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7.1 inderfinite integral — Maths STD 12 Science — Question

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

Answer

Correct option: B.
$\frac{x}{{\log x}} + c$
b
(b)$\int_{}^{} {\left[ {\frac{1}{{\log x}} - \frac{1}{{{{(\log x)}^2}}}} \right]} \,dx = \int_{}^{} {\frac{1}{{\log x}}\,dx - \int_{}^{} {\frac{1}{{{{(\log x)}^2}}}\,dx} } $
$ = \frac{x}{{\log x}} + \int_{}^{} {\frac{1}{{{{(\log x)}^2}}}\,.\,\frac{1}{x}x\,dx} - \int_{}^{} {\frac{1}{{{{(\log x)}^2}}}} dx + c = \frac{x}{{\log x}} + c$.

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