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x^6 y^5 z^3 w^2 (x - x y) (x - x y z) (x - x y z w) (x y -
x y z) (x y - x y z w) (x y z - x y z w) Dt[x] Dt[y] Dt[z] Dt[
w] // Factor
% /. {x -> u^(1/13), y -> v^(1/9), z -> s^(1/5),
w -> t^(1/3)} // Simplify
1/1755*NIntegrate[(1755 %)/(Dt[s] Dt[t] Dt[u] Dt[v]) // Evaluate, {u,
0, 1}, {v, 0, 1}, {s, 0, 1}, {t, 0, 1},
Method -> "AdaptiveMonteCarlo"]
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