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