Integral of 2ydy dx

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

   $$\int 2 y 1\, dy = 2 \int y\, dy$$

   1. The integral of $y^{n}$ is $\frac{y^{n + 1}}{n + 1}$ when $n \neq -1$:

      $$\int y\, dy = \frac{y^{2}}{2}$$

   So, the result is: $y^{2}$

2. Add the constant of integration:

   $$y^{2}+ \mathrm{constant}$$

The answer is:

$$y^{2}+ \mathrm{constant}$$