It’s a simple, elementary thing to differentiate $ f(x)=\log(\sin(x))\log(\cos(x))$ by the well-known formulae one learns in high school, and Mathematica 9 perfectly does it. However, when integrating $ f'(x)$ , one might have the big surprise to find Mathematica 9 gives a long answer in terms of logarithms and polylogarithms with complex argument. Question: CouldRead more