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## Homework Statement

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.

## Homework Equations

I(λ,T) = (2πhc^2)/(λ^5)*(1/(e^(hc/λkBT))-1)

## 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.