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Lecture

7.4 Integration of Rational Functions by Partial Fractions Question #4 (Medium)

Department
Mathematics
Course Code
MAT136H1
Professor
all

This preview shows half of the first page. to view the full 1 pages of the document. 7.4 Integration Techniques
Partial Fractions for Rational Functions
Question #4 (Medium): Rationalizing Substitutions
Strategy
Non-rational functions are rationalized through substitution. Assign root function to a variable, then
convert non-rational function into rational function. Then rest is same as working with rational functions.
Remember to substitute back in the original root expression at the end.
Sample Question
Apply substitution to express the integral as a rational function, then evaluate the integral.

 
Solution
Let    
, then    so that    and   
So  
 and    , then    
Then:

 
 
 
Using the long division, the quotient is    and remainder , thus:
   

   
 
   
Substitute back in    
:
 
 
 
  
 
 
 
  
Therefore, the integral is evaluated as:

 
 
 
 
  
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