Integral of (0.4-0.08x)dx dx

1. Integrate term-by-term:

   1. The integral of a constant is the constant times the variable of integration:

      $$\int \frac{2}{5}\, dx = \frac{2 x}{5}$$

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

      $$\int \left(- \frac{2 x}{25}\right)\, dx = - \frac{2 \int x\, dx}{25}$$

      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: $- \frac{x^{2}}{25}$

   The result is: $- \frac{x^{2}}{25} + \frac{2 x}{5}$

2. Now simplify:

   $$\frac{x \left(10 - x\right)}{25}$$

3. Add the constant of integration:

   $$\frac{x \left(10 - x\right)}{25}+ \mathrm{constant}$$

The answer is:

$$\frac{x \left(10 - x\right)}{25}+ \mathrm{constant}$$