Integral of e^(x/y) dx

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

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

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

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

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

      1. The integral of the exponential function is itself.

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

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

   Now substitute $u$ back in:

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

2. Add the constant of integration:

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

The answer is:

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