Verified answer

b.

Factor the radical to

integral sqrt(8)sqrt(x). since sqrt (8) is a constant, you can factor that outside the integrand to get

sqrt(8) integral sqrt(x). Sqrt (x) is just x^(1/2), so use the power rule to integrate it. Its integral is

sqrt(8)*(2/3)*(x^(3/2)). Simplify sqrt (8) to 2 sqrt(2) and combine to get

(4sqrt(2)x^(3/2))/3. this doesn't match your answers but if you realize that x^(3/2) is the same as x*sqrt(x) then you can rewrite this as

(4x*sqrt(2x))/3 +C, which is b