\[\iiint_V e^{\left(x^2 + y^2 + z^2\right)^{3/2}} \, dV = \iiint_V e^{\left(\rho^2\right)^{3/2}} \rho^2 \sin\phi \, d\rho \, d\phi \, d\theta.\]
Mathbot Says...
I wasn't able to parse your question, but the HE.NET team is hard at work making me smarter.