Function Expression :
\[f(x)=\frac{2}{x(x^2+1 )} \]Domain
\[\left]-\infty, 0\right[ \cup \left]0, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{2 \left(- 3 x^{2} - 1\right)}{x^{2} \left(x^{2} + 1\right)^{2}} \]\[f^{\,\prime}(x)=\frac{2 \left(- 3 x^{2} - 1\right)}{x^{2} \left(x^{2} + 1\right)^{2}} \]
\[ \]
Integral
\[F(x) = 2 \log{\left(x \right)} - \log{\left(x^{2} + 1 \right)} \]Sign Table
Variation Table
Plot
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