<p>1/ln(x) is somewhat like sin(x)/x, which can be integrated, but only into a series, I believe. I know that if you convert sin(x) into a series, then divide each term by x, you can integrate each term separately. But I dunno if there's an analogous method of integrating 1/ln(x), and even if there were, the series would be in the denominator so the fraction couldn't be split. </p>
<p>Perhaps you could introduce an intermediary variable b, to represent 1/ln(x) in terms of e and b, and then you could substitute with the definition of e, and then integrate...? Just a thought.</p>
<p>Check out mathworld: <a href="http://mathworld.wolfram.com/NaturalLogarithm.html%5B/url%5D">http://mathworld.wolfram.com/NaturalLogarithm.html</a></p>
<p>Good luck.</p>