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[tex]L_T = \int_0^{\infty} e^{-(r/a)^{1/4}} r^2 dr[/tex]

estimate the radius [tex]r(a)[/itex] corresponding to half of the total luminosity.

This would be to integrate from zero to r and get a function [itex]r(a,L)[/itex] but this is impossible so anyone got an idea on how to estimate this?