Blackbody radiation equations

[Abdul.119]

Homework Statement

Show that the total energy of the radiation in a volume V at temperature T is

Hint:

Homework Equations

The Attempt at a Solution

The hint doesn't make sense to me, and those are the equation that I found to be perhaps relevant. Do I integrate the second equation? I'm not sure how to start this problem.
I think the hint is to help in integrating the second "relevant" equation, so integrating f^3 / exp(hf/K_BT)-1 from zero to infinity should equal pi^4/15?

 

[SteamKing]

Homework Statement

Show that the total energy of the radiation in a volume V at temperature T is

Hint:

Homework Equations

The Attempt at a Solution

The hint doesn't make sense to me, and those are the equation that I found to be perhaps relevant. Do I integrate the second equation? I'm not sure how to start this problem.
I think the hint is to help in integrating the second "relevant" equation, so integrating f^3 / exp(hf/K_BT)-1 from zero to infinity should equal pi^4/15?

Yes, you need to integrate the equation for dU/df.

Make the substitution x = hf / K_bT and use the Hint.

 

[Abdul.119]

Yes, you need to integrate the equation for dU/df.

Make the substitution x = hf / K_bT and use the Hint.

Then
x = hf / K_b T
dx = h / K_b T * df
df = K_b T / h * du
performing the integral then gives pi^4/15 * (K_b T / h)
then together with the rest of the constants it gives [8pi^5V K_b T] / [15c^3] , which doesn't look look like the final answer, did I do something wrong or are there additional steps?

Edit: Oops sorry there is a mistake in the first equation given in the problem. The pi has an exponent of 5 not 2, and the k_B has an exponent of 4 not 2.

But still I can't seem to obtain that equation, all I get is [8pi^5V K_b T] / [15c^3], the h is missing