Function Expression :
\[f(x)=x+2\frac{1}{x^2+2} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{4 x}{\left(x^{2} + 2\right)^{2}} + 1 \]\[f^{\,\prime}(x)=- \frac{4 x}{\left(x^{2} + 2\right)^{2}} + 1 \]
\[f^{\,\prime}(x)=\frac{- 4 x + \left(x^{2} + 2\right)^{2}}{\left(x^{2} + 2\right)^{2}} \]
Integral
\[F(x) = \frac{x^{2}}{2} + \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)} \]Sign Table
Variation Table
Plot
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