${I_{m,n}} = \mathop {\smallint \,\,}\limits_0^1 {x^m}\,\,{\left( {\ln \,\,x} \right)^n}\,\,dx = $

$\frac{n}{{n + 1}}\,\,{I_{m,\,n - 1}}$

$\frac{{ - \,m}}{{n + 1}}\,\,{I_{m,n - 1}}$

$\frac{m}{{n + 1}}\,\,{I_{m,n - 1}}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

{I_{m,n}} = \mathop {\int \,\,}\limits_0^1 {x^m}\,\,{\left( {\ln \,\,x} \right)^n}\,\,dx =

View answer and explanation

Correct option: C

\frac{{ - \,\,n}}{{m + 1}}\,\,{I_{m,n - 1}}

Option C (

\frac{{ - \\,n}}{{m + 1}}\\,,{I_{m,n - 1}}

) is correct because it is the result of applying integration by parts to the given integral.

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