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Q.∫sin⁡xsin⁡x+cos⁡x dx=\int \dfrac{\sin x}{\sin x + \cos x} \, dx =

a
x−tan⁡−1(sin⁡x+cos⁡x)+Cx - \tan^{-1}(\sin x + \cos x) + C
b
12tan⁡−1(sin⁡x+cos⁡x2)+C\dfrac{1}{\sqrt{2}} \tan^{-1}\left(\dfrac{\sin x + \cos x}{\sqrt{2}}\right) + C
c
x+ln⁡∣sin⁡x+cos⁡x∣+Cx + \ln|\sin x + \cos x| + C
d
ln⁡∣sin⁡x+cos⁡x∣+C\ln|\sin x + \cos x| + C

Correct Answer: Option D

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

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