Function Expression :
\[f(x)=\frac{1}{2}x^2-ln x \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=x - \frac{1}{x} \]\[f^{\,\prime}(x)=\frac{x^{2} - 1}{x} \]
Integral
\[F(x) = \frac{x^{3}}{6} - x \log{\left(x \right)} + x \]Sign Table
Variation Table
Plot
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