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Problem : Compute dx.

The denominator x2 - 3x + 2 factors as (x - 1)(x - 2). We set

+ = ,    

or


5x - 7=A(x - 2) + B(x - 1)  
 =(A + B)x + (- 2A - B)  

Solving the system


A + B=5  
-2A - B=-7  

we find that A = 2, B = 3. Thus


dx=dx + dx  
 =2 log(x - 1) + 3 log(x - 2) + C  

Problem : Compute dx using change of variables and partial fraction decomposition.

Letting u = ex, we have


du=du + du  
 =2 log(u - 4) + log(u + 2) + C  
 =2 log(ex -4) + log(ex + 2) + C  

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