Bremiher — Errors Affecting LQgarithviic Computations. 41-0 

 The limits will bo 



1/6 1/6 



in place of which oo may again be substituted since tliis limit 



becomes infinite with r. Moreover the function to be inte- 

 grated remains the same whether x has its positive or negative 

 value, hence may be put as the inferior limit ?nd "the integral 

 doubicd. Thus we have 



J 



sin cz\/ 6_ 

 7, = ^ I e -<^-'^ V _ ^^ „. .^.) —-I dz [11] 



which can be considered as the sum of two integrals and com- 

 puted by the assistance of the ordinary formula 



.6 ^' 



e ^ ^ cos2/5a; dx = i s— 



JFor by integration between and I with respect to ^ this gives 





which is the desired reduction for the first part of the integraL 

 Whence 



e-^^'dz. [12] 



