symbolic math - Multifold integration with Matlab -

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this question may seem silly cannot find way solve myself. need multifold integrations (at least 4 fold) range infinite matlab, , did not found suitable functions.

for example, how should following integral:

integrate[f(x,y,z,w),{x,-\infty,\infty},{y,-\infty,\infty},{z,-\infty,\infty},{w,-\infty,\infty}]

where function f may defined as

f=1/(x-y)*1/(z-w)exp(-0.25(x^2+y^2+z^2+w^2))

in matlab, 1 needs add dot behind arguments function can executed, confused about.

i appreciate if help.

i assume mean symbolic integration. that

  1. define symbolic variables.
  2. define function of symbolic variables.
  3. apply int repeatedly integrate respect each variable. assumes function satisfies hypotheses of fubini's theorem (which example function).

so:

>> syms x y z w                           %// step 1 >> f = exp(-x^2-y^2-z^2-w^2)              %// step 2 f = exp(- w^2 - x^2 - y^2 - z^2) >> f = f f = exp(- w^2 - x^2 - y^2 - z^2) >> f = int(f,x,-inf,inf)                  %// step 3: x f = pi^(1/2)*exp(-w^2)*exp(-y^2)*exp(-z^2) >> f = int(f,y,-inf,inf)                  %// step 3: y f = pi*exp(- w^2 - z^2) >> f = int(f,z,-inf,inf)                  %// step 3: z f = pi^(3/2)*exp(-w^2) >> f = int(f,w,-inf,inf)                  %// step 3: w f = pi^2

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