Answer :

Given


Rewriting, we get


Expressing the integral




Consider


By partial fraction decomposition,



x – 2 = A (2x – 1) + Bx


x – 2 = 2Ax – A + Bx


x – 2 = (2A + B) x – A


A = 2 and 2A + B = 1


B = 1 – 4 = -3


Thus,




Consider


We know that



And consider


Let u = 2x – 1 dx = 1/2 du



We know that



Then,




Then,




We know that




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