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