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Question Number 44697 by manish09@gmail.com last updated on 03/Oct/18
prove that:−  ∫_0 ^∞ (t^(a−1) /(1+t))dt = (𝛑/(sin(𝛑a)))
$$\boldsymbol{{prove}}\:\boldsymbol{{that}}:− \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{{t}}^{\boldsymbol{{a}}−\mathrm{1}} }{\mathrm{1}+\boldsymbol{{t}}}\boldsymbol{{dt}}\:=\:\frac{\boldsymbol{\pi}}{\boldsymbol{{sin}}\left(\boldsymbol{\pi{a}}\right)} \\ $$

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