Integral of $$$\frac{e^{x}}{x}$$$

The calculator will find the integral/antiderivative of $$$\frac{e^{x}}{x}$$$, with steps shown.

Related calculator: Definite and Improper Integral Calculator

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Find $$$\int \frac{e^{x}}{x}\, dx$$$.


This integral (Exponential Integral) does not have a closed form:

$${\color{red}{\int{\frac{e^{x}}{x} d x}}} = {\color{red}{\operatorname{Ei}{\left(x \right)}}}$$


$$\int{\frac{e^{x}}{x} d x} = \operatorname{Ei}{\left(x \right)}$$

Add the constant of integration:

$$\int{\frac{e^{x}}{x} d x} = \operatorname{Ei}{\left(x \right)}+C$$

Answer: $$$\int{\frac{e^{x}}{x} d x}=\operatorname{Ei}{\left(x \right)}+C$$$