Integrals — Class 12 Maths Solution

: Let $I = \int {\left( {\cfrac{{{x^3} - {x^2} + x - 1}}{{x - 1}}} \right)dx} = \int {\cfrac{{{x^2}\left( {x - 1} \right) + \left( {x - 1} \right)}}{{x - 1}}} dx$

$= \int {\left( {{x^2} + 1} \right)dx} = \cfrac{{{x^3}}}{3} + x + C$