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Question Number 149156 by gsk2684 last updated on 03/Aug/21

if ∫(dx/( (((1+x^2 )^(1012) (2+x^2 )^(3012) ))^(1/(2012)) ))=(α/(2β))(1−f(x))^(β/α)   then find α,β,f(x)

$${if}\:\int\frac{{dx}}{\:\sqrt[{\mathrm{2012}}]{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{1012}} \left(\mathrm{2}+{x}^{\mathrm{2}} \right)^{\mathrm{3012}} }}=\frac{\alpha}{\mathrm{2}\beta}\left(\mathrm{1}−{f}\left({x}\right)\right)^{\frac{\beta}{\alpha}} \\ $$$${then}\:{find}\:\alpha,\beta,{f}\left({x}\right) \\ $$

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