TS EAMCET · Maths · Indefinite Integration
If \(f_n(x)=\log \log \log \ldots \log x \quad(\log\) is repeated \(n\)-times), then \(\int\left(x f_1(x) f_2(x) \ldots f_n(x)\right)^{-1} d x\) is equal to
- A \(f_{n+1}(x)+c\)
- B \(\frac{f_{n+1}(x)}{n+1}+c\)
- C \(n f_n(x)+c\)
- D \(\frac{f_n(x)}{n}+c\)
Answer & Solution
Correct Answer
(A) \(f_{n+1}(x)+c\)
Step-by-step Solution
Detailed explanation
\(f_n(x)=\log \cdot \log \cdot \log \ldots \cdot \log x\) (upto \(n\) times) \(f_1(x)=\log x\) \(f_2(x)=\log \log x\) \(f_3(x)=\log \log \log x\) \(f_{n-1}(x)=\log \log \log \ldots \ldots \log x\) (up to \((n-1)\) times) Now,…
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