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STD 12 - 7.1 inderfinite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {\frac{1}{{{x^3}}}{{[\log {x^x}]}^2}\;dx = } $
  • A
    $\frac{{{x^3}}}{3}(\log x) + x + c$
  • ✓
    $\frac{1}{3}{(\log x)^3} + c$
  • C
    $3\log (\log x) + c$
  • D
    None of these
✓

Answer

Correct option: B.
$\frac{1}{3}{(\log x)^3} + c$
b
(b)$\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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