If \( f: \mathbb{R} \rightarrow \mathbb{R} \) is a function satisfying the following: (i) \( f(-....

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If \( f: \mathbb{R} \rightarrow \mathbb{R} \) is a function satisfying the following:
\( \mathrm{P} \)
(i) \( f(-x)=-f(x) \)
W.
(ii) \( f(x+1)=f(x)+1 \)
(iii) \( f\left(\frac{1}{x}\right)=\frac{f(x)}{x^{2}} \forall x \neq 0 \)
then \( \int e^{x} f(x) d x \) is equal to
(1) \( e^{x}(x-1)+c \)
(2) \( e^{x} \log x+c \)
(3) \( \frac{e^{x}}{x}+c \)
(4) \( \frac{e^{x}}{x+1}+c \)



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