f(x)=2sinx(sinx+cosx)
=2sin²x+2sinxcosx
=1-cos(2x)+sin(2x)
=√2sin(2x-π/4)+1
當(dāng)2kπ-π/2≤2x-π/4≤2kπ+π/2,k∈Z
即kπ-π/8≤x≤kπ+3π/8,k∈Z時(shí),f(x)為增函數(shù)；
當(dāng)2kπ+π/2＜2x-π/4＜2kπ+3π/2,k∈Z
即kπ+3π/8＜x＜kπ+7π/8,k∈Z時(shí),f(x)為減函數(shù),
∴函數(shù)的增區(qū)間為[kπ-π/8,kπ+3π/8],減區(qū)間為（kπ+3π/8,kπ+7π/8）,k∈Z.