1. Integrating Rational Functions by the Method of Partial Fraction

2. Examples I When the power of the polynomial of the numerator is less than that of the denominator

3. Example 1

4. The denominator

8. Example 2

11. Example 3

14. Examples II When the power of the polynomial of the numerator is equal or greater than that of the denominator

15. Example 1

17. Notice We can use the same method used in this example as an alternative way to write the given rational function as a sum of simpler rational functions (partial fractions). Going back to examples. Notice the following:

20. Question ( Use two methods)

21. Example 2

23. Examples III Sometimes it is easier to find the constants not by solving a system of linear equations but rather by substituting a different appropriate value for x, in each of these equationsز

24. Example 1