## Integration

Integration is one of the most important and frequently used tools of calculus, finding its way into many applications of science and engineering. Unfortunately, itâ€™s often the case where only the simplest of expressions are easy to integrate by hand. In the past this could mean that if you came across an expression that could not be integrated using the elementary methods and tricks taught in calculus, you would have to dig out some heavy book and search endless tables to find the answer. If you were lucky some 19th century mathematician had done the hard work for you and you would find what you were looking for. Luckily for us, Mathematica shines when computing integrals of all kinds, and can be used to quickly determine the answer whether the problem at hand involves a definite or indefinite integral. Answers to indefinite integrals are reported symbolically in functional form just like you would write them on a piece of paper. Integrals can be computed using any coordinate system you desire. So instead of taking a trip to the library or bookstore to leaf through a heavy table of integrals, you can simply type in the integral you are trying to compute and let Mathematica do the hard work. In this chapter we will consider how to use Mathematica to integrate several well-known functions. This will be done in two ways. First we investigate the use of symbolic input that lets you enter the functions you want to inte-

you might expect to enter data into a computer program. Here the trade-off is giving up some of the familiarity for a bit of power.