Let $g:(0,\infty) \rightarrow R$ be a differentiable function such that
$\int \left( \frac{x(\cos x - \sin x)}{e^x + 1} + \frac{g(x)(e^x + 1 - xe^x)}{(e^x + 1)^2} \right) dx = \frac{x \, g(x)}{e^x + 1} + c \text{ for all } x > 0 \text{, where } c \text{ is an arbitrary constant. Then :}$
