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calculate-A-0-cos-4-x-x-2-2-2-dx-2-find-the-value-of-0-cos-4-x-x-2-3-2-dx-




Question Number 136406 by mathmax by abdo last updated on 21/Mar/21
calculate  A_λ =∫_0 ^∞   ((cos^4 x)/((x^2  +λ^2 )^2 ))dx  2) find the value of ∫_0 ^∞  ((cos^4 x)/((x^2  +3)^2 ))dx
$$\mathrm{calculate}\:\:\mathrm{A}_{\lambda} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{cos}^{\mathrm{4}} \mathrm{x}}{\left(\mathrm{x}^{\mathrm{2}} \:+\lambda^{\mathrm{2}} \right)^{\mathrm{2}} }\mathrm{dx} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}^{\mathrm{4}} \mathrm{x}}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$
Commented by mathmax by abdo last updated on 21/Mar/21
λ>0
$$\lambda>\mathrm{0} \\ $$

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