Integration by Substitution

1
Integration by Substitution

• Lesson 5.5

2
Substitution with Indefinite Integration

• This is the backwards version of the chain rule
  
• Recall
• Then

3
Substitution with Indefinite Integration

• In general we look at the f(x) and split it
• into a g(u) and a du/dx
• So that

4
Substitution with Indefinite Integration

• Note the parts of the integral from our example

5
Example

• Try this
• what is the g(u)?
• what is the du/dx?
• We have a problem

Where is the 4 which we need?
6
Example

• We can use one of the properties of integrals
• We will insert a factor of 4 inside and a factor
  of ¼ outside to balance the result

7
Can You Tell?

• Which one needs substitution for integration?
• Go ahead and do the integration.

8
Try Another
9
Assignment

• Page 362
• Problems1, 5, 7, 9, 15, 17, 21, 25, 31, 37, 41