(* 4.382.1 *)

Integrate[Log[Abs[(x+a)/(x-a)]]*Sin[b*x],{x,0,Infinity},Assumptions->(a<0)&&(b>0)]//FullSimplify

(* This matches the table *)

f1[a_,b_]:=NIntegrate[Log[Abs[(x+a)/(x-a)]]*Sin[b*x],{x,0,Infinity}];

f2[a_,b_]:=N[((π Sin[a b])/b)];

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

s1:=RandomReal[{2,2.0001},10];

s2:=RandomReal[{2,2.0001},10];

s1

s2

s1[[1]]

s2[[1]]

f1[s1[[1]],s2[[1]]]

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

(* Correct *)