A) 1
B) 0
C) \[c{{e}^{x}}\]
D) \[\log x\]
Correct Answer: C
Solution :
\[\int_{{}}^{{}}{f(x)dx=x{{e}^{\log \left| \frac{1}{x} \right|}}+f(x)\Rightarrow \int_{{}}^{{}}{f(x)dx=\frac{x}{|x|}+f(x)}}\] On differentiating both sides , we get \[f(x)=0+f'(x)\] We know \[\frac{d}{dx}({{e}^{x}})={{e}^{x}},\,\,\therefore \,\,f(x)=c{{e}^{x}}\].
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