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Understanding Integration Rules: Fitting Integrals to Basic Rules

Explore and apply integration rules such as the log rule, arctangent rule, and long division principle to fit integrals. Discover disguises of the log rule, power rule, and trig identities in integration problems. Review basic integration rules and procedures for fitting integrands to rules.

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Understanding Integration Rules: Fitting Integrals to Basic Rules

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  1. Basic IntegrationRules Lesson 8.1

  2. Fitting Integrals to Basic Rules • Consider these similar integrals • Which one uses … • The log rule • The arctangent rule • The rewrite with long division principle

  3. Try It Out • Decide which principle to apply …

  4. The Log Rule in Disguise • Consider • The quotient suggests possible Log Rule, but the du = exis not present • We can manipulate this to make the Log Rule apply • Add and subtract ex in the numerator

  5. The Power Rule in Disguise • Here's another integral that doesn't seem to fit the basic options • What are the options for u ? • Best choice is

  6. The Power Rule in Disguise • Thenbecomes and power rule applies • Note review of basic integration rules pg 520 • Note procedures for fitting integrands to basic rules, pg 521

  7. Disguises with Trig Identities • What rules might this fit? • Note that tan2 u is not on the list … • However sec2uis on the list • This suggests one of the pythagorean identities and we have

  8. Assignment • Lesson 8.1 • Page 522 • Exercises 1 – 49 EOO

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