If ∫cosxcos2xcos5xdx
=A1sin2x+A2sin4x+A3sin6x+A4sin8x+C
then
A1=12,A2=14
A1=14,A2=18
A2=116,A3=18
A1=18, A4=132
(cosxcos2x)cos5x=12(cosx+cos3x)cos5x
=14[cos4x+cos6x]+14[cos2x+cos8x]=14cos2x+14cos4x+14cos6x+14cos8x
∫cosxcos2xcos5xdx=18sin2x+116sin4x+124sin6x+132sinx+C