Function Expression :
\[f(x)=x+\frac{1}{2}-ln(x )+\frac{1}{2}(ln x )^2-x \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\log{\left(x \right)}}{x} - \frac{1}{x} \]\[f^{\,\prime}(x)=\frac{\log{\left(x \right)} - 1}{x} \]
\[ \]
Integral
\[F(x) = \frac{x \log{\left(x \right)}^{2}}{2} - 2 x \log{\left(x \right)} + \frac{5 x}{2} \]Sign Table
Variation Table
Plot
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