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Question Number 187528 by sciencestudentW last updated on 18/Feb/23

$$\underset{\frac{9\pi }{2}}{\stackrel{\frac{7\pi }{1.5}}{\int }}\frac{dx}{\sqrt{1-sinx}}=?$$

Answered by ARUNG_Brandon_MBU last updated on 18/Feb/23

$$I=\int \frac{dx}{\sqrt{1-\sin x}}$$$$=\int \frac{dx}{\mid \cos \frac{x}{2}-\sin \frac{x}{2}\mid }=\frac{1}{\sqrt{2}}\int \frac{dx}{\cos (\frac{x}{2}+\frac{\pi }{4})}$$$$=\frac{1}{2}\ln \mid \sec (\frac{x}{2}+\frac{\pi }{4})+\tan (\frac{x}{2}+\frac{\pi }{4})\mid +C$$

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