Evaluate: `int(x^3-x^2+x-1)/(x-1)\ dx`

Explanation

Solution:

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

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

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

=`\int(x^{2}+1) d x`

=`\int(x^{2}+x^{0}) d x`

=`\int x^{2} d x+\int x^{0} d x`

=`\frac{x^{2+1}}{2+1}+\frac{x^{0+1}}{0+1}+C`

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