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If I(n)=int("In "x)^(n)dx, " then " I(n)...

If `I_(n)=int("In "x)^(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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OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Solved Example
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  20. Let f(x) be a quadratic function such that f(0)=1 and int(f(x))/(x^2(x...

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