Integral of $$$\frac{e^{x}}{x}$$$
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Your Input
Find $$$\int \frac{e^{x}}{x}\, dx$$$.
Solution
This integral (Exponential Integral) does not have a closed form:
$${\color{red}{\int{\frac{e^{x}}{x} d x}}} = {\color{red}{\operatorname{Ei}{\left(x \right)}}}$$
Therefore,
$$\int{\frac{e^{x}}{x} d x} = \operatorname{Ei}{\left(x \right)}$$
Add the constant of integration:
$$\int{\frac{e^{x}}{x} d x} = \operatorname{Ei}{\left(x \right)}+C$$
Answer: $$$\int{\frac{e^{x}}{x} d x}=\operatorname{Ei}{\left(x \right)}+C$$$