Chapter 16
Integration Techniques for Experts
IN THIS CHAPTER
Breaking down integrals into parts and finding trigonometric integrals
Returning to your roots with SohCahToa
Understanding the As, Bs, and Cs of partial fractions
Looking at LIATE
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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