So i dont really know where to paste this.(adsbygoogle = window.adsbygoogle || []).push({});

I'm reading a example in my modern physics book and i dont understand what they did.

[tex]\int[/tex] (2(pi)hc^{2})/([tex]\lambda[/tex]^{5}(e^{hc/[tex]\lambda[/tex]kT}-1))d[tex]\lambda[/tex]

if we make the change of variable x=hc/[tex]\lambda[/tex]kT

(2(pi)k^{4}T^{4})/(c^{2}h^{3})[tex]\int[/tex]((x^{3})/(e^{x}-1))dx

so how did they get to this:

(2(pi)k^{4}T^{4})/(c^{2}h^{3})[tex]\int[/tex]((x^{3})/(e^{x}-1))dx

when I solve for [tex]\lambda[/tex] in x=hc/[tex]\lambda[/tex]kT and plug it into the first ingetral I get:

(2(pi)x^{5}k^{5}T^{5})/(h^{4}c^{3})

basically, i'm off by 1 power for everything except for x (that i'm off by 2).

can someone explain this?

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# Homework Help: Help with ingetral

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