记为f(P)=Lf()l(=L(p 实际上,原函数当为f(t)H(t) 例(1)求L1L1=1e"M=、1, (2)求L Ll=eh、1r tdl(em)=--[t·em e Pdt P P (3)求Le M[e"=et.ep'dt=(p-s)dt e (P-s)|∞ p-s Re p> re s例 (1) 求 L[1] . 1 1 [1] 1 0 0 p e p e dt pt pt =  = − = −   −  L (2) 求 L[t] . 1 1 1 [ ] 1 ( ) 1 [ ] 0 0 2 0 0  0     −  −  −  − − =  = −  = −  + = = p e dt p e dt p t e p t d e p t t e dt p t p t p t p t p t L 记为 f ( p) = L[ f (t)], ( ) [ ( )]. 1 f t f p − = L 实际上，原函数当为 f (t)H (t) (3) 求 [ ] st L e . 1 1 [ ] 0 ( ) 0 0 ( ) p s e p s e e e dt e dt s t s t p t p s t p s t − = − =  = = − − −    − − −   L Re P  Re s