Evaluate the following integrals \[ \int \frac{\left(2 x^{2}+5 x+9\right) d x}{(x+1) \sqrt{x^{2}...

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Evaluate the following integrals
\[
\int \frac{\left(2 x^{2}+5 x+9\right) d x}{(x+1) \sqrt{x^{2}+x+1}}
\]
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