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If g(0,oo) to R is a differentiable func...

If `g(0,oo) to R` is a differentiable function `int[(x.(cos-sinx))/(e^x+1)+g(x)(e^x+1-xe^x)/(e^x+1)^2]dx=(xg(x))/(e^x+1)+c` for all `x gt 0` here c=constant , then

A

`g(x)` is decreasing in `(0,pi/4)`

B

`g(x)` is increasing in `(0,pi/4)`

C

`g+g'` is increasing in `(0,pi/2)`

D

`g-g'` is decreasing in `(0,pi/2)`

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