Answer
$ 2x^\frac {1}{2} + x + \frac{2x^\frac{3}{2}}{3} + C$
Work Step by Step
We can split the fraction into three different terms that can be simplified and are easier to take the integral of:
$\int \frac{1 + \sqrt x + x}{\sqrt x} dx =\int( \frac{1}{\sqrt x} + \frac{\sqrt x}{\sqrt x} + \frac{x}{\sqrt x} )dx = \int (x^\frac{-1}{2} + 1 + x^\frac{1}{2}) dx$
We can now evaluate the integral, which results in $\frac {x^\frac{1}{2}}{\frac{1}{2}} + x + \frac {x^\frac{3}{2}}{\frac{3}{2}} + C $ which can be simplified further to
$ 2x^\frac {1}{2} + x + \frac{2x^\frac{3}{2}}{3} + C$
*Note: Since it is an indefinite integral, we must include a general constant $C$ in our answer
