What kinds of functions can be integrated using partial fraction decomposition?
we will assume that we have a rational function in which degree of p (x) < degree of q (x). If this is not the case, we can always perform long division.
For example, if we were given the fraction .
We would perform long division to obtain
We then would apply partial fraction decomposition to .
(1) q(x) is a product of distinct linear factors.
Let us assume that q (x) is a product of n distinct linear factors that is
q (x) =() ):::()
Finding the decomposition amounts to finding the coefficient A1, ..., An. This can be done two different ways.
(2)q(x) is a product of linear factors, some being repeated
The factors which are not repeated will be decomposed as above.
Suppose that q (x) also contains that is ax + b is repeated m times.
The decomposition for this factor will be