integrand := (1 - exp(-(t - x1 - x3))) * (1 - exp(-(t - x1 - x4))) * (1 - exp(-(t - x2 - x3))) *
             (1 - exp(-(t - x2 - x4))) * exp(-x1) * exp(-x2) * exp(-x3) * exp(-x4);
F6T := int(int(int(int(integrand, x4 = 0 .. t - x1), x3 = 0 .. t - x1), x2 = 0 .. x1), x1 = 0 .. t) +
       int(int(int(int(integrand, x4 = 0 .. t-x2), x3 = 0 .. t-x2), x2 = x1 .. t), x1=0 .. t);
F6T := simplify(F6T);
mean := int(1 - F6T, t = 0 .. infinity);