Evaluate the following integrals:
Question:

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

Solution:

Given, $\int \frac{x^{2}-x^{2}+x-1}{x-1} d x$.

$=\int \frac{x^{2}(x-1)+x-1}{x-1} d x$

$=\int \frac{(x-1)\left[x^{2}+1\right]}{x-1} d x$

$=\int\left(x^{2}+1\right) d x\left[\right.$ since, $\left.\int x^{n} d x=\frac{x^{n+1}}{n+1}\right]$

$=\frac{x^{3}}{3}+x+c$

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