Function Expression :
\[f(x)=\frac{(-x^3+(-x )^2-1 )}{(-x )^2-1} \]Domain
\[\left]-\infty, -1\right[ \cup \left]-1, 1\right[ \cup \left]1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \overset{<}{\rightarrow-1} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = -\infty \]
\[\lim_{x \overset{<}{\rightarrow1} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{2 x \left(\left(- x\right)^{2} - x^{3} - 1\right)}{\left(\left(- x\right)^{2} - 1\right)^{2}} + \frac{- 3 x^{2} + 2 x}{\left(- x\right)^{2} - 1} \]\[f^{\,\prime}(x)=\frac{x^{2} \cdot \left(3 - x^{2}\right)}{x^{4} - 2 x^{2} + 1} \]
\[ \]
Integral
\[F(x) = - \frac{x^{2}}{2} + x - \frac{\log{\left(x^{2} - 1 \right)}}{2} \]Sign Table
Variation Table
Plot
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