720 BELL SYSTEM TECHNICAL JOURNAL 



with their known solutions, accompanied by the corresponding 

 operational equation and its explicit solution. All of these solutions 

 are directly applicable to important technical problems. It may be 

 remarked in passing that the infinite integrals have for the most 

 part been e\aluated by ad\anced mathematical methods which need 

 not concern us here. 



Table of Infinite Integrals, the Corresponding Operational Equations, 

 and Their Explicit Solutions 



1 



(a) r 



Jo 



e-p'e-Wt = ^. , ^ , 

 p-\-\ 



P 



h=^-^=e-^'. 



P+\ 



(b) r e-P'^.dl=^\/p''+\ 

 Jo n\ 





r°° \ 1 



(c) / e-P'^dl=~, 

 J<i y/wt Vp 



(2»-l)y'^/ pny/p' 



.Vp_^ (2/)" 1 



/>'■ 1.3.5... (2n- 1)^7/* 



(e) re-P'^;,e-^'dt = -^^ 



(P+X) 

 (/>+X)"+' «!' • 



>+i 



(f) 



^■^t\n 



(g) / e-P'^dl = '-~~, 



,_ , _ p-\ll 



h = Vpe-'^'I^P=, .^. 

 Wirt 



