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Q.∫cos⁡x−sin⁡x+1sin⁡x+cos⁡x+2 dx\int \dfrac{\cos x - \sin x + 1}{\sin x + \cos x + \sqrt{2}} \, dx equals

a
x−log⁡∣sin⁡x+cos⁡x+2∣+Cx - \log|\sin x + \cos x + \sqrt{2}| + C
b
x+log⁡∣sin⁡x+cos⁡x+2∣+Cx + \log|\sin x + \cos x + \sqrt{2}| + C
c
log⁡∣sin⁡x+cos⁡x+2∣+C\log|\sin x + \cos x + \sqrt{2}| + C
d
12log⁡∣sin⁡x+cos⁡x+2∣+C\dfrac{1}{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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