Question

Find the following integrals.
$\int \frac{x^3-x^2+x-1}{(x-1)}dx.$

Answer 1

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