Evaluate: ∫⁡ ⁡sin6x+cos6xsin2x⋅cos2xdx

Let I = ∫ sin6x + cos6xsin2xcos2x dx = ∫ (sin2x)3 + (cos2x)3sin2xcos2x dx = ∫ (sin2x + cos2x)(sin4x + cos4x − sin2xcos2x)sin2xcos2x dx = ∫ (sin2x + cos2x)2 ⁡⁡⁡−sin2xcos2xsin2xcos2x dx = ∫ (1sin2xcos2x ⁡⁡⁡) dx = ∫ sin2 + cos2xsin2xcos2x dx ⁡⁡⁡ x + C = ∫ sec2x dx + ∫ cosec2x dx ⁡⁡⁡ x + C I = tanx − cotx ⁡⁡⁡ x + C