TS EAMCET · Maths · Indefinite Integration
\(\int\left(\frac{1-\log x}{1+(\log x)^2}\right)^2 d x=\)
- A \(\frac{1}{1+(\log x)^2}+c\)
- B \(\frac{\log x}{1+(\log x)^2}+c\)
- C \(\frac{x}{1+(\log x)^2}+c\)
- D \(\frac{x^2}{1+(\log x)^2}+\mathrm{c}\)
Answer & Solution
Correct Answer
(C) \(\frac{x}{1+(\log x)^2}+c\)
Step-by-step Solution
Detailed explanation
\(\frac{d}{dx}\left(\frac{x}{1+(\log x)^2}\right)\) \(=\frac{1 \cdot (1+(\log x)^2) - x \cdot (2\log x \cdot \frac{1}{x})}{(1+(\log x)^2)^2}\) \(=\frac{1+(\log x)^2 - 2\log x}{(1+(\log x)^2)^2}\) \(=\frac{(1-\log x)^2}{(1+(\log x)^2)^2}\)…
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