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## Homework Statement

Starting with the Planck distribution:

[tex] R(\lambda,T) = \frac{c}{4} \frac{8 \pi}{\lambda^4} (\frac{hc}{\lambda})(\frac{1}{e^{hc/(\lambda kT)}-1})[/tex]

Derive the blackbody Stefan-Boltzmann law (ie total flux is proportional to T

^{4}) by integrating the above expression over all wavelengths. Thus show that

R(T) = [tex] \frac{2 \pi^5 k^4}{15h^3 c^2} T^4 [/tex]

and [tex]\int[/tex] [tex] \frac{x^3}{e^x -1} dx = \frac{\pi^4}{15}[/tex]

## The Attempt at a Solution

I know I need to substitute [tex]x = \frac{hc}{kT} \frac{1}{\lambda}[/tex]. And somehow I think I can use the form KR([tex]\lambda[/tex],T) = A([tex]\lambda[/tex])B([tex]\lambda[/tex])