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If lr(x) means log log log ......x, the log being repeated r times, then

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1 Answer

+2 votes
by (15.1k points)

Take first two pairs

x logx

Let logx = a

So (1/x)dx = da

⇒ dx = xda

Putting the assumed value the equation is reduced to

Now x cancels out so

⇒ 

Again repeat above procedure and keep doing until this equation reduced to 1 term only i.e

Some 

Where p = (log(log(log(log)…r times)))

So integration will give logp

So now putting the value answer is

Log(log(log(log(log)))) r+1 times

So answer is lr+1

Correct option is (a)

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