Evaluate the integral from 0 to 1 of (6+4x sqrt(x))

I keep getting 8 on this problem, and it is wrong. Will someone please help me with this problem.

Thanks!

Separate the integral since it is two integrals: Integral from 0 to 1 (6 dx) + Integral from 0 to 1 (4x * x^(1/2) dx)

Distribute x^(1/2): Integral from 0 to 1 (6 dx) + Integral from 0 to 1 (4x^(3/2) dx)

Evaluate the integral: 6x from 0 to 1 + (8/5)x^(5/2) from 0 to 1

Simplify: 6(1) - 6(0) + (8/5)(1) - (8/5)(0) = 6 + 8/5 = 30/5 + 8/5 = 38/5

∫(6 + 4x√x) dx from 0 to 1

∫(6 + 4x^(3/2)) dx from 0 to 1

6x + 8/5*x^(5/2) eval. from 0 to 1

= 6 + 8/5 = 38/5