Volume of Sphere: Find Integral Solution

[cad2blender]

Find the volume of the sphere:

f(x,y,z)=e^(x^2+y^2+z^2) over x^2+y^2+z^2≤9 using spherical coordinates

After working trough I get this enormous number 228965, when I know its 113.097 using the simple volume formula for a sphere. I think I am having trouble with the integration of e^(rho^2)*rho... Any tips guys?

 

[rochfor1]

Integration by parts!

 

[Office_Shredder]

You might have better luck with the substitution u=rho²

 

[rochfor1]

Which is of course correct. Apologies for my confusion.