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Category: Integration

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-

Question Number 4298 by Yozzii last updated on 08/Jan/16 $${Find}\:{Q}=\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{3}} }{{e}^{{x}/{T}} −\mathrm{1}}{dx}\:,{where}\:{Q}\:{is} \\ $$$${assumed}\:{finite}\:{for}\:{T}\:{being}\:{a}\: \\ $$$${positive}\:{constant},\:{and}\:{Q}\:{taking}\:{the} \\ $$$${form}\:{Q}={KT}^{{n}} \:,{where}\:{K}={constant} \\ $$$${and}\:{n}\in\mathbb{Z}. \\ $$$$…

x-2-3x-cos-x-dx-

Question Number 135259 by leena12345 last updated on 11/Mar/21 $$\int\left({x}^{\mathrm{2}} +\mathrm{3}{x}\right)\mathrm{cos}\:\left({x}\right){dx} \\ $$ Answered by Ar Brandon last updated on 11/Mar/21 $$\mathcal{I}=\int\left(\mathrm{x}^{\mathrm{2}} +\mathrm{3x}\right)\mathrm{cosxdx} \\ $$$$\:\:\:=\left(\mathrm{x}^{\mathrm{2}}…