The value of \( \mathrm{P}^{12 i} \) \( \int \frac{1+x}{x\left(1+x ...

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The value of
\( \mathrm{P}^{12 i} \) \( \int \frac{1+x}{x\left(1+x e^{x}\right)^{2}} d x=\log \left|\frac{f(x)}{g(x)}\right|+\frac{1}{g(x)}+C \) then value

W of \( g(x)-f(x) \) is
(1) \( \frac{1}{2} \)
(2) 1
(3) 2
(4) 4
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