7.4 Integration Techniques
Partial Fractions for Rational Functions
Question #2 (Medium): Evaluating the Definite Integral Using Partial Fractions
Before evaluating the definite integral, rational function needs to be decomposed by partial fractions.
Once the numerator coefficients are determined, taking the anti-derivative is easy. To decompose as
much as possible, factored binomials with power greater than 1 must be written by that number of
Evaluate the definite integral using partial fractions.
( ) ( )
Since the denominator is already factored, coefficients need to be determined to evaluate the integral.
So, ( ) ( ) ( ) ( ) ( ). Since ( ) is of order 2, it needs to be written twice. Then
the numerators are written as: ( )( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )