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