Integral of 4/sqrt(x) dx

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

   $$\int \frac{4}{\sqrt{x}}\, dx = 4 \int \frac{1}{\sqrt{x}}\, dx$$

   1. Let $u = \sqrt{x}$.

      Then let $du = \frac{dx}{2 \sqrt{x}}$ and substitute $2 du$:

      $$\int 2\, du$$

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

         $$\text{False}$$

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

            $$\int 1\, du = u$$

         So, the result is: $2 u$

      Now substitute $u$ back in:

      $$2 \sqrt{x}$$

   So, the result is: $8 \sqrt{x}$

2. Add the constant of integration:

   $$8 \sqrt{x}+ \mathrm{constant}$$

The answer is:

$$8 \sqrt{x}+ \mathrm{constant}$$