Question: Get a integral out

Dear Forum

I'm trying to evaluate the following expression:

Int(Int(Int(N*exp(-alpha*r^2)*N*exp(-alpha*r^2)*r^2,r=0..infinity) *sin(t), t=0..Pi),p=0..2*Pi)

The value of the integral should equal 1 and from that the value of the normalization constant N can be obtained. It should equal sqrt(alpha^3/pi).

How do i need to enter the integral such that it just becomes evaluated? Instead I get this:

What is signum(sin(pi)) trying to tell me here?

Any suggestions/hints are greatly welcomed.

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