Integral of [ ln(1 + cosx) - xtan x/2] dx (A) x tan x/2 + C  (B) ln (1+ cosx) + C  (C) x ln (1+ cosx) + C  (D) none of these

Dear student

In questions like these, it is easier to differentiate the options and then check the result with the question

In this case, differentiating option C, we get

   ddxx ln 1+cos x+c=ddxx ln 1+cos x=ln1+x+x×11+cos x×-sin x=ln1+x-x sin x1+cos x=ln1+x-x× 2 sinx/2 cosx/22 cos2x/2=ln1+x-x × 2 sinx/22 cosx/2=ln1+x-x tanx2

Regards

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