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