1. 9.4 Integrals of Rational Functions
Rita Korsunsky

2. Partial fraction decomposition.
Info from Algebra I:
If numerator has lower degree than denominator
and denominator is the product of all linear terms, then:
Partial Fractions

3. Example 1 Evaluate: Since numerator has lower degree than denominator+ +
For x = 0:
For x = -3:
For x = 1:
Thus; +C =

4. Example 2 Cover (x-1)!!! Evaluate: For A, set x = 1
For C, set x = 3 and cover x-3; OR
For B, set x = 2 and cover x-2;

5. Example 3 Evaluate: For A, set x = 0 and cover x;
For C, set x = -5 and cover x+5;
For B, set x = 2 and cover x-2;

6. Example 4:
Power of numerator is greater than denominator
Evaluate:

7. Factor the denominator: Thus:
If factored terms are not all linear:Example 5 (not in AP test)
Note that in:
Evaluate:
Factor the denominator:
Thus:
Since C = -5;
A = 3; B = 1
For C; Set x = ;
C = -5;