Integral of 3xt^2 dt

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

   $$\int 3 t^{2} x\, dt = 3 x \int t^{2}\, dt$$

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

      $$\int t^{2}\, dt = \frac{t^{3}}{3}$$

   So, the result is: $t^{3} x$

2. Add the constant of integration:

   $$t^{3} x+ \mathrm{constant}$$

The answer is:

$$t^{3} x+ \mathrm{constant}$$