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If l^r(x) means logloglog.......x being ...

If `l^r(x)` means `logloglog.......x` being repeated `r` times, then `int [ (x l(x) l^2(x) l^3(x) .... l^r (x)]^(-1) dx` is equal to :

A

`l^(r+1) (x) +c`

B

`(l^(r+1)(x))/(r+1)+c`

C

`l^(r)(x) +c`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`int(1)/(xl(x)l^(2)(x)....l^(r-1)(x)l^(r)(x))dx`
f(x)=t
`rArr(1)/(l^(r-1)x.l^(r-2)x...x)dx=dt`
`:. int(dt)/(t)=ln|t|+c`
`" " l^(r+1)(x)+c`
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