`int (5x-2) / (x-2)^2 dx` Use partial fractions to find the indefinite integral

Expert Answers
gsarora17 eNotes educator| Certified Educator


Let's use partial fraction decomposition on the integrand,




comparing the coefficients of the like terms,



Plug in the value of A in the above equation,





So now `int(5x-2)/(x-2)^2dx=int(5/(x-2)+8/(x-2)^2)dx`

Now apply the sum rule,


Take the constant's out,


Now let's evaluate each of the above two integrals separately,


Apply integral substitution `u=x-2`



Use the common integral :`int1/xdx=ln|x|`


Substitute back `u=x-2`


Now evaluate the second integral,


Apply integral substitution:`v=x-2`




Apply the power rule,




Substitute back `v=x-2`



Add a constant C to the solution,


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