How do I normalize a wavefunction in three dimensions?

[Lily Wright]

Homework Statement

2. Homework Equations [/B]
Uploaded as a picture as it's pretty hard to type out

The Attempt at a Solution

So to normalise a wavefunction it has to equal 1 when squared.
A is the normalisation factor so we have:
A.x²e^-x/2a0.x²e^-x/2a0 = 1
∫ψ*ψdx = A²∫x⁴e^-axdx = 1

Then I've been given the integral of this between 0 and ∞: ∫xⁿe^-axdx = n!/aⁿ⁺¹
∫ψ*ψdx = A².4!/a⁵
= A².24/a⁵
A = √a⁵/24

Have I done this right? I don't even know where to start with (ii). Any help would be greatly appreciated!

 

[mfb]

"." is an unusual multiplication sign, "*" is better (or use LaTeX for the best result).
(i) looks right.

(ii) is like (i), just with a more complicated function and in three dimensions, but the approach is exactly the same.