1. Find Find Find Find Find
INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS
Rational function:
Example
Example
Find
Find
Example
Find
Example
Example
Find
Find

2. INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS

3. INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS

4. INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS

5. 1 2 3 INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS Example
Multiply by 1
subsitute
subsitute
Match coeff 2 3
The Heaviside
“Cover-up”
subsitute

6. INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS1
Use long division 2
Check if we can use subsitution 3
Factor q(x) as linear factors or irreducible quadratic
Express p(x)/q(x) as a sum of partial fraction 4
q(x)= product of linear factor
q(x)= product of quadratic (irred)
All distinct
Some repeated
repeated
All distinct
case1
case2
case3
case4

7. INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS
q(x)= product of linear factor
Example
Find
All distinct
Some repeated
case1
case2
Example
Find

8. INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS
q(x)= product of linear factor
All distinct
Some repeated
case1
case2
Example
Example
Find

9. case3 case4 INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS
q(x)= product of quadratic (irred)
repeated
All distinct
case3
case4
Example
Example

10. Expand by partial fraction
INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS
q(x)= product of quadratic (irred)
Example
repeated
Find
All distinct
case3
case4
Example
Expand by partial fraction
Example
Find

11. INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS

12. INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS
TERM-101
Solution:

13. INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS

14. INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS