Prove

Question:

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

Solution:

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

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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