Function Expression :
\[f(x)=(ln x-1 )(e^{2ln x}-1 ) \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=2 x \left(\log{\left(x \right)} - 1\right) + \frac{x^{2} - 1}{x} \]\[f^{\,\prime}(x)=2 x \log{\left(x \right)} - x - \frac{1}{x} \]
\[f^{\,\prime}(x)=\frac{2 x^{2} \log{\left(x \right)} - x^{2} - 1}{x} \]
Integral
\[F(x) = \frac{x^{3} \log{\left(x \right)}}{3} - \frac{4 x^{3}}{9} - x \log{\left(x \right)} + 2 x \]Sign Table
Variation Table
Plot
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