Speed of Symbolic Integration

Hi, I have a long expression composed of sines and cosines of three variables. The expression needs to be volume averaged using a symbolic triple integral. I need to use symbolic in order to get exact solutions.

I've attached an example expression needed to be integrated. All variables are symbolic.

I need to perform the volume integral of this expression. Ordinarily, I assign this symbolic expression to variable II and operate successive "int" commands...

int(int(int(II.*sin(THETA),THETA,0,pi),PHI,0,2*pi),ZETA,0,2*pi)

This procedure takes more than 20 hours to run on my computer. I am using 32 GB memory with an 8-core i7 processor. The CPU utilization is around 20% at 3.27 GHz.

Perhaps there is away to partition the sum? Any other suggestions would be appreciated.

[Walter Roberson]

Can all variables be assumed to be real-valued ?

[Christopher Kube]

Yes, all variables are real.

[Christopher Kube]

Does anyone have any suggestions? I am currently using Matlab2013b.