$\int \frac{x^{3}-x^{2}+x-1}{x-1} d x$
On dividing, we obtain
$=\int\left(x^{2}+1\right) d x$
$=\int x^{2} d x+\int 1 d x$
$=\frac{x^{3}}{x}+x+\mathrm{C}$
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