Calculus II For Dummies, 2nd Edition

Chapter 6

Integration by Parts

In This Chapter

Making the connection between the Product Rule and integration by parts

Knowing how and when integration by parts works

Integrating by parts by using the DI-agonal method

Practicing the DI-agonal method on the four most common products of functions

In Calculus I, you find that the Product Rule allows you to find the derivative of any two functions that are multiplied together. (I review this in Chapter 2, in case you need a refresher.) But integrating the product of two functions isn’t quite as simple. Unfortunately, no formula allows you to integrate the product of any two functions. As a result, a variety of techniques have been developed to handle products of functions on a case-by-case basis.

In this chapter, I show you the most widely applicable technique for integrating products, called integration by parts. First, I demonstrate how the formula for integration by parts follows the Product Rule. Then I show you how the formula works in practice. After that, I give you a list of the products of functions that are likely to yield ...