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.