It's still good to have A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev (who works since years with Wolfram): Integrals and Series (Moscow 1981, russian) on the book shelf, and there in ยง 1.2.5 no. 9, p. 31:
Integrate[1/(x (x + a)), x] = Log[Abs[x/(x+a)]]/a
it's the same thing as discussed in Doing an integral ... mentioned above. To make a long story short: use the Prudnikov et. al. solution as long as
$x$ is real.
Two of the integral table workers (Brychkow and Marichev) wrote an interesting blog article New Derivatives of the Bessel Functions Have Been Discovered with the Help of the Wolfram Language! Enjoy!