[tex]\LARGE\begin{aligned}&t=\dfrac{2}{x}\\&dt=-\dfrac{2}{x^2}\, dx\\&dx=-\dfrac{x^2}{2}\,dt\\\\&\int \dfrac{e^{\frac{2}{x}}}{x^2}\, dx=\int -\dfrac{e^t}{2}\, dt=-\dfrac{1}{2}\int e^t\, dt=\\&=-\dfrac{1}{2}e^t +C=-\dfrac{1}{2}e^{\frac{2}{x}} +C\end[/tex]
