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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Indefinite Integration

NDA 2013 · Mathematics · Indefinite Integration

What is ∫ (d x)/(x x) equal to ? where c is the constant of...

What is ∫dxxln⁡x\int \frac{d x}{x \ln x} equal to ? where cc is the constant of integration.

Options

  1. Aln⁡(ln⁡x)+c\ln (\ln x)+c
  2. Bln⁡x+c\ln x+c
  3. C(ln⁡x)2+c(\ln x)^2+c
  4. DNone of the above

Correct answer

A. ln⁡(ln⁡x)+c\ln (\ln x)+c

Step-by-step solution

∫dxxln⁡x\int \frac{d x}{x \ln x} Put \quadln⁡x=t1xdx=dt∫1tdt=ln⁡t+c=ln⁡ln⁡x+c\begin{aligned} \ln x & =t \\ \frac{1}{x} d x & =d t \\ \int \frac{1}{t} d t & =\ln t+c=\ln \ln x+c\end{aligned}$$
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