Integral Calculus Question 466
Question: $ \int_{{}}^{{}}{\frac{1}{x^{3}}{{[\log x^{x}]}^{2}}\ dx=} $
Options:
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
Show Answer
Answer:
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} $ .
BETA
