Integral of e^(x)*cos(y) dy

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

   $$\int e^{x} \cos{\left(y \right)}\, dy = e^{x} \int \cos{\left(y \right)}\, dy$$

   1. The integral of cosine is sine:

      $$\int \cos{\left(y \right)}\, dy = \sin{\left(y \right)}$$

   So, the result is: $e^{x} \sin{\left(y \right)}$

2. Add the constant of integration:

   $$e^{x} \sin{\left(y \right)}+ \mathrm{constant}$$

The answer is:

$$e^{x} \sin{\left(y \right)}+ \mathrm{constant}$$