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The Calculus Lifesaver by Adrian Banner

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CHAPTER 18 _____________________________

Techniques of Integration, Part One

Let’s kick off the process of building up a virtual toolkit of techniques to find antiderivatives. In this chapter, we’ll look at the following three techniques:

• the method of substitution (otherwise known as “change of variables”);

• integration by parts; and

• using partial fractions to integrate rational functions.

Then, in the next chapter, we’ll look at some more techniques involving trig functions.

18.1 Substitution

Using the chain rule, we can easily differentiate ex2 with respect to x and see that

Images

The factor 2x is the derivative of x2, which appears in the exponent. ...

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