∫(sinx)^2 *(cosx)^4dx
=∫(sinx^2*cosx^2)*cosx^2dx
=∫(1/4)(sin2x)^2 cosx^2 dx
=(1/4)∫(sin2x)^2*[(1+cos2x)/2]dx
=(1/8)∫(sin2x)^2 dx +(-1/16)∫(sin2x)^2dsin2x
=(1/8)∫(1-cos4x)/2 dx +(-1/48)(sin2x)^3
=(1/8)x+(-1/64)sin4x+(-1/48)(sin2x)^3+C
∫(sinx)^2 *(cosx)^4dx
=∫(sinx^2*cosx^2)*cosx^2dx
=∫(1/4)(sin2x)^2 cosx^2 dx
=(1/4)∫(sin2x)^2*[(1+cos2x)/2]dx
=(1/8)∫(sin2x)^2 dx +(-1/16)∫(sin2x)^2dsin2x
=(1/8)∫(1-cos4x)/2 dx +(-1/48)(sin2x)^3
=(1/8)x+(-1/64)sin4x+(-1/48)(sin2x)^3+C