Function Expression :
\[f(x)=(x-3 )ln(x-3 )-x \]Domain
\[\left]3, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow3} }f(x) = -3 \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\log{\left(x - 3 \right)} \]\[f^{\,\prime}(x)=\log{\left(x - 3 \right)} \]
\[ \]
Integral
\[F(x) = \frac{x^{2} \log{\left(x - 3 \right)}}{2} - \frac{3 x^{2}}{4} - 3 x \log{\left(x - 3 \right)} + \frac{3 x}{2} + \frac{9 \log{\left(x - 3 \right)}}{2} \]Sign Table
Variation Table
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