答：
∫ (sint)^2 * (cost)^4 dt
=∫ (sintcost)^2 *(cost)^2 dt
=(1/4) ∫ (sin2t)^2 *(1/2)*(cos2t+1) dt
=(1/8) ∫ (cos2t+1)(sin2t)^2 dt
=(1/16) ∫ (sin2t)^2 d(sin2t) +(1/16) ∫ (1-cos4t) dt
=(1/48) (sin2t)^3 + t /16 -(1/64)sin4t +C