1. The Natural Log Function: Integration
Lesson 5.7

2. Log Rule for Integration
Because
Then we know that
And in general, when u is a differentiable function in x:

3. Try It Out
Consider these . . .

4. Finding Area
Given
Determine the area under the curve on the interval [2, 4]

5. Using Long Division Before Integrating
Use of the log rule is often in disguised form
Do the division on this integrand and alter it's appearance

6. Using Long Division Before Integrating
Calculator also can be used
Now take the integral

7. Change of Variables Consider So we have Then u = x – 1 and du = dx
But x = u and x – 2 = u – 1
So we have
Finish the integration

8. Integrals of Trig Functions
Note the table of integrals, pg 357
Use these to do integrals involving trig functions

9. Assignment
Assignment 5.7
Page 358
Exercises 1 – 37 odd , 71, 73