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