Function Expression :
\[f(x)=ln(x^2+4 )-x \]Domain
\[\left]-\infty, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{2 x}{x^{2} + 4} - 1 \]\[f^{\,\prime}(x)=\frac{- x^{2} + 2 x - 4}{x^{2} + 4} \]
\[ \]
Integral
\[F(x) = - \frac{x^{2}}{2} + x \log{\left(x^{2} + 4 \right)} - 2 x + 4 \operatorname{atan}{\left(\frac{x}{2} \right)} \]Sign Table
Variation Table
Plot
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