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

1 Answer
Apr 14, 2016

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.