Evaluate the following integrals:


To Find :


Now, let be written as (2x – 4) -1 and split


Therefore ,


=


=


Now solving,


Let = u dx =


Thus, becomes


Now , = = =


=


Now solving,


=


=


Let x – 2 = y dx = dy


Then becomes


Formula Used: = log |x +|+ C


Since is in the form of with change in variable.


Hence = log |y +|+ C


= log |y +|+ C


Now, since x – 2 = y and dx = dy


= log |(x-2) +|+ C


Hence = log |(x-2) +|+ C


Therefore , =


log |(x-2) +|+ C


=


log |x - 2 +|+ C


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