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