Some integrals with problematic evaluation

[quinyu]

So, back to it.

Code:

int(1/(x*(1-ln(x))),x)

This is a particular case of the general form

Code:

int(1/(a+b*ln(c(d(e+fx)^p)^q)*(g+hx)),x)

with a=1, b=-1, c=1, d=1, e=0, f=1, g=0, h=1, p=1, q=1. That integral, IF fg-eh=0, can be written as

Code:

ln(a+b*ln(c(d(e+fx)^p)^q))/(bhpq)

So ln(1-1*ln(1(1(0+1x)^1)^1))/(-1), which simplifies to

Code:

-ln(1-ln(x))

The same applies to the integral after it, with int(1/(x*(1+ln(x/a))),x).