Function Expression :
\[f(x)=\frac{6-2x^3+2x}{2-x^2} \]Domain
\[\left]-\infty, - \sqrt{2}\right[ \cup \left]- \sqrt{2}, \sqrt{2}\right[ \cup \left]\sqrt{2}, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow- \sqrt{2}} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow- \sqrt{2}} }f(x) = +\infty \]
\[\lim_{x \overset{<}{\rightarrow\sqrt{2}} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow\sqrt{2}} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{2 x \left(\left(-1\right) 2 x^{3} + 2 x + 6\right)}{\left(2 - x^{2}\right)^{2}} + \frac{2 - 6 x^{2}}{2 - x^{2}} \]\[f^{\,\prime}(x)=\frac{2 \left(x^{4} - 5 x^{2} + 6 x + 2\right)}{x^{4} - 4 x^{2} + 4} \]
\[ \]
Integral
\[F(x) = x^{2} + \left(1 - \frac{3 \sqrt{2}}{2}\right) \log{\left(x - \sqrt{2} \right)} + \left(1 + \frac{3 \sqrt{2}}{2}\right) \log{\left(x + \sqrt{2} \right)} \]Sign Table
Variation Table
Plot
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