Function Expression :
\[f(x)=-x+2-x(ln x )^2 \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = 2 \]\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \log{\left(x \right)}^{2} - 2 \log{\left(x \right)} - 1 \]\[f^{\,\prime}(x)=- \log{\left(x \right)}^{2} - 2 \log{\left(x \right)} - 1 \]
\[ \]
Integral
\[F(x) = - \frac{x^{2} \log{\left(x \right)}^{2}}{2} + \frac{x^{2} \log{\left(x \right)}}{2} - \frac{3 x^{2}}{4} + 2 x \]Sign Table
Variation Table
Plot
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