How does Planck's blackbody law follow from the radiation formula?

[robertjford80]

I don't see how this follows.

 

[phyzguy]

What don't you see? If you do the substitution, the h's cancel, one of the c's cancel, and one of the lambda's cancel, leaving the result. What are you missing?

 

[jtbell]

If your problem is with the approximation in the second line, consider the power series for e^x:

$$e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + ...$$