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Question Number 156961 by MathSh last updated on 17/Oct/21

𝛀 =∫_( 0) ^( ∞)  ((cos^2 (x) - sin^2 (x))/((1 + x^4 )^3 )) dx = ?

$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}\right)\:-\:\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)}{\left(\mathrm{1}\:+\:\mathrm{x}^{\mathrm{4}} \right)^{\mathrm{3}} }\:\mathrm{dx}\:=\:? \\ $$

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