Integrate (3x^2-x^3)dx

With integration like this, you can look at each appearance of x individually.  Firstly there is a rule to follow that is the power of X in each case increases by 1 and then that increase power divides the case: 

eg. integral of x² = x²⁺¹/(2+1)

in this case, the integral of 3x² -> 3x²⁺¹/3 = x³ and x³ -> x⁽³⁺¹⁾/(3+1) = x⁴/(4)

you must always remember when integrating to add a constant to the end ( +c)

so we have x³ + x⁴/4 + C

as our final integration