I entered
Integral[Exp[I x t - a (u-x) ] , {x,-Infinity, u}] // Simplify
%% (Where I stands for the imaginary unit i) And got the correct answer but with a weird condition:
E^(I t u)/(a+I t) if Re(a)>Im(t)\[And]Re(a (u+1000345))>=1000345 Im(t)\[And]Re(a (u+1000503))>=1000503 Im(t)
Looks as if infinity equals the number 1000345 ?
The purpose here was to find the characteristic function of a Laplace distribution.
