ABSTRACT
This chapter discusses integration by substitution, integration by parts, the use of reduction formulae and the use of partial fractions to simplify the task of integrating rational functions. It shows how these same techniques may be used to find antiderivatives which are just functions, and definite integrals which are numbers. The chapter deals with a discussion of differentiation under the integral sign and the integration of trigonometric functions involving multiple angles. Possibly the most frequently used technique of integration is that in which the variable under the integral sign is changed in a manner which simplifies the task of finding the antiderivative. This process is known as integration by substitution or integration by change of variable. Integration by substitution depends for its success on transforming an integrand in one variable into one of simpler form in another variable.
