Question

How do you integrate `x^3/(x-2)`?

Answer 1

Do the division, then integrate to get `x^3/3 + x^2 +4x +8ln abs(x-2) + C`

Explanation:

Perform the division:

`x^3/(x-2) = x^2 + 2x +4 +8/(x-2)`

So
`int x^3/(x-2) dx = int (x^2 + 2x +4 +8/(x-2)) dx`

`= x^3/3 + x^2 +4x +8ln abs(x-2) + C`