In[]:=
LT[f_,t_,s_]:=ft
∞
∫
-∞
-st
In[]:=
LT[-UnitStep[-t],t,s]
-a*t
Out[]=
★
ConditionalExpression,Re[a+s]<0
1
a+s
In[]:=
LT[UnitStep[t],t,s]
-a*t
Out[]=
★
ConditionalExpression,Re[a+s]>0
1
a+s
(*TwoDifferentTimeSignalsGivingthesame'LaplaceTransform★'withDifferentROC*)