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Evaluate: int(x^4+x^2+1)/(x^2-x+1)\ dx...

Evaluate: `int(x^4+x^2+1)/(x^2-x+1)\ dx`

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Solution:
`\int \frac{x^{4}+x^{2}+1}{x^{2}-x+1} d x=\int \frac{x^{4}+2 x^{2}+1-x^{2}}{x^{2}-x+1} d x`
=`\int \frac{(x^{2}+1)-x^{2}}{x^{2}-x+1} d x=\int \frac{(x^{2}+1+x)(x^{2}+1-x)}{x^{2}-x+1} d x`
=`\int(x^{2}+x+1)`
=`\frac{x^{3}}{3}+\frac{x^{2}}{2}+x+C`
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