let-f-t-0-1-e-t-1-x-2-1-x-2-dx-with-t-0-find-a-simple-form-of-f-t-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 35587 by abdo mathsup 649 cc last updated on 20/May/18

let f(t) =∫_0 ^1 (e^(−t(1+x^2 )) /(1+x^2 ))dx with t≥0 find a simple form of f(t) .

$${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{e}^{−{t}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:{with}\:{t}\geqslant\mathrm{0} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({t}\right)\:. \\ $$

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let-f-t-0-1-e-t-1-x-2-1-x-2-dx-with-t-0-find-a-simple-form-of-f-t-

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