g[x_]  :=   Sin[x]^4 Cos[x]^2

TraditionalForm[g[x]]

computer  =  ∫g[x] \[DifferentialD]x

goodman  =   (x/16) - 
        (1/64) Sin[4 x]   -  (1/48) Sin[2  x]^3

Simplify[computer  -  goodman]