1. Section 6.2: Integration by Substitution
Objectives: Students will be able to…
Use substitution in indefinite integrals
Use substitution in definite integrals
Solve separable differential equations

2. Find the indefinite integral
What if we had to find ?

3. Find indefinite integral
NOTICE ANYTHING??????

4. If you have You can use the substitution method:
Choose a substitution : u = g(x)
Compute du = g’(x)dx
Rewrite the integral in terms of the variable u.
Replace u by g(x) to obtain an antiderivative in terms of x
Check your answer by differentiating
Integrating by substitution is to integration, as the chain rule is to differentiation 

5. Let’s revisit the last problem…

6. Examples: Find the indefinite integral.

7. Sometimes you need to solve for dx:

8. Find the indefinite integral
1) 2) 3)

9. What about u? Having difficulty deciding what u should be?
Check to see if you have one of the following
cases.
The quantity under a root or raised to a power
The quantity in the denominator
The exponent on e
*Remember some integrands may need to be rearranged to fit one of these

10. Find the indefinite integral: