Consider
given integration,
⇒∫cos4xdx
⇒∫(cos2x)2dx
⇒∫(1+cos2x2)2dx
⇒∫(1+cos2x)24dx
⇒∫(1+cos22x+2cos2x)4dx
⇒∫(1+1+cos2.2x2+2cos2x)4dx
⇒∫(2+cos4x+4cos2x)8dx
⇒18∫(2+cos4x+4cos2x)dx
⇒18(2x+sin4x4+4sin2x2)+C
⇒18(2x+sin4x4+sin2x)+C
Hence, this is the
answer.