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Monday, October 7, 2013

Integration - Algebraic Substitution, 5

Category: Integral Calculus, Algebra

"Published in Newark, California, USA"

Evaluate


Solution:

Consider the given equation above


Since the denominator consists of a binomial and a radical equation, then we cannot integrate it by simple integration. We need to simplify first the given equation by eliminating the radical sign by algebraic substitution.

Let




then it follows that


Hence, the above equation becomes




The denominator at the right side of the equation can be factored as follows


Since the denominator is already factored, then we can rewrite the above equation into partial fractions as follows


Consider



Multiply both sides of the equation by their Least Common Denominator (LCD), we have


 
 

Equate u:


 

Equate u0:



but


The above equation becomes






Substitute the values of A and B to the original equation, we have


 
 
 
 

but



Therefore,