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