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If In=int( lnx)^n dx then In+nI(n-1)...

If `I_n=int( lnx)^n dx` then `I_n+nI_(n-1)`

A

`(xlogx)^(n)`

B

`x(logx)^(n)`

C

`n(logx)^(n)`

D

`(logx)^(n-1)`

Text Solution

Verified by Experts

The correct Answer is:
b
Let `I_(n)=intunderset(I)((logx)^(n))*underset(II)(1)dx`
`rArrI_(n)=x(logx)^(n)=intxn(logx)^(n-1)(1)/(x)dx`
`rArr I_(n)=x(logx)^(n)-nI_(n-1)`
`rArrI_(n)+nI_(n-1)=x(logx)^(n)`
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