Problem:
Evaluate the following integral:

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Solution:

1. We first write
   
   

2. Adding the terms together, we obtain
   
   

3. Hence, the two numerators are equal
   
   

4. Equating the coefficients of like powers of x, we obtain the following system of three equations in three unknowns:
   
   

5. The solution of this system of equations is
   
   

6. We can now integrate