Evaluate ( ).

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

Evaluate ∫0π/2ln⁡(1+asin⁡x1−asin⁡x)dxsin⁡x\int_{0}^{\pi/2} \ln \left( \frac{1+a \sin x}{1-a \sin x} \right) \frac{dx}{\sin x} ( ∣a∣<1|a| < 1 ).

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