It's hard to debug a picture. Can you attach a clean notebook with just the code that needs to be debugged?
It's possible that Integrate doesn't know how to solve the integral. Does the order of integration matter in this case? If not, try switching the order of integration. You might also try replacing the floating point values in the integrand (like 0.3333333) with rational values (like 1/3).
It looks like your integral has a matrix in it? Make sure that the integrand is a vector. I see you are also using MattrixForm or some special formatting funcitons. Try removing these.
One thing I do is try to find the smallest integrand which reproduces the problem. That is, I strip away parts of the integrand until I get the smallest integrand that won't integrate. This helps me understand what in particular is difficult about the integral.
Have you tried numerically solving the integral with NSolve?