Do the math with your pen and see what you can get.

I simplified the above formula to:

This is a question that my friend gave me at that time. If I do it right, I will get a reward. Science students seem to have a natural love for mathematics, just like some people don't like it, but because of their age, these integral knowledge are almost forgotten.

All I know is that there seems to be some connection between integral and derivative.

Then according to my guess, I find a function whose derivative can be: sin x/x, and then I substitute it into positive infinity to get a value, and subtract the value obtained by substituting it into O, which is the result of this integral.

So the key to the problem is to find this function, and its derivative is: sin x/x.

I won't. I can ask my friends. So I got these answers.

This hope of directly calculating the results with advanced formulas seems to be stuck.

Trying again seems to have failed.

This friend gave me a screenshot directly and told me three facts:

(1) This function has no original function, so it can't be done as I said.

(2) But this integral can really be found, but I don't know how to use it.

(3) This integral has very important application value in the fields of probability theory, number theory, optics and Fourier analysis.

The problem is deadlocked, from a clue to nothing, what should I do?

The great god was born.

After a while, another picture.

It is quite possible that this man named Dirichlet found the answer in this way.

The problem seems to have been solved, and the final answer to this game is:

This great god, no screenshots, no superfluous words, just a few words, hit the floor.

He said:

"This is not to do so.

The derivative of elementary function is not this.

Using residue theorem

Residue must understand real integral. This topic is a very basic example of residue theorem.

Look at a Baidu library or something and it will be solved.

In fact, knowing the residue theorem, this is a verbal calculation, π/2 "

What is the charm of mathematics?

It should be a sense of pleasure and accomplishment brought by finding a simpler iterative upgrade method to solve the problem. I can solve problems that the whole world can't solve quickly and simply, so I have a sense of superiority that seems to be the best in the world.

It should be a personal hobby and fun, just like some people like to smell their smelly socks. You may not understand it, but it does exist.

It should be love after understanding that mathematics has changed the world!

After all the mathematical operation methods and major problems are solved, it will bring about the leap-forward development of physics, and their major discoveries will eventually directly turn into more convenient mobile phones, more convenient transportation and smarter and richer lives. It's just that the connection is too far and the time span is too long, which makes it difficult for us to connect today's high-tech and convenience with mathematics that we hate. Moreover, it seems that mathematics has benefited all future generations, and at most they can win an award and get some money, and then the theorem and proof of this problem are named after themselves. Not many people know and not many people admire, which makes life clear. And these people often have different talents and different ways of thinking. They are gods from the future or from outer space, and their mission in life seems to be to challenge the creator and unlock a little secret of nature.

Pay tribute to mathematics and pay tribute to the founders of today's life.

Finally, I'll give you a question. You can leave the results at the bottom of this article. I don't need to publish the answer. See why other people's answers are different from their own, and you will know which one is correct!