Skip over navigation

Computing Integrals

Problems

Partial Fraction Decomposition

How to Cite This SparkNote

Problem : Compute dx .

The denominator x 2 - 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 = e x , we have


du = du + du  
  = 2 log(u - 4) + log(u + 2) + C  
  = 2 log(e x -4) + log(e x + 2) + C  

Follow Us