Function Expression :
\[f(x)=1+x-\sqrt{x^2-4} \]Domain
\[\left]-\infty, -2\right] \cup \left[2, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow-2} }f(x) = -1 \]
\[\lim_{x \overset{>}{\rightarrow2} }f(x) = 3 \]
\[\lim_{x \rightarrow+\infty}f(x) = 1 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{x}{\sqrt{x^{2} - 4}} + 1 \]\[f^{\,\prime}(x)=- \frac{x}{\sqrt{x^{2} - 4}} + 1 \]
\[f^{\,\prime}(x)=\frac{- x + \sqrt{x^{2} - 4}}{\sqrt{x^{2} - 4}} \]
Integral
\[F(x) = \frac{x^{2}}{2} - \frac{x \sqrt{x^{2} - 4}}{2} + x + 2 \operatorname{acosh}{\left(\frac{x}{2} \right)} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0027 seconds