A) \[e\]
B) \[\ln \,(1+e)\]
C) \[e+\ln (1+e)\]
D) \[e-\ln (1+e)\]
Correct Answer: D
Solution :
[d] \[I=\int\limits_{1}^{e}{\left( \frac{1}{x}+1 \right)}dx-\int\limits_{1}^{e}{\frac{1+\ln x}{1+x\ln x}dx}\] \[={{[\ln x+x]}_{1}}^{e}-[\ln (1+x\ln x)]_{1}^{e}\] \[=e-\ln (1+e)\]
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