Basic Integration Rules Lesson 8.1

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

Try It Out Decide which principle to apply …

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

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

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

Disguises with Trig Identities What rules might this fit? Note that tan2 u is not on the list … However sec2u is on the list This suggests one of the pythagorean identities and we have

Assignment Lesson 8.1 Page 522 Exercises 1 – 49 EOO