f(x)=sin²(x)+(√3)sin(x)cos(x)+2cos²(x)
=3/2+√3/2sin2x+1/2cos2x
=3/2+sin(2x+π/6)
函数f(x)的最小正周期T=2π/2=π
2kπ-π/2≤ 2x+π/6≤2kπ+π/2,k∈Z
kπ-π/3≤ x≤kπ+π/6,k∈Z
∴f(x)单调增区间是
[kπ-π/3,kπ+π/6】k∈Z