Function Expression :
\[f(x)=ln(x^3-x ) \]Domain
\[\left]-1, 0\right[ \cup \left]1, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{3 x^{2} - 1}{x^{3} - x} \]\[f^{\,\prime}(x)=\frac{3 x^{2} - 1}{x \left(x^{2} - 1\right)} \]
Integral
\[F(x) = x \log{\left(x^{3} - x \right)} - 3 x - \log{\left(x - 1 \right)} + \log{\left(x + 1 \right)} \]Sign Table
Variation Table
Plot
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