Integral of 2y^4 dy

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

   $$\int 2 y^{4}\, dy = 2 \int y^{4}\, dy$$

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

      $$\int y^{4}\, dy = \frac{y^{5}}{5}$$

   So, the result is: $\frac{2 y^{5}}{5}$

2. Add the constant of integration:

   $$\frac{2 y^{5}}{5}+ \mathrm{constant}$$

The answer is:

$$\frac{2 y^{5}}{5}+ \mathrm{constant}$$