Function Expression :
\[f(x)=-\frac{ln(-x )}{x+1}-1 \]Domain
\[\left]-\infty, -1\right[ \cup \left]-1, 0\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -1 \]\[\lim_{x \overset{<}{\rightarrow-1} }f(x) = 0 \]
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = 0 \]
\[\lim_{x \overset{<}{\rightarrow0} }f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\log{\left(- x \right)}}{\left(x + 1\right)^{2}} - \frac{1}{x \left(x + 1\right)} \]\[f^{\,\prime}(x)=\frac{x \log{\left(- x \right)} - x - 1}{x \left(x + 1\right)^{2}} \]
\[ \]
Integral
\[F(x) = - x + \operatorname{Li}_{2}\left(\left(x + 1\right) e^{2 i \pi}\right) \]Sign Table
Variation Table
Plot
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