ExamBro
ExamBro
AP EAMCET · Maths · Indefinite Integration

\(\int\left[\frac{1}{\log x}-\frac{1}{(\log x)^2}\right] d x=\)

  1. A \(x \log x+c\)
  2. B \(-x \log x+c\)
  3. C \(\frac{\log x}{x}+c\)
  4. D \(\frac{x}{\log x}+c\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{x}{\log x}+c\)

Step-by-step Solution

Detailed explanation

\(\int\left(\frac{1}{\log x}-\frac{1}{(\log x)^2}\right) d x\) Put, \(\log x=t\) \(\begin{array}{l} x=e^t \\ d x=e^t d t \\ \int\left(\frac{1}{t}+\frac{-1}{t^2}\right) e^t d t \end{array}\) We have,…