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$\int \frac{\sin 2 x}{a^{2} \sin^{2} x + b^{2} \cos^{2} x} d x$

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1a2+b2loga2sin2x+b2cos2x+C

1a2−b2loga2sin2x+b2cos2x+C

1a2−b2loga2sin2x−b2cos2x+C

1a2+b2loga2sin2x−b2cos2x+C

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detailed solution

Correct option is B

ddxa2sin2⁡x+b2cos2⁡x=a2−b2sin⁡2x Now, ∫sin⁡2xa2sin2⁡x+b2cos2⁡xdx=1a2−b2∫a2−b2sin⁡2xa2sin2⁡x+b2cos2⁡xdx=1a2−b2∫ddxa2sin2⁡x+b2cos2⁡xa2sin2⁡x+b2cos2⁡xdx=1a2−b2log⁡a2sin2⁡x+b2 cos2x+C

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∫sin2xa2sin2x+b2cos2xdx

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$\int \frac{\sin 2 x}{a^{2} \sin^{2} x + b^{2} \cos^{2} x} d x$