NEW FUNCTION

Function Expression :

\[f(x)=e(x-xln x )+\frac{x^2}{2} \]

Domain

\[\left]0, \infty\right[ \]

Limits

\[\lim_{x \overset{>}{\rightarrow0} }f(x) = 0 \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]

Derivate

\[f^{\,\prime}(x)=x - e \log{\left(x \right)} \]
\[f^{\,\prime}(x)=x - e \log{\left(x \right)} \]
\[ \]

Integral

\[F(x) = \frac{x^{3}}{6} + e \left(- \frac{x^{2} \log{\left(x \right)}}{2} + \frac{3 x^{2}}{4}\right) \]

Sign Table


Variation Table


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