Integral of cos(x)cos(y) dx

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

   $$\int \cos{\left(x \right)} \cos{\left(y \right)}\, dx = \cos{\left(y \right)} \int \cos{\left(x \right)}\, dx$$

   1. The integral of cosine is sine:

      $$\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$$

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

2. Add the constant of integration:

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

The answer is:

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