Integrating
irrational functions

Integration of
irrational functions of the form 


where,
R
is a rational function and, p_{1},
q_{1},
p_{2},
q_{2},
. . . are integers, we
can solve 
using substitution 

where
the power n
is the least common multiple of q_{1},
q_{2},
. . . .



Integration of
irrational functions examples

Example:
Evaluate 




Example:
Evaluate 




Integration of
irrational functions of the form 


where
P_{n}(x)
is an nth
degree polynomial. 
Set 


where
Q_{n }_{}_{
1}(x) is an (n

1) th
degree polynomial of undetermined
coefficients and l
is a constant.

Coefficients
of the polynomial Q
and the constant l
we obtain by deriving the above identity. 


Solution:





Example:
Evaluate 


Solution:





Integration of
irrational functions of the form 


Given
integral can be solved using the substitution
x

a
= 1 / t.


Example:
Evaluate 



