6.7 Integration By Partial Fractions
If an algebraic fraction is expressed in terms of two or more simpler fractions, then this simple fractions are called partial fractions.
![](c53a.gif)
In many problems, if we resolve an algebraic fraction into partial fractions, its integration becomes much simpler.
Let the fraction to be resolved into partial fraction is . Then there are two cases
(1) Degree of P (x) < degree of Q (x).
This algebraic fraction is known as the proper fraction.
(2) Degree of P(x) > degree of Q (x).
This type of algebraic fraction is known as an improper fraction.
Consider these cases :
(a) To each linear factor (a1x2
+ b1) of
Q (x), there will be a corresponding partial fraction in the form ![](c54a.gif)
(b) To each quadratic factor (a1x2
+ b1x
+ c1), there
will be a corresponding partial fraction in the form ![](c54b.gif)
(c) To each repeated linear factor (a1x
+ b1)n
of Q (x), there will be ‘n’ corresponding partial fractions of the
form ![](c54c.gif)
(d) To each repeated Quadratic factor (a1x2
+ b1 +
c1
)n there will be corresponding ‘ n ’ partial fractions
as
terms
|