What is the value of this?
In[]:=
EnsureHeld[
Integrate[x,{x,-Infinity,Infinity}]
q
]
Out[]=
Hold
∞
∫
-∞
xx
q

In[]:=
ReleaseHoldHold
∞
∫
-∞
xx
q

Integrate
:Integral of x does not converge on {-∞,∞}.
Out[]=
∞
∫
-∞
xx
q
We can use the Cauchy principal value to find out:
In[]:=
Integrate[x,{x,-Infinity,Infinity},PrincipalValue->True]
q
Out[]=
1
The integral is 0 with the Cauchy principal value:
In[]:=
Integrate[x,{x,-Infinity,Infinity},PrincipalValue->True]
Out[]=
0
So we have
In[]:=
Inactivate[
0
q
==1]
Out[]=
q^01
In[]:=
HoldForm[
0
q
1]
Out[]=
0
q
1
In[]:=
TraditionalForm[HoldForm[
0
q
1]]
Out[]//TraditionalForm=
0
q
1
In[]:=
Inactivate[
Integrate[x,{x,-Infinity,Infinity},PrincipalValue->True]
q

0
q
1,Integrate]
Out[]=
Integrate[x,{x,-∞,∞},PrincipalValueTrue]
q
11