Question

How do you integrate `int (x-5)/(x-2)^2` using partial fractions?

Answer 1

`int (x-5)/((x-2)^2) dx = ln abs (x-2) +3 /(x-2) + C`

Explanation:

We do not really need partial fractions here as we can separate the numerator by writing:

`int (x-5)/((x-2)^2) dx = int (x-2-3)/((x-2)^2) dx = int (dx)/(x-2) -3 int (dx)/((x-2)^2)`

now, as `d(x-2) = dx` we can solve the integrals directly

`int (x-5)/((x-2)^2) dx = ln abs (x-2) +3 /(x-2) + C`