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find-the-value-of-0-cos-x-2n-1-x-2-1-dx-and-0-sin-x-2n-1-x-2-1-dx-




Question Number 25765 by abdo imad last updated on 14/Dec/17
find the value of ∫_0 ^∞  cos(x^(2n) )(1+x^2 )^(−1) dx and ∫_0 ^∞  sin( x^(2n) )^ (1+x^2 )^(−1) dx
$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{\mathrm{2}{n}} \right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{−\mathrm{1}} {dx}\:{and}\:\int_{\mathrm{0}} ^{\infty} \:{sin}\left(\:{x}^{\mathrm{2}{n}} \right)^{} \left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{−\mathrm{1}} {dx} \\ $$

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