<s>[INST] Evaluating the integral $\int\frac{3x^{2}-x+2}{x-1}\;dx$ 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?
 [/INST] 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}
</s>