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Question Number 73230 by mathmax by abdo last updated on 08/Nov/19

calculate A_n =∫_0 ^∞   ((1+x^n )/(2+x^(2n) ))dx  and J_n =∫_0 ^∞   ((2+x^(3n) )/(5+x^(7n) ))dx  with n integr natural not 0

$${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{1}+{x}^{{n}} }{\mathrm{2}+{x}^{\mathrm{2}{n}} }{dx}\:\:{and}\:{J}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{2}+{x}^{\mathrm{3}{n}} }{\mathrm{5}+{x}^{\mathrm{7}{n}} }{dx} \\ $$$${with}\:{n}\:{integr}\:{natural}\:{not}\:\mathrm{0} \\ $$

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