Integral of cos(x+yy) dx

1. Let $u = x + y y$.

   Then let $du = dx$ and substitute $du$:

   $$\int \cos{\left(u \right)}\, du$$

   1. The integral of cosine is sine:

      $$\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$$

   Now substitute $u$ back in:

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

2. Now simplify:

   $$\sin{\left(x + y^{2} \right)}$$

3. Add the constant of integration:

   $$\sin{\left(x + y^{2} \right)}+ \mathrm{constant}$$

The answer is:

$$\sin{\left(x + y^{2} \right)}+ \mathrm{constant}$$