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