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$\int \frac{2 x + \sqrt{\tan^{- 1} x}}{1 + x^{2}} d x =$

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log(1+x2)

log(1+x2)+tan−1x32+C

log(1+x2)+cot−1x32+C

log(1+x2)+23tan−1x32+C

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detailed solution

Correct option is D

I=∫2x+tan−1⁡x1+x2dxI=∫2x1+x2dx+∫tan−1⁡x1+x2dx=∫2x1+x2dx+∫tdt ∵tan−1⁡x=t,11+x2dx=dt=log⁡1+x2+23t32+C=log⁡1+x2+23tan−1⁡x32+C

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∫2x+tan−1x1+x2dx=

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$\int \frac{2 x + \sqrt{\tan^{- 1} x}}{1 + x^{2}} d x =$