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If l^r(x) means logloglog...... x , the ...

If `l^r(x)` means `logloglog...... x ,` the `log` being repeated `r` times, then `int[x l(x)l^2(x)l^3(x)..... l^r(x)]^(-1)d x` is equal to `l^(r+1)(x)+C` (b) `(l^(r+1)(x))/(r+1)+C` (c)`l^r(x)+C` (d) none of these

A

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

B

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

C

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

D

non of these

Text Solution

Verified by Experts

The correct Answer is:
A
Putting `l^(r+1)(x)=t`
and `(1)/(xl(x)l^(2)(x) ...l^(r)(x))dx=dt,` we get
`int(dx)/(xl^(2)(x)l^(3)(x) ...l^(r)(x))=int 1 dt=t+C=l^(r+1)(x)+C`
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