Question

Find the integral: $\int \frac{x^3-x^2+x-1}{x-1}dx$

Answer 1

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

Where $C$ is constant of integration