The integration you are trying to compute will not give you any answer because the constant 'sigma v' has a subscript v which is considered as a variable v which runs from (-) Infinity to (+) Infinity. As Mathematica does not know that it is a subscript or a notation,it can not compute. That is why it is convenient to use another symbol say, 'a' instead of 'sigma v'.
Integrate[Exp[(-v^2/a^2)/2]/(Sqrt[2 Pi] a), {v, -Infinity, Infinity}]
Perhaps this will work. See the attachment.
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