Function Expression :
\[f(x)=\frac{x^3+2x^2+1}{x^2-4} \]Domain
\[\left]-\infty, -2\right[ \cup \left]-2, 2\right[ \cup \left]2, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow-2} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow-2} }f(x) = -\infty \]
\[\lim_{x \overset{<}{\rightarrow2} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow2} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{2 x \left(x^{3} + 2 x^{2} + 1\right)}{\left(x^{2} - 4\right)^{2}} + \frac{3 x^{2} + 4 x}{x^{2} - 4} \]\[f^{\,\prime}(x)=\frac{x \left(x^{3} - 12 x - 18\right)}{x^{4} - 8 x^{2} + 16} \]
\[ \]
Integral
\[F(x) = \frac{x^{2}}{2} + 2 x + \frac{17 \log{\left(x - 2 \right)}}{4} - \frac{\log{\left(x + 2 \right)}}{4} \]Sign Table
Variation Table
Plot
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