A) \[\frac{1}{2}\log x+c\]
B) \[\frac{1}{2}{{(\log x)}^{2}}+c\]
C) \[\frac{1}{2}\log {{(x)}^{2}}+c\]
D) \[\log x+c\]
Correct Answer: B
Solution :
\[I=\int_{{}}^{{}}{\frac{1}{x}\log x\,dx}\]. Put \[\log x=t\Rightarrow \frac{1}{x}\,dx=dt\] \[\therefore \,\,\,I\int_{{}}^{{}}{t\,dt}=\frac{{{t}^{2}}}{2}+c=\frac{{{(\log x)}^{2}}}{2}+c\].
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