Function Expression :
\[f(x)=-\frac{x}{2}+ln(\frac{x-1}{(x )} ) \]Domain
\[\left]-\infty, 0\right[ \cup \left]1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{x \left(\frac{1}{x} - \frac{x - 1}{x^{2}}\right)}{x - 1} - \frac{1}{2} \]\[f^{\,\prime}(x)=\frac{x \left(1 - x\right) + 2}{2 x \left(x - 1\right)} \]
\[ \]
Integral
\[F(x) = - \frac{x^{2}}{4} + x \log{\left(1 - \frac{1}{x} \right)} - \log{\left(x - 1 \right)} \]Sign Table
Variation Table
Plot
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