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explicite-f-t-0-e-t-1-x-2-1-x-2-dx-with-t-0-




Question Number 136033 by mathmax by abdo last updated on 18/Mar/21
explicite f(t)=∫_0 ^∞  (e^(−t(1+x^2 )) /(1+x^2 ))dx  with t≥0
$$\mathrm{explicite}\:\mathrm{f}\left(\mathrm{t}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{e}^{−\mathrm{t}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)} }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}\:\:\mathrm{with}\:\mathrm{t}\geqslant\mathrm{0} \\ $$

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