\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Verify that the function \(F(x) = \dfrac{-1}{x^2+x+1}\) is an antiderivative of \(f(x) = \dfrac{2x+1}{(x^2+x+1)^2}\) on \(\mathbb{R}\).
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