72 C. V. L. Chaiiier 



The integral T may be represented through f|j aud its first differeutialquotient. 

 We have indeed 



f-=-p-f. 



so that 



(167) T=K,{\-2qi^-{:2-^<fW]. 



48. For the study of è it is suggested to use the integraUogarifhmus. This 

 function is defined by the formula (Compare e. g. Nielsen : Théorie des Integral- 

 logaritlimus) 



li X 



1 



X 



dt 



\ogf 



u 



or 



lie 



or, somewhat more generally, 

 (16&) lie 



- t 



— X le dt 



t 



X 



-xy l e dt 



Besides the integrallogarithmus we introduce also the integralsinus and the 

 integralcosinus, defined by the integrals 



00 



(169) sicc=-f^f/^, 



t 



X 



(169*) cix = — ^^dt, 



t 



X 



which give 



IX 



(170) lie =c\x-{-is\x. 



