Question

How do you find the indefinite integral of `int (2x)/(x-1)^2`?

Answer 1

`2 ln |x-1| - 2/(x-1) +c`

Explanation:

Substitute `u=x-1`. Then `dx=du`, `x=u+1`:

`int(2(u+1))/u^2 du`
`=2int 1/u du + 2 int (du)/u^2`
`= 2ln|u| -2/u +c`
`=2ln|x-1|-2/(x-1)+c`