Abstract
This chapter discusses how one can recognize classes of functions that can be integrated in the sense of actually finding a recognizable antiderivative. There are many techniques which have evolved over a period of decades particular to the detection of particular integrals. The most notable of such techniques is called integration by parts; it is derived from the product rule of differentiation. Thereafter, it is possible to simplify a large number of complicated-looking integrals by making an appropriate trigonometric substitution. There are sometimes two or more ways to integrate a rational function with a quadratic denominator. Many other types of expressions can be integrated by making appropriate substitution, but there is no obvious way to find the one substitution that works, and it is often necessary to resort to trial and error. There are extensive tables of integrals made available at present to the student for aid in applications.
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