由欧拉公式得
cos(wt)=(1/2)*[e^iwt+e^(-iwt)]
L(coswt)=(1/2)L[e^iwt+e^(-iwt)]
=(1/2)*[L(e^iwt)+L(e^-iwt)]
又L(e^at)=1/(s-a)
所以原式=(1/2)[1/(s-iw)+1/(s+iw)]
=s/(s^2+w^2)