Integral of Complex exp of dot product

[SuperNoob]

[tex] S(\vec{q})= \int_0^r exp(i\vec{q}\cdot\vec{x})4\pi x^2 \ dx[/tex]

How would one approach this integral?
I tried to "ignore" the dot product and proceeded with [tex]exp(i\vec{q}\cdot \vec{x})=exp(iqx) [/tex] and got a wrong answer.

 

[waht]

If this integral is to be done in 3D, one may switch to spherical coordinates which has the volume element

[tex] dV = r^2 sin(\theta)\; dr\; d\theta\; d\phi [/tex]

and also, the dot product is

[tex] |x||q|\; cos(\theta) [/tex]

if x = r and play around with substitution, this integral might be easier to do.

 

[SuperNoob]

Thanks!