(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to minimize the function Etrial[a]

trial[x_] := E^(-a*x^2)

Etrial[a_] :=

NIntegrate[1/2*D[trial[x], x]^2 + x^4*trial[x]^2, {x, -\[Infinity], \[Infinity]}]/

NIntegrate[trial[x]^2, {x, -\[Infinity], \[Infinity]}]

2. Relevant equations

3. The attempt at a solution

I have used NMinimize[Etrial[a],a] and Minimize[Etrial[a],a], as well as FindMiminum[Etrial[a],{a,.5}], since when I plot it, the minimum is pretty obviously around .7, so I arbitrarily chose .5 as a close starting point.

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# Homework Help: Mathematica returns non-numerical integrand while minimizing

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