Find the antiderivative of f(x) = ln (ln x) + (ln x) –2 who…

Maths Indefinite Integral Integration by Parts, Integral of the Form ex(F(x) + F(x)) dx, Integral of the Form ekx(kF(x)+F(x)) dx Subjective Type

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Find the antiderivative of f(x) = ln (ln x) + (ln x) –2 whose graph passes through (e, e).

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The correct answer is:

CHECK THE SOLUTION.

y = x + 2e

Sol. =

Put  nx = t ⇒ x = e t ⇒ dx = e t dt

= = = e t + C ⇒ y = x + C

 it passes through (e, e) ⇒ C = 2e

Hence, y = x + 2e

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