are traditioanlly known as Nonelementary Functions but it doesn't given clear explanation that what was the reason behind it to call such function as Nonelementary Functions, whereas the name Nonelementary Integrals are the clear explanation that it has been originated from integration and there must be relation between elementary function and integration, when we call an integral nonelementary. In fact nonelementary integrals are those antiderivatives of elementary functions, which cann't be expressed in terms of elementary functions. This book contains the basic theorems and properties related to integration and these are not found in general textbooks. I collected these material from different resources, which have been given as references in the last chapter in the book.