Chapter 9, Problem 9.31E

Integrate Planck’s law (equation 9.23) from the wavelength limits $\lambda =0$ to $\lambda =\infty$ to get equation 9.24. You will have to rewrite the expression by redefining the variable (and its infinitesimal) and use the following integral:

${\displaystyle \underset{0}{\overset{\infty }{\int }}\left(\frac{x^3}{e^x-1}\right)dx=\frac{{\pi }^4}{15}}$ (9.43)