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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{{dx}}{{x + x\log x}} = } $
  • ✓
    $\log (1 + \log x)$
  • B
    $\log \log (1 + \log x)$
  • C
    $\log x + \log (\log x)$
  • D
    None of these
✓

Answer

Correct option: A.
$\log (1 + \log x)$
a
(a)$\int_{}^{} {\frac{{dx}}{{x + x\,\,\log x}}} = \int_{}^{} {\frac{{dx}}{{x(1 + \log x)}}} $Now putting $1 + \log x = t \Rightarrow \frac{1}{x}\,dx = dt,$ it reduces to$\int_{}^{} {\frac{{dt}}{t}} = \log (t) = \log (1 + \log x)$.

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