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Question Number 35593 by abdo.msup.com last updated on 20/May/18

let f(a)=∫_0 ^∞   e^(−( t^2  +(a/t^2 ))) dt witha>0  find the value of f(a).

$${let}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\left(\:{t}^{\mathrm{2}} \:+\frac{{a}}{{t}^{\mathrm{2}} }\right)} {dt}\:{witha}>\mathrm{0} \\ $$ $${find}\:{the}\:{value}\:{of}\:{f}\left({a}\right). \\ $$

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