In calculus, the easiest way to deal with roots is to turn them into fraction powers. A square root will become a ½ power, a cube root will become a 1/3 power and so on. There is a basic formula to follow when taking the integral of an expression with a power 1/(n+1) x^(n+1).
Re-write the cube root into a fraction power: x^(1/3).
Add one to the power: x^(4/3).
Multiply the expression by the reciprocal of the power. A reciprocal is simply a fraction flipped. For example the reciprocal of 4/3 is 3/4. Multiplying by 3/4 yields: 3/4 x^(4/3).