The value of $$2$$∫$$sin$$⁡xdxsin⁡x−π$$4$$ is equal to

Correct option is 4x+log⁡sin⁡x−π4+C

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The value of $\sqrt{2} \int \frac{\sin xdx}{\sin (x - \frac{π}{4})}$ is equal to

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x−log⁡cos⁡x−π4+C

x+log⁡cos⁡x−π4+C

x−log⁡sin⁡x−π4+C

x+log⁡sin⁡x−π4+C

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detailed solution

Correct option is D

Let I=2∫sin⁡xsin⁡x−π4dxPut, x=π4=t⇒dx=dt∴I=2∫sin⁡π4+tdtsin⁡t=2∫12cot⁡t+12dt=log⁡|sin⁡t|+t+C=x+log⁡sin⁡x−π4+C

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The value of 2∫sin⁡xdxsin⁡x−π4 is equal to

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The value of $\sqrt{2} \int \frac{\sin xdx}{\sin (x - \frac{π}{4})}$ is equal to