Question

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

Answer 1

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

On dividing, we obtain

= $\int (x^2+1)dx$

= $\int x^2dx+ \int 1dx$

= $\frac{x^3}{3}+x+C$