Function Expression :
\[f(x)=\frac{ln(e^{x^2-1} )}{x^3} \]Domain
\[\left]-\infty, 0\right[ \cup \left]0, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{2 x e^{1 - x^{2}} e^{x^{2} - 1}}{x^{3}} - \frac{3 \log{\left(e^{x^{2} - 1} \right)}}{x^{4}} \]\[f^{\,\prime}(x)=\frac{2 x^{2} - 3 \log{\left(e^{x^{2}} \right)} + 3}{x^{4}} \]
\[ \]
Integral
\[F(x) = \log{\left(x \right)} + \frac{1}{2 x^{2}} \]Sign Table
Variation Table
Plot
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