f(x)=2根号3sinxcosx+cos2x+1
=根号3sin2x+cos2x+1
=2sin(2x+π/6)+1
T=2π/2=π
单调递减区间
2kπ+π/2<=2x+π/6<=2kπ+3π/2
kπ-π/6<=x<=kπ+2π/3
单调递减区间[kπ-π/6,kπ+2π/3
]