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