Find-Q-0-x-3-e-x-T-1-dx-where-Q-is-assumed-finite-for-T-being-a-positive-constant-and-Q-taking-the-form-Q-KT-n-where-K-constant-and-n-Z-

Tinku Tara June 3, 2023 Integration 0 Comments

Question Number 4298 by Yozzii last updated on 08/Jan/16

Find Q=∫_0 ^∞ (x^3 /(e^(x/T) −1))dx ,where Q is assumed finite for T being a positive constant, and Q taking the form Q=KT^n ,where K=constant and n∈Z.

$${Find}\:{Q}=\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{3}} }{{e}^{{x}/{T}} −\mathrm{1}}{dx}\:,{where}\:{Q}\:{is} \\ $$$${assumed}\:{finite}\:{for}\:{T}\:{being}\:{a}\: \\ $$$${positive}\:{constant},\:{and}\:{Q}\:{taking}\:{the} \\ $$$${form}\:{Q}={KT}^{{n}} \:,{where}\:{K}={constant} \\ $$$${and}\:{n}\in\mathbb{Z}. \\ $$$$ \\ $$

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Find-Q-0-x-3-e-x-T-1-dx-where-Q-is-assumed-finite-for-T-being-a-positive-constant-and-Q-taking-the-form-Q-KT-n-where-K-constant-and-n-Z-

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