Function Expression :
\[f(x)=ln(x^2-1 )+x \]Domain
\[\left]-\infty, -1\right[ \cup \left]1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow-1} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{2 x}{x^{2} - 1} + 1 \]\[f^{\,\prime}(x)=\frac{x^{2} + 2 x - 1}{x^{2} - 1} \]
\[ \]
Integral
\[F(x) = \frac{x^{2}}{2} + x \log{\left(x^{2} - 1 \right)} - 2 x + 2 \log{\left(x + 1 \right)} - \log{\left(x^{2} - 1 \right)} \]Sign Table
Variation Table
Plot
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