[Solved] Help for calculating triple definite integral, please.

Questions
1

Hello everybody. I cannot calculate following problem. My software in my PC evaluates very long, but answer is not exist. Please, help me to calculate this problem:

Integrate[Sqrt[(2*Delta*J*(3 - Cos[Pi*x] - Cos[Pi*y] - Cos[Pi*z]) + J^2*(3 - Cos[Pi*x] - Cos[Pi*y] - Cos[Pi*z])^2)],{x,0,1},{y,0,1},{z,0,1}]
2

It may be that the integral does not exist. If so, you can still obtain numerical results:

int[Delta_, J_] := 
 NIntegrate[
  Sqrt[(2*Delta*J*(3 - Cos[Pi*x] - Cos[Pi*y] - Cos[Pi*z]) + 
     J^2*(3 - Cos[Pi*x] - Cos[Pi*y] - Cos[Pi*z])^2)], {x, 0, 1}, {y, 
   0, 1}, {z, 0, 1}]

int[1, 1]

(* 3.853312214951417` *)

I used your code as written, but it is usually best to begin user-defined variables in lower case to prevent colliding with reserved words.

Kind regards,
David

3

Thank you a lot. It succesfully work.