restart;
dp:=(p,q)->int(p*q,x=-1..1);
nm:=p->sqrt(dp(p,p));
N:=3;
for n from 0 to N
do
   tv[n]:=x^n-add(dp(x^n,tv[k])*tv[k],k=0..n-1);
   v[n]:=tv[n]/nm(tv[n]);
end;
xs:=[solve(v[3]=0,x)];
ws:=[seq(w[k],k=0..2)];
q:=f->add(ws[k]*f(xs[k]),k=1..3);
eq1:=int(1,x=-1..1)=q(x->1);
eq2:=int(x,x=-1..1)=q(x->x);
eq3:=int(x^2,x=-1..1)=q(x->x^2);
S:=solve({eq1,eq2,eq3},ws);
a1:=subs(S[1],q(f));
with(codegen):
C(a1);
solve((x-b)/(b-a)+(x-a)/(b-a)=u,x);
evalf(int(exp(-x^2),x=-1..1));