INTEGRAL - evaluate!!?

Question

take the integral of

(( 12x^2 + 12x^(3/2) +8x + 3) / (sqrt(x))) dx

Answer 1

A u-substitution is unnecessary here, just evaluate the expression as is using the power rule:

∫(12x² + 12x^(3/2) + 8x + 3)/√x dx
∫12x^(3/2) + 12x + 8√x + 3/√x dx
24x^(5/2)/5 + 6x² + 16x^(3/2)/3 + 6√x + C

Answer 2

set u = sqrt x and you'll get a polynomial in u.