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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
$\int \frac{d x}{x \log _e x}$ is equal to :
  • A
    $|\log x|+C$
  • B
    $\frac{1}{x}+ C$
  • ✓
    $\log |\log x|+C$
  • D
    $-\frac{1}{x^2}+C$
✓

Answer

Correct option: C.
$\log |\log x|+C$
(C)
$\int \frac{d x}{x \log _e x}$
Let $\log _{ e } x=t$
$
\begin{aligned}
\frac{1}{x} d x & =d t \\
\int \frac{d t}{t} & =\log |t|+C \\
& =\log |\log x|+C
\end{aligned}
$
Hence option (C) is correct.

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