Question

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

Answer 1

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