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