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Question Number 201037    Answers: 1   Comments: 1

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Prove that ∫_0 ^∞ ((2arctan((t/x)))/(e^(2𝛑t) βˆ’1))dt=Inπšͺ(x)βˆ’xIn(x)+xβˆ’(1/2)In(((2𝛑)/x)) Michael faraday

$$\boldsymbol{{Prove}}\:\boldsymbol{{that}} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{2}\boldsymbol{{arctan}}\left(\frac{\boldsymbol{{t}}}{\boldsymbol{{x}}}\right)}{\boldsymbol{{e}}^{\mathrm{2}\boldsymbol{\pi{t}}} βˆ’\mathrm{1}}\boldsymbol{{dt}}=\boldsymbol{{In}\Gamma}\left(\boldsymbol{{x}}\right)βˆ’\boldsymbol{{xIn}}\left(\boldsymbol{{x}}\right)+\boldsymbol{{x}}βˆ’\frac{\mathrm{1}}{\mathrm{2}}\boldsymbol{{In}}\left(\frac{\mathrm{2}\boldsymbol{\pi}}{\boldsymbol{{x}}}\right) \\ $$$$\boldsymbol{{Michael}}\:\boldsymbol{{faraday}} \\ $$

Question Number 201008    Answers: 1   Comments: 0

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Question Number 200964    Answers: 1   Comments: 0

Question Number 200961    Answers: 2   Comments: 0

βˆ’x^3 +1=((βˆ’x+1))^(1/3) β‡’x=?

$$\: \\ $$$$\:\:\:\:\:βˆ’{x}^{\mathrm{3}} +\mathrm{1}=\sqrt[{\mathrm{3}}]{βˆ’{x}+\mathrm{1}}\:\Rightarrow{x}=? \\ $$$$ \\ $$

Question Number 200960    Answers: 3   Comments: 0

Question Number 200958    Answers: 2   Comments: 0

Question Number 200954    Answers: 0   Comments: 1

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