AP EAMCET · Maths · Indefinite Integration
\(\int\left[\frac{1}{\log x}-\frac{1}{(\log x)^2}\right] d x=\)
- A \(x \log x+c\)
- B \(-x \log x+c\)
- C \(\frac{\log x}{x}+c\)
- D \(\frac{x}{\log x}+c\)
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,…
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