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Question Number 65825 by ~ À ® @ 237 ~ last updated on 04/Aug/19

let consider  two real numbers p and such as p^2 −q^2 =pq  Prove that     J= ∫_0 ^∞     (dv/(^q (√((1+^q (√(v^p  )) )^p ))))= 1

$${let}\:{consider}\:\:{two}\:{real}\:{numbers}\:{p}\:{and}\:{such}\:{as}\:{p}^{\mathrm{2}} −{q}^{\mathrm{2}} ={pq} \\ $$$${Prove}\:{that} \\ $$$$\:\:\:{J}=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dv}}{\:^{{q}} \sqrt{\left(\mathrm{1}+\:^{{q}} \sqrt{{v}^{{p}} \:}\:\right)^{{p}} }}=\:\mathrm{1} \\ $$$$ \\ $$

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