Function Expression :
\[f(x)=x+ln(1+\frac{1}{(x )} ) \]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
\[f^{\,\prime}(x)=1 - \frac{1}{x^{2} \cdot \left(1 + 1 \cdot \frac{1}{x}\right)} \]\[f^{\,\prime}(x)=\frac{x \left(x + 1\right) - 1}{x \left(x + 1\right)} \]
\[ \]
Integral
\[F(x) = \frac{x^{2}}{2} + x \log{\left(1 + \frac{1}{x} \right)} + \log{\left(x + 1 \right)} \]Sign Table
Variation Table
Plot
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