I am trying to solve the following integral: $$\int \frac{\arctan x}{(x-2)^2} \,dx$$
My idea:
First of all, I tried to divide it into a multiplication of functions, therefore, applying the integration by parts I got the following form: $$\frac{\arctan x}{2-x} - \int \frac{1}{(1+x^2)(2-x)} dx$$
Here I am stuck in fact I tried to split this integral into multiplication of functions in order to use one more time integration by parts but I don't have any interesting result.
I would like to solve it. Thank you very much.