Function Expression :
\[f(x)=\frac{1}{3x}e^{x^3} \]Domain
\[\left]-\infty, 0\right[ \cup \left]0, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=3 \cdot \frac{1}{3 x} x^{2} e^{x^{3}} - \frac{e^{x^{3}}}{3 x^{2}} \]\[f^{\,\prime}(x)=\frac{\left(x^{3} - \frac{1}{3}\right) e^{x^{3}}}{x^{2}} \]
\[f^{\,\prime}(x)=\frac{\left(3 x^{3} - 1\right) e^{x^{3}}}{3 x^{2}} \]
Integral
\[F(x) = \frac{\operatorname{Ei}{\left(x^{3} \right)}}{9} \]Sign Table
Variation Table
Plot
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