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If $\int \frac{x + \sin x}{1 + \cos x} d x = f (x) \tan \frac{x}{2} + C$ then

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f(x)=x2

f(x)=x

f(x)=1+cos⁡x

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detailed solution

Correct option is B

∫x+sin⁡x1+cos⁡xdx=12∫xsec2⁡x2dx+∫sin⁡x1+cos⁡xdx=122xtan⁡x2−2∫tan⁡x2+∫tan⁡x2dx=xtan⁡x2+C.

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If ∫x+sin⁡x1+cos⁡xdx=f(x)tan⁡x2+C then

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If $\int \frac{x + \sin x}{1 + \cos x} d x = f (x) \tan \frac{x}{2} + C$ then