Question

How do you integrate `int 1/(xlnx)` using substitution?

Answer 1

`ln(ln(x)) + C`

Explanation:

Let `u=ln(x) implies du = 1/xdx`

So

`int (dx)/(xln(x)) = int (du)/(u)`

`int (du)/(u) = ln(u) + C = ln(ln(x)) + C`