Function Expression :
\[f(x)=x+\frac{1-(ln x )^2}{x} \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=1 - \frac{1 - \log{\left(x \right)}^{2}}{x^{2}} - \frac{2 \log{\left(x \right)}}{x^{2}} \]\[f^{\,\prime}(x)=\frac{x^{2} + \log{\left(x \right)}^{2} - 2 \log{\left(x \right)} - 1}{x^{2}} \]
\[ \]
Integral
\[F(x) = \frac{x^{2}}{2} - \frac{\log{\left(x \right)}^{3}}{3} + \log{\left(x \right)} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0379 seconds