Function Expression :
\[f(x)=\frac{6-x^3}{2+x^2} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{3 x^{2}}{x^{2} + 2} - \frac{2 x \left(6 - x^{3}\right)}{\left(x^{2} + 2\right)^{2}} \]\[f^{\,\prime}(x)=\frac{x \left(- x^{3} - 6 x - 12\right)}{x^{4} + 4 x^{2} + 4} \]
\[ \]
Integral
\[F(x) = - \frac{x^{2}}{2} + \log{\left(x^{2} + 2 \right)} + 3 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)} \]Sign Table
Variation Table
Plot
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