Integral of 1000x0,5 dx

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

   $$\int 1000 x 0.5\, dx = 500.0 \int x\, dx$$

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

      $$\int x\, dx = \frac{x^{2}}{2}$$

   So, the result is: $250.0 x^{2}$

2. Add the constant of integration:

   $$250.0 x^{2}+ \mathrm{constant}$$

The answer is:

$$250.0 x^{2}+ \mathrm{constant}$$