A) \[x{{\log }_{10}}x+c\]
B) \[x({{\log }_{10}}x+{{\log }_{10}}e)+c\]
C) \[{{\log }_{10}}x+c\]
D) \[x({{\log }_{10}}x-{{\log }_{10}}e)+c\]
Correct Answer: D
Solution :
\[\int_{{}}^{{}}{{{\log }_{10}}x\,dx}=\int_{{}}^{{}}{\frac{\log x}{\log 10}\,dx}\] \[=\frac{1}{\log 10}[x\log x-x]=x[{{\log }_{10}}x-{{\log }_{10}}e]+c\].
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