Introduce a new variable:
u = 4x^3 + 2
They you can get dx=du/12x^2. You insert both of these two into you initial equation and get:
x^2*u^3*du/12x^2
Due to new variable you must change limits into 2 to 6, getting final equation
u^4/48Inserting the limits you obtain the result 26.67 or 80/3.