Mathematica returns non-numerical integrand while minimizing

[physstudent.4]

Homework Statement

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]}]

Homework Equations

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.

 

[vela]

Use Integrate instead of NIntegrate. Also, you can actually do the integrals and write the expressions down in closed form. If you define Etrial using those results, it'll be a lot faster since Mathematica won't have to repeatedly perform the integrations.

 

[physstudent.4]

I ended up just writing a separate loop that found the minimum. I discovered if I had written my trial function as a function of both x and a, then used partial derivatives, Mathematica can handle that easier. Thanks anyway though!