Integral of 3z^2 dx

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

   $$\int 3 z^{2}\, dz = 3 \int z^{2}\, dz$$

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

      $$\int z^{2}\, dz = \frac{z^{3}}{3}$$

   So, the result is: $z^{3}$

2. Add the constant of integration:

   $$z^{3}+ \mathrm{constant}$$

The answer is:

$$z^{3}+ \mathrm{constant}$$