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