Function Expression :
\[f(x)=x+ln(\frac{3-x}{1+x} ) \]Domain
\[\left]-1, 3\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = +\infty \]\[\lim_{x \overset{<}{\rightarrow3} }f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=1 + \frac{\left(x + 1\right) \left(- \frac{3 - x}{\left(x + 1\right)^{2}} - \frac{1}{x + 1}\right)}{3 - x} \]\[f^{\,\prime}(x)=\frac{\left(x - 3\right) \left(x + 1\right) + 4}{\left(x - 3\right) \left(x + 1\right)} \]
\[ \]
Integral
\[F(x) = \frac{x^{2}}{2} + x \log{\left(- \frac{x}{x + 1} + \frac{3}{x + 1} \right)} - 4 \log{\left(x + 1 \right)} - 3 \log{\left(- \frac{x}{x + 1} + \frac{3}{x + 1} \right)} \]Sign Table
Variation Table
Plot
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