How do you find the integral of e^((-1/2)*x)?

$- 2 {e}^{- \frac{1}{2} x} + C$
$t = - \frac{1}{2} x \implies \mathrm{dt} = - \frac{1}{2} \mathrm{dx} \implies \mathrm{dx} = - 2 \mathrm{dt}$
$I = \int {e}^{- \frac{1}{2} x} \mathrm{dx} = \int {e}^{t} \cdot \left(- 2 \mathrm{dt}\right) = - 2 \int {e}^{t} \mathrm{dt} = - 2 {e}^{t} + C$
$I = - 2 {e}^{- \frac{1}{2} x} + C$