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∫ (sin^2 x/(sin^4 x + cos^4 x)) for x ∈ [0,π/2]

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∫ (sin2 x/(sin4 x + cos4 x)) for x ∈ [0,π/2]

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= |tan–1 (tan x)| for x ∈ [0,π/2]

= ((π/2) – 0) 

= π/2

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