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1-calculate-cos-x-n-x-2-x-1-dx-with-n-integr-natural-2-find-the-value-of-cos-x-2n-x-2-x-1-dx-3-calculate-cos-pi-x-3-




Question Number 34593 by abdo mathsup 649 cc last updated on 08/May/18
1) calculate  ∫_(−∞) ^(+∞)    ((cos(αx^n ))/(x^2  +x +1)) dx  with n integr  natural  2) find the value of   ∫_(−∞) ^∞     ((cos( α x^(2n) ))/(x^2  +x +1))dx  3) calculate  ∫_(−∞) ^(+∞)     ((cos(π x^3 ))/(x^2  +x +1)) dx
$$\left.\mathrm{1}\right)\:{calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left(\alpha{x}^{{n}} \right)}{{x}^{\mathrm{2}} \:+{x}\:+\mathrm{1}}\:{dx}\:\:{with}\:{n}\:{integr} \\ $$$${natural} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\:\int_{−\infty} ^{\infty} \:\:\:\:\frac{{cos}\left(\:\alpha\:{x}^{\mathrm{2}{n}} \right)}{{x}^{\mathrm{2}} \:+{x}\:+\mathrm{1}}{dx} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{cos}\left(\pi\:{x}^{\mathrm{3}} \right)}{{x}^{\mathrm{2}} \:+{x}\:+\mathrm{1}}\:{dx} \\ $$

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