Function Expression :
\[f(x)=x. x. x. x(ln x-1 )(ln x-1 ) \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = 0 \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=4 x^{3} \left(\log{\left(x \right)} - 1\right)^{2} + 2 x^{3} \left(\log{\left(x \right)} - 1\right) \]\[f^{\,\prime}(x)=2 x^{3} \left(\log{\left(x \right)} - 1\right) \left(2 \log{\left(x \right)} - 1\right) \]
\[ \]
Integral
\[F(x) = \frac{x^{5} \log{\left(x \right)}^{2}}{5} - \frac{12 x^{5} \log{\left(x \right)}}{25} + \frac{37 x^{5}}{125} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0285 seconds