Calculus: Integration of Rational functions
Calculus: Integration of Rational functions
A rational function is by definition the quotient of two polynomials. For example
are all rational functions. Remember in the definition of a rational
function, you will not see 
neither 
or |x| for
example. Note that integration by parts will not be enough to help
integrate a rational function. Therefore, a new technique is needed
to do the job. This technique is called
Decomposition of
rational functions into a sum of partial fractions (in short
Partial Fraction Decomposition).
Let us summarize the practical steps how to integrate the rational
function 
:
, perform
polynomial long-division.
Otherwise go to step 2.
Remark: The main difficulty encountered in general when using this technique is in dealing with step 2 and step 3. Therefore, it is highly recommended to do a serious review of partial decomposition technique before adventuring into integrating fractional functions.
The following examples illustrate cases in
which you will be required to use Partial Fraction Decomposition technique:
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