Can Anyone Stump My All-Knowing Dad?

[heman]

The integral of x*sec(x) cannot be expressed as an elementary function- meaning usual nice finite combinations of exponentials, logarithms, polynomials, trig functions, etc. This is the same situation as the more common e^(-x^2).

I know its solution and i very well know its solution contain polylog function and other adhoc complex functions,but i don't care about the complexity involved!
Do you know how to solve it??
I have tried this question more than any question i can think of!

I don't agree with what you say about e^(-x^2)
Its a very easy question which can be solved trivially with the help of Polar Coordiantes and further with change of variables!

I guess you must have been pointing to x^x,its solution can't be written in form of elementary functions!

 

[heman]

Ask him what women want.

Tell me what do you want??

 

[honestrosewater]

Tell me what do you want??

If you have to ask, you don't really want to know.


Hey, I'm getting the hang of this inscrutable psyche stuff[/size]

 

[heman]

If you have to ask, you don't really want to know.


Hey, I'm getting the hang of this inscrutable psyche stuff[/size]

So...Hmmmm...Ok...Well ...Yeah


I have observed all through that women reveal only when they are asked!

 

[shmoe]

I know its solution and i very well know its solution contain polylog function and other adhoc complex functions,but i don't care about the complexity involved!
Do you know how to solve it??
I have tried this question more than any question i can think of!

Write sec(x) in terms of exponentials, sec(x)=2/(e^{ix}+e^{-ix}), then a change of variables, e^{ix}=t. Using partial fractions you can then write the integral in terms of dilog say, which is an integral you can't express in elementary terms. This isn't really anymore satisfying than the original form though, but I guess this is the find of thing you're looking for. I wouldn't call rearranging this integral into some other arbitrary looking integral, that necessarily has no elementary solution, "solving" anything, but that's just me.

Or if you like you can express x*sec(x) as a power series and integrate that (keeping mind of the interval of convergence). Again, this is somewhat unsatisfying and not in elementary terms (which implies a finite number of terms).

I don't agree with what you say about e^(-x^2)
Its a very easy question which can be solved trivially with the help of Polar Coordiantes and further with change of variables!

You can work out \int_{-\infty}^{\infty}e^{-x^2}dx exactly by polar coordinates or other tricks. This is not what I said was impossible. You cannot express an antiderivative of e^{-x^2} in terms of elementary functions (for the usual definition of "elementary function"), this is not debatable. There is a difference between expressing an antiderivative in terms of elementary functions and evaluating a definite integral exactly.

 

[gravenewworld]

Ask your dad this simple question-" Why do hotdogs come in packages of 10 and hot dog buns come in packs of 8?" Guaranteed he will be stumped.

 

[BobG]

Ask your dad this simple question-" Why do hotdogs come in packages of 10 and hot dog buns come in packs of 8?" Guaranteed he will be stumped.

You've obviously never had a weinie roast on a beach. Guaranteed, one hot dog will fall into the fire and be unretrievable. A different hot dog will fall into the sand.

Whether this hot dog is still edible or not depends on whether or not there's a least one person at the party you don't like and whether or not that person saw you drop the hot dog.

This makes the problem of why there is only 8 buns in a package instead of 9 a little more complex and is unsolvable through normal beach party math. It's because bun packagers belong to the conservative, pro-family segment of society. They assume the hot dog in the beach is unusable and the thought of a bunch of single people assembling on the beach together is such a totally repugnant thought that they never get as far as debating whether the sandy hot dog is still usable or not.

 

[honestrosewater]

You've obviously never had a weinie roast on a beach. Guaranteed, one hot dog will fall into the fire and be unretrievable. A different hot dog will fall into the sand.

Haha, that's true, but you forgot the part about someone trying to douse the fire with their beer.

Whether this hot dog is still edible or not depends on whether or not there's a least one person at the party you don't like and whether or not that person saw you drop the hot dog.

This makes the problem of why there is only 8 buns in a package instead of 9 a little more complex and is unsolvable through normal beach party math. It's because bun packagers belong to the conservative, pro-family segment of society. They assume the hot dog in the beach is unusable and the thought of a bunch of single people assembling on the beach together is such a totally repugnant thought that they never get as far as debating whether the sandy hot dog is still usable or not.

Ah, but the pro-family people surely realize that there will be a baby in the family who will be served the cut up hot dog without a bun. So the mystery lives!

 

[BobG]

Haha, that's true, but you forgot the part about someone trying to douse the fire with their beer.
Ah, but the pro-family people surely realize that there will be a baby in the family who will be served the cut up hot dog without a bun. So the mystery lives!

At least that's better than some parties where some guy tries to douse the fire and winds up getting hauled off by the police for indecent exposure.

The pro-family segment realizes that at the typical family weinie roast, all of the hot dogs wind up in the fire or the sand, the buns get fed to the ducks and geese, and the family goes to MacDonald's to eat.

 

[honestrosewater]

At least that's better than some parties where some guy tries to douse the fire and winds up getting hauled off by the police for indecent exposure.

Sorry to hear that - I hope the cops didn't mistreat you.

The pro-family segment realizes that at the typical family weinie roast, all of the hot dogs wind up in the fire or the sand, the buns get fed to the ducks and geese, and the family goes to MacDonald's to eat.

Right, how could I forget... good times.

 

[Lisa!]

I have been trying for quite some time now to stump my dad on just one question. I've tryed out physics, Astronomy & Cosmology, Mathematics, Philosophy, logic, tecnology, almost every subject! It is getting to the point where i stay up late on the internet trying to find something. can anyone suggest a question please?

Invite him to PF.Then we can examine him.
And if he would be able to answer every question, it will be great to have him here.

 

[honestrosewater]

Invite him to PF.Then we can examine him.
And if he would be able to answer every question, it will be great to have him here.

That's the most logical thing anyone's said all day.

 

[quantumdude]

What is the air-speed velocity of an unladen swallow?

 

[honestrosewater]

What is the air-speed velocity of an unladen swallow?

Nice try, but this guy sounds like a nerd, i.e., he has the script on disk somewhere.

I'm right, aren't I, Shippo?