If $I_n=\int_\limits 1^e(\log x)^n d x$, then $I_n+n I_{n-1}$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Analyzing +4 | -1

I_n=\int\limits_{1}^e(\log x)^n d x

, then

I_n+n I_{n-1}

is equal to

View answer and explanation

Correct option: B

e

Option B (

e

) is correct because integrating by parts simplifies the expression and leads to the result

I_n + nI_{n-1} = e

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