What is the integral of e^{2/x} ?

The integral of e^{2/x} is e^{2/x}x-2\Ei(2/x)+C

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integral of e^{2/x}

integral

e^{\frac{2}{x}}

e^{\frac{2}{x}} x - 2 Ei (\frac{2}{x}) + C

Solution steps

\int e^{\frac{2}{x}} d x

Apply Integration By Parts

: e^{\frac{2}{x}} x - \int - \frac{2 e ^{\frac{2}{x}}}{x} d x

= e^{\frac{2}{x}} x - \int - \frac{2 e ^{\frac{2}{x}}}{x} d x

\int - \frac{2 e ^{\frac{2}{x}}}{x} d x = 2 Ei (\frac{2}{x})

= e^{\frac{2}{x}} x - 2 Ei (\frac{2}{x})

Add a constant to the solution

= e^{\frac{2}{x}} x - 2 Ei (\frac{2}{x}) + C

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What is the integral of e^{2/x} ?
The integral of e^{2/x} is e^{2/x}x-2\Ei(2/x)+C