I am trying to calculate an expression which has the following form
Sum[(-1)^(n+1) Bionomial[4,n] NIntegrate[S[n,x] Q[n,x] V[n,x] F[x], {x,0,2000} , WorkingPercision -> 5 ] , {n, 4} ]
Where we have :
G[x_ ] := 2 Pi x p[x] Exp[-2 Pi Integrate[t p[t], {t, 0, x}]]
p[x_ ] := Piecewise[ {{0 , x > 140}} , Exp[ -0.0071* x] ];
S[n_ ,x_ ] := Exp[ -n x];
Q[n_ ,x_ ] := Product[ Exp[-2 Pi Integrate [1 - 1/(n x)^4 p[t] t , {t,x, Infinity }]] ,{n,4} ]
V[n_ ,x_ ] := Product[ Exp[-2 Pi Integrate [1 - 1/(n x / t^2 )^4 (1-p[t]) t , {t, x^2 , Infinity }]] ,{n,4} ]
F[x_ ] := G[x] Exp[Integrate[ -2 Pi (1- p[t]) t , {t, 0 , x }]]
Unfortunately the evaluation takes so much time. Is there any way to break this expression into pieces and perform calculation separately ?
p.s. I also tried limiting WorkingPercision and MaxRecursion but it didn't work.
The acceptable WorkingPercision is 5 and the acceptable evaluation time is less than half an hour !
I appreciate your suggestions.