I've seen that (tough) integrals may be broken into answers in logarithmic form. In other words, many integrals have an alternate answer that is in the form of a function involving logarithms. An example is this question, which gives an alternate answer in terms of logarithms.
I'd like to know much more about breaking integrals into logarithms. Is there a method that can accomplish this without luck? I've read a reference (actually pictures of a book, I believe) that stated something like any integral can be broken into this logarithmic form. I'd like to know what is known about this, and I'd be delighted if someone could reference this research.
I'm looking into an algorithm to do very tough integration, and wonder if this technique is anywhere close to feasible.