# How to calculate an integral in Mathematica?

I have the next integral, and I would like to know what is the best way to define it in mathematica:

$\int_{0}^{\infty}{du}\int_{0}^{\infty}{dv} \frac{u}{u^2+v^2}(\int_{0}^{0.8}\int_{0}^{\infty} xe^{-2\sqrt{x^2+y^2}} J_{0}(ux)[cos(\pi y/0.8)]^2 cos(yv) {dy}{dx})^2$

Because I am a beginnner, my first idea was touse the next code:

   NIntegrate[ (u/(u^2 + v^2))*r*x*  Exp[-2*0.2*(Sqrt[r^2 + z^2] + Sqrt[x^2 + y^2])]*BesselJ[0, u*r]*  BesselJ[0, u*x]*Cos[v*z]*Cos[y*v]*(Cos[Pi*z/1.6]*Cos[Pi*y/1.6])^2, {u, 0, Infinity}, {v, 0,Infinity}, {r, 0, Infinity}, {x, 0, Infinity}, {z, 0, 0.8}, {y, 0, 0.8}]


But I get warnings about the oscillatory behavior of the integrand.

What would be another way to define the integral in order to gain time and not warnings

I find another way to calculate it, using the Adative MonteCarlo strategy, but each time that I evaluate he cell, I got a different result. What is the origin of this problem?

Thank you for all your help

• where did the r and y come from? Mar 12, 2018 at 18:28
• instead of the square of the integral, in the code I put the the product of two integrals, one using r and z and the other with x and y.
– rafa
Mar 13, 2018 at 6:47
• that is not a valid transformation Mar 13, 2018 at 11:15
• But I am applying the Fubini theorem
– rafa
Mar 13, 2018 at 11:57
• so edit the question to show exactly what you are doing and what you are actually trying to accomplish. Mar 13, 2018 at 13:43

      Quiet[NIntegrate[(u/(u^2 + v^2))*r*x*