A) \[{{(\log x)}^{2}}\]
B) \[\frac{1}{2}{{(\log x)}^{2}}\]
C) \[\frac{\log {{x}^{2}}}{2}\]
D) None of these
Correct Answer: A
Solution :
\[I=\int_{1}^{x}{\frac{2\log x}{x}dx}\] Let \[\log x=t\] Þ \[\frac{dx}{x}=dt\] \[\therefore I=2\int_{0}^{\log x}{t\,dt=2\,\left[ \frac{{{t}^{2}}}{2} \right]}_{0}^{\log x}={{(\log x)}^{2}}\].
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