7.4 Integration Techniques
Partial Fractions for Rational Functions: Overview
Rational functions are functions with a polynomial in the numerator and the denominator, so that:
( ) ( )
If the degree of ( ) is less than ( ), it is called proper rational function.
If the degree of ( ) is greater than ( ), it is called improper rational function. Then before
proceeding to applying partial fractions, it must be written in the form of ) ( ) ( ) ( ),
( ) ( )
where ( ) is the remainder obtained from long division.
4 Cases of Rational Functions
Case 1: When the function in the denominator can be factored into linear functions. Then split the
function in the numerator and integrate separately.
Case 2: Similar to Case 1, but some of the factored terms in the denominator have order greater than 1.
Then write out each power occurrence, and decompose the numerator accordingly, and then integrate
Case 3: When the factored ter