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Q.∫dxsin⁡x−cos⁡x+2\int \dfrac{dx}{\sin x - \cos x + \sqrt{2}} equals

a
12log⁡∣tan⁡(x2+π8)∣+C\dfrac{1}{\sqrt{2}} \log \left| \tan \left( \dfrac{x}{2} + \dfrac{\pi}{8} \right) \right| + C
b
log⁡∣tan⁡(x+π/42)∣+C\log \left| \tan \left( \dfrac{x + \pi/4}{2} \right) \right| + C
c
12log⁡∣sin⁡x−cos⁡x+2∣+C\frac{1}{\sqrt{2}} \log \left| \sin x - \cos x + \sqrt{2} \right| + C
d
2log⁡∣sin⁡x−cos⁡x+2∣+C\sqrt{2} \log |\sin x - \cos x + \sqrt{2}| + C

Correct Answer: Option A

The correct solution involves applying the fundamental concept to derive the final value step by step...

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