A) \[\frac{{{x}^{3}}}{3}(\log x)+x+c\]
B) \[\frac{1}{3}{{(\log x)}^{3}}+c\]
C) \[3\log (\log x)+c\]
D) None of these
Correct Answer: B
Solution :
\[\int_{{}}^{{}}{\frac{1}{{{x}^{3}}}{{[\log {{x}^{x}}]}^{2}}\,dx}=\int_{{}}^{{}}{\frac{1}{{{x}^{3}}}{{[x\log x]}^{2}}dx}\] \[=\int_{{}}^{{}}{\frac{1}{x}{{(\log x)}^{2}}dx}=\frac{1}{3}{{(\log x)}^{3}}+c\], {Putting \[\log x=t\}\].
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