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