y=2cosx(sinx+cosx)
=sin2x+cos2x+1
=根号2*sin(2x+π/4)
对称轴为
2x+π/4=kπ+π/2
x=kπ/2+π/8
对称中心为
2x+π/4=kπ
x=kπ/2-π/8