Please find the integral of the following:

numerator(x -4) can be written as (x-2 - 2) and then break into 2 parts we get

 

[ 1/(x-2)² - 2/(x-2)³ ] e^x , Now it can be seen that integration of [ f(x) + f^'(x) ] e^x = f(x) e^x

 

So thee above expression has f(x) = 1/(x-2)² , Answer is 1/(x-2)² .e^x