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
Plot
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