How to calculate the following complex integration

I want to integrate something similar to the following:

 int_0^inf(exp(c*int_z^inf(1- int_0^inf(1/(x*y) dx))*ydy))dz

I tried the following:

syms x y z

g = int(1/(x*y),x,0,inf);

f = int((1-g)*y,y,z,inf);

f = @(x,y,z) exp(c*f);

h = integral(@(z) f(x,y,z) , 0,inf)

but I get the following error:

Error using integralCalc/finalInputChecks (line 511)

Input function must return 'double' or 'single' values. Found 'sym'.

Error in integralCalc/iterateScalarValued (line 315)

                  finalInputChecks(x,fx);

Error in integralCalc/vadapt (line 132)

              [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 83)

          [q,errbnd] = vadapt(@AToInfInvTransform,interval);

Error in integral (line 88)

Q = integralCalc(fun,a,b,opstruct);

[David Goodmanson]

Hi Hesham, this is problematic since the g integral does not converge.

[Hesham]

Hi David,

Assuming it does converge, what would be the syntax used?

[David Goodmanson]

Hi Hesham,

I can't assume the impossible as a working hypothesis. The syntax is correct, though, and should give you the result g = Inf/y

Answer 1

[Walter Roberson]

syms x y z c
g = int(1/(x*y),x,0,inf);
f = int((1-g)*y,y,z,inf);
f2 = exp(c*f);
h = int(f2,z,0,inf)