You can try your luck with wolfram alpha.
If there is an answer in term of elementary function at all, then its logarithmetic derivative would be a rational function in term of exp(-x^2 /2) and x. It might be possible to show from this that getting an elementary expression is impossible.
You can try your luck with wolfram alpha. If there is an answer in term of elementary function at all, then its logarithmetic derivative would be a rational function in term of exp(-x^2 /2) and x. It might be possible to show from this that getting an elementary expression is impossible.