In[]:=
$Version
Out[]=
15.0.0 for Microsoft Windows (64-bit) (May 19, 2026)
In[]:=
A=(1/((b-a)+(d-c)))(Integrate[1/x,{x,a,b},Assumptions->{a,b}∈Reals]+Integrate[1/x,{x,c,d},Assumptions->{c,d}∈Reals])
Out[]=
Log
b
a
+Log
d
c

-a+b-c+d
if b>0&&(0<a<b||a>b)&&d>0&&(0<c<d||c>d)
In[]:=
Limit[A,{a,b,c,d}->{-Infinity,0,0,Infinity},Direction->{Reals,-1,1,Reals}]
Out[]=
Undefined
(*---OR:--------------------------*)
In[]:=
B=Assuming[{a,b,c,d}∈Reals,(1/((b-a)+(d-c)))(Integrate[1/x,{x,a,b}]+Integrate[1/x,{x,c,d}])]
Out[]=
Log
b
a
+Log
d
c

-a+b-c+d
if a>0&&a≠b&&b>0&&c>0&&c≠d&&d>0
In[]:=
Limit[B,{a,b,c,d}->{-Infinity,0,0,Infinity},Direction->{Reals,-1,1,Reals}]
Out[]=
Undefined