令t=tanx,则dt=sec²xdx
sec²x=1+tan²x=1+t²
∫ sinxcosx/[1+(sinx)^4] dx.分子分母同除于cosx^4
=∫ tanxsec²x/[(secx)^4+1] dx
=∫ t/[1+(1+t²)²]dt
=0.5 ∫ 1/[1+(1+t²)²] d(1+t²)
=0.5 arctan(1+t²)+C
=0.5 arctan[sec²x]+C