This thread is for pros!

Here is how it works: it starts with me giving you an integral to solve.

**If you have a complete and correct solution, post it. Otherwise do not post anything please!**
So you post your solution and also your own problem (integral of course!) for others to solve. It goes on like this until this thread has 100 posts. If after 48 hours nobody solved your problem, which

is not very likely, you'll post your solution and again it'll be your turn to challenge us with a new problem. Finally whoever earns the right to post in this thread can also post his solution, if he has a

different one of course, to any problem that has already been solved in this thread.

**Make sure your problem is interesting and definitely not very easy to solve. Do not give any hint please!**
Let's get started: Evaluate $\displaystyle I=\int_{\frac{-\pi}{4}}^{\frac{\pi}{4}} \frac{4x - \pi}{1 - \cot x} \ dx.$