(* 4.383.1 *)

Integrate[Log[(1+ Exp[-a*x])]*Cos[b*x],{x,0,Infinity},Assumptions->Re[a]>0&&b>0&&Im[a]>0]

f1[a_,b_]:=NIntegrate[Log[(1+ Exp[-a*x])]*Cos[b*x],{x,0,Infinity}];

f2[a_,b_]:=N[((a-b π Csch[((b π)/a)])/(2 (b^2)))];

f[a_,b_]:=f1[a,b]/f2[a,b];

s1:=RandomReal[{0,100},10];

s2:=RandomReal[{0,100},10];

s1

Table[f[s1[[i]],s2[[j]]],{i,1,3},{j,1,3}]

(* Correct *)