Question

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

Answer 1

$\frac{x^3-x^2+x+1}{x-1}$

$=x^2+1$

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

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

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