∫dxsin⁡x−$$cos$$⁡$$x+2$$ is equal to

Correct option is 312cot⁡x2+π8+C

Questions

$\int \frac{dx}{\sin x - \cos x + \sqrt{2}}$ is equal to

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−12tan⁡x2+π8+C

12tan⁡x2+π8+C

12cot⁡x2+π8+C

−12cot⁡x2+π8+C

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detailed solution

Correct option is C

∫dxsin⁡x−cos⁡x+2=∫dxsin⁡x22−cos⁡x22+2=∫dx2sin⁡xsin⁡π4−cos⁡xcos⁡π4+1=12∫dx1−cos⁡x+π4=12∫dx1−cos⁡2x2+π8=12∫dx2sin2⁡x2+π8=122∫cosec2⁡x2+π8dx=−122⋅−cot⁡x2+π812+C=12cot⁡x2+π8+C

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∫dxsin⁡x−cos⁡x+2 is equal to

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$\int \frac{dx}{\sin x - \cos x + \sqrt{2}}$ is equal to