Usually, u sub is used when you find a suitable u such that it is easy to differentiate and its derivatives will be seen as factors of f. In this problem, using u sub would only make it more complicated.
If we expand it, we'll get
∫ [tex] \frac{ x^2-2x+1}{ x^2 } [/tex] dx
= ∫ [tex] \frac{ x^2 }{ x^2 } [/tex] dx - ∫ [tex] \frac{-2x}{ x^2 } [/tex] dx + ∫ 1/x² dx
= ∫ dx + 2∫ 1/x dx + ∫1/x² dx
= x +2lnx -1/x
