2 - Indefinite Integrals of Elementary Functions

Abstract

This chapter provides an introduction to indefinite integrals of elementary functions followed by its forms. Elementary functions include rational functions, algebraic functions, exponential function, hyperbolic function, trigonometric functions, logarithms and inverse-hyperbolic functions, and inverse trigonometric functions. When certain functions are integrated, the logarithm of the absolute value is obtained. In such formulas, the absolute-value bars in the argument of the logarithm are omitted for simplicity in writing. In certain cases, it is important to give the complete form of the primitive function. Such primitive functions, written in the form of definite integrals, are given. Closely related to these formulas are formulas in which the limits of integration and the integrand depend on the same parameter. A number of formulas lose their meaning for certain values of the constants (parameters) or for certain relationships among these constants. These values of the constants and the relationships among them are for the most part completely clear from the very structure of the right hand member of the formula. Therefore, throughout the chapter, remarks to this effect are omitted. The constant of integration in all the formulas of this chapter is also omitted. Therefore, the equality sign (=) means that the functions on the left and right of this symbol differ by a constant.