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## Homework Statement

Show that the radial function R[tex]_{31}[/tex] is normalized.

## Homework Equations

[tex]\frac{1}{a_{0}^{3/2}}\frac{4}{81\sqrt{6}}\left(6-\frac{r}{a_{0}}\right)\frac{r}{a_{0}}e^{-r/3a_{0}}[/tex]

[tex]\int^{\infty}_{0}r^{2}R_{31}*R_{31}dr=1[/tex]

## The Attempt at a Solution

So I plugged that radial function in and got [tex]\int^{\infty}_{0}a_{0}^{2}u^{2}\left(6u-u^{2}\right)^{2}e^{-2u/3}du=1[/tex] all multiplied by some constant and [tex]u=\frac{r}{a_{0}}[/tex]

I'm getting [tex]\frac{243}{4}[/tex] times the constant, and that does not equal one. So I feel like I'm not using the right equation for this one.

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