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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {\frac{1}{{{{\log }_x}e}}dx = } $
  • A
    $\log {\log _x}e + c$
  • B
    $\frac{1}{{{{({{\log }_x}e)}^2}}} + c$
  • ✓
    $x\log \left( {\frac{x}{e}} \right) + c$
  • D
    None of these
✓

Answer

Correct option: C.
$x\log \left( {\frac{x}{e}} \right) + c$
c
(c)$\int_{}^{} {\frac{1}{{{{\log }_x}e}}\,dx = \int_{}^{} {{{\log }_e}x\,dx} = x\log x - x + c} $
$ = x({\log _e}x - {\log _e}e) + c = x{\log _e}\left( {\frac{x}{e}} \right) + c.$

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