........help please

(a) Consider the improper function f(x)= (x^4+x^3+2x^2+x-1)/(x^3-x^2+x-1). Use long division to convert f(x) into a polynomial plus a proper rational function. -->I ended up with : (x+2) + (3x^2-2x-3)/(x^3-x^2+x-1) (b) Factor the polynomial Q(x) = x^3 - x...

Hello, Thank you very much for your help with my question. If it's possible, could you please explain why you multiply 1/2 with 2(x)/(x^2+1) in this part: = ∫ x+2 + 2/(x-1) + (1/2) * (2x)/(x^2+1) + 1/(x^2+1) dx