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∫ (sin^–1 √x – cos^–1 √x/(sin^–1 √x + cos^–1 √x)) dx

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∫ (sin–1 √x – cos–1 √x/(sin–1 √x + cos–1 √x)) dx

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where x = sin2 θ

= (2/π) (– sin–1 (√x) (1 – 2x2) + √x √(1 – x) – x + c

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