Chapter 16

Integration Techniques for Experts

In This Chapter

arrow Breaking down integrals into parts and finding trigonometric integrals

arrow Returning to your roots with SohCahToa

arrow Understanding the As, Bs, and Cs of partial fractions

arrow LIATE: Lilliputians In Africa Tackle Elephants

I figure it wouldn’t hurt to give you a break from the kind of theoretical groundwork stuff that I lay on pretty thick in Chapter 15, so this chapter cuts to the chase and shows you just the nuts and bolts of several integration techniques. In Chapter 15, you saw three basic integration methods: the reverse rules, the guess-and-check method, and substitution. Now you graduate to four advanced techniques: integration by parts, trigonometric integrals, trigonometric substitution, and partial fractions. Ready?

Integration by Parts: Divide and Conquer

Integrating by parts is the integration version of the product rule for differentiation. Just take my word for it. The basic idea of integration by parts is to transform an integral you can’t do into a simple product minus an integral you can do. Here’s the formula:

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