Have a good weekend everybody!

I have couple of problems for you to look at! First one is a chess problem. Can you find the solution of the mate in 5 moves? It's whites turn in the diagram and white wins in 5 moves if played correctly!

This is considerably easy problem for a 5 moves chess problems.

Now a physics problem

3 workers carrying a long wood plank. Two of them holds from 2 ends of the wood plank and one holds in the middle. what are the forces acting on them? All carries the same a moon? -or do you think there is some injustice for the middle guy?

Lets not forget math

Here is an integral to tackle with:

$\underset{0}{\overset{1}{\int \; <!--\; integral\; -->}}\frac{{\tan }^{-1}\left(\sqrt{2+x^2}\right)\mathrm{dx}}{\left(1+x^2\right)\times \; <!--\; multiplication\; sign\; -->\sqrt{2+x^2}}=?$

This is famous integral. it's called "Ahmed's integral" . it's proposed in 2002 by indian mathematician Zafar Ahmed. You can google it find answer if you want. But if you want to play with it first, I recommend starting with Feymann's differentiating under integral sign trick.

$I=\underset{0}{\overset{1}{\int \; <!--\; integral\; -->}}\frac{{\tan }^{-1}\left(u\sqrt{2+x^2}\right)\mathrm{dx}}{\left(1+x^2\right)\times \; <!--\; multiplication\; sign\; -->\sqrt{2+x^2}}=?\times \; <!--\; multiplication\; sign\; -->\frac{dI}{du}=?$