Question

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. non of these

Answer 1

Correct Answer - 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`