Integral of e^(x/2) dx

1. Let $u = \frac{x}{2}$.

   Then let $du = \frac{dx}{2}$ and substitute $2 du$:

   $$\int 2 e^{u}\, du$$

   1. The integral of a constant times a function is the constant times the integral of the function:

      $$\text{False}$$

      1. The integral of the exponential function is itself.

         $$\int e^{u}\, du = e^{u}$$

      So, the result is: $2 e^{u}$

   Now substitute $u$ back in:

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

2. Now simplify:

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

3. Add the constant of integration:

   $$2 e^{\frac{x}{2}}+ \mathrm{constant}$$

The answer is:

$$2 e^{\frac{x}{2}}+ \mathrm{constant}$$