now have a look at this post. It shows you how to apply the integrating factor method.
That is a linear equation and, as you say, has an "integrating factor".
That means there exist some function u(x) such that multiplying the entire equation by u(x), the left side becomes an "exact derivative":
Do the differentiation on the right side, using the product rule, and compare:
We must have , a separable equation for u(x): . Integrating both sides of that, ln|u|= -ln|x-1| so is the integrating factor:
Now integerate both sides of that.