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Question Number 69375 by mathmax by abdo last updated on 22/Sep/19
let f(α) =∫_0 ^∞   ((cos(α(1+x^2 )))/(1+x^2 ))dx  1)determine a explicit form of f(α)  2) calculate ∫_0 ^∞   ((cos(2+2x^2 ))/(x^2  +1))dx
$${let}\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\alpha\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right){determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left(\alpha\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\mathrm{2}+\mathrm{2}{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$

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