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If $f_{n} (x) = \log \log \dots \log x$ (log is repeated n times)
then $\int {[x f_{1} (x) f_{2} (x) \dots f_{n} (x)]}^{- 1} d x$ is equal to

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fn+1(x)+C

fn+1(x)n+1+C

nfn(x)+C

none of these

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detailed solution

Correct option is A

Put fn(x)=t,dtdx=1xf1(x)…fn−1(x)So ∫xf1(x)…fn(x)−1dx=∫dtt=log⁡t+C=fn+1(x)+C.

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If fn(x)=log⁡log⁡…log⁡x (log is repeated n times)then ∫xf1(x)f2(x)…fn(x)−1dx is equal to

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Ready to Test Your Skills?

free study material

If $f_{n} (x) = \log \log \dots \log x$ (log is repeated n times)
then $\int {[x f_{1} (x) f_{2} (x) \dots f_{n} (x)]}^{- 1} d x$ is equal to