Take first two pairs

*x* log*x*

Let log*x* = a

So (1/*x*)d*x* = da

⇒ d*x* = *x*da

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 l**^{r+1}

**Correct option is (a)**