1. The problem statement, all variables and given/known data The total intensity I(T) radiated from a blackbody (at all wavelengths λ) is equal to the integral over all wavelengths, 0 < λ < ∞, of the Planck distribution (4.28). (a) By changing variables to x = hc/λkBT, show that ¡(T) has the form I(T) = σT4 where a is a constant independent of temperature. This result is called Ste fan’s fourth-power law, after the Austrian physicist Josef Stefan. 2. Relevant equations I(λ,T) = (2πhc^2)/(λ^5)*(1/(e^(hc/λkBT))-1) 3. The attempt at a solution I understand that I need to substitute x into the equation and the easy part that I get: 1/(e^x)-1 out of the second part. However the first part seems to be just inflating the equation by substitution to which it will merely increase continually. I did end up substituting: hc=xλkBT into the numerator to get: =2π(kBTx)c/λ^5 just not sure where to go from here.