Integral of 0,1875sqrt(x) dx

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

   $$\int 0.1875 \sqrt{x}\, dx = 0.1875 \int \sqrt{x}\, dx$$

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

      $$\int \sqrt{x}\, dx = \frac{2 x^{\frac{3}{2}}}{3}$$

   So, the result is: $0.125 x^{\frac{3}{2}}$

2. Add the constant of integration:

   $$0.125 x^{\frac{3}{2}}+ \mathrm{constant}$$

The answer is:

$$0.125 x^{\frac{3}{2}}+ \mathrm{constant}$$