# Integrate: x^4+x^2+1 / x^2+x+1

Solution:

$I=\int \frac{x^{4}+x^{2}+1}{x^{2}+x+1}dx\\ \\ \Rightarrow \hspace{1cm}I=\int \frac{(x^{2}+x+1)(x^{2}-x+1)}{x^{2}+x+1}dx\\ \\ \Rightarrow \hspace{1cm}I=\int (x^{2}-x+1)dx \\ \\ \Rightarrow \hspace{1cm}I=\frac{x^{3}}{3}-\frac{x^{2}}{2}+x+c$

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