1. Partial Fractions Section 8-5
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Section 8-5

2. Adding Fractions: Find a common denominator1.
Reverse process: Decomposition of a Rational Expression

3. Guidelines for partial fraction decomposition
Factor the denominator
Assume there are constants A,B and C
Find a common denominator and add the fractions then cancel the denominator
Because the resulting equation is true for all x, substitute convenient values for A and B
Solve for A, B and C

4. There are 3 main types of partial fractions
Linear factors in the denominator
Repeated linear term in the denominator
Quadratic factors in the denominator
Use partial fractions to decompose a rational function into an integratable form

5. Sometimes splitting a single fraction into two makes integration easier2.

6. Linear Factors 3.

7. 4.

8. 5.

9. 6.

10. 7. Integrate these four “look-alike” integrals
7. Integrate these four “look-alike” integrals. Although they have similar appearances, they will require you to use three completely different integration formulas.
a. b. c d.

11. Assignment
Page 561
Problems # 7-13 all and worksheet 8-5