A) \[\frac{1}{\log x}+c\]
B) \[\frac{x}{\log x}+c\]
C) \[\frac{x}{{{(\log x)}^{2}}}\]
D) None of these
Correct Answer: B
Solution :
\[\int_{{}}^{{}}{\left[ \frac{1}{\log x}-\frac{1}{{{(\log x)}^{2}}} \right]}\,dx=\int_{{}}^{{}}{\frac{1}{\log x}\,dx-\int_{{}}^{{}}{\frac{1}{{{(\log x)}^{2}}}\,dx}}\] \[=\frac{x}{\log x}+\int_{{}}^{{}}{\frac{1}{{{(\log x)}^{2}}}\,.\,\frac{1}{x}x\,dx}-\int_{{}}^{{}}{\frac{1}{{{(\log x)}^{2}}}}dx+c=\frac{x}{\log x}+c\].
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