QM integration question

[sniffer]

if i want to calculate mean square radius by using:
$$\rho^2=\frac{\int \mid\psi\mid^2 r^2 dr}{\int |\psi|^2 dr}$$
with $\psi=\sum_{k} a_k exp(ikr)$.

How do I solve the numerator part?

 

[CarlB]

Have you considered integrating by parts?

Carl