Calculus II Workbook For Dummies

Chapter 9

Integration by Parts

IN THIS CHAPTER

Understanding the formula for integration by parts

Knowing how to assign u and dv values

Evaluating integrals by applying integration by parts multiple times

Integration by parts provides a formula for rewriting integrals in a way that makes evaluating them more accessible. It allows you to integrate a function by splitting it into factors, differentiating one factor and integrating the other, and then piecing together the results.

In this chapter, I first show you the formula for integration by parts to give you practice using it. Next, I give you guidance on when and how to use this strategy. Finally, you see how to apply integration by parts more than once to evaluate a single integral.

Using the Formula for Integration by Parts

Here’s the formula for integration by parts:

In this formula, both u and v are functions of x.

Integration by parts is commonly used to integrate a product of two functions. For example:

Q. Evaluate