HELP!!! ): How do you anti-differentiate ∫√x(2+x) dx

Please explain how you got the answer in detail.
I don't understand how to do it. ):

∫ √x(2 + x) dx

= ∫ (2√x + x√x) dx

= ∫ (2x^1/2 + x^3/2) dx

= {(2x^(3/2)) / (3/2)} + {(x^(5/2)) / (5/2)} + C

= (4/3)x√x + (2/5)x²√x + C

I'm assuming you mean:
∫ x^(1/2) * (2 + x) dx

Distribute the x^(1/2):
∫ (2x^(1/2) + x^(3/2)) dx

Integrate using the power rule:
(4/3)x^(3/2) + (2/5)x^(5/2) + c