Function Expression :
\[f(x)=ln(\frac{x+1}{x-1} ) \]Domain
\[\left]-\infty, -1\right[ \cup \left]1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow-1} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\left(x - 1\right) \left(\frac{1}{x - 1} - \frac{x + 1}{\left(x - 1\right)^{2}}\right)}{x + 1} \]\[f^{\,\prime}(x)=- \frac{2}{x^{2} - 1} \]
\[ \]
Integral
\[F(x) = x \log{\left(\frac{x}{x - 1} + \frac{1}{x - 1} \right)} + 2 \log{\left(x + 1 \right)} - \log{\left(\frac{x}{x - 1} + \frac{1}{x - 1} \right)} \]Sign Table
Variation Table
Plot
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