Question

What is the indefinite integral of `ln(ln x)`?

Answer 1

`int ln(lnx) dx = xln(lnx) - int 1/lnx dx`

Explanation:

Using integration by parts with `u = ln(lnx)` and `dv = dx`, we get

`int ln(lnx) dx = xln(lnx) - int 1/lnx dx`

The antiderivative of `1/lnx` is called the logarithmic integral function, and is denoted `li(x)` It is generally not included in an introductory calculus course (or sequence of courses). You can read more about it at Wikipedia.