The value of ∫$$sin$$⁡x−$$cos$$⁡xsin⁡$$2x$$−$$1/2dx$$ is

Correct option is 2−log⁡|(sin⁡x+cos⁡x)+sin⁡2x−1/2|+C

Questions

The value of $\int \frac{\sin x - \cos x}{\sqrt{\sin 2 x - 1 / 2}} d x$ is

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log⁡|(sin⁡x+cos⁡x)+sin⁡2x|+C

−log⁡|(sin⁡x+cos⁡x)+sin⁡2x−1/2|+C

−12log⁡|(sin⁡x+cos⁡x)+sin⁡2x−1/2|+C

none of these

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detailed solution

Correct option is B

The given integral can be written as∫sin⁡x−cos⁡x(sin⁡x+cos⁡x)2−3/2dx=−∫dtt2−3/2(t=sin⁡x+cos⁡x)=−log⁡t+t2−3/2+C=−log⁡|sin⁡x+cos⁡x+sin⁡2x−1/2|+C

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The value of ∫sin⁡x−cos⁡xsin⁡2x−1/2dx is

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The value of $\int \frac{\sin x - \cos x}{\sqrt{\sin 2 x - 1 / 2}} d x$ is