Question

Evaluate: $\int \frac{x^3-x^2+x-1}{x-1}dx$

Answer 1

$\int \frac{x^3-x^2+x-1}{x-1}dx=$ $\int \frac{x^2(x-1)+1(x-1)}{x-1}dx$

$\Rightarrow \int \frac{(x-1)(x^2+1)}{x-1}dx=\int x^2+1dx$

$\Rightarrow \frac{x^3}{3}+x+c$