Function Expression :
\[f(x)=\frac{x^3}{x^2-x-2} \]Domain
\[\left]-\infty, -1\right[ \cup \left]-1, 2\right[ \cup \left]2, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow-1} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = +\infty \]
\[\lim_{x \overset{<}{\rightarrow2} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow2} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{x^{3} \cdot \left(1 - 2 x\right)}{\left(x^{2} - x - 2\right)^{2}} + \frac{3 x^{2}}{x^{2} - x - 2} \]\[f^{\,\prime}(x)=\frac{x^{2} \cdot \left(3 x^{2} - x \left(2 x - 1\right) - 3 x - 6\right)}{\left(- x^{2} + x + 2\right)^{2}} \]
\[ \]
Integral
\[F(x) = \frac{x^{2}}{2} + x + \frac{8 \log{\left(x - 2 \right)}}{3} + \frac{\log{\left(x + 1 \right)}}{3} \]Sign Table
Variation Table
Plot
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