f(x)=sin^2ωx+√3sinωxsin(ωx+π/2)=f(x)=sin^2ωx+√3sinωxcos(ωx)=√3/2sin2ωx-1/2cos2ωx+1/2
=sin(2ωx-π/6)+1/2
最小正周期为π,2π/2ω=π,ω=1
f(x)=sin(2x-π/6)+1/2
令2x-π/6=kπ+π/2,x=kπ/2+π/3,对称轴为直线x=kπ/2+π/3（k为整数）
令2x-π/6=kπ,x=kπ/2+π/12,对称中心为（x=kπ/2+π/12,1/2）（k为整数）
令2kπ-π/2≤2x-π/6≤2kπ+π/2,kπ-π/6≤x≤kπ+π/3
单调递增区间[kπ-π/6,kπ+π/3],（k为整数）