sin^6x+cos^6x+3sin^2xcos^2x+4=(sin^2x+cos^2)(sin^4x-sin^2xcos^2x+cos^4x)+3sin^2xcos^2x+4
=(sin^2+cos^2x)^2-3sin^2xcos^2x+3sin^2xcos^2x+4
=1+4
=5