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If In=int(logx)^n dx, then In+nI(n-1) i...

If `I_n=int(logx)^n dx, ` then` I_n+nI_(n-1)` is equal to

A

`x(logx)^n`

B

`(xlogx)^n`

C

`(logx)^(n-1)`

D

`n(logx)^n`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If I_(n)=int_(1)^(e)(log x)^(n) d x, then I_(n)+nI_(n-1) equal to

    A
    `(1)/(e)`
    B
    e
    C
    `e-1`
    D
    None of these

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    A
    `tan^n x`
    B
    `cot^n x`
    C
    `tan^(n-1) x`
    D
    `cot^(n-1) x`

  • If I_(n)-int(lnx)^(n)dx, then I_(10)+10I_(9) is equal to (where C is the constant of integration)

    A
    `x(lnx)^(10)+C`
    B
    `10(lnx)^(9)+C`
    C
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    D
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