A) \[\log {{\log }_{x}}e+c\]
B) \[\frac{1}{{{({{\log }_{x}}e)}^{2}}}+c\]
C) \[x\log \left( \frac{x}{e} \right)+c\]
D) None of these
Correct Answer: C
Solution :
\[\int_{{}}^{{}}{\frac{1}{{{\log }_{x}}e}\,dx=\int_{{}}^{{}}{{{\log }_{e}}x\,dx}=x\log x-x+c}\] \[=x({{\log }_{e}}x-{{\log }_{e}}e)+c=x{{\log }_{e}}\left( \frac{x}{e} \right)+c.\]You need to login to perform this action.
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