The value of ∫$$cos$$⁡xsin⁡$$x+$$$$cos$$⁡xdx is

Correct option is 212(x+log⁡|sin⁡x+cos⁡x|)+C

Questions

The value of $\int \frac{\cos x}{\sin x + \cos x} d x$ is

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x22+log⁡|sin⁡x+cos⁡x|+C

12(x+log⁡|sin⁡x+cos⁡x|)+C

2log⁡|sin⁡x+cos⁡x|+x+C

none of these

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detailed solution

Correct option is B

∫cos⁡xsin⁡x+cos⁡xdx=12∫cos⁡x+sin⁡x+cos⁡x−sin⁡xsin⁡x+cos⁡xdx=12∫1+cos⁡x−sin⁡xsin⁡x+cos⁡xdx=(1/2)(x+log⁡|sin⁡x+cos⁡x|)+C

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The value of ∫cos⁡xsin⁡x+cos⁡xdx is

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The value of $\int \frac{\cos x}{\sin x + \cos x} d x$ is