Answer
$-e^{2/x}+C$
Work Step by Step
$I=\displaystyle \int\frac{2e^{2/x}}{x^{2}}dx$
Substitute: $\left[\begin{array}{llll}
u & =\dfrac{2}{x}=2x^{-1} & & \\
& & & \\
du & =-2x^{-2}dx & \Rightarrow & \dfrac{2dx}{x^{2}}=-du
\end{array}\right]$
$I=\displaystyle \int(e^{2/x})(\frac{2dx}{x^{2}})=$ apply the substitution $=\displaystyle \int e^{u}(-du)$
$=-e^{u}+C$
bring back the variable $x$
= $-e^{2/x}+C$
