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Question Number 67931 by mathmax by abdo last updated on 02/Sep/19

let A_n =∫_0 ^(π/4)   x^n {1+cosx +cos(2x)}^2 dx  find a relation of recurrence betwedn the A_n

$${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:{x}^{{n}} \left\{\mathrm{1}+{cosx}\:+{cos}\left(\mathrm{2}{x}\right)\right\}^{\mathrm{2}} {dx} \\ $$$${find}\:{a}\:{relation}\:{of}\:{recurrence}\:{betwedn}\:{the}\:{A}_{{n}} \\ $$

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