integrand := (1 - exp(-t + x7)) * (1 - exp(-t + x4)) * (1 - exp(-t + x2 + x4)) * (1 - exp(-t + x2)) *
             exp(-x1) * exp(-x2) * exp(-x3) * exp(-x4) * exp(-x5) * exp(-x6) * exp(-x7);
F1 := int(int(int(int(int(int(int(integrand, x7 = 0 .. t - x5 - x1), x6 = 0 .. t - x1),
      x5 = 0 .. t - x1), x4 = 0 .. t - x2), x3 = 0 .. x1 - x2), x2 = 0 .. x1), x1 = 0 .. t);
F2 := int(int(int(int(int(int(int(integrand, x7 = 0 .. t - x5 - x3 - x2),  x6 = 0 .. t - x3 - x2),
      x5 = 0 .. t - x3 - x2), x4 = 0 .. t - x2), x3 = x1 - x2 .. t - x2), x2 = 0 .. x1), x1 = 0 .. t);
F3 := int(int(int(int(int(int(int(integrand, x7 = 0 .. t - x5 - x3 - x2), x6 = 0 .. t - x3 - x2),
      x5 = 0 .. t - x3 - x2), x4 = 0 .. t - x2), x3 = 0 .. t - x2), x2 = x1 .. t), x1 = 0 .. t);
F6T := simplify(F1 + F2 + F3);
mean := int(1 - F6T, t = 0 .. infinity);