1. Basic Integration Rules
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 = ex is 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
Then becomes 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 sec2u is on the list
This suggests one of the pythagorean identities and we have

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