Evaluate dx, where λ n (x) = log e

Maths Indefinite Integral General Subjective Type

Published on: August 11, 2026

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

Sol. We have,

d{ λ (x)} = d(log x) = dx

d{ λ 2 (x)} = d {log e (log e x)} = dx = dx

d{ λ 3 (x)} = d{log (log (log e x)}

= dx and so on.

∴ d { λ n (x)} =

Thus,

= , where t = λ n (x)

= log e (t) + C

= log e { λ n (x)} + C

= λ n+1 (x) + C

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