f(x)=1+sin2x+2cos^2x
=1+sin2x+1+cos2x
=√2sin(2x+π/4)+2
2kπ-π/2≤2x+π/4≤2kπ+π/2
kπ-3π/8≤x≤kπ+π/8
[0,π/8]