I tired to Integrate with several dimensions but it calculate so slow. I wait for 20 minutes but calculate so much. Therefore I want to know how can I integrate several times in a quick methods. in below I tried to integrate
for 3 dimension
Integrate[Integrate[Integrate[(1 + Subscript[c, 1]*Subscript[x, 1] +
Subscript[c, 2]*Subscript[x, 2] +
Subscript[c, 3]*Subscript[x, 3])^(-4), {Subscript[x, 1], 0, 1}],{Subscript[x,2],0,1}],{Subscript[x,3],0,1]
for 4 dimension
Integrate[Integrate[Integrate[Integrate[
exp (-Sum[
Subscript[c, i]^2*(Subscript[x, i] - Subscript[u, i])^2, {i, 1,
4}]), {Subscript[x, 1], 0, 1}],{Subscript[x,2],0,1}],{Subscript[x,3],0,1}],{Subscript[x,4],0,1}]]
For 5 dimension
Integrate[Integrate[Integrate[Integrate[Integrate[
exp (-Sum[
Subscript[c, i]*Abs[Subscript[x, i] - Subscript[u, i]], {i, 0,
5}]), {Subscript[x, 1], 0, 1}], {Subscript[x, 2], 0, 1}], {Subscript[x, 3], 0, 1}]], {Subscript[x, 4], 0, 1}]], {Subscript[x, 5], 0, 1}]]