Function Expression :
\[f(x)=\frac{x^4+2x^2+1}{x^2+2} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{2 x \left(x^{4} + 2 x^{2} + 1\right)}{\left(x^{2} + 2\right)^{2}} + \frac{4 x^{3} + 4 x}{x^{2} + 2} \]\[f^{\,\prime}(x)=\frac{2 x \left(x^{4} + 4 x^{2} + 3\right)}{x^{4} + 4 x^{2} + 4} \]
\[ \]
Integral
\[F(x) = \frac{x^{3}}{3} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} \]Sign Table
Variation Table
Plot
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