One of my interests is integral calculus so when I conceived of a problem such as

$\displaystyle \int dx/(1 + cosx)(1 + sinx)$

that resists methods such as integration by parts or a substitution, this gets me interested as it's so far been challenging to me.

Even though I feel that a simple (closed) solution exists for this problem, I haven't found one to date so I figure that others may want to take a look and try their hand at it.

Any ideas?