The antiderivative of ƒ(x) = log (log x) + (log x) –2 whose…

Maths Indefinite Integral General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

The antiderivative of ƒ(x) = log (log x) + (log x) –2 whose graph passes through (e, e) is –

x (log (log x) + (log x) –1 )

x (–log (log x) + (log x) –1 ) + e

x (log (log x) – (log x) –1 ) + 2e

None of these

Text Solution

Verified by Experts

The correct answer is:

An antiderivative of ƒ(x) = F(x) =

dx + c

= x log (log x) – dx+ dx + c

(integrating by parts the first term log x is)

= x log (log x) – [x (log x) –1 + dx]

+ dx + c

(again integrating by parts (log x) –1 as first term)

= x log (log x) – x (log x) –1 + c

Putting x = e, we have e = 0 – e + c so c = 2e

Thus F (x) = x (log (log x) – (log x) –1 + 2e.

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