Function Expression :
\[f(x)=\frac{1}{(x+1 )(x+2 )} \]Domain
\[\left]-\infty, -2\right[ \cup \left]-2, -1\right[ \cup \left]-1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow-2} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow-2} }f(x) = -\infty \]
\[\lim_{x \overset{<}{\rightarrow-1} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\frac{1}{\left(x + 1\right) \left(x + 2\right)} \left(- 2 x - 3\right)}{\left(x + 1\right) \left(x + 2\right)} \]\[f^{\,\prime}(x)=\frac{- 2 x - 3}{\left(x + 1\right)^{2} \left(x + 2\right)^{2}} \]
\[ \]
Integral
\[F(x) = \log{\left(x + 1 \right)} - \log{\left(x + 2 \right)} \]Sign Table
Variation Table
Plot
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