7.4 Integration of Rational Functions by Partial Fractions
Partial fraction decomposition is the reversal of combining fractions.
A fraction broken down into its component parts is much easier to integrate. In fact, it may not
even be possible to integrate without the decomposition taking place.
There are four cases considered in this section, we will only look at the first two.
To apply the techniques of partial fraction decomposition, the degree of the numerator must be
less than the degree of the denominator. If this is not the case, you must perform long division
before the decomposition process can proceed.
Consider
:
( )
( )
( ),
( ) are polynomials.
( )
P x
f x
P x
Q x
Q x
=
CASE I  Q(x) is a product of distinct linear factors.
In this case, you will set up a fraction for each factor of the denominator.
1
2
3
1
2
3
numerator
A
B
C
F
F
F
F
F
F
=
+
+
⋅
⋅
It doesn’t matter how many factors there are; each one gets a fraction, from two on up to
however many you need.
There’s actually more than one way to solve for A,B,C, etc. We’ll look at both as we progress.
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 Fall '08
 Estrada
 Division, Fractions, Rational Functions, Fraction, Rational function

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