Put fraction in "arctan-friendly" form – math.stackexchange.com

Put fraction in "arctan-friendly" form – math.stackexchange.com

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I would like to put $\int\frac{1}{(2x^2+x+1)}dx$ into something like $\int\frac{1}{(u^2+1)}dx$. What is the quickest way to proceed? I know that previous fraction can be rewritten as $2t^2+t+1 = ...

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