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