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

Question

As the title suggests, the following integral has been given to me

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

Yet I still get the wrong answer every time.

Can someone calculate it step-by-step so I can compare it to my own answer?

Answer 1

HINT: $$\frac{3x^2-x+2}{x-1}=\frac{(x-1)3x+(x-1)2+4}{x-1}=3x+2+\frac4{x-1}$$

Answer 2

Another hint :

\begin{align} \frac{3x^{2}-x+2}{x-1}&=\frac{3x^{2}-3x+2x+2}{x-1}\\ &=\frac{3x^{2}-3x}{x-1}+\frac{2x}{x-1}+\frac{2}{x-1}\\ &=\frac{3x(x-1)}{x-1}+2\left(\frac{x-1+1}{x-1}\right)+\frac{2}{x-1}\\ &=3x+2\left(1+\frac{1}{x-1}\right)+\frac{2}{x-1}\\ \end{align}