# $\int \ln (\cos x)\,dx$

Why is $\ln( \cos x)$ a function that cannot be integrated symbolically? From what I have read, it's integral would produce a result that is not an elementary function, but I don't see why getting something like a polylogarithm is so bad. Further, $\int\ln( u)\, du$ can be solved, so why not use $u$-sub and evaluate it in this manner?

Thank you for your help in advance.

• $u = \cos x$ produces an additional $\sin(x)$ term since that's the jacobian of this substitution, so it doesn't help – mm-aops Jun 25 '14 at 13:55