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