What is the easiest way to calculate the triple definite integral of a symbolic vector over arbitrary domain without using for loop?

What is the easiest way to calculate the triple integral of a symbolic vector over arbitrary domain without using for loop? e,g, -1<x,y,z<1

syms x y z
V=[sin(x*y*z), cos(z)*z*x, x*y*z^3, x+cos(z)*x]

Answer 1

[David Hill]

syms x y z
V=[x,y,z];
I=int(int(int(V,x),y),z);%recognize the definite integrals do not exist for many integrals (this works but your V would be in terms in integrals)

[David Hill]

syms x y z
V=[sin(x*y*z), cos(z)*z*x, x*y*z^3, x+cos(z)*x];
vpaintegral(vpaintegral(vpaintegral(V,x,-1,1),y,-1,1),z,-1,1)

[Mehdi]

Nice!