JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

F_n(x)=\int(\log x)^n d x

and

\phi_n=F_n+n F_{n-1}

, then

\phi_n(e)-\phi_n(1)

is equal to

View answer and explanation

Correct option: D

e

Option D is correct because by using integration by parts, we find that φ_n(x) = x(log x)^n + c, and then φ_n(e) - φ_n(1) = e.

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