f(x)=sin⁴x+2sinxcosx-cos⁴x
=sin(2x)-(cos⁴x-sin⁴x)
=sin(2x)-(sin²x+cos²x)(cos²x-sin²x)
=sin(2x)-(cos²x-sin²x)
=sin(2x)-cos(2x)
=√2sin(2x-π/4)
2kπ-π/2≤2x-π/4≤2kπ+π/2 (k∈Z)时,函数单调递增,此时
kπ-π/8≤x≤kπ+3π/8 (k∈Z)
函数的单调递增区间为[kπ-π/8,kπ+3π/8] (k∈Z).