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