Function Expression :
\[f(x)=(xln x )^2 \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = 0 \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{x^{2} \log{\left(x \right)}^{2} \cdot \left(2 \log{\left(x \right)} + 2\right)}{x \log{\left(x \right)}} \]\[f^{\,\prime}(x)=2 x \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} \]
\[ \]
Integral
\[F(x) = \frac{x^{3} \log{\left(x \right)}^{2}}{3} - \frac{2 x^{3} \log{\left(x \right)}}{9} + \frac{2 x^{3}}{27} \]Sign Table
Variation Table
Plot
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